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Table of Contents
Introduction to Mathematics
Calculus and Analysis
Real Analysis
Complex Analysis
Fourier Analysis
Inequalities
Proof: A Many-Splendored Thing
The Four-Colour Problem
Geometry, Fractals, and Topology
Linear Algebra
Algebra
Multivariable Calculus
Ordinary Differential Equations
Partial Differential Equations
Functional Analysis
Discrete Mathematics
Combinatorics
Number Theory
Graph Theory
Network Science
Logic and Set Theory
Thoughts, Ideas, Opinions, Surveys, and Blogs
History of Mathematics
Modeling and Simulation
Probability
Probability and Statistics
Statistics
Thomas Bayes: Life and Work
Bayesian Statistics
Statistical Programming Using R
Experimental Math and Math Computing
LaTeX
People and Places
Ramanujan – Life and Work
Elements de Mathematique by N. Bourbaki
Mathematical Fun
Legal Matters
Reference Material
Additional Web Resources
Online Publications – Directly
Odds & Ends
Introduction to Mathematics =============
Precalculus + College Algebra + College Trigonometry
Carl Stitz and Jeff Zeager
http://stitz-zeager.com/
MATHematics Illuminated
http://www.learner.org/courses/mathilluminated/
Algebra Through Problem Solving
Abraham P. Hillman and Gerald I. Alexanderson
http://www.thiel.edu/mathproject/atps/default.htm
Roots of Modern Technology: An Elegant Survey of the
Basic Mathematical and Scientific Concepts
Siegfried Wendt
Springer, 2010, ISBN 978-3-642-12062-6
http://dx.doi.org/10.1007/978-3-642-12062-6
Symmetry: A Mathematical Exploration
Kristopher Tapp
Springer, 2012, ISBN 978-1-4614-0299-2
http://dx.doi.org/10.1007/978-1-4614-0299-2
How to Think Like a Mathematician:
A Companion to Undergraduate Mathematics
Kevin Houston
Cambridge University Press, 2009, ISBN 9780511808258
http://dx.doi.org/10.1017/CBO9780511808258
A Mathematical Odyssey:
Journey from the Real to the Complex
Steven G. Kranz and Harold R. Parks
Springer, 2014, ISBN 978-1-4614-8939-9
http://dx.doi.org/10.1007/978-1-4614-8939-9
Bridging the Gap to University Mathematics
Martin Gould and Edward Hurst
Springer, 2009, ISBN 978-1-84800-290-6
http://dx.doi.org/10.1007/978-1-84800-290-6
A Readable Introduction to Real Mathematics
Daniel Rosenthal, David Rosenthal, and Peter Rosenthal
Springer, 2014, ISBN 978-3-319-05654-8
http://dx.doi.org/10.1007/978-3-319-05654-8
Figuring It Out:
Entertaining Encounters with Everyday Math
Nuno Grato
Springer, 2010, ISBN 978-3-642-04833-3
http://dx.doi.org/10.1007/978-3-642-04833-3
Number Story: From Counting to Cryptography
Peter M. Higgins
Springer, 2008, ISBN 978-1-84800-001-8
http://dx.doi.org/10.1007/978-1-84800-001-8
The Language of Mathematics: Utilizing Math in Practice
Robert Laurence Baber
Wiley, 2011, ISBN 9781118061770
http://dx.doi.org/10.1002/9781118061770
All the Mathematics You Missed:
But Need to Know for Graduate School
Thomas A. Garrity
Cambridge University Press, 2001, ISBN 9780511800498
http://dx.doi.org/10.1017/CBO9780511800498
Mathematics: Form and Function
Saunders Mac Lane
Springer, 1986, ISBN 978-1-4612-4872-9
http://dx.doi.org/10.1007/978-1-4612-4872-9
Chance Rules:
An Informal Guide to Probability, Risk and Statistics,
Second Edition
Brian Everitt
Springer, 2008, ISBN 978-0-387-77415-2
http://dx.doi.org/10.1007/978-0-387-77415-2
Probabilities: The Little Numbers that Rule Our Lives
Peter Olofsson
Wiley, 2007, ISBN 9780470099797
http://dx.doi.org/10.1002/0470099798
A Mathematician’s Apology
G. H. Hardy
http://www.math.ualberta.ca/~mss/misc/
Cambridge University Press, 1992, ISBN 9781139644112
http://dx.doi.org/10.1017/CBO9781139644112
Wikipedia:
http://en.wikipedia.org/wiki/G._H._Hardy
Mathematical Writing
Franco Vivaldi
Springer, 2014, ISBN 978-1-4471-6527-9
http://dx.doi.org/10.1007/978-1-4471-6527-9
Numbers, Groups and Codes, Second Edition
J. F. Humphreys and M. Y. Priest
Cambridge University Press, 2004, ISBN 9780511812187
http://dx.doi.org/10.1017/CBO9780511812187
Back to the Table of Contents
=======================================
Calculus and Analysis ====================
Introduction to Calculus I and II
J.H. Heinbockel
http://www.math.odu.edu/~jhh/counter10.html
Active Calculus
Matthew Boelkins, David Austin, and Steven Schlicker
http://scholarworks.gvsu.edu/books/10/
Community Calculus
Calculus: Early Transcendentals (Single Variable Calculus)
Calculus: Early Transcendentals (Multiariable Calculus)
Calculus: Late Transcendentals (Single Variable Calculus)
Calculus: Late Transcendentals (Multiariable Calculus)
David Guichard and friends
http://communitycalculus.org
Inside Calculus
George R. Exner
Springer, 2000, ISBN 978-0-387-22646-0
http://dx.doi.org/10.1007/b97700
Calculus Light
Menahem Friedman and Abraham Kandel
Springer, 2011, ISBN 978-3-642-17848-1
http://dx.doi.org/10.1007/978-3-642-17848-1
Calculus With Applications, Second Edition
Peter D. Lax and Maria Shea Terrell
Springer, 2014, ISBN 978-1-4614-7946-8
http://dx.doi.org/10.1007/978-1-4614-7946-8
Advanced Calculus: A Geometric View
James J. Callahan
Springer, 2010, ISBN 978-1-4419-7332-0
http://dx.doi.org/10.1007/978-1-4419-7332-0
Advanced Calculus: A Differential Forms Approach
Harold M. Edwards
Springer, 2014, ISBN 978-0-8176-8412-9
http://dx.doi.org/10.1007/978-0-8176-8412-9
From Calculus to Analysis
Steen Pedersen
Springer, 2015, ISBN 978-3-319-13641-7
http://dx.doi.org/10.1007/978-3-319-13641-7
Numbers and Functions: Steps into Analysis, Second Edition
R. P. Burn
Cambridge University Press, 2004, ISBN 9780511755248
http://dx.doi.org/10.1017/CBO9780511755248
Introduction to Calculus and Classical Analysis, Second Edition
Omar Hijab
Springer, 2007, ISBN 978-0-387-69316-3
http://dx.doi.org/10.1007/978-0-387-69316-3
Calculus for the Ambitious
T. W. Korner
Cambridge University Press, 2014, ISBN 9781107517271
http://dx.doi.org/10.1017/CBO9781107517271
From Calculus to Analysis
Rinaldo B. Schinazi
Springer, 2012, ISBN 978-0-8176-8289-7
http://dx.doi.org/10.1007/978-0-8176-8289-7
A Concise Introduction to Mathematical Analysis
Mangatiana A. Robdera
Springer, 2003, ISBN 978-0-85729-347-3
http://dx.doi.org/10.1007/978-0-85729-347-3
Mathematical Analysis Fundamentals
A. E. Bashirov
Elsevier, 2014, ISBN 978-0-12-801001-3
http://www.sciencedirect.com/science/book/9780128010013
Foundations of Mathematical Analysis
S. Ponnusamy
Springer, 2012, ISBN 978-0-8176-8292-7
http://dx.doi.org/10.1007/978-0-8176-8292-7
A Course in Mathematical Analysis, Volume I:
Foundations and Elementary Real Analysis
D. J. H. Garling
Cambridge University Press, 2013, ISBN 9781139424493
http://dx.doi.org/10.1017/CBO9781139424493
A Course in Mathematical Analysis, Volume II:
Metric and Topological Spaces, Functions of a Vector Variable
D. J. H. Garling
Cambridge University Press, 2013, ISBN 9781139424509
http://dx.doi.org/10.1017/CBO9781139424509
A Course in Mathematical Analysis, Volume III:
Complex Analysis, Measure and Integration
D. J. H. Garling
Cambridge University Press, 2014, ISBN 9781139424516
http://dx.doi.org/10.1017/CBO9781139424516
Mathematical Analysis I, Second Edition
Claudio Canuto and Anita Tabacco
Springer, 2015, ISBN 978-3-319-12757-9
http://dx.doi.org/10.1007/978-3-319-12772-9
Mathematical Analysis II, Second Edition
Claudio Canuto and Anita Tabacco
Springer, 2015, ISBN 978-3-319-12757-6
http://dx.doi.org/10.1007/978-3-319-12757-6
A Course in Calculus and Real Analysis
Sudhir R. Ghorpade and Balmohan V. Limaye
Springer, 2006, ISBN 978-0-387-36425-4
http://dx.doi.org/10.1007/0-387-36425-0
Calculus of One Variable
** Terse, use of Maple is recommended **
Keith E. Hirst
Springer, 2006, ISBN 978-1-884628-222-5
http://dx.doi.org/10.1007/1-84628-222-5
From Real to Complex Analysis
R. H. Dyer and D. E. Edmunds
Springer, 2014, ISBN 978-3-319-06209-9
http://dx.doi.org/10.1007/978-3-319-06209-9
The Integral: A Crux for Analysis
Steven G. Krantz
Morgan & Claypool, 2011, ISBN 9781608456147
http://dx.doi.org/10.2200/S00327ED1V01Y201101MAS009
Real Analysis: Measures, Integrals and Applications
Boris Makarov and Anatolii Podkorytov
Springer, 2013, ISBN 978-1-4471-5122-7
http://dx.doi.org/10.1007/978-1-4471-5122-7
Measure, Integral, Derivative: A Course in Lebesgue’s Theory
Sergei Ovchinnikov
Springer, 2013, ISBN 978-1-4614-7196-7
http://dx.doi.org/10.1007/978-1-4614-7196-7
A Course on Integration Theory:
including more than 150 exercises with detailed answers
Nicolas Lerner
Springer, 2014, ISBN 978-3-0348-0694-7
http://dx.doi.org/10.1007/978-3-0348-0694-7
Mathematical Analysis: Approximation and Discrete Processes
Mariano Giaquinta and Giuseppe Modica
Springer, 2004, ISBN 978-0-8176-4414-7
http://dx.doi.org/10.1007/978-0-8176-4414-7
Discovering Mathematics:
A Problem-Solving Approach to Mathematical Analysis with
MATHEMATICA and Maple
Jiri Gregor and Jaroslav Tiser
Springer, 2011, ISBN 978-0-85729-064-9
http://dx.doi.org/10.1007/978-0-85729-064-9
Functional Analysis:
An Introduction to Metric Spaces, Hilbert Spaces,
and Banach Algebras
Joseph Muscat
Springer, 2014, ISBN 978-3-319-06728-5
http://dx.doi.org/10.1007/978-3-319-06728-5
An Introduction to Modern Analysis
Vicente Montesinos, Peter Zizler, and Vaclav Zizler
Springer, 2015, ISBN 978-3-319-12481-0
http://dx.doi.org/10.1007/978-3-319-12481-0
Exercises in Analysis, Part I
Leszek Gazinski and Nikolaos S. Papageorgiou
Springer, 2014, ISBN 978-3-319-06176-4
http://dx.doi.org/10.1007/978-3-319-06176-4
Examples and Theorems in Analysis
Peter Walker
Springer, 2004, ISBN 978-0-85729-380-0
http://dx.doi.org/10.1007/978-0-85729-380-0
Back to the Table of Contents
=======================================
Real Analysis ==========================
Lectures on Real Analysis
Finnur Larusson
Cambridge University Press, 2012, ISBN 9781139208604
http://dx.doi.org/10.1017/CBO9781139208604
Real Analysis for the Undergraduate:
With an Invitation to Functional Analysis
Matthew A. Pons
Springer, 2014, ISBN 978-1-4614-9638-0
http://dx.doi.org/10.1007/978-1-4614-9638-0
Real and Convex Analysis
Erhan Cinlar and Robert J. Vanderbei
Springer, 2013, ISBN 978-1-4614-5257-7
http://dx.doi.org/10.1007/978-1-4614-5257-7
The Real Numbers and Real Analysis
Ethan D. Bloch
Springer, 2011, ISBN 978-0-387-72177-4
http://dx.doi.org/10.1007/978-0-387-72177-4
Real Analysis on Intervals
A.D.R. Choudary and Constantin P. Niculescu
Springer, 2014, ISBN 978-81-322-2148-7
http://dx.doi.org/10.1007/978-81-322-2148-7
Problems in Real Analysis: Advanced Calculus on the Real Axis
Teodora-Liliana T. Radulescu, Vicentiu D. Radulecu,
and Titu Andrrescu
Springer, 2009, ISBN 978-0-387-77379-7
http://dx.doi.org/10.1007/978-0-387-77379-7
A Problem Book in Real Analysis
Asuman G. Aksoy and Mohamed A. Khamsi
Springer, 2010, ISBN 978-1-4419-1296-1
http://dx.doi.org/10.1007/978-1-4419-1296-1
Basic Real Analysis
Anthony W. Knapp
Springer, 2005, ISBN 978-0-8176-4441-3
http://dx.doi.org/10.1007/0-8176-4441-5
Advanced Real Analysis
Anthony W. Knapp
Springer, 2005, ISBN 978-0-8176-4442-0
http://dx.doi.org/10.1007/0-8176-4442-3
The Continuum:
A Constructive Approach to Basic Concepts of Real Analysis
Rudolf Taschner
Springer, 2005, ISBN 978-3-322-82036-5
http://dx.doi.org/10.1007/978-3-322-82036-5
Set Theoretical Aspects of Real Analysis
Alexander B. Kharazishvili
CRC Press, 2015, ISBN 978-1-4822-4202-7
http://dx.doi.org/10.1201/b17298
Back to the Table of Contents
=======================================
Complex Analysis =======================
Complex Analysis and Differential Equations
Luis Barreira and Claudia Valls
Springer, 2012, ISBN 978-1-4471-4008-5
http://dx.doi.org/10.1007/978-1-4471-4008-5
Complex Analysis: In the Spirit of Lipman Bers, Second Edition
Rubi E. Rodriguez, Irwin Kra, and Jane P. Gilman
Springer, 2013, ISBN 978-1-4419-7323-8
http://dx.doi.org/10.1007/978-1-4419-7323-8
A Course in Complex Analysis:
From Basic Results to Advanced Topics
Wolfgang Fischer and Ingo Lieb
Springer, 2012, ISBN 978-3-8348-8661-3
http://dx.doi.org/10.1007/978-3-8348-8661-3
Geometric Function Theory: Explorations in Complex Analysis
Steven G. Krantz
Springer, 2006, ISBN 978-0-8176-4440-6
http://dx.doi.org/10.1007/0-8176-4440-7
Back to the Table of Contents
=======================================
Fourier Analysis ========================
An Introduction to Laplace Transform and Fourier Series,
Second Edition
Phil Dyke
Springer, 2014, ISBN 978-1-4471-6395-4
http://dx.doi.org/10.1007/978-1-4471-6395-4
An Intuitive Explanation of Fourier Theory
Steven Lehar
http://cns-alumni.bu.edu/~slehar/fourier/fourier.html
Classical Fourier Analysis, Third Edition
Loukas Grafakos
Springer, 2014, ISBN 978-1-4939-1194-3
http://dx.doi.org/10.1007/978-1-4939-1194-3
Modern Fourier Analysis, Third Edition
Loukas Grafakos
Springer, 2014, ISBN 978-1-4939-1230-8
http://dx.doi.org/10.1007/978-1-4939-1230-8
Digital Fourier Analysis: Fundamentals
Ken’iti Kido
Springer, 2015, ISBN 978-1-4614-9260-3
http://dx.doi.org/10.1007/978-1-4614-9260-3
Digital Fourier Analysis: Advanced techniques
Ken’iti Kido
Springer, 2015, ISBN 978-1-4939-1127-1
http://dx.doi.org/10.1007/978-1-4939-1127-1
Fourier Analysis and Its Applications
Anders Vretblad
Springer, 2003, ISBN 978-0-387-21723-9
http://dx.doi.org/10.1007/b97452
The Fourier Transform and its Applications
(Lecture Notes for EE 261)
Brad Osgood
Electrical Engineering Department, Stanford University
http://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf
Course Home
http://see.stanford.edu/see/courseInfo.aspx?coll=84d174c2d74f-493d-92ae-c3f45c0ee091
Stanford Engineering Everywhere (SEE)
http://see.stanford.edu/
Hermitian Analysis:
From Fourier Series to Cauchy-Riemann Geometry
John P. D’Angelo
Springer, 2013, ISBN 978-1-4614-8526-1
http://dx.doi.org/10.1007/978-1-4614-8526-1
An introduction to wavelets
Amara Graps
IEEE Computational Science & Engineering,
Volume 2, Number 2 (Summer 1995)
http://dx.doi.org/10.1109/99.388960
Wavelets for Kids: A Tutorial Introduction
Brani Vidakovic and Peter Mueller
http://gtwavelet.bme.gatech.edu/wp/kidsA.pdf
Wavelets Made Easy
Yves Nivergelt
Springer, 2013 (2001), ISBN 978-1-4614-6006-0
http://dx.doi.org/10.1007/978-1-4614-6006-0
A Friendly Guide to Wavelets
Gerald Kaiser
Springer, 2011 (1994), ISBN 978-0-8176-8111-1
http://dx.doi.org/10.1007/978-0-8176-8111-1
An introduction to Wavelets Through Linear Algebra
Michael W. Frazier
Springer, 1999, ISBN 978-3-642-85570-2
http://dx.doi.org/10.1007/978-3-642-85570-2
Applied Mathematics: Data Compression, Spectral Methods,
Fourier Analysis, Wavelets, and Applications
Charles K. Chui and Quingtang Jiang
Springer, 2013, ISBN 978-94-6239-009-6
http://dx.doi.org/10.2991/978-94-6239-009-6
A Mathematical Introduction to Wavelets
P. Wojtaszczyk
Cambridge University Press, 1997, ISBN 0780511623790
http://dx.doi.org/10.1017/CBO9780511623790
Wavelets: from Math to Practice
Desanka P. Radunovic
Springer, 2009, ISBN 978-3-642-00614-2
http://dx.doi.org/10.1007/978-3-642-00614-2
A Wavelet Tour of Signal Processing: The Sparse Way
Stephane Mallat
Elsevier, 2009, ISBN 978-0-12-374370-1
http://www.sciencedirect.com/science/book/9780123743701
Wavelet Transforms and Their Applications, Second Edition
Lokenath Debnath and Firdous Ahmad Shah
Springer, 2015, ISBN 978-0-8176-8418-1
http://dx.doi.org/10.1007/978-0-8176-8418-1
Discrete Fourier Analysis
M.W. Wong
Springer, 2011, ISNM 978-3-0348-0116-4
http://dx.doi.org/10.1007/978-3-0348-0116-4
Mastering the Discrete Fourier Transform in One, Two or
Several Dimensions: Pitfalls and Artifacts
Issav Amidror
Springer, 2013, ISBN 978-1-4471-5167-8
http://dx.doi.org/10.1007/978-1-4471-5167-8
Decay of the Fourier Transform:
Analytic and Geometric Aspects
Alex Iosevich and Elijah Liflyand
Springer, 2014, ISBN 978-3-0348-0625-1
http://dx.doi.org/10.1007/978-3-0348-0625-1
Excursions in Harmonic Analysis, Volume 1:
The February Fourier Talks at the Norbert Wiener Center
Travis D. Andrews, Radu Balan, John J. Benedetto,
Wojciech Czaja, and Kasso A. Okoudjou (Editors)
Springer, 2013, ISBN 978-0-8176-8376-4
http://dx.doi.org/10.1007/978-0-8176-8376-4
Excursions in Harmonic Analysis, Volume 2:
The February Fourier Talks at the Norbert Wiener Center
Travis D. Andrews, Radu Balan, John J. Benedetto,
Wojciech Czaja, and Kasso A. Okoudjou (Editors)
Springer, 2013, ISBN 978-0-8176-8379-5
http://dx.doi.org/10.1007/978-0-8176-8379-5
Wavelets and Multiscale Analysis: Theory and Applications
Jonathan Cohen and Ahmed I. Zayed (Editors)
Springer, 2011, ISBN 978-0-8176-8095-4
http://dx.doi.org/10.1007/978-0-8176-8095-4
Shearlets: Multiscale Analysis for Multivariate Data
Gitta Kutyniok and Demetrio Labate (Editors)
Springer, 2012, ISBN 978-0-8176-8316-0
http://dx.doi.org/10.1007/978-0-8176-8316-0
Unified Signal Theory
Gianfranco Cariolaro
Springer, 2011, ISBN 978-0-85729-464-7
http://dx.doi.org/10.1007/978-0-85729-464-7
Fast Fourier Transform: Algorithms and Applications
K.R. Rao, D.N. Kim, and J.J. Hwang
Springer, 2010, ISBN 978-1-4020-6629-0
http://dx.doi.org/10.1007/978-1-4020-6629-0
A First Course in Statistics for Signal Analysis, Second Edition
Springer, 2011, ISBN 978-0-8176-8101-2
Wojbor A. Woyczynski
http://dx.doi.org/10.1007/978-0-8176-8101-2
A Basis Theory Primer: Expanded Edition
Christopher Heil
Springer, 2011, ISBN 978-0-8176-4687-5
http://dx.doi.org/10.1007/978-0-8176-4687-5
Distributions: Theory and Applications
J.J. Dustremaat and J.A.C. Kolk
Springer, 2010, ISBN 978-0-8176-4675-2
http://dx.doi.org/10.1007/978-0-8176-4675-2
Introduction to Hyperfunctions and Their Integral Transforms:
An Applied and Computational Approach
Urs Graf
Springer, 2010, ISBN 978-3-0346-0408-6
http://dx.doi.org/10.1007/978-3-0346-0408-6
Explorations in Harmonic Analysis: With Applications to
Complex Function Theory and the Heisenberg Group
Steven G. Krantz
Springer, 2009, ISBN 978-0-8176-4669-1
http://dx.doi.org/10.1007/978-0-8176-4669-1
Principles of Harmonic Analysis
Anton Deitmar and Siegfried Echterhoff
Springer, 2009, ISBN 978-0-387-85469-4
http://dx.doi.org/10.1007/978-0-387-85469-4
The Evolution of Applied Harmonic Analysis:
Models of the Real World
Elena Prestini
Springer, 2004, ISBN 978-0-8176-8140-1
http://dx.doi.org/10.1007/978-0-8176-8140-1
Fourier Analysis and Approximation of Functions
Roald M. Trigub and Eduard S. Bellinsky
Springer, 2004, ISBN 978-1-4020-2876-2
http://dx.doi.org/10.1007/978-1-4020-2876-2
Applied Mathematics: Data Compression, Spectral Methods,
Fourier Analysis, Wavelets, and Applications
Charles K. Chui and Quingtang Jiang
Springer, 2013, ISBN 978-94-6239-009-6
http://dx.doi.org/10.2991/978-94-6239-009-6
Back to the Table of Contents
=======================================
Inequalities ============================
Inequalities: Theorems, Techniques and Selected Problems
Zdravko Cvetkovski
Springer, 2012, ISBN 978-3-642-23792-8
http://dx.doi.org/10.1007/978-3-642-23792-8
Equations and Inequalities:
Elementary Problems and Theorems in Algebra and Number
Theory
Jiri Herman, Radan Kucera, and Jaromir Simsa
Springer, 2000, ISBN 978-1-4612-1270-6
http://dx.doi.org/10.1007/978-1-4612-1270-6
Inequalities: With Applications to Engineering, Second Edition
Michael J. Cloud, Byron C. Drachman, and Leonid P. Lebedev
Springer, 2014, ISBN 978-3-319-05311-0
http://dx.doi.org/10.1007/978-3-319-05311-0
The Cauchy-Schwarz Master Class:
An Introduction to the Art of Mathematical Inequalities
J. Michael Steele
Cambridge University Press, 2004, ISBN 9780511917106
http://dx.doi.org/10.1017/CBO9780511817106
Inequalities
E. F. Beckenbach and R. Bellman
Springer, 1965, ISBN 978-3-642-64971-4
http://dx.doi.org/10.1007/978-3-642-64971-4
Back to the Table of Contents
=======================================
Proof: A Many-Splendored Thing ==========
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Book of Proof, Second Edition
Richard Hammack (2013)
http://www.people.vcu.edu/~rhammack/BookOfProof/
Home Page of Richard Hammack
http://www.people.vcu.edu/~rhammack/
A Gentle Introduction to the Art of Mathematics
Joseph E. Fields (2013)
http://ares.southernct.edu/~fields/GIAM/
Home Page of Joe Fields
http://ares.southernct.edu/~fields/
Mathematical Reasoning: Writing and Proof
Ted Sundstrom (2014)
https://sites.google.com/site/mathematicalreasoning3ed/
Home Page of Ted Sundstrom
https://sites.google.com/site/tedsundstrom/
The Art of Proof:
Basic Training for Deeper Mathematics
Matthias Beck and Ross Geoghegan
Springer, 2010, ISBN 978-1-4419-7023-7
http://dx.doi.org/10.1007/978-1-4419-7023-7
The Proof is in the Pudding:
The Changing Nature of Mathematical Proof
Steven G. Krantz
Springer, 2011, ISBN 978-0-387-48744-1
http://dx.doi.org/10.1007/978-0-387-48744-1
Proof Patterns
Mark Joshi
Springer, 2015, ISBN 978-3-319-16250-8
http://dx.doi.org/10.1007/978-3-319-16250-8
Proof: A Many-Splendored Thing
Israel Kleiner and Nitsa Movshovitz-Hadat
Mathematical Intelligencer,
Volume 19, Number 3 (June 1997)
http://dx.doi.org/10.1007/BF03025344
Proofs from THE BOOK, Fifth Edition
Martin Aigner and Gunther M. Ziegler
Springer, 2014, ISBN 978-3-662-44205-0
http://dx.doi.org/10.1007/978-3-662-44205-0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Deduction, Computation, Experiment:
Exploring the Effectiveness of Proof
Rosella Lupacchini and Giovanna Corsi (Editors)
Springer, 2008, ISBN 978-88-470-0784-0
http://dx.doi.org/10.1007/978-88-470-0784-0
Proofs (Not) from the Book
S. Tabachnikov
Mathematical Intelligencer, Volume 36, Number 2 (June 2014)
http://dx.doi.org/10.1007/s00283-013-9424-2
A Logical Introduction to Proof
Daniel W. Cunningham
Springer, 2012, ISBN 978-1-4614-3631-7
http://dx.doi.org/10.1007/978-1-4614-3631-7
Informal Logic
http://dx.doi.org/10.1007/978-1-4419-7127-2_1
Strategies for Proofs
http://dx.doi.org/10.1007/978-1-4419-7127-2_2
Proofs and Fundamentals:
A First Course in Abstract Mathematics, Second Edition
Ethan D. Bloch
Springer, 2011, ISBN 978-1-4419-7127-2
http://dx.doi.org/10.1007/978-1-4419-7127-2
Introduction to Mathematical Structures and Proofs,
Second Edition
Larry J. Gerstein
Springer, 2012, ISBN 978-1-4614-4265-3
http://dx.doi.org/10.1007/978-1-4614-4265-3
Is it Plausible?
Barry Mazur
Mathematical Intelligencer,
Volume 36, Number 1 (February 2014)
http://dx.doi.org/10.1007/s00283-013-9398-0
Paradigms of Proof
Johnston Anderson and Keith Austin
The Mathematical Gazette,
Volume 79, Number 486 (November 1995)
http://www.jstor.org/stable/3618075
Introduction – Creativity, Thought and Mathematical Proof
Ian Winchester (Editor)
Special Issue: Creativity, Thought and Mathematical Proof
Interchange, Volume 21, Number 1 (Spring 1990)
http://dx.doi.org/10.1007/BF01809603
Why Do We Prove Theorems?
Yehuda Ray
Philosophia Mathematica, Volume 7, Issue 1 (February 1999)
http://dx.doi.org/10.1093/philmat/7.1.5
Back to the Table of Contents
=======================================
The Four-Colour Problem ================
Problem: Can every map be coloured with at most four
colours in such a way that neighbouring countries are
coloured differently?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The existence of unavoidable sets of geographically good
configurations
K. Appel and W. Haken
Illinois Journal of Mathematics, Volume 20, Number 2 (1976)
http://www.projecteuclid.org/euclid.ijm/1256049898
The Four-Color Problem
Kenneth Appel and Wolfgang Haken
http://dx.doi.org/10.1007/978-1-4613-9435-8_7
Mathematics Today: Twelve Informal Essays
Lynn Arthur Steen (Editor)
Springer, 1978, ISBN 978-1-4613-9435-8
http://dx.doi.org/10.1007/978-1-4613-9435-8
An Unavoidable Set of Configurations in Planar Triangulations
K. Appel and W. Haken
Journal of Combinatorial Theory B,
Volume 26, Number 1 (February 1979)
http://dx.doi.org/10.1016/0095-8956(79)90038-8
The Four Color Proof Suffices
K. Appel and W. Haken
Mathematical Intelligencer,
Volume 8, Number 1 (March 1986)
http://dx.doi.org/10.1007/BF03023914
A Digest of the Four Color Theorem
Frank R. Bernhart
Journal of Graph Theory, Volume 1, Number 3 (Fall 1977)
http://dx.doi.org/10.1002/jgt.3190010305
The Four-Color Theorem
Rudolf Fritsch and Gerda Fritsch
Springer, 1998, ISBN 978-1-4612-1720-6
http://dx.doi.org/10.1007/978-1-4612-1720-6
Map Color Theorem
Gerhard Ringel
Springer, 1974, ISBN 978-3-642-65759-7
http://dx.doi.org/10.1007/978-3-642-65759-7
Chapter 3 On Proof and Progress in Mathematics
William P. Thurston
http://dx.doi.org/10.1007/0-387-29831-2_3
Chapter 7 Computers and the Sociology of Mathematical
Proof
Donald Mackenzie
http://dx.doi.org/10.1007/0-387-29831-2_7
18 Unconventional Essays on the Nature of Mathematics
Reuben Hersh (Editor)
Springer, 2006, ISBN 978-0-387-29831-3
http://dx.doi.org/10.1007/0-387-29831-2
Back to the Table of Contents
=======================================
Geometry, Fractals, and Topology =========
Mysteries of the Equilateral Triangle
Brian J. McCartin
http://www.m-hikari.com/bmp.html
The Four Pillars of Geometry
John Stillwell
Springer, 2005, ISBN 978-0-387-29052-2
http://dx.doi.org/10.1007/0-387-29052-4
Gems of Geometry, Second Edition
John Barnes
Springer, 2012, ISBN 978-3-642-30964-9
http://dx.doi.org/10.1007/978-3-642-30964-9
An Axiomatic Approach to Geometry: Geometric Trilogy I
Francis Borceux
Springer, 2014, ISBN 978-3-319-01730-3
http://dx.doi.org/10.1007/978-3-319-01730-3
An Algebraic Approach to Geometry: Geometric Trilogy II
Francis Borceux
Springer, 2014, ISBN 978-3-319-01733-4
http://dx.doi.org/10.1007/978-3-319-01733-4
A Differential Approach to Geometry: Geometric Trilogy III
Francis Borceux
Springer, 2014, ISBN 978-3-319-01736-5
http://dx.doi.org/10.1007/978-3-319-01736-5
Shaping Space:
Exploring Polyhedra in Nature, Art, and the
Geometrical Imagination
Marjorie Senechal (Editor)
Springer, 2013, IS N978-0-387-92714-5
http://dx.doi.org/10.1007/978-0-387-92714-5
Manifold Mirrors:
The Crossing Paths of the Arts and Mathematics
Felipe Cucker
Cambridge University Press, 2013, ISBN 9781139014632
http://dx.doi.org/10.1017/CBO9781139014632
The Art of Science:
From Perspective Drawing to Quantum Randomness
Rossella Lupacchini and Annarita Angelini (Editors)
Springer, 2014, ISBN 978-3-319-02111-9
http://dx.doi.org/10.1007/978-3-319-02111-9
Perspectives on Projective Geometry:
A Guided Tour Through Real and Complex Geometry
Jurgen Richter-Gebert
Springer, 2011, ISBN 978-3-642-17286-1
http://dx.doi.org/10.1007/978-3-642-17286-1
Symmetry and Pattern in Projective Geometry
Eric Lord
Springer, 2013, ISBN 978-1-4471-4631-5
http://dx.doi.org/10.1007/978-1-4471-4631-5
Geometry Revealed:
A Jacob’s Ladder to Modern Higher Geometry
Marcel Berger
Springer, 2010, ISBN 978-3-540-70997-8
http://dx.doi.org/10.1007/978-3-540-70997-8
Curves and Surfaces
Marco Abate and Francesca Tovena
Springer, 2012, ISBN 978-88-470-1941-6
http://dx.doi.org/10.1007/978-88-470-1941-6
Dense Sphere Packings: A blueprint for formal proofs
Thomas C. Hales
Cambridge University Press, 2012, ISBN 9781139193894
http://dx.doi.org/10.1017/CBO9781139193894
The Colours of Infinity:
The Beauty and Power of Fractals
Nigel Lesmoir-Gordon (Editor)
Springer, 2011, ISBN 978-1-84996-486-9
http://dx.doi.org/10.1007/978-1-84996-486-9
Chaos and Fractals: New Frontiers of Science, Second Edition
Heinz-Otto Peitgen, Hartmut Jurgens, and Dietmar Saupe
Springer, 2004, ISBN 978-0-387-21823-6
http://dx.doi.org/10.1007/b97624
The Science of Fractal Images
Heinz-Otto Peitgen and Dietmar Saupe (Editors)
Springer, 1988, ISBN 978-1-4612-3784-6
http://dx.doi.org/10.1007/978-1-4612-3784-6
The Beauty of Fractals:
Images of Complex Dynamical Systems
H.-O. Peitgen and P.H. Richter
Springer, 1986, ISBN 978-3-642-61717-1
http://dx.doi.org/10.1007/978-3-642-61717-1
Superfractals
Michael Fielding Barnsley
Cambridge University Press, 2006, ISBN 9781107590168
http://dx.doi.org/10.1017/CBO9781107590168
Fractal Geometry
Steven G. Krantz
Mathematical Intelligencer,
Volume 11, Number 4 (Fall 1989)
http://dx.doi.org/10.1007/BF03025877
Some “Facts” That Evaporate Upon Examination
Benoit B. Mandelbrot
Mathematical Intelligencer,
Volume 11, Number 4 (Fall 1989) Pages 17-19
http://dx.doi.org/10.1007/BF03025878
Art Meets Mathematics in the Fourth Dimension, Second
Edition
Stephen Leon Lipscomb
Springer, 2014, ISBN 978-3-319-06254-9
http://dx.doi.org/10.1007/978-3-319-06254-9
Introduction to Topology and Geometry, Second Edition
Saul Stahl and Catherine Stenson
Wiley, 2013, ISBN 9781118545904
http://dx.doi.org/10.1002/9781118545904
A Course in Point Set Topology
John B. Conway
Springer, 2014, ISBN 978-3-319-02368-7
http://dx.doi.org/10.1007/978-3-319-02368-7
Measure, Topology, and Fractal Geometry, Second Edition
Gerald Edgar
Springer, 2008, ISBN 978-0-387-74749-1
http://dx.doi.org/10.1007/978-0-387-74749-1
Explorations in Topology:
Map Coloring, Surfaces, and Knots; Second Edition
David A. Gay
Elsevier, 2014, ISBN 978-0-12-416648-6
http://www.sciencedirect.com/science/book/9780124166486
The Four-Color Theorem:
History, Topological Foundations, and Idea of Proof
Rudolf Fritsch and Gerda Fritsch
Springer, 1998, ISBN 978-1-4612-1720-6
http://dx.doi.org/10.1007/978-1-4612-1720-6
A Short Course in Computational Geometry and Topology
Herbert Edelsbrunner
Springer, 2014, ISBN 978-3-319-05957-0
http://dx.doi.org/10.1007/978-3-319-05957-0
Ideals, Varieties, and Algorithms:
An Introduction to Computational Algebraic Geometry and
Commutative Algebra, Fourth Edition
David A. Cox, John Little, and Donal O’Shea
Springer, 2015, ISBN 978-3-319-16721-3
http://dx.doi.org/10.1007/978-3-319-16721-3
Convex Analysis
Steven G. Krantz
CRC Press, 2015, ISBN 978-1-4987-0638-4
http://dx.doi.org/10.1201/b17694
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lie Groups, Lie Algebras, and Representations:
An Elementary Introduction; Second Edition
Brian Hall
Springer, 2015, ISBN 978-3-319-13467-3
http://dx.doi.org/10.1007/978-3-319-13467-3
Back to the Table of Contents
=======================================
Linear Algebra =========================
Linear Algebra
David Cherney, Tom Denton, and Andrew Waldron
https://www.math.ucdavis.edu/~linear/
Linear Algebra Done Right, Third Edition
Sheldon Axler
Springer, 2015, ISBN 978-3-319-11080-6
http://dx.doi.org/10.1007/978-3-319-11080-6
Linear Algebra:
Algorithms, Applications, and Techniques; Third Edition
Richard Bronson, Gabriel B. Costa, and John T. Saccoman
Elsevier, 2014, ISBN 978-0-12-391420-0
http://www.sciencedirect.com/science/book/9780123914200
Linear Algebra: for everyone
Lorenzo Robbiano
Springer, 2011, ISBN 978-88-470-1839-6
http://dx.doi.org/10.1007/978-88-470-1839-6
Finite-Dimensional Vector Spaces
Paul R. Halmos
Springer, 1987, ISBN 978-1-4612-6387-6
http://dx.doi.org/10.1007/978-1-4612-6387-6
Vectors, Pure and Applied:
A General Introduction to Linear Algebra
T. W. Körner
Cambridge University Press, 2013, ISBN 9781139520034
http://dx.doi.org/10.1017/CBO9781139520034
A First Course in Linear Algebra
Robert A. Beezer (2004-2013)
http://linear.ups.edu/download.html
Linear Algebra Thoroughly Explained
Milan Vujicic
Springer, 2007, ISBN 978-3-540-74639-3
http://dx.doi.org/10.1007/978-3-540-74639-3
Linear Algebra: Concepts and Methods
Martin Anthony and Michele Harvey
Cambridge University Press, 2012, ISBN 9780511844249
http://dx.doi.org/10.1017/CBO9780511844249
A Concise Introduction to Linear Algebra
Geza Schay
Springer, 2012, ISBN 978-0-8176-8325-2
http://dx.doi.org/10.1007/978-0-8176-8325-2
Linear Algebra
Peter Petersen
Springer, 2012, ISBN 978-1-4614-3612-6
http://dx.doi.org/10.1007/978-1-4614-3612-6
The Linear Algebra a Beginning Graduate Student Ought to
Know, Third Edition
Jonathan S. Golan
Springer, 2012, ISBN 978-94-007-2636-9
http://dx.doi.org/10.1007/978-94-007-2636-9
Applied Linear Algebra and Matrix Analysis
Thomas Shores
Springer, 2007, ISBN 978-0-387-48947-6
http://dx.doi.org/10.1007/978-0-387-48947-6
Matrix Analysis, Second Edition
Roger A. Horn and Charles R. Johnson
Cambridge University Press, 2013, ISBN 9781139020411
http://dx.doi.org/10.1017/CBO9781139020411
Matrix Reference Manual
Mike Brookes
http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/
Home Page
http://www.ee.ic.ac.uk/hp/staff/dmb/
A Concise Text on Advanced Linear Algebra
Yisong Yang
Cambridge University Press, 2015, ISBN 9781316103845
http://dx.doi.org/10.1017/CBO9781316103845
Advanced Linear Algebra
Nicholas Loehr
CRC Press, 2014, ISBN 978-1-4665-5902-8
http://dx.doi.org/10.1201/b16505
Advanced Linear Algebra, Third Edition
Steven Roman
Springer, 2008, ISBN 978-0-387-72831-5
http://dx.doi.org/10.1007/978-0-387-72831-5
Algebra and Number Theory: An Integrated Approach
Martyn R. Dixon, Leonid A. Kurdachenko,
and Igor Ya. Subbotin
Wiley, 2010, ISBN 9780470640548
http://dx.doi.org/10.1002/9780470640548
Linear Algebra and Geometry
Igor R. Shafarevich and Alexey O. Remizov
Springer, 2013, ISBN 978-3-642-30994-6
http://dx.doi.org/10.1007/978-3-642-30994-6
Separable Type Representations of Matrices and Fast
Algorithms
Volume 1: Basics. Completion Problems.
Multiplication and Inversion Algorithms
Yuli Eidelman, Israel Goldberg, and Julian Haimovici
Springer, 2014, ISBN 978-3-0348-0606-0
http://dx.doi.org/10.1007/978-3-0348-0606-0
Separable Type Representations of Matrices and Fast
Algorithms
Volume 2: Eigenvalue Method
Yuli Eidelman, Israel Goldberg, and Julian Haimovici
Springer, 2014, ISBN 978-3-0348-0612-1
http://dx.doi.org/10.1007/978-3-0348-0612-1
Back to the Table of Contents
=======================================
Algebra ===============================
Classical Algebra: Its Nature, Origins, and Uses
Roger Cooke
Wiley, 2008, ISBN 9780470277980
http://dx.doi.org/10.1002/9780470277980
Basic Algebra
Anthony W. Knapp
Springer, 2006, ISBN 978-0-8176-4529-8
http://dx.doi.org/10.1007/978-0-8176-4529-8
Advanced Algebra
Anthony W. Knapp
Springer, 2007, ISBN 978-0-8176-4613-4
http://dx.doi.org/10.1007/978-0-8176-4613-4
Groups:
An Introduction to Ideas and Methods of the Theory of Groups
Antonio Machi
Springer, 2012, ISBN 978-88-470-2421-2
http://dx.doi.org/10.1007/978-88-470-2421-2
Basic Modern Algebra with Applications
Mahima Ranjan Adhikari and Avishek Adhikari
Springer, 2014, ISBN 978-81-322-1599-8
http://dx.doi.org/10.1007/978-81-322-1599-8
Drawing with Complex Numbers
Michael Eastwood and Roger Penrose
The Mathematical Intelligencer,
Volume 22, Number 4 (December 2000)
http://dx.doi.org/10.1007/BF03026760
Why do Mathematicians Need Different Ways of Presenting
Mathematical Objects? The Case of Cayley Graphs
Irina Starikova
http://dx.doi.org/10.1007/s11245-009-9065-4
Mathematical Knowledge: Intuition, visualization, and
understanding (special issue)
Leon Horsten and Irina Starikova(Editors)
Topoi, Volume 29, Number 1 (April 2010)
Exterior Analysis: Using Applications of Differential Forms
Erdogan S. Suhubi
Elsevier, 2013, ISBN 978-0-12-415902-0
http://www.sciencedirect.com/science/book/9780124159020
Representation Theory: A Homological Algebra Point of View
Alexander Zimmerman
Springer, 2014, ISBN 978-3-319-07968-4
http://dx.doi.org/10.1007/978-3-319-07968-4
Category Theory
Steve Awodey
Oxford University Press, 2006, ISBN 9780198568612
http://dx.doi.org/10.1093/acprof:oso/9780198568612.001.000
1
Abstract Algebra: Structure and Applications
David R. Finston and Patrick J. Morandi
Springer, 2014, ISBN 978-3-319-04498-9
http://dx.doi.org/10.1007/978-3-319-04498-9
An Invitation to General Algebra and Universal Constructions,
Second Edition
George M. Bergman
Springer, 2015, ISBN 978-3-319-11478-1
http://dx.doi.org/10.1007/978-3-319-11478-1
Back to the Table of Contents
=======================================
Multivariable Calculus ===================
Mathematical Analysis:
An Introduction to Functions of Several Variables
Mariano Giaquinta and Guiseppe Modica
Springer, 2009, ISBN 978-0-8176-4612-7
http://dx.doi.org/10.1007/978-0-8176-4612-7
A Course in Multivariable Calculus and Analysis
Sudhir R. Ghorpade and Balmohan V. Limaye
Springer, 2010, ISBN 978-1-4419-1621-1
http://dx.doi.org/10.1007/978-1-4419-1621-1
Differential Forms: Theory and Practice, Second Edition
Steven H. Weintraub
Elsevier, 2014, ISBN 978-0-12-394403-0
http://www.sciencedirect.com/science/book/9780123944030
A Geometric Approach to Differential Forms
David Bachman
Springer, 2006, ISBN 978-0-8176-4520-5
http://dx.doi.org/10.1007/978-0-8176-4520-5
Introduction to Tensor Analysis and the Calculus of Moving
Surfaces
Pavel Grinfeld
Springer, 2013, ISBN 978-1-4614-7867-6
http://dx.doi.org/10.1007/978-1-4614-7867-6
Back to the Table of Contents
=======================================
Ordinary Differential Equations ===========
Introductory Differential Equations, Fourth Edition
Martha L. Abell and James P. Braselton
Elsevier, 2014, ISBN 978-0-12-417219-7
http://www.sciencedirect.com/science/book/9780124172197
Ordinary Differential Equations:
Analysis, Qualitative Theory and Control
Hartmut Logemann and Eugene P. Ryan
Springer, 2014, ISBN 978-1-4471-6398-5
http://dx.doi.org/10.1007/978-1-4471-6398-5
Differential Equations: A Primer for Scientists and Engineers
Christian Constanda
Springer, 2013, ISBN 978-1-4614-7297-1
http://dx.doi.org/10.1007/978-1-4614-7297-1
A First Course in Differential Equations, Second Edition
J. David Logan
Springer, 2011, ISBN 978-1-4419-7592-8
http://dx.doi.org/10.1007/978-1-4419-7592-8
An Introduction to Ordinary Differential Equations
Ravi P. Agarwal and Donal O’Regan
Springer, 2008, ISBN 978-0-387-71276-5
http://dx.doi.org/10.1007/978-0-387-71276-5
Differential Equations:
Theory and Applications, Second Edition
David Bettounes
Springer, 2010, ISBN 978-1-4419-1163-6
http://dx.doi.org/10.1007/978-1-4419-1163-6
A Textbook on Ordinary Differential Equations
Shair Ahmad and Antonio Ambroscetti
Springer, 2014, ISBN 978-3-319-02129-4
http://dx.doi.org/10.1007/978-3-319-02129-4
A First Course in Ordinary Differential Equations:
Analytical and Numerical Methods
Martin Hermann and Masoud Saravi
Springer, 2014, ISBN 978-81-322-1835-7
http://dx.doi.org/10.1007/978-81-322-1835-7
Ordinary Differential Equations and Mechanical Systems
Jan Awrejcewicz
Springer, 2014, ISBN 978-3-319-07659-1
http://dx.doi.org/10.1007/978-3-319-07659-1
Back to the Table of Contents
=======================================
Partial Differential Equations =============
Introduction to Partial Differential Equations
Peter J. Olver
Springer, 2014, ISBN 978-3-319-02099-0
http://dx.doi.org/10.1007/978-3-319-02099-0
Partial Differential Equations, Second Edition
Emmanuele DiBenedetto
Springer, 2010, ISBN 978-0-8176-4552-6
http://dx.doi.org/10.1007/978-0-8176-4552-6
Partial Differential Equations, Third Edition
Jurgen Jost
Springer, 2013, ISBN 978-1-4614-4809-9
http://dx.doi.org/10.1007/978-1-4614-4809-9
Lectures on Partial Differential Equations
Vladimir I. Arnold
Springer, 2004, ISBN 978-3-662-05441-3
http://dx.doi.org/10.1007/978-3-662-05441-3
Solving Numerical PDEs: Problems, Applications, Exercises
Luca Formaggia, Fausto Saleri, and Alessandro Veneziani
Springer, 2012, ISBN 978-88-470-2412-0
http://dx.doi.org/10.1007/978-88-470-2412-0
Applied Partial Differential Equations
J. David Logan
Springer, 2015, ISBN 978-3-319-12493-3
http://dx.doi.org/10.1007/978-3-319-12493-3
Back to the Table of Contents
=======================================
Functional Analysis =====================
Real Analysis for the Undergraduate:
With an Invitation to Functional Analysis
Matthew A. Pons
Springer, 2014, ISBN 978-1-4614-9638-0
http://dx.doi.org/10.1007/978-1-4614-9638-0
An Introduction to Modern Analysis
Vicente Montesinos, Peter Zizler, and Vaclav Zizler
Springer, 2015, ISBN 978-3-319-12481-0
http://dx.doi.org/10.1007/978-3-319-12481-0
Functional Analysis: Fundamentals and Applications
Michel Willem
Springer, 2013, ISBN 978-1-4614-7004-5
http://dx.doi.org/10.1007/978-1-4614-7004-5
Functional Analysis:
An Introduction to Metric Spaces, Hilbert Spaces,
and Banach Algebras
Joseph Muscat
Springer, 2014, ISBN 978-3-319-06728-5
http://dx.doi.org/10.1007/978-3-319-06728-5
A Primer on Hilbert Space Theory:
Linear Spaces, Topological Spaces, Metric Spaces,
Normed Spaces, and Topological Groups
Carlo Alabiso and Ittay Weiss
Springer, 2015, ISBN 978-3.319-03713-4
http://dx.doi.org/10.1007/978-3-319-03713-4
Functional Analysis, Calculus of Variations and
Optimal Control
Francis Clarke
Springer, 2013, ISBN 978-1-4471-4820-3
http://dx.doi.org/10.1007/978-1-4471-4820-3
Methods of Nonlinear Analysis:
Applications to Differential Equations, Second Edition
Pavel Drabek and Jaroslav Milota
Springer, 2013, ISBN 978-3-0348-0387-8
http://dx.doi.org/10.1007/978-3-0348-0387-8
A Glimpse at Hilbert Space Operators:
Paul R. Hamos in Memoriam
Sheldon Axler, Peter Rosenthal, and Donald Sarason (Editors)
Birkhauser, 2010, ISBN 978-3-0346-0347-8
http://dx.doi.org/10.1007/978-3-0346-0347-8
Wikipedia:
http://en.wikipedia.org/wiki/Paul_Halmos
The Elements of Operator Theory, Second Edition
Carlos S. Kubrusly
Springer, 2011, ISBN 978-0-8176-4998-2
http://dx.doi.org/10.1007/978-0-8176-4998-2
Basic Operator Theory
Israel Gohberg and Seymour Goldberg
Springer, 1980, ISBN 978-1-4612-5985-5
http://dx.doi.org/10.1007/978-1-4612-5985-5
Back to the Table of Contents
=======================================
Discrete Mathematics ===================
Also see:
the Solving Mathematical Problems section.
Applied Discrete Structures
Alan Doerr and Kenneth Levasseur (2013)
http://faculty.uml.edu/klevasseur/ads2/
Home Page of Ken Levasseur
http://faculty.uml.edu/klevasseur/
Chapter 1 The Bridge Between Continuous and Discrete
http://dx.doi.org/10.1007/978-0-387-33062-4_1
Mathematical Masterpieces:
Further Chronicles by the Explorers
Arthur Knoebel, Reinhad Laubenbacher, Jerry Lodder,
and David Pengelley
Springer, 2007, ISBN 978-0-387-33062-4
http://dx.doi.org/10.1007/978-0-387-33062-4
Sets, Logic and Maths for Computing, Second Edition
David Makinson
Springer, 2012, ISBN 978-1-4471-2500-6
http://dx.doi.org/10.1007/978-1-4471-2500-6
Fundamentals of Discrete Math for Computer Science:
A Problem-Solving Primer
Tom Jenkyns and Ben Stephenson
Springer, 2013, ISBN 978-1-4471-4069-6
http://dx.doi.org/10.1007/978-1-4471-4069-6
Mathematics of Discrete Structures for Computer Science
Gordon J. Pace
Springer, 2012, ISBN 978-3-642-29840-0
http://dx.doi.org/10.1007/978-3-642-29840-0
A Beginner’s Guide to Discrete Mathematics, Second Edition
W.D. Wallis
Springer, 2012, ISBN 978-0-8176-8286-6
http://dx.doi.org/10.1007/978-0-8176-8286-6
A First Course in Discrete Mathematics
Ian Anderson
Springer, 2002, ISBN 978-0-85729-315-2
http://dx.doi.org/10.1007/978-0-85729-315-2
Transfinite Numbers – What Is Infinity?
S M Srivastava
Resonance, Volume 2, Number 3 (March 1997)
http://dx.doi.org/10.1007/BF02838969
The Logic of Infinity
Barnaby Sheppard
Cambridge University Press, 2014, ISBN 9781107415614
http://dx.doi.org/10.1017/CBO9781107415614
The Mathematics of Infinity:
A Guide to Great Ideas, Second Edition
Theodore G. Faticoni
Wiley, 2012, ISBN 9781118243879
http://dx.doi.org/10.1002/9781118243879
In Search of Infinity
N. Ya. Vilenkin
Springer, 1995, ISBN 978-1-4612-0837-2
http://dx.doi.org/10.1007/978-1-4612-0837-2
Introduction to Finite Mathematics
John G. Kemeny, J. Laurie Snell, and Gerald L. Thompson
http://www.math.dartmouth.edu/~doyle/docs/finite/cover/co
ver.html
Topics in Finite and Discrete Mathematics
Sheldon M. Ross
Cambridge University Press, 2000, ISN 9780511755354
http://dx.doi.org/10.1017/CBO9780511755354
Mathematics Is Not a Spectator Sport
George M. Phillips
Springer, 2005, ISBN 978-0-387-28697-7
http://dx.doi.org/10.1007/0-387-28697-7
Discrete Mathematics: Elementary and Beyond
L. Lovasz, J. Pelikan, and K. Vesztergombi
Springer, 2003, ISBN 978-0-387-21777-2
http://dx.doi.org/10.1007/b97469
Looking at Numbers
Tom Johnson and Franck Jedrzejewski
Springer, 2014, ISBN 978-3-0438-0554-4
http://dx.doi.org/10.1007/978-3-0348-0554-4
The Last Recreations:
Hydras, Eggs, and Other Mathematical Mystifications
Martin Gardner
Springer, 1997, ISBN 978-0-387-30389-5
http://dx.doi.org/10.1007/978-0-387-30389-5
Difference Equations: From Rabbits to Chaos
Paul Cull, Mary Flahive, and Robby Robson
Springer, 2005, ISBN 978-0-387-27645-9
http://dx.doi.org/10.1007/0-387-27645-9
An Introduction to Difference Equations, Third Edition
Saber Elaydi
Springer, 2005, ISBN 978-0-387-23059-7
http://dx.doi.org/10.1007/0-387-27602-5
The Thrills of Abstraction
P. R. Halmos
The Two-Year College Mathematics Journal,
Volume 13, Number 4 (September 1982)
http://www.jstor.org/stable/3027126
The Truth about Venn Diagrams
Ian Stewart
The Mathematical Gazette,
Volume 60, Number 411 (March 1976)
http://www.jstor.org/stable/3615644
Is the Venn Diagram Good Enough?
Mou-liang Kung and George C. Harrison
The College Mathematics Journal,
Volume 15, Number 1 (January 1984)
http://www.jstor.org/stable/3027430
On Picture-Writing
George Polya
The American Mathematical Monthly,
Volume 63, Number 10 (December 1956)
http://www.jstor.org/stable/2309555
The On-Line Encyclopedia of Integer Sequences (OEIS)
https://oeis.org/
Website of Neil J. A. Sloane
http://neilsloane.com/
Website of Herbert Wilf
http://www.math.upenn.edu/~wilf/
Problems from the Discrete to the Continuous:
Probability, Number Theory, Graph Theory, and
Combinatorics
Ross G. Pinsky
Springer, 2014, ISBN 978-3-319-07965-3
http://dx.doi.org/10.1007/978-3-319-07965-3
Computing the Continuous Discretely:
Integer-Point Enumeration in Polyhedra
Matthias Beck and Sinai Robins
Springer, 2007, ISBN 978-0-387-46112-0
http://dx.doi.org/10.1007/978-0-387-46112-0
The Surprising Mathematics of Longest Increasing
Subsequences
Dan Romik
Cambridge University Press, 2014, ISBN 9781139872003
http://dx.doi.org/10.1017/CBO9781139872003
Back to the Table of Contents
=======================================
Combinatorics =========================
Combinatorics Through Guided Discovery
Kenneth P. Bogart (2004)
http://www.math.dartmouth.edu/newsresources/electronic/kpbogart/
Foundations of Combinatorics with Applications
Edward A. Bender and S. Gill Williamson
Dover, 2006, ISBN 0-486-44603-4
http://www.math.ucsd.edu/~ebender/CombText/
Applied Combinatorics: Preliminary Edition
Michael T. Keller and William T. Trotter (2014)
http://people.math.gatech.edu/~trotter/
generatingfunctionology, Second Edition
Academic Press, 1994
Herbert Wilf
http://www.math.upenn.edu/~wilf/DownldGF.html
Website of Herbert Wilf
http://www.math.upenn.edu/~wilf/
The Combinatorial Object Server
http://www.theory.csc.uvic.ca/~cos/
Website of Neil J. A. Sloane
http://neilsloane.com/
A Walk Through Combinatorics:
An Introduction to Enumeration and Graph Theory,
Second Edition
Miklos Bona
World Scientific, 2006, ISBN 981-256-885-9
**** Some pages missing ***
https://books.google.com/books?isbn=9789814335232
How to Count: An Introduction to Combinatorics and Its
Applications
Robert A. Beeler
Springer, 2015, ISBN 978-3-319-13844-2
http://dx.doi.org/10.1007/978-3-319-13844-2
Combinatorics of Permutations, Second Edition
Miklos Bona
CRC Press, 2012, ISBN 978-1-4398-5052-7
http://dx.doi.org/10.1201/b12210
Combinatorics of Set Partitions
Toufik Mansour
CRC Press, 2013, ISBN 978-1-4398-6334-3
http://dx.doi.org/10.1201/b12691
On Picture-Writing
George Polya
The American Mathematical Monthly,
Volume 63, Number 10 (December 1956)
http://www.jstor.org/stable/2309555
Constructive Combinatorics
Dennis Stanton and Dennis White
Springer, 1986, ISBN 978-1-4612-4968-9
http://dx.doi.org/10.1007/978-1-4612-4968-9
Counting: The Art of Enumerative Combinatorics
George E. Martin
Springer, 2001, ISBN 978-1-4757-4878-9
http://dx.doi.org/10.1007/978-1-4757-4878-9
An Introduction to Enumeration
Alan Camina and Barry Lewis
Springer, 2011, ISBN 978-0-85729-599-6
http://dx.doi.org/10.1007/978-0-85729-600-9
Combinatorics, Second Edition
Russell Merris
Wiley, 2003, Online ISBN 978-0-471-44968-3
http://dx.doi.org/10.1002/0471449687
Problem-Solving Methods in Combinatorics:
An Approach to Olympiad Problems
Pablo Soberon
Springer, 2013, ISBN 978-3-0348-0597-1
http://dx.doi.org/10.1007/978-3-0348-0597-1
Counting and Configurations:
Problems in Combinatorics, Arithmetic, and Geometry
Jiri Herman, Radan Kucera, and Jaromir Simsa
Springer, 2003, ISBN 978-1-4757-3925-1
http://dx.doi.org/10.1007/978-1-4757-3925-1
Algebraic Combinatorics: Walks, Trees, Tableaux, and More
Richard P. Stanley
Springer, 2013, ISBN 978-1-4614-6998-8
http://dx.doi.org/10.1007/978-1-4614-6998-8
Proofs and Confirmations: The Story of the Alternating Sign
Matrix Conjecture
David M. Bressoud
Cambridge University Press, 1999, ISBN 9780511613449
http://dx.doi.org/10.1017/CBO9780511613449
Inverse Relations and Combinatorial Identities
John Riordan
American Mathematical Monthly,
Volume 71, Number 5 (May 1964)
http://www.jstor.org/stable/2312584
The Pigeonhole Principle (What It Is, How It Works, and How It
Applies to Map Coloring)
Kenneth R. Rebman
The Two-Year College Mathematics Journal,
Volume 10, Number 1 (January 1979)
http://www.jstor.org/stable/3026807
Notes on Introductory Combinatorics
George Polya, Robert E. Tarjan, and Donald R. Woods
Springer, 2010, ISBN 978-0-8176-4953-1
http://dx.doi.org/10.1007/978-0-8176-4953-1
Combinatorial Enumeration of Groups,
Graphs, and Chemical Compounds
G. Polya and R.C. Read
Springer, 1987, ISBN 978-1-4612-4664-0
http://dx.doi.org/10.1007/978-1-4612-4664-0
Combinatorics: The Rota Way
Joseph P. S. King, Gian-Carlo Rota, and Catherine H. Yan
Cambridge University Press, 2009, ISBN 9780511803895
http://dx.doi.org/10.1017/CBO9780511803895
Combinatorial Snapshots
Gian-Carlo Rota
The Mathematical Intelligencer,
Volume 21, Number 2 (June 1999)
http://dx.doi.org/10.1007/BF03024840
On the foundations of combinatorial theory I. Theory of
Mobius Functions
Gian-Carlo Rota
Probability Theory and Related Fields,
Volume 2, Number 4 (1964)
http://dx.doi.org/10.1007/BF00531932
A Course in Enumeration
Martin Aigner
Springer, 2007, ISBN 978-3-540-39032-9
http://dx.doi.org/10.1007/978-3-540-39035-0
Enumerative Combinatorics, Volume 1, Second Edition
Richard P. Stanley
Cambridge University Press, 2012, ISBN 9781139058520
http://dx.doi.org/10.1017/CBO9781139058520
Enumerative Combinatorics, Volume 2
Richard P. Stanley
Cambridge University Press, 1999, ISBN 978-0-511-60958-9
http://dx.doi.org/10.1017/CBO9780511609589
Combinatorial Theory
Martin Aigner
Springer, 1997, ISBN 978-3-642-59101-3
http://dx.doi.org/10.1007/978-3-642-59101-3
A Course in Combinatorics, Second Edition
J. H. van Lint and R. M. Wilson
Cambridge University Press, 2001, ISBN 9780511987045
http://dx.doi.org/10.1017/CBO9780511987045
Combinatorial Theory, Second Edition
Marshall Hall, Jr.
Wiley, 1983 (1998), ISBN 9781118032862
http://dx.doi.org/10.1002/9781118032862
Partition bijections, a survey
Igor Pak
The Ramanujan Journal, Volume 12, Number 1 (August 2006)
http://dx.doi.org/10.1007/s11139-006-9576-1
Permutations, matrices, and generalized Young
tableaux
Donald E. Knuth
Pacific Journal of Mathematics, Volume 34, Number 3 (1970)
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=
Display&handle=euclid.pjm/1102971948
Advanced Combinatorics: The Art of Finite and Infinite
Expansions; Revised and Enlarged Edition
Louis Comtet
Springer, 1974, ISBN 978-94-010-2196-8
http://dx.doi.org/10.1007/978-94-010-2196-8
Analytic Combinatorics
Philippe Flajolet and Robert Sedgewick
Cambridge University Press, 2009, ISBN 9780511801655
http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.h
tml
http://dx.doi.org/10.1017/CBO9780511801655
Geometric Etudes in Combinatorial Mathematics
Alexander Soifer
Springer, 2010, ISBN 978-0-387-75469-7
http://dx.doi.org/10.1007/978-0-387-75470-3
Ramsey Theory: Yesterday, Today, and Tomorrow
Alexander Soifer (Editor)
Springer, 2011, ISBN 978-0-8176-8092-3
http://dx.doi.org/10.1007/978-0-8176-8092-3
Configurations from a Graphical Viewpoint
Tomaz Pisanski and Brigitte Servatius
Springer, 2013, ISBN 978-0-8176-8364-1
http://dx.doi.org/10.1007/978-0-8176-8364-1
Matroids: A Geometric Introduction
Gary Gordon and Jennifer McNulty
Cambridge University Press, 2012, ISBN 9781139049443
http://dx.doi.org/10.1017/CBO9781139049443
The Last Recreations:
Hydras, Eggs, and Other Mathematical Mystifications
Martin Gardner
Springer, 1997, ISBN 978-0-387-30389-5
http://dx.doi.org/10.1007/978-0-387-30389-5
Games of No Chance
Richard J. Nowakowski (Editor)
http://library.msri.org/books/Book29/
More Games of No Chance
Richard J. Nowakowski (Editor)
http://library.msri.org/books/Book42/
Games of No Chance 3
Michael H. Albert and Richard J. Nowakowski (Editors)
Cambridge University Press, 2009, ISBN 9780511807251
http://dx.doi.org/10.1017/CBO9780511807251
Combinatorial Games: Tic-Tac-Toe Theory
Jozsef Beck
Cambridge University Press, 2008, ISBN 978-0-511-73520-2
http://dx.doi.org/10.1017/CBO9780511735202
Back to the Table of Contents
=======================================
Number Theory ========================
The Whole Truth About Whole Numbers:
An Elementary Introduction to Number Theory
Sylvia Forman and Agnes M. Rash
Springer, 2015, ISBN 978-3-319-11035-6
http://dx.doi.org/10.1007/978-3-319-11035-6
Elementary Number Theory in Nine Chapters, Second Edition
James J. Tattersall
Cambridge University Press, 2005, ISBN 9780511756344
http://dx.doi.org/10.1017/CBO9780511756344
Number Theory: Structures, Examples, and Problems
Dorin Andrica and Titu Andreescu
Springer, 2009, ISBN 978-0-8176-4645-5
http://dx.doi.org/10.1007/b11856
An Introduction to Diophantine Equations:
A Problem-Based Approach
Titu Andreescu, Dorin Andrica, and Ion Cucurezeanu
Springer, 2010, ISBN 978-0-8176-4549-6
http://dx.doi.org/10.1007/978-0-8176-4549-6
Complex Numbers From A to … Z, Second Edition
Titu Andreescu and Dorin Andrica
Springer, 2014, ISBN 978-0-8176-8415-0
http://dx.doi.org/10.1007/978-0-8176-8415-0
Number Theory: An Introduction to Mathematics
William A. Coppel
Springer, 2009, ISBN 978-0-387-89486-7
http://dx.doi.org/10.1007/978-0-387-89486-7
A Comprehensive Course in Number Theory
Alan Baker
Cambridge University Press, 2012, ISBN 9781139093835
http://dx.doi.org/10.1017/CBO9781139093835
Equations and Inequalities:
Elementary Problems and Theorems in Algebra and Number
Theory
Jiri Herman, Radan Kucera, and Jaromir Simsa
Springer, 2000, ISBN 978-1-4612-1270-6
http://dx.doi.org/10.1007/978-1-4612-1270-6
Arithmetic Tales
Olivier Bordelles
Springer, 2012, ISBN 978-1-4471-4096-2
http://dx.doi.org/10.1007/978-1-4471-4096-2
An Introduction to Number Theory
Graham Everest and Thomas Ward
Springer, 2005, ISBN 978-1-84628-044-3
http://dx.doi.org/10.1007/b137432
PRIMES: What is Riemann’s Hypothesis?
Barry Mazur and William Stein (2014)
http://wstein.org/books/rh/
Elementary Number Theory: Primes, Congruences, and Secrets
William Stein (2011)
http://wstein.org/ent/
Number Theory: An Introduction via the Distribution of Primes
Benjamin Fine and Gerhard Rosenberger
Springer, 2006, ISBN 978-0-8176-4541-0
http://dx.doi.org/10.1007/978-0-8176-4541-0
Prime Numbers: A Computational Perspective, Second Edition
Richard Crandall and Carl Pomerance
Springer, 2005, ISBN 978-0-387-28979-8
http://dx.doi.org/10.1007/0-387-28979-8
Number Theory in Science and Communication:
With Applications in Cryptography, Physics, Digital
Information, Computing, and Self-Similarity; Fifth Edition
Manfred Schroeder
Springer, 2009, ISBN 978-3-540-85298-8
http://dx.doi.org/10.1007/978-3-540-85298-8
Algebraic Number Theory
Frazer Jarvis
Springer, 2014, ISBN 978-3-319-07545-7
http://dx.doi.org/10.1007/978-3-319-07545-7
Algebraic Number Theory, A Computational Approach
William Stein (2012)
http://wstein.org/books/ant/ant.pdf
Introduction to Modern Number Theory
Yuri Ivanovic Manin and Alexei A. Panchishkin
Springer, 2005, ISBN 3-540-27692-0
http://dx.doi.org/10.1007/3-540-27692-0
A Primer of Analytic Number Theory:
From Pythagoras to Riemann
Jeffrey Stopple
Cambridge University Press, 2003, ISBN 9780511755132
http://dx.doi.org/10.1017/CBO9780511755132
On Certain Sequences of Integers Defined by Sieves
Verna Gardiner, R. Lazarus, N. Metropolis, and S. Ulam
Mathematics Magazine,
Volume 29, Number 3 (January-February 1956)
http://www.jstor.org/stable/3029719
A Visual Display of Some Properties of the Distribution of
Primes
M. L. Stein, S. M. Ulam, and M. B. Wells
American Mathematical Monthly,
Volume 71, Number 5 (May 1964)
http://www.jstor.org/stable/2312588
An Introduction to Sieve Methods and Their Applications
Alina Carmen Cojocaru and M. Ram Murty
Cambridge University Press, 2005, ISBN 978-0-511-61599-3
http://dx.doi.org/10.1017/CBO9780511615993
Neverending Fractions:
An Introduction to Continued Fractions
Jonathan Borwein, Alf Van der Poorten, Jeffrey Shallit,
and Wadim Zudilin
Cambridge University Press, 2014, ISBN 9780511902659
http://dx.doi.org/10.1017/CBO9780511902659
Transcendental Numbers
M. Ram Murty and Purusottam Rath
Springer, 2014, ISBN 978-1-4939-0832-5
http://dx.doi.org/10.1007/978-1-4939-0832-5
Lattice Theory: Foundation
George Gratzer
Springer, 2011, ISBN 978-3-0348-0018-1
http://dx.doi.org/10.1007/978-3-0348-0018-1
Lattice Theory: Special Topics and Applications, Volume 1
George Gratzer and Friedrich Wehrung (Editors)
Springer, 2014, ISBN 978-3-319-06413-0
http://dx.doi.org/10.1007/978-3-319-06413-0
Reciprocity Laws: From Euler to Eisenstein
Franz Lemmermeyer
Springer, 2000, ISBN 978-3-662-12893-0
http://dx.doi.org/10.1007/978-3-662-12893-0
The Quadratic Reciprocity Law: A Collection of Classical Proofs
Oswald Baumgart
Springer, 2015, ISBN 978-3-319-16283-6
http://dx.doi.org/10.1007/978-3-319-16283-6
Introduction to Classical Mathematics I: From the Quadratic
Reciprocity Law to the Uniformization Theorem
Helmut Koch
Springer, 1991, ISBN 978-94-011-3218-3
http://dx.doi.org/10.1007/978-94-011-3218-3
Back to the Table of Contents
=======================================
Graph Theory ==========================
A Beginner’s Guide to Graph Theory, Second Edition
W. D. Wallis
Springer, 2007, ISBN 978-0-8176-4580-9
http://dx.doi.org/10.1007/978-0-8176-4580-9
Combinatorics and Graph Theory, Second Edition
John M. Harris, Jeffry L. Hirst, and Michael J. Mossinghoff
Springer, 2008, ISBN 978-0-387-79711-3
http://dx.doi.org/10.1007/978-0-387-79711-3
Graph Theory with Algorithms and Its Applications:
In Applied Science and Technology
Santanu Saha Ray
Springer, 2013, ISBN 978-81-322-0750-4
http://dx.doi.org/10.1007/978-81-322-0750-4
A Textbook of Graph Theory, Second Edition
R. Balakrishnan and K. Ranganathan
Springer, 2012, ISBN 978-1-4614-4529-6
http://dx.doi.org/10.1007/978-1-4614-4529-6
Covering Walks in Graphs
Futaba Fujie and Ping Zhang
Springer, 2014, ISBN 978-1-4939-0305-4
http://dx.doi.org/10.1007/978-1-4939-0305-4
Magic Graphs, Second edition
Alison M. Marr and W.D. Wallis
Springer, 2013, ISBN 978-0-8176-8391-7
http://dx.doi.org/10.1007/978-0-8176-8391-7
Graphs and Cubes
Sergei Ovchinnikov
Springer, 2011, ISBN 978-1-4614-0797-3
http://dx.doi.org/10.1007/978-1-4614-0797-3
The Mathematical Coloring Book: Mathematics of
Coloring and the Colorful Life of Its Creators
Alexander Soifer
Springer, 2009, ISBN 978-0-387-74642-5
http://dx.doi.org/10.1007/978-0-387-74642-5
Thirty Essays on Geometric Graph Theory
Janos Pach (Editor)
Springer, 2013, ISBN 978-1-4614-01110-0
http://dx.doi.org/10.1007/978-1-4614-0110-0
The Four-Color Theorem:
History, Topological Foundations, and Idea of Proof
Rudolf Fritsch and Gerda Fritsch
Springer, 1998, ISBN 978-1-4612-1720-6
http://dx.doi.org/10.1007/978-1-4612-1720-6
Graph Theory Applications
L.R. Foulds
Springer, 1992, ISBN 978-1-4612-0933-1
http://dx.doi.org/10.1007/978-1-4612-0933-1
Spectral Radius of Graphs
Dragan Stevanovic
Elsevier, 2015, ISBN 9780-12-802068-5
http://www.sciencedirect.com/science/book/9780128020685
Back to the Table of Contents
=======================================
Network Science =======================
Also see:
the Biological Networks shelf in the
Biophysics, Bioinformatics, … section;
the Computational Social Science shelf in the
Computer Science, … section.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Network Science
Albert-Laszlo Barabasi
Center for Complex Network Research,
Northeastern University
http://barabasilab.neu.edu/networksciencebook/
Network Science
Albert-Laszlo Barabasi
More Is Different Conference
Nanyang Technological University, Singapore (2012)
https://www.youtube.com/watch?v=NCq1kpuCUq4
The Architecture of Complexity:
From the Topology of the WWW to Human Diseases
Albert-Laszlo Barabasi
Institute for Mathematics and Its Applications (April 2009)
https://www.youtube.com/watch?v=KOfRITP9o5U
Catching the “Network Science” Bug: Insight and Opportunity
for the Operations Researcher
Operations Research, Volume 56, Number 5 (Sep/Oct 2008)
http://dx.doi.org/10.1287/opre.1080.0606
Complex Networks: An Algorithmic Perspective
Kayhan Erciyes
CRC Press, 2015, ISBN 089-1-4665-7167-9
http://dx.doi.org/10.1201/b17409
Complex networks: Structure and dynamics
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez,
and D.-U. Hwang
Physics Reports, Volume 424 (2006)
http://dx.doi.org/10.1016/j.physrep.2005.10.009
Computational Network Science: An Algorithmic Approach
Henry Hexmoor
Elsevier, 2015, ISBN 978-0-12-800891-1
http://www.sciencedirect.com/science/book/9780128008911
Exploring complex networks
Steven H. Strogatz
Nature, Volume 410, Number 6825 (8 March 2001)
http://dx.doi.org/10.1038/35065725
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Algebraic connectivity of graphs
Miroslav Fiedler
Czechoslovak Mathematical Journal,
Volume 23, Number 2 (1973)
http://dml.cz/handle/10338.dmlcz/101168
Community detection in graphs
Santo Fortunato
Physics Reports, Volume 486 (2010)
http://dx.doi.org/10.1016/j.physrep.2009.11.002
Eigenvectors of acyclic matrices
Miroslav Fiedler
Czechoslovak Mathematical Journal,
Volume 25, Number 4 (1975)
http://dml.cz/handle/10338.dmlcz/101356
Evolution of networks
S.N. Dorogovtsev and J.F.F. Mendes
Advances in Physics, Volume 51 (2002)
http://arxiv.org/abs/cond-mat/0106144
A fast and efficient heuristic algorithm for detecting
community structures in complex networks
Duanbing Chen, Yan Fu, and Mingsheng Shang
Physica A, Volume 388, Number 13 (1 July 2009)
http://dx.doi.org/10.1016/j.physa.2009.03.022
Frontiers in Network Science (special issue)
Bernd Blasius and Dirk Brockmann (Guest Editors)
European Physical Journal B,
Volume 84, Number 4 (December 2011)
http://link.springer.com/journal/10051/84/4/
Graph clustering
Satu Elisa Schaeffer
Computer Science Review, Volume 1 (2007)
http://dx.doi.org/10.1016/j.cosrev.2007.05.001
Lectures on Complex Networks
S. N. Dorogovtsev
Clarendon Press, 2010
https://sites.google.com/site/sergeydorogovtsev/lectures_on_
complex_networks
Network Science: Complexity in Nature and Technology
Ernesto Estrada, Maria Fox, Desmond J. Higham,
and Gian-Luca Oppo (Editors)
Springer, 2010, ISBN 978-1-84996-396-1
http://dx.doi.org/10.1007/978-1-84996-396-1
Networks: An Introduction
M.E.J. Newman
Oxford University Press, 2010, ISBN 9780199206650
http://dx.doi.org/10.1093/acprof:oso/9780199206650.001.000
1
Network Science, Nonlinear Science and Infrastructure
Systems
Terry L. Friesz (Editor)
Springer, 2007, ISBN 978-0-387-71134-8
http://dx.doi.org/10.1007/0-387-71134-1
Performance Analysis of Complex Networks and Systems
Piet van Mieghem
Cambridge University Press, 2014, ISBN 9781107415874
http://dx.doi.org/10.1017/CBO9781107415874
A property of eigenvectors of nonnegative symmetric matrices
and its application to graph theory
Miroslav Fiedler
Czechoslovak Mathematical Journal,
Volume 25, Number 4 (1975)
http://dml.cz/handle/10338.dmlcz/101357
Spectral methods for graph clustering – A survey
Maria C.V. Nascimento and Andre C.P.L.F. de Carvalho
European Journal of Operational Research,
Volume 2011, Number 2 (1 June 2011)
http://dx.doi.org/10.1016/j.ejor.2010.08.012
Statistical mechanics of complex networks
Reka Albert and Albert-Laszlo Barabasi
Reviews of Modern Physics, Volume 74 (2002)
http://arxiv.org/abs/cond-mat/0106096
Structural Equation Models: From Paths to Networks
J. Christopher Westland
Springer, 2015, ISBN 978-3-319-16507-3
http://dx.doi.org/10.1007/978-3-319-16507-3
The structure and function of complex networks
M. E. J. Newman
SIAM Review, Volume 45 (2003)
http://arxiv.org/abs/cond-mat/0303516
A survey of kernel and spectral methods for clustering
Maurizio Filippone, Francesco Camastra, Francesco Masulli,
and Stefano Rovetta
Pattern Recognition, Volume 41, Number 1 (January 2008)
http://dx.doi.org/10.1016/j.patcog.2007.05.018
Synchronization in complex networks
Alex Arenas, Albert Diaz-Guilera, Jurgen Kurths,
Yamir Moreno, and Changsong Zhou
Physics Reports, Volume 469, Number 3 (December 2008)
http://dx.doi.org/10.1016/j.physrep.2008.09.002
A very fast algorithm for detecting community structures in
complex networks
Xutao Wang, Guanrong Chen, and Hongtao Lu
Physica A, Volume 384 (2007)
http://dx.doi.org/10.1016/j.physa.2007.05.013
Weak Links: The Universal Key to the Stability of Networks
and Complex Systems
Peter Csermely
Springer, 2009, ISBN 978-3-540-31157-7
http://dx.doi.org/10.1007/978-3-540-31157-7
Back to the Table of Contents
=======================================
Logic and Set Theory ====================
forallx: Cambridge 2014-2015
(with a complete solutions booklet)
P.D. Magnus (modified by Tim Button for Cambridge)
and
Metatheory for truth-functional logic
Tim Button
http://people.ds.cam.ac.uk/tecb2/logicebooks.shtml
Tim Button’s Home Page
http://people.ds.cam.ac.uk/tecb2/index.shtml
forallx: An Introduction to Formal Logic
P.D. Magnus
http://www.fecundity.com/logic/
The Three Laws of Thought, Plus One: The Law of Comparisons
Thomas L. Saaty
Axioms, Volume 3, Number 1 (2014)
http://dx.doi.org/10.3390/axioms3010046
Sets, Relations, Functions
Ivo Düntsch and Günther Gediga (2000)
http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.ht
ml
Propositional and Predicate Calculus: A Model of Argument
Derek Goldrei
Springer, 2005, ISBN 978-1-84628-229-4
http://dx.doi.org/10.1007/1-84628-229-2
Logic and Structure, Fifth Edition
Dirk van Dalen
Springer, 2013, ISBN 978-1-4471-4558-5
http://dx.doi.org/10.1007/978-1-4471-4558-5
Elements of Logical Reasoning
Jan Von Plato
Cambridge University Press, 2013, ISBN 97851139567862
http://dx.doi.org/10.1017/CBO9781139567862
First-Order Logic
Raymond M. Smullyan
Springer, 1968, ISBN 978-3-642-86718-7
http://dx.doi.org/10.1007/978-3-642-86718-7
Lectures in Logic and Set Theory, Volume 1: Mathematical
Logic
George Tourlakis
Cambridge University Press, 2003, ISBN 9780511615559
http://dx.doi.org/10.1017/CBO9780511615559
Lectures in Logic and Set Theory, Volume 2: Set Theory
George Tourlakis
Cambridge University Press, 2003, ISBN 9780511615566
http://dx.doi.org/10.1017/CBO9780511615566
Mathematical Logic
George Tourlakis
Wiley, 2008, ISBN 9781118032436
http://dx.doi.org/10.1002/9781118032435
A Course in Mathematical Logic for Mathematicians
Yu. I. Manin
Springer, 2010, ISBN 978-1-4419-0615-1
http://dx.doi.org/10.1007/978-1-4419-0615-1
Proofs and Computations
Helmut Schwichtenberg and Stanley S. Wainer
Cambridge University Press, 2012, ISBN 9781139031905
http://dx.doi.org/10.1017/CBO9781139031905
Type Theory and Formal Proof: An Introduction
Rob Nederpelt and Herman Geuvers
Cambridge University Press, 2014, ISBN 9781139567725
http://dx.doi.org/10.1017/CBO9781139567725
Introduction to Mathematical Logic
Vilnis Detlovs and Karlis Podnieks
http://www.ltn.lv/~podnieks/mlog/ml.htm
What is Mathematics: Godel’s Theorem and Around
Karlis Podnieks
http://www.ltn.lv/~podnieks/gt.html
Website
http://www.ltn.lv/~podnieks/
Computability and Logic, Fifth Edition
George S. Boolos, John P. Burgess, and Richard C. Jeffrey
Cambridge University Press, 2007, ISBN 9780511804076
http://dx.doi.org/10.1017/CBO9780511804076
The Completeness Theorem of Godel:
1. An Introduction to Mathematical Logic
S. M. Srivastava
Resonance, Volume 6, Number 7 (July 2001)
http://dx.doi.org/10.1007/BF02835268
The Completeness Theorem of Godel:
2. Henkin’s Proof for First Order Logic
S. M. Srivastava
Resonance, Volume 6, Number 8 (August 2001)
http://dx.doi.org/10.1007/BF02902516
Godel’s Proof: 1. An Introduction to Mathematical Logic
S M Srivastava
Resonance, Volume 12, Number 2 (February 2007)
http://dx.doi.org/10.1007/s12045-007-0028-z
Godel’s Proof:
2. Semantics of First order Theory and Hilbert’s program
S M Srivastava
Resonance, Volume 12, Number 3 (March 2007)
http://dx.doi.org/10.1007/s12045-007-0018-1
Godel’s Proof: 3. Incompleteness Theorems
S M Srivastava
Resonance, Volume 12, Number 5 (May 2007)
http://dx.doi.org/10.1007/s12045-007-0052-z
An Introduction to Godel’s Theorems, Second Edition
Peter Smith
Cambridge University Press, 2013, ISBN 9781139149105
http://dx.doi.org/10.1017/CBO9781139149105
Kurt Godel: Essays for His Centennial
Solomon Feferman, Charles Parsons, and Stephen G. Simpson
(Editors)
Cambridge University Press, 2010, ISBN 9780511750762
http://dx.doi.org/10.1017/CBO9780511750762
The Mathematics of Logic:
A guide to completeness theorems and their applications
Richard Kaye
Cambridge University Press, 2007, ISBN 9780511619243
http://dx.doi.org/10.1017/CBO9780511619243
Formal Languages in Logic: A Philosophical and Cognitive
Analysis
Catarina Dutilh Novaes
Cambridge University Press, 2012, ISBN 9781139108010
http://dx.doi.org/10.1017/CBO9781139108010
Set Theory: Exploring Independence and Truth
Ralf Schindler
Springer, 2014, ISBN 978-3-319-06725-4
http://dx.doi.org/10.1007/978-3-319-06725-4
Set Theory: With an Introduction to Real Point Sets
Abhijit Dasgupta
Springer, 2014, ISBN 978-1-4614-8854-5
http://dx.doi.org/10.1007/978-1-4614-8854-5
The Joy of Sets: Fundamentals of Contemporary Set Theory,
Second Edition
Keith Devlin
Springer, 1993, ISBN 978-1-4612-0903-4
http://dx.doi.org/10.1007/978-1-4612-0903-4
In Search of Infinity
N. Ya. Vilenkin
Springer, 1995, ISBN 978-1-4612-0837-2
http://dx.doi.org/10.1007/978-1-4612-0837-2
The Mathematics of Infinity: A Guide to Great Ideas,
Second Edition
Theodore G. Faticoni
Wiley, 2012, ISBN 9781118243879
http://dx.doi.org/10.1002/9781118243879
Sets for Mathematics
F. William Lawvere and Robert Rosebrugh
Cambridge University Press, 2003, ISBN 9780511755460
http://dx.doi.org/10.1017/CBO9780511755460
Ordered Sets: An Introduction
Bernd S. W. Schroder
Springer, 2003, ISBN 978-1-4612-0053-6
http://dx.doi.org/10.1007/978-1-4612-0053-6
Classical Descriptive Set Theory
Alexander S. Kechris
Springer, 1995, ISBN 978-1-4612-4190-4
http://dx.doi.org/10.1007/978-1-4612-4190-4
Labyrinth of Thought:
A History of Set Theory and Its Role in Modern Mathematics
Jose Ferreiros
Springer, 2007, ISBN 978-3-7643-8350-3
http://dx.doi.org/10.1007/978-3-7643-8350-3
The Elements of Cantor Sets – With Applications
Robert W. Vallin
Wiley, 2013, ISBN 9781118405710
http://dx.doi.org/10.1002/9781118548745
The Logical Status of Diagrams
Sun-Joo Shin
Cambridge University Press, 1995, ISBN 9780511574696
http://dx.doi.org/10.1017/CBO9780511574696
Visual Reasoning with Diagrams
Amiouche Moktefi and Sun-Joo Shin (Editors)
Springer, 2013, ISBN 978-3-0348-0600-8
http://dx.doi.org/10.1007/978-3-0348-0600-8
Principia Mathematica to *56
Alfred North Whitehead and Bertrand Russell
Cambridge University Press, 1997, ISBN 9780511623585
http://dx.doi.org/10.1017/CBO9780511623585
The Evolution of Principia Mathematica:
Bertrand Russell’s Manuscripts and Notes for the Second
Edition
Bernard Linsky
Cambridge University Press, 2011, ISBN 9780511760181
http://dx.doi.org/10.1017/CBO9780511760181
A Course in Model Theory
Katrin Tent and Martin Ziegler
Cambridge University Press, 2012, ISBN 9781139015417
http://dx.doi.org/10.1017/CBO9781139015417
Practical Foundations for Programming Languages
Robert Harper
Cambridge University Press, 2013, ISBN 9781139342131
http://dx.doi.org/10.1017/CBO9781139342131
Apartness and Uniformity: A Constructive Development
Douglas S. Bridges and Luminita Vita
Springer, 2011, ISBN 978-3-642-22415-7
http://dx.doi.org/10.1007/978-3-642-22415-7
Elementary Set Theory with a Universal Set
Randall Holmes
http://math.boisestate.edu/~holmes/holmes/head.pdf
Randall Holmes’s Home Page
http://math.boisestate.edu/~holmes/
Kripke’s Worlds: An Introduction to Modal Logics via Tableaux
Olivier Gasquet, Andreas Herzig, Bilal Said,
and Francois Schwarzentruber
Springer, 2014, ISBN 978-3-7643-8504-0
http://dx.doi.org/10.1007/978-3-7643-8504-0
Universal Logic as a Science of Patterns
Brian R. Gaines
http://dx.doi.org/10.1007/978-3-319-10193-4_7
The Road to Universal Logic:
Festschrift for 50th Birthday of Jan-Yves Beziau, Volume I
Arnold Kozlow and Arthur Buchsbaum (Editors)
Springer, 2015, ISBN 978-3-319-10193-4
http://dx.doi.org/10.1007/978-3-319-10193-4
Back to the Table of Contents
=======================================
Thoughts, Ideas, Opinions, Surveys, and Blogs
=======================================
Math Trek Blog
https://www.sciencenews.org/search?st=math+trek&=Search
Science News Magazine
http://www.sciencenews.org/
Discrete Thoughts:
Essays on Mathematics, Science, and Philosophy
Mark Kac, Gian-Carlo Rota, and Jacob T. Schwartz
Springer, 2008, ISBN 978-0-8176-4775-9
http://dx.doi.org/10.1007/978-0-8176-4775-9
The Mathematics of Paul Erdos I, Second Edition
Ronald L. Graham, Jaroslav Nesetril, and Steve Butler (Editors)
Springer, 2013, ISBN 978-1-4614-7258-2
http://dx.doi.org/10.1007/978-1-4614-7258-2
The Mathematics of Paul Erdos II, Second Edition
Ronald L. Graham, Jaroslav Nesetril, and Steve Butler (Editors)
Springer, 2013, ISBN 978-1-4614-7254-4
http://dx.doi.org/10.1007/978-1-4614-7254-4
The Crossing of Heaven: Memoirs of a Mathematician
Karl Gustafson
Springer, 2012, ISBN 978-3-642-22558-1
http://dx.doi.org/10.1007/978-3-642-22558-1
A Mathematician Reflects on the Useful and Reliable Illusion of
Reality in Mathematics
Keith Devlin
Pages 359-379
Erkenntnis, Volume 68, Number 3 (May 2008)
http://dx.doi.org/10.1007/s10670-008-9105-2
Mathematics – The Music of Reason
Jean Diedonne
Springer, 1992, ISBN 978-3-662-35358-5
http://dx.doi.org/10.1007/978-3-662-35358-5
Mathematics: Queen and Servant of the Sciences
Michael Atiyah
Proceedings of the American Philosophical Society,
Volume 137, Number 4 (December 1993) Pages 527-531
http://www.jstor.org/stable/987071
MATHKNOW:
Mathematics, Applied Sciences and Real Life
Michele Emmer and Alfio Quarteroni (Editors)
Springer, 2009, ISBN 978-88-470-1122-9
http://dx.doi.org/10.1007/978-88-470-1122-9
Imagine Math: Between Culture and Mathematics
Michele Emmer (Editor)
Springer, 2012, ISBN 978-88-470-2427-4
http://dx.doi.org/10.1007/978-88-470-2427-4
Imagine Math 2: Between Culture and Mathematics
Michele Emmer (Editor)
Springer, 2013, ISBN 978-88-470-2889-0
http://dx.doi.org/10.1007/978-88-470-2889-0
The Mathematician as a Type
William Story
http://aleph0.clarku.edu/~djoyce/story/MathAsType.html
William Edward Story - Biography
http://www.gap-system.org/~history/Biographies/Story.html
David E. Joyce, Professor of Mathematics and Computer Science,
Clark University
http://aleph0.clarku.edu/~djoyce/
Truth as a Value and Duty: Lessons of Mathematics
Pages 37-49
**** Includes a question and answer period ****
Yuri Manin
http://dx.doi.org/10.1007/978-1-4020-9896-3_3
Truth in Science, the Humanities, and Religion:
Balzan Symposium 2008
M.E.H. Nicolette Mout and Werner Stauffacher (Editors)
Springer, 2010, ISBN 978-1-4020-9896-3
http://dx.doi.org/10.1007/978-1-4020-9896-3
Georg Cantor and his heritage
Yuri I. Manin
arXiv.org > math > arXiv:math/0209244
http://arxiv.org/abs/math/0209244
Mathematical knowledge: internal, social and cultural aspects
Yu. I. Manin
arXiv.org > math > arXiv:math/0703427v1
http://arxiv.org/abs/math/0703427v1
Comments on a recent item by Yu I Manin
Elemer E Rosinger
arXiv.org > math > arXiv:math/0703547
http://arxiv.org/abs/math/0703547
The Mathematical Truth
Enrico Bombiery, Institute for Advanced Study
Slides of a lecture at Swiss Federal Institute of Technology
(November 24, 2008)
http://www.math.ethz.ch/news_events/bombieri_math_truth.pdf
Mathematics, Matter and Method, Philosophical Papers, Volume I,
Second Edition
Hilary Putnam
Cambridge University Press, 1979, ISBN 9780511625268
http://dx.doi.org/10.1017/CBO9780511625268
Unfashionable Pursuits
Freeman J. Dyson
The Mathematical Intelligencer,
Volume 5, Number 3 (September 1983)
http://dx.doi.org/10.1007/BF03026573
Birds and Frogs
Freeman Dyson
Notices of the AMS,
Volume 56, Number 2 (February 2009)
http://www.ams.org/notices/200902/rtx090200212p.pdf
Wikipedia:
http://en.wikipedia.org/wiki/Freeman_Dyson
A Revolution in Mathematics?
What Really Happened a Century Ago and Why It Matters Today
Frank Quinn
Notices of the AMS, Volume 59, Number 1 (January 2012)
http://www.ams.org/notices/201201/rtx120100031p.pdf
Encounters with Science: Dialogues in Five Parts
Lars Garding
http://dx.doi.org/10.1007/3-540-30434-7_14
Perspectives in Analysis:
Essays in Honor of Lennart Carleson’s 75th Birthday
Michael Benedicks, Peter W. Jones, Stanislaw Smirnov,
and Bjorn Winckler (Editors)
Springer, 2005, ISBN 978-3-540-30434-0
http://dx.doi.org/10.1007/3-540-30434-7
The Hilbert-Brouwer controversy resolved?
Pages 243-256
Per Martin-Lof
http://dx.doi.org/10.1007/978-3-7643-8653-5_15
One Hundred years of Intuitionism (1907-2007) –
The Cerisy Conference
Mark van Atten, et al. (Editors)
Springer, 2008, ISBN 978-3-7643-8653-5
http://dx.doi.org/10.1007/978-3-7643-8653-5
18 Unconventional Essays on the Nature of
Mathematics
Reuben Hersh (Editor)
Springer, 2006, ISBN 978-0-387-29831-3
http://dx.doi.org/10.1007/0-387-29831-2
The Two Cultures of Mathematics
http://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf
When are two proofs essentially the same?
http://gowers.wordpress.com/2007/10/04/when-are-two-proofsessentially-the-same/
Prof. W.T. Gowers, FRS,
Royal Society 2010 Anniversary Research Professor
Department of Pure Mathematics and Mathematical Statistics,
University of Cambridge
http://www.dpmms.cam.ac.uk/people/w.t.gowers/
Weblog
http://gowers.wordpress.com/
Mathematical Events of the Twentieth Century
**** The Russian perspective ****
A.A. Bolibruch, Yu. S.Osipov, and Ya. G. Sinai (Editors)
Springer, 2006, ISBN 978-3-540-23235-3
http://www.springerlink.com/content/978-3-540-23235-3/contents/
Contemporary Debates on the Nature of Mathematics
A.N. Kolmogorov (1929)
Problems of Information Transmission,
Volume 42, Number 4 (October-December 2006)
http://dx.doi.org/10.1134/S0032946006040107
Unified Foundations for Mathematics
Mark Burgin
arXiv:math/0403186v1
http://arxiv.org/abs/math/0403186
The Abel Prize: 2003-2007 The First five Years
Helge Holden and Ragni Piene (Editors)
Springer, 2010, ISBN 978-3-642-01372-0
http://dx.doi.org/10.1007/978-3-642-01373-7
Proof, Computation and Agency - Logic at the Crossroads - First Indian
Conference on Logic and its Relationship with Other Disciplines
Johan van Benthem, Amitabha Gupta, and Rohit Parikh (Editors)
Springer, 2011, ISBN 978-94-007-0079-6
http://dx.doi.org/10.1007/978-94-007-0080-2
Computational Discovery in Pure Mathematics
Simon Colton
http://dx.doi.org/10.1007/978-3-540-73920-3_9
Computational Discovery
Saso Dzeroski and Ljupco Todorovski (Editors)
Springer, 2007, ISBN 978-3-540-73919-7, LNCS 4660
http://dx.doi.org/10.1007/978-3-540-73920-3
Risk and Reward: The Science of Casino Blackjack
N. Richard Werthamer
Springer, 2009, ISBN 978-1-4419-0252-8
http://dx.doi.org/10.1007/978-1-4419-0253-5
Calculated Bets:
Computers, Gambling, and Mathematical Modeling to Win
Steven Skiena
Cambridge University Press, 2001, ISBN 9780511547089
http://dx.doi.org/10.1017/CBO9780511547089
Mixing Apples and Oranges:
What Poetry and Applied Mathematics Have in Common
Joel E. Cohen
Proceedings of the American Philosophical Society,
Volume 155, Number 2 (June 2011) pages 189-202
http://www.amphilsoc.org/sites/default/files/6Cohen1550206.pdf
Back to the Table of Contents
=======================================
History of Mathematics ==================
5000 Years of Geometry: Mathematics in History and Culture
Christoph J. Scriba and Peter Schreiber
Springer, 2015, ISBN 978-3-0348-0898-9
http://dx.doi.org/10.1007/978-3-0348-0898-9
The Scholar and the State: In Search of Van der Waerden
Alexander Soifer
Springer, 2015, ISBN 978-3-0348-0712-8
http://dx.doi.org/10.1007/978-3-0348-0712-8
Mathematical Encounters of the Second Kind
Philip J. Davis
Springer, 1997, ISBN 978-1-4612-2462-4
http://dx.doi.org/10.1007/978-1-4612-2462-4
Journey through Mathematics: Creative Episodes in Its History
Enrique A. Gonzalez- Velasco
Springer, 2011, ISBN 978-0-387-92154-9
http://dx.doi.org/10.1007/978-0-387-92154-9
Mathematics and Its History
John Stillwell
Springer, 2010, ISBN 978-1-4419-6053-5
http://dx.doi.org/10.1007/978-1-4419-6053-5
Sources in the Development of Mathematics: Infinite Series
and Products from the Fifteenth to the Twenty-first Century
Ranjan Roy
Cambridge University Press, 2011, ISBN 9780511844195
http://dx.doi.org/10.1017/CBO9780511844195
Geometry: Our Cultural Heritage, Second Edition
Audun Holme
Springer, 2010, ISBN 978-3-642-14441-7
http://dx.doi.org/10.1007/978-3-642-14441-7
Worlds Out of Nothing:
A Course in the History of Geometry in the 19th Century
Jeremy Gray
Springer, 2010, ISBN 978-0-85729-060-1
http://dx.doi.org/10.1007/978-0-85729-060-1
Analysis by Its History
E. Hairer and G. Wanner
Springer, 2008, ISBN 978-0-387-77036-9
http://dx.doi.org/10.1007/978-0-387-77036-9
Gauss: A Biographical Study
W. K. Buhler
Springer, 1981, ISBN 978-3-642-49207-5
http://dx.doi.org/10.1007/978-3-642-49207-5
A History of Chinese Mathematics
Jean-Claude Martzloff
Springer, 2006, ISBN 978-3-540-33783-6
http://dx.doi.org/10.1007/978-3-540-33783-6
Throwing Some Light on the Vast Darkness that is Analysis:
Niels Henrik Abel’s Critical Revision and the Concept of
Absolute Convergence
Henrik Kragh Sorensen
Centaurus – An International Journal of the History of Science
and Its Cultural Aspects, Volume 52, Issue 1 (February 2010)
http://dx.doi.org/10.1111/j.1600-0498.2009.00163.x
The Battle for Cantorian Set Theory
Joseph W. Dauben
http://dx.doi.org/10.1007/0-387-28272-6_10
Hilbert and his Twenty-Four Problems
Rudiger Thiele
http://dx.doi.org/10.1007/0-387-28272-6_11
Mathematics and the Historian’s Craft – The Kenneth O. May
Lectures
Glen Van Brummelen and Michael Kinyon (Editors)
Springer, 2005, ISBN 978-0-387-25284-1
http://dx.doi.org/10.1007/0-387-28272-6
A History of the Central Limit Theorem:
From Classical to Modern Probability Theory
Hans Fischer
Springer, 2011, ISBN 978-0-387-87856-0
http://dx.doi.org/10.1007/978-0-387-87857-7
A History of Algebra: From al-Khwarizmi to Emmy Noether
B.L. van der Waerden
Springer, 1985, ISBN 978-3-642-51599-6
http://dx.doi.org/10.1007/978-3-642-51599-6
Science Awakening I
B.L. van der Waerden
Springer, 1988, ISBN 978-94-009-1379-0
http://dx.doi.org/10.1007/978-94-009-1379-0
The World as a Mathematical Game:
John von Neumann and Twentieth Century Science
Giorgio Israel and Ana Milan Gasca
Springer, 2009, ISBN 978-3-7643-9896-5
http://dx.doi.org/10.1007/978-3-7643-9896-5
Hilbert
Constance Reid
Springer, 1996, ISBN 978-1-4612-0739-9
http://dx.doi.org/10.1007/978-1-4612-0739-9
Sur les problems futures des mathematiques
David Hilbert
Deuxieme Congres International des Mathematiciens (1900)
http://mathunion.org/ICM/ICM1900/
ICM Proceedings 1893-2010
http://mathunion.org/ICM/
International Mathematical Union
http://mathunion.org/
Back to the Table of Contents
=======================================
Modeling and Simulation ================
Ways of Thinking, Ways of Seeing:
Mathematical and Other Modelling in Engineering and
Technology
Chris Bissell and Chris Dillon (Editors)
Springer, 2012, ISBN 978-3-642-25209-9
http://dx.doi.org/10.1007/978-3-642-25209-9
Modeling and Simulation:
An Application-Oriented Introduction
Hans-Joachim Bungartz, Stefan Zimmer, Martin Bucholz,
and Dirk Pfluger
Springer, 2014, ISBN 978-3-642-39524-6
http://dx.doi.org/10.1007/978-3-642-39524-6
Principles of Modeling and Simulation:
A Multidisciplinary Approach
John A. Sokolowski and Catherine M. Banks (Editors)
Wiley, 2009, ISBN 9780470403563
http://dx.doi.org/10.1002/9780470403563
Modeling Reality: How Computers Mirror Life
Iwo Bialynicki-Birual and Iwona Bialynicka-Birula
Oxford University Press, 2004, ISBN 9780198531005
http://dx.doi.org/10.1093/acprof:oso/9780198531005.001.000
1
Handbook of Real-World Applications in Modeling and
Simulation
John A. Sokolowski and Catherine M. Banks (Editors)
Wiley, 2012, ISBN 9781118241042
http://dx.doi.org/10.1002/9781118241042
Discrete and Continuous Simulation: Theory and Practice
Susmita Bandyopadhyay and Ranjan Bhattacharya
CRC Press, 2014, ISBN 978-1-4665-9640-5
http://dx.doi.org/10.1201/b17127
It’s a Nonlinear World
Richard H. Enns
Springer, 2011, ISBN 978-0-387-75340-9
http://dx.doi.org/10.1007/978-0-387-75340-9
Mathematics and Technology
Christiane Rousseau and Yvan Saint-Aubin
Springer, 2008, ISBN 978-0-387-69216-6
http://dx.doi.org/10.1007/978-0-387-69216-6
The Mathematics of Medical Imaging: A Beginner’s Guide
Timothy G. Freeman
Springer, 2010, ISBN 978-0-387-92712-1
http://dx.doi.org/10.1007/978-0-387-92712-1
Back to the Table of Contents
=======================================
Probability ============================
Chance Rules: An Informal Guide to Probability,
Risk and Statistics; Second Edition
Brian Everitt
Springer, 2008, ISBN 978-0-387-77415-2
http://dx.doi.org/10.1007/978-0-387-77415-2
Probabilities: The Little Numbers that Rule Our Lives
Peter Olofsson
Wiley, 2007, ISBN 9780470099797
http://dx.doi.org/10.1002/0470099798
A Basic Course in Measure and Probability
Ross Leadbetter, Stamatis Cambanis, and Vladas Pipiras
Cambridge University Press, 2014, ISBN 9781139103947
http://dx.doi.org/10.1017/CBO9781139103947
Elementary Probability, 2nd Edition
David Stirzaker
Cambridge University Press, 2003, ISBN 9780511755309
http://dx.doi.org/10.1017/CBO9780511755309
The Unity and Diversity of Probability
Glenn Shafer
http://www.jstor.org/stable/2245372
Comment by Hirotugu Akaike
http://www.jstor.org/stable/2245373
Comment by David Aldous
http://www.jstor.org/stable/2245374
Comment by George Box
http://www.jstor.org/stable/2245375
Comment by A. P. Dempster
http://www.jstor.org/stable/2245376
Comment by B. Efron
http://www.jstor.org/stable/2245377
Comment by Ian Hacking
http://www.jstor.org/stable/2245378
Comment by David S. Moore
http://www.jstor.org/stable/2245379
Rejoinder by Glenn Shafer
http://www.jstor.org/stable/2245380
Statistical Science, Volume 5, Number 4 (1990)
Understanding Probability, Third Edition
Henk Tijms
Cambridge University Press, 2012, ISBN 9781139206990
http://dx.doi.org/10.1017/CBO9781139206990
Introduction to Probability, Second Edition
George G. Roussas
Elsevier, 2014, ISBN 978-0-12-800041-0
http://www.sciencedirect.com/science/book/9780128000410
Subjective Probability: The Real Thing
Richard Jeffrey
Cambridge University Press, 2004, ISBN 9780511816161
http://dx.doi.org/10.1017/CBO9780511816161
Basic Probability Theory with Applications
Mario Lefebvre
Springer, 2009, ISBN 978-0-387-74995-2
http://dx.doi.org/10.1007/978-0-387-74995-2
40 Puzzles and Problems in Probability and Mathematical
Statistics
Wolfgang Schwarz
Springer, 2008, ISBN 978-0-387-73512-2
http://dx.doi.org/10.1007/978-0-387-73512-2
An introduction to Measure-Theoretic Probability,
Second Edition
George G. Roussas
Elsevier, 2014, ISBN 978-0-12-800042-7
http://www.sciencedirect.com/science/book/9780128000427
Probability and Random Variables: A Beginner’s Guide
David Stirzaker
Cambridge University Press, 1999, ISBN 9780511813627
http://dx.doi.org/10.1017/CBO9780511813627
Analysis and Probability
Aurel Spataru
Elsevier, 2013, ISBN 978-0-12-401665-1
http://www.sciencedirect.com/science/book/9780124016651
Probability Theory: A Comprehensive Course, Second Edition
Achim Klenke
Springer, 2014, ISBN 978-1-4471-5361-0
http://dx.doi.org/10.1007/978-1-4471-5361-0
The Theory of Probability
Santosh S. Venkatesh
Cambridge University Press, 2013, ISBN 9781139169325
http://dx.doi.org/10.1017/CBO9781139169325
A Probability Path
Sidney I. Resnick
Springer, 2014, ISBN 978-0-8176-8409-9
http://dx.doi.org/10.1007/978-0-8176-8409-9
Fundamentals of Applied Probability and Random Processes,
Second Edition
Oliver C. Ibe
Elsevier, 2014, ISBN 978-0-12-800852-2
http://www.sciencedirect.com/science/book/9780128008522
Exercises in Probability: A Guided Tour from Measure Theory
to Random Processes, via Conditioning, Second Edition
Loic Chaumont and Marc Yor
Cambridge University Press, 2012, ISBN 9781139135351
http://dx.doi.org/10.1017/CBO9781139135351
Fundamentals of Probability: A First Course
Anirban DasGupta
Springer, 2010, ISBN 978-1-4419-5780-1
http://dx.doi.org/10.1007/978-1-4419-5780-1
Introduction to Probability Models, Eleventh Edition
Sheldon M. Ross
Elsevier, 2014, ISBN 978-0-12-407948-9
http://www.sciencedirect.com/science/book/9780124079489
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A Treatise on Probability
John Maynard Keynes (1921)
http://www.archive.org/details/treatiseonprobab007528
mbp
Wikipedia:
http://en.wikipedia.org/wiki/John_Maynard_Keynes
Back to the Table of Contents
=======================================
Probability and Statistics =================
Probability and Statistics by Example I:
Basic probability and Statistics, Second Edition
Yuri Suhov and Mark Kelbert
Cambridge University Press, 2014, ISBN 9781139087773
http://dx.doi.org/10.1017/CBO9781139087773
Probability and Statistics by Example, Volume 2
Yuri Suhov and Mark Kelbert
Cambridge University Press, 2008, ISBN 9780521612341
http://dx.doi.org/10.1017/CBO9780511813641
A Modern Introduction to Probability and Statistics:
Understanding Why and How
F.M. Dekking, C. Kraaikamp, H.P. Lopuhaa, and L.E. Meester
Springer, 2005, ISBN 978-1-84628-168-6
http://dx.doi.org/10.1007/1-84628-168-7
Back to the Table of Contents
=======================================
Statistics ==============================
Chance Rules: An Informal Guide to Probability,
Risk and Statistics; Second Edition
Brian Everitt
Springer, 2008, ISBN 978-0-387-77415-2
http://dx.doi.org/10.1007/978-0-387-77415-2
Past, Present, and Future of Statistical Science
Xihong Lin, Christian Genest, David L. Banks, Geert
Molenberghs,
David W. Scott, and Jane-Ling Wang (Editors)
CRC Press, 2014, ISBN 978-1-4822-0498-8
http://dx.doi.org/10.1201/b16720
Normal and Student’s t Distributions and Their Applications
Mohammad Ahsanullah, B. M. Golam Kibria,
and Mohammad Shakil
Springer, 2014, ISBN 978-94-6239-061-4
http://dx.doi.org/10.2991/978-94-6239-061-4
Regression: Models, Methods and Applications
Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, and Brian Marx
Springer, 2013, ISBN 978-3-642-34333-9
http://dx.doi.org/10.1007/978-3-642-34333-9
Do We Really Need the S-word?
Megan D. Higgs
American Scientist,
Volume 101, Number 1 (January-February 2013)
http://dx.doi.org/10.1511/2013.100.6
What Everyone Should Know about Statistical
Correlation
Vladica M. Velickovic
American Scientist,
Volume 103, Number 1 (January-February 2015)
http://dx.doi.org/10.1511/2015.112.26
To Throw Away Data: Plagiarism as a Statistical Crime
Andrew Gelman and Thomas Basboll
American Scientist, Volume 101, Number 3 (May-June 2013)
http://www.americanscientist.org/issues/pub/2013/3/tothrow-away-data-plagiarism-as-a-statistical-crime
Outlier Analysis
Charu C. Aggarwal
Springer, 2013, ISBN 978-1-4614-6396-2
http://dx.doi.org/10.1007/978-1-4614-6396-2
Data is a singular noun (2010)
Norman Gray
http://nxg.me.uk/note/2005/singular-data/
Website
http://nxg.me.uk/
The Art of Data Science
Matthew J. Graham
http://dx.doi.org/10.1007/978-1-4614-3323-1_4
Astrostatistics and Data Mining
Luis Manuel Sarro, Laurent Eyer, William O’Mullane,
and Joris De Ridder (Editors)
Springer, 2012, ISBN 978-1-614-3323-1
http://dx.doi.org/10.1007/978-1-4614-3323-1
The Future of Data Analysis
John W. Tukey
Annals of Mathematical Statistics,
Volume 33, Number 1 (March 1962)
http://www.jstor.org/stable/2237638
Symmetry Studies:
An Introduction to the Analysis of Structured Data in
Applications
Marlos A. G. Viana
Cambridge University Press, 2008, ISBN 9780511755477
http://dx.doi.org/10.1017/CBO9780511755477
An Introduction to Categorical Data Analysis, Second Edition
Alan Agresti
Wiley, 2007, ISBN 9780470114759
http://dx.doi.org/10.1002/0470114754
Categorical Data Analysis, Second Edition
Alan Agresti
Wiley, 2002, ISBN 9780471249689
http://dx.doi.org/10.1002/0471249688
First Link in the Markov Chain: Probability and poetry
were unlikely partners in the creation of a
computational tool
Brian Hayes
American Scientist, Volume 101, Number 2 (March-April 2013)
http://www.americanscientist.org/issues/pub/2013/2/firstlinks-in-the-markov-chain
Understanding Markov Chains: Examples and Applications
Nicolas Privault
Springer, 2013, ISBN 978-981-4451-51-2
http://dx.doi.org/10.1007/978-981-4451-51-2
Finite Markov Chains and Algorithmic Applications
Olle Haggstrom
Cambridge University Press, 2002, ISBN 9780511613586
http://dx.doi.org/10.1017/CBO9780511613586
Markov Chains
R. Norris
Cambridge University Press, 1998
http://www.statslab.cam.ac.uk/~james/Markov/
Probability and Information: An Integrated Approach,
Second Edition
David Applebaum
Cambridge University Press, 2008, ISBN 978-0-511-75526-2
http://dx.doi.org/10.1017/CBO9780511755262
Informal Introduction to Stochastic Processes with Maple
Jan Vrbik and Paul Vrbik
Springer, 2013, ISBN 978-1-4614-4057-4
http://dx.doi.org/10.1007/978-1-4614-4057-4
Introduction to Probability and Stochastic Processes
with Applications
Liliana Blanco Castaneda, Viswanathan Arunachalam,
and Delvamuthu Dharmaraja
Wiley, 2012, ISBN 9781118344972
http://dx.doi.org/10.1002/9781118344972
An Introduction to Markov Processes, Second Edition
Daniel W. Stroock
Springer, 2014, ISBN 978-3-642-40523-5
http://dx.doi.org/10.1007/978-3-642-40523-5
Markov Processes for Stochastic Modeling, Second Edition
Oliver C. Ibe
Elsevier, 2013, ISBN 978-0-12-407795-9
http://www.sciencedirect.com/science/book/9780124077959
Multivariate Statistics: Exercises and Solutions, Second edition
Wolfgang Hardle and Zdenek Hlavka
Springer, 2015, ISBN 978-3-642-36005-3
http://dx.doi.org/10.1007/978-3-642-36005-3
Applied Multivariate Statistical Analysis, Fourth Edition
Wolfgang Karl Hardle and Leopold Simar
Springer, 2015, ISBN 978-3-662-45171-7
http://dx.doi.org/10.1007/978-3-662-45171-7
Fundamentals of Modern Statistical Methods:
Substantially Improving Power and Accuracy, Second Edition
Rand R. Wilcox
Springer, 2010, ISBN 978-1-4419-5525-8
http://dx.doi.org/10.1007/978-1-4419-5525-8
Chi-Squared Goodness of Fit Tests with Applications
V. Voinov, M. Nikulin, and N. Balakrishnan
Elsevier, 2013, ISBN 978-0-12-397194-4
http://www.sciencedirect.com/science/book/9780123971944
Numerical Methods of Statistics, Second Edition
John F. Monahan
Cambridge University Press, 2011, ISBN 9780511977176
http://dx.doi.org/10.1017/CBO9780511977176
A Matrix Handbook for Statisticians
George A. F. Seber
Wiley, 2008, ISBN 9780470226797
http://dx.doi.org/10.1002/9780470226797
Data Representations, Transformations, and Statistics for
Visual Reasoning
Ross MacieJewski
Morgan & Claypool, 2011, ISBN 9781608456260
http://dx.doi.org/10.2200/S00357ED1V01Y201105VIS002
Essential Statistical Inference: Theory and Methods
Dennis D. Boos and L.A. Stefanski
Springer, 2013, ISBN 978-1-4614-4818-1
http://dx.doi.org/10.1007/978-1-4614-4818-1
Principles of Statistical Inference
D. R. Cox
Cambridge University Press, 2006, ISBN 9780511813559
http://dx.doi.org/10.1017/CBO9780511813559
Statistical Theory and Inference
David J. Olive
Springer, 2014, ISBN 978-3-319-04972-4
http://dx.doi.org/10.1007/978-3-319-04972-4
Statistical Inference: The Minimum Distance Approach
Ayanendranath Basu, Hiroyuki Shioya, and Chanseok Park
CRC Press, 2011, ISBN 978-1-4200-9966-9
http://dx.doi.org/10.1201/b10956
Applied Statistical Inference: Likelihood and Bayes
Leonhard Held and Daniel Sabanes Bove
Springer, 2014, ISBN 978-3-642-37887-4
http://dx.doi.org/10.1007/978-3-642-37887-4
Foundations of Inference
Kevin H. Knuth and John Skilling
Axioms, Volume 1, Number 1 (June 2012)
http://dx.doi.org/10.3390/axioms1010038
The Significance Test Controversy Revisited:
The Fiducial Bayesian Alternative
Bruno Lecoutre and Jacques Poitevineau
Springer, 2014, ISBN 978-3-662-44046-9
http://dx.doi.org/10.1007/978-3-662-44046-9
Statistical Modeling and Computation
Dirk P. Kroese and Joshua C.C. Chan
Springer, 2014, ISBN 978-1-4614-8775-3
http://dx.doi.org/10.1007/978-1-4614-8775-3
Matrix Tricks for Linear Statistical Models:
Our Personal Top Twenty
Simo Puntanen, George P. H. Styan, and Jarko Isotalo
Springer, 2011, ISBN 978-3-642-10473-2
http://dx.doi.org/10.1007/978-3-642-10473-2
The Big Picture (Chapter 4)
http://dx.doi.org/10.1007/0-387-34239-7_4
Estimation of Dependences Based on Empirical Data
Vladimir Vapnik
Springer, 2006, ISBN 978-0-387-34329-9
http://dx.doi.org/10.1007/0-387-34239-7
Fisher, Neyman, and the Creation of Statistics
Erich L. Lehmann
Springer, 2011, ISBN 978-1-4419-9500-1
http://dx.doi.org/10.1007/978-1-4419-9500-1
Principal Component Analysis, Second Edition
I.T. Jolliffe
Springer, 2002, ISBN 978-0-387-22440-4
http://dx.doi.org/10.1007/b98835
Probability Theory As Extended Logic
****************************************************
Edwin T. Jaynes was one of the first people to realize that
probability theory, as originated by Laplace is a generalization
of Aristotelian logic that reduces to deductive logic in the
special case that our hypotheses are either true or false. This
website has a large selection of his articles, as well as articles
by a number of other people who use probability theory in
this way
****************************************************
http://bayes.wustl.edu/
Statistics in Food Science and Nutrition
Are Hugo Pripp
Springer, 2013, ISBN 978-1-4614-5010-8
http://dx.doi.org/10.1007/978-1-4614-5010-8
Statistics for Anthropology, Second Edition
Lorena Madrigal
Cambridge University Press, 2012, ISBN 9781139022699
http://dx.doi.org/10.1017/CBO9781139022699
Statistical Modeling and Computation
Dirk P. Kroese and Joshua C.C. Chan
Springer, 2014, ISBN 978-1-4614-8775-3
http://dx.doi.org/10.1007/978-1-4614-8775-3
The Foundations of Statistics: A Simulation-based Approach
Shravan Vasishth and Michael Broe
Springer, 2011, ISBN 978-3-642-16313-5
http://dx.doi.org/10.1007/978-3-642-16313-5
Explorations in Monte Carlo Methods
Ronald W. Shonkwiler and Franklin Mendivil
Springer, 2009, ISBN 978-0-387-87837-9
http://dx.doi.org/10.1007/978-0-387-87837-9
Essentials of Monte Carlo Simulation:
Statistical Methods for Building Simulation Models
Nick T. Thomopoulos
Springer, 2013, ISBN 978-1-4614-6022-0
http://dx.doi.org/10.1007/978-1-4614-6022-0
Foundations of Applied Statistical Methods
Hang Lee
Springer, 2014, ISBN 978-3-319-02402-8
http://dx.doi.org/10.1007/978-3-319-02402-8
Principles of Applied Statistics
D. R. Cox and Christal A. Donnelly
Cambridge University Press, 2011, ISBN 9781139005036
http://dx.doi.org/10.1017/CBO9781139005036
Statistical Principles for the Design of Experiments
R. Mead, S. G. Gilmour, and A. Mead
Cambridge University Press, 2012, ISBN 9781139020879
http://dx.doi.org/10.1017/CBO9781139020879
Lies, Damned Lies and Statistics
http://www.york.ac.uk/depts/maths/histstat/lies.htm
Material for the History of Statistics
http://www.york.ac.uk/depts/maths/histstat/welcome.htm
A Career in Statistics: Beyond the Numbers
Gerald J. Hahn and Necip Doganaksov
Wiley, 2011, ISBN 9781118490143
http://dx.doi.org/10.1002/9781118490143
Strength in Numbers:
The Rising of Academic Statistics Departments in the U.S.
Alan Agresti and Xiao-Li Meng (Editors)
Springer, 2013, ISBN 978-1-4614-3649-2
http://dx.doi.org/10.1007/978-1-4614-3649-2
Odds Are, It’s Wrong:
Science fails to face the shortcomings of statistics
Tom Siegfried
Science News, Volume 177, Number 7 (March 27, 2010)
http://www.sciencenews.org/view/feature/id/57091/descripti
on/Odds_Are_Its_Wrong
The Dilemma of Statistics:
Rigorous Mathematical Methods Cannot Compensate Messy
Interpretations and Lousy Data
Peter Schuster
Complexity, Volume 20, Number 1 (September-October 2014)
http://dx.doi.org/10.1002/cplx.21553
The Pleasures of Statistics:
The Autobiography of Frederick Mosteller
Frederick Mosteller
Springer, 2010, ISBN 978-0-387-77956-0
http://dx.doi.org/10.1007/978-0-387-77956-0
Wikipedia:
http://en.wikipedia.org/wiki/Frederick_Mosteller
Reminiscences of a Statistician: The Company I Kept
E. L. Lehman
Springer, 2007, ISBN 978-0-387-71597-1
http://dx.doi.org/10.1007/978-0-387-71597-1
An Accidental Statistician:
The Life and Memories of George E.P. Box
George E.P. Box
Wiley, 2013, ISBN 9781118514948
http://dx.doi.org/10.1002/9781118514948
Mathematical Statistics with Applications in R, Second Edition
Kandethody M. Ramachandran and Chris P. Tsokos
Elsevier, 2015, ISBN 978-0-12-417113-8
http://www.sciencedirect.com/science/book/9780124171138
Basics of Modern Mathematical Statistics
Vladimir Spokoiny and Thorsten Dickhaus
Springer, 2014, ISBN 978-3-642-39909-1
http://dx.doi.org/10.1007/978-3-642-39909-1
Basics of Modern Mathematical Statistics: Exercises and
Solutions
Wolfgang Karl Hardle, Vladimir Spokoiny, Vladimir Panov,
and Weining Wang
Springer, 2014, ISBN 978-3-642-36850-9
http://dx.doi.org/10.1007/978-3-642-36850-9
Mathematical Statistics
B.L. van der Waerden
Springer, 1969, ISBN 978-3-662-22137-2
http://dx.doi.org/10.1007/978-3-662-22137-2
40 Puzzles and Problems in Probability and Mathematical
Statistics
Wolfgang Schwarz
Springer, 2008, ISBN 978-0-387-73512-2
http://dx.doi.org/10.1007/978-0-387-73512-2
Understanding Uncertainty, Revised Edition
Dennis V. Lindley
Wiley, 2014, ISBN 9781118650158
http://dx.doi.org/10.1002/9781118650158
Back to the Table of Contents
=======================================
Thomas Bayes: Life and Work =============
The Reverend Thomas Bayes, FRS:
A Biography to Celebrate the Tercentenary of His Birth
D. R. Bellhouse
http://projecteuclid.org/euclid.ss/1089808271
Special Issue: Bayes Then and Now
Statistical Science, Volume 19, Number 4 (February 2004)
http://projecteuclid.org/euclid.ss/1089808267
Most Honourable Remenbrance:
The Life and Work of Thomas Bayes
Andrew I. Dale
Springer, 2003, ISBN 978-0-387-21561-7
http://dx.doi.org/10.1007/b97274
A History of Inverse Probability:
From Thomas Bayes to Carl Pearson
Andrew I. Dale
Springer, 1991, ISBN 978-1-4684-4115-9
http://dx.doi.org/10.1007/978-1-4684-0415-9
An Essay towards Solving a Problem in the Doctrine of
Chances.
By the Late Rev. Mr. Bayes, F. R. S. Communicated by
Mr. Price, in a Letter to John Canton, A. M. F. R. S.
Philosophical Transactions, Volume 53 (1763)
http://dx.doi.org/10.1098/rstl.1763.0053
Bayes’ Theorem in the 21st Century
Bradley Efron
Science, Volume 340, Number 6137 (7 June 2013)
http://dx.doi.org/10.1126/science.1236536
Thomas Bayes’s Bayesian Inference
Stephen M. Steiger
Journal of the Royal Statistical Society, Series A,
Volume 145, Number 2 (1982)
http://www.jstor.org/stable/2981538
Was Bayes a Bayesian?
Donald A. Gillies
Historia Mathematca, Volume 14 (1987)
http://dx.doi.org/10.1016/0315-0860(87)90065-6
Bayes’ Bayesianism
John Earman
Studies in History and Philosophy of Science Part A,
Volume 21, Number 3 (September 1990)
http://dx.doi.org/10.1016/0039-3681(90)90001-O
Who Discovered Bayes’s Theorem?
Stephen M. Stigler
The American Statistician,
Volume 37, Number 4 (November 1983)
http://www.jstor.org/stable/2682766
Laplace’s 1774 Memoir on Inverse Probability
Stephen M. Steiger
Statistical Science, Volume 1, Number 3 (1986)
http://projecteuclid.org/euclid.ss/1177013620
Pierre-Simon Laplace: Philosophical Essay on Probabilities
Andrew I. Dale
Springer, 1995, ISBN 978-1-4612-4184-3
http://dx.doi.org/10.1007/978-1-4612-4184-3
An Intuitive Explanation of Bayes’ Theorem
http://yudkowsky.net/rational/bayes
A Technical Explanation of Technical Explanation
http://yudkowsky.net/rational/technical
Eliezer S. Yudkowsky, Research Fellow,
Singularity Institute for Artificial Intelligence
http://yudkowsky.net/
Bayesian Essentials with R, Second Edition
Jean-Michel Marin and Christian P. Robert
Springer, 2014, ISBN 978-1-4614-8687-9
http://dx.doi.org/10.1007/978-1-4614-8687-9
Bayesian Probability Theory: Applications in the Physical
Sciences
Wolfgang von der Linden, Volker Dose, and Udo von Toussaint
Cambridge University Press, 2014, ISBN 9781139565608
http://dx.doi.org/10.1017/CBO9781139565608
Introduction to Bayesian Statistics, Second Edition
William M. Bolstad
Wiley, 2007, ISBN 9780470181188
http://dx.doi.org/10.1002/9780470181188
Bayes Linear Statistics: Theory and Methods
Michael Goldstein and David Wooff
Wiley, 2007, ISBN 9780470065662
http://dx.doi.org/10.1002/9780470065662
Bayesian Theory and Methods with Applications
Vladimir P. Savchuk and Chris P. Tsokos
Springer, 2011, ISBN 978-94-91216-14-5
http://dx.doi.org/10.2991/978-94-91216-14-5
Introduction to Probability and Statistics:
From a Bayesian Viewpoint, Part 2 Inference
D. V. Lindley
Cambridge University Press, 1965, ISBN 9780511662973
http://dx.doi.org/10.1017/CBO9780511662973
Bayesian Inference: With Ecological Examples
William A. Link and Richard J. Barker
Elsevier, 2010, ISBN 978-0-12-374854-6
http://www.sciencedirect.com/science/book/9780123748546
Bayesian Inference in Statistical Analysis
George E.P. Box and George C. Tiao
Wiley, 1973, ISBN 9781118033197
http://dx.doi.org/10.1002/9781118033197
Bayesian Networks: An Introduction
Timo Koski and John M. Noble
Wiley, 2009, ISBN 9780470684023
http://dx.doi.org/10.1002/9780470684023
Interpreting Probability:
Controversies and Developments in the Early Twentieth
Century
David Howie
Cambridge University Press, 2002, ISBN 9780511498840
http://dx.doi.org/10.1017/CBO9780511498480
A History of Probability and Statistics and Their Applications
before 1750
Anders Hald
Wiley, 2003, ISBN 9780471725169
http://dx.doi.org/10.1002/0471725161
Back to the Table of Contents
=======================================
Bayesian Statistics ======================
The Mathematics of Making Up Your Mind
Will Hively
Discover (May 1996)
http://discovermagazine.com/1996/may/themathematicsof76
0
A Primer on Bayesian Statistics in Health Economics and
Outcomes Research
Anthony O’Hagan and Bryan R. Luce
MEDTAP International (2003)
http://www.paceinitiative.org/Resources_Pubs.html
Doing Bayesian Data Analysis:
A Tutorial with R, JAGS, and STAN; Second Edition
John K. Kruschke
Elsevier, 2015, ISBN 978-0-12-405888-0
http://www.sciencedirect.com/science/book/9780124058880
Bayesian Data Analysis in Ecology Using Linear Models with R,
BUGS, and Stan
Franzi Korner-Nievergelt, et al.
Elsevier, 2015, ISBN 978-0-12-801370-0
http://www.sciencedirect.com/science/book/9780128013700
The Bayesian Choice:
From Decision-Theoretic Foundations to Computational
Implementation, Second Edition
Christian P. Robert
Springer, 2007, ISBN 978-0-387-71599-5
http://dx.doi.org/10.1007/0-387-71599-1
Bayesian Networks for Probabilistic Inference and Decision
Analysis in Forensic Science, Second Edition
Franco Taroni, Alex Biedermann, Silvia Bozza,
Paolo Garbolino, and Colin Aitken
Wiley, 2014, ISBN 9781118914762
http://dx.doi.org/10.1002/9781118914762
Bayesian Probability Theory: Applications in the Physical
Sciences
Wolfgang von der Linden, Volker Dose, and Udo von Toussaint
Cambridge University Press, 2014, ISBN 9781139565608
http://dx.doi.org/10.1017/CBO9781139565608
Bayesian Methods for the Physical Sciences:
Learning from Examples in Astronomy and Physics
Stefano Anderson and Brian Weaver
Springer, 2015, ISBN 978-3-319-15287-5
http://dx.doi.org/10.1007/978-3-319-15287-5
Back to the Table of Contents
=======================================
Statistical Programming Using R ===========
The R Project for Statistical Computing
http://www.r-project.org/
The Art of R Programming
Norman Matloff (2009)
http://heather.cs.ucdavis.edu/~matloff/132/NSPpart.pdf
The R Book, Second Edition
Michael J. Crawley
Wiley, 2013, ISBN 9781118448908
http://dx.doi.org/10.1002/9781118448908
Beginning R: An Introduction to Statistical Programming
Larry Pace
Springer, 2012, ISBN 978-1-4302-4555-1
http://dx.doi.org/10.1007/978-1-4302-4555-1
Understanding Statistics Using R
Randall Schumacker and Sara Tomek
Springer, 2013, ISBN 9781-4614-6227-9
http://dx.doi.org/10.1007/978-1-4614-6227-9
Using R for Statistics
Sarah Stowell
Springer, 2014, ISBN 978-1-4842-0139-8
http://dx.doi.org/10.1007/978-1-4842-0139-8
Bayesian Computation with R, Second Edition
Jim Albert
Springer, 2009, ISBN 978-0-387-92298-0
http://dx.doi.org/10.1007/978-0-387-92298-0
Statistics and Data with R:
An applied approach through examples
Yosef Cohen and Jeremiah Y. Cohen
Wiley, 2008, ISBN 9780470758052
http://dx.doi.org/10.1002/9780470721896
R Quick Syntax Reference
Margot Tollefson
Springer, 2014, ISBN 978-1-4302-6641-9
http://dx.doi.org/10.1007/978-1-4302-6641-9
A Tiny Handbook of R
Mike Allerhand
Springer, 2011, ISBN 978-3-642-17980-8
http://dx.doi.org/10.1007/978-3-642-17980-8
Advanced R
Hadley Wickham
CRC Press, 2015, ISBN 978-1-4665-8696-3
http://dx.doi.org/10.1201/b17487
Beginning Data Science with R
Manas A. Pathak
Springer, 2014, ISBN 978-3-319-12066-9
http://dx.doi.org/10.1007/978-3-319-12066-9
R for Cloud Computing: An Approach for Data Scientists
A. Ohri
Springer, 2014, ISBN 978-1-4939-1702-0
http://dx.doi.org/10.1007/978-1-4939-1702-0
Guide to Programming and Algorithms Using R
Ozgur Ergul
Springer, 2013, ISBN 978-1-4471-5328-3
http://dx.doi.org/10.1007/978-1-4471-5328-3
Data Mining and Business Analytics with R
Johannes Ledolter
Wiley, 2013, ISBN 9781118596289
http://dx.doi.org/10.1002/9781118596289
XML and Web Technologies for Data Sciences with R
Deborah Nolan and Duncan Temple Lang
Springer, 2014, ISBN 978-1-4614-7900-0
http://dx.doi.org/10.1007/978-1-4614-7900-0
Analyzing Compositional Data with R
K. Gerald van den Boogaart and Raimon Tolosana-Delgado
Springer, 2013, ISBN 978-3-642-36809-7
http://dx.doi.org/10.1007/978-3-642-36809-7
Statistical Analysis of Network Data with R
Eric D. Kolaczyk and Gabor Csardi
Springer, 2014, ISBN 978-1-4939-0983-4
http://dx.doi.org/10.1007/978-1-4939-0983-4
Statistical Methods for Ranking Data
Mayer Alvo and Philip L.H. Yu
Springer, 2014, ISBN 978-1-4939-1471-5
http://dx.doi.org/10.1007/978-1-4939-1471-5
**** A companion set of R programs ****
http://web.hku.hk/~plhyu/StatMethRank/
Bayesian Essentials with R, Second Edition
Jean-Michel Marin and Christian P. Robert
Springer, 2014, ISBN 978-1-4614-8687-9
http://dx.doi.org/10.1007/978-1-4614-8687-9
Mathematical Statistics with Applications in R, Second Edition
Kandethody M. Ramachandran and Chris P. Tsokos
Elsevier, 2015, ISBN 978-0-12-417113-8
http://www.sciencedirect.com/science/book/9780124171138
Data Mining Applications with R
Yanchang Zhao and Yonghua Cen
Elsevier, 2014, ISBN 978-0-12-411511-8
http://www.sciencedirect.com/science/book/9780124115118
Introduction to Data Analysis and Graphical Presentation in
Biostatistics with R: Statistics in the Large
Thomas W. MacFarland
Springer, 2014, ISBN 978-3-319-02532-2
http://dx.doi.org/10.1007/978-3-319-02532-2
Bayesian Data Analysis in Ecology Using Linear Models with R,
BUGS, and Stan
Franzi Korner-Nievergelt, et al.
Elsevier, 2015, ISBN 978-0-12-801370-0
http://www.sciencedirect.com/science/book/9780128013700
Data Analysis and Graphics Using R – an Example-Based
Approach, Third Edition
John Maindonald and W. John Braun
Cambridge University Press, 2010, ISBN 9781139194648
http://dx.doi.org/10.1017/CBO9781139194648
Guidebook to R Graphics Using Microsoft® Windows
Kunio Takezawa
Wiley, 2012, ISBN 9781118270165
http://dx.doi.org/10.1002/9781118270165
Six Sigma with R:
Statistical Engineering for Process Improvement
Emilio L. Cano, Javier M. Moguerza, and Andres Redchuk
Springer, 2012, IS N978-1-4614-3652-2
http://dx.doi.org/10.1007/978-1-4614-3652-2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
10 How computing has changed statistics
Brian D. Ripley
http://dx.doi.org/10.1093/acprof:oso/9780198566540.003.001
1
Celebrating Statistics:
Papers in honour of Sir David Cox on his 80th birthday
Anthony Davison, Yadolah Dodge, and Nanny Wermuth
(Editors)
Oxford University Press, 2005, ISBN 9780198566540
http://dx.doi.org/10.1093/acprof:oso/9780198566540.001.000
1
Introduction to Bayesian Scientific Computing:
Ten Lectures on Subjective Computing
Daniela Calvetti and Erkki Somersalo
Springer, 2007, ISBN 978-0-387-73394-4
http://dx.doi.org/10.1007/978-0-387-73394-4
Using R for Numerical Analysis in Science and Engineering
Victor A. Bloomfield
CRC Press, 2014, ISBN 978-1-4398-8449-2
http://www.crcnetbase.com/isbn/978-1-4398-8448-5
Computational Actuarial Science with R
Arthur Charpentier (Editor)
CRC Press, 2015, ISBN 978-1-4665-9260-5
http://www.crcnetbase.com/isbn/978-1-4665-9259-9
Text Analysis with R for Students of Literature
Matthew L. Jockers
Springer, 2014, ISBN 978-3-319-03164-4
http://dx.doi.org/10.1007/978-3-319-03164-4
Modeling Count Data
Joseph M. Hilbe
Cambridge University Press, 2014, ISBN 9781139236065
http://dx.doi.org/10.1017/CBO9781139236065
Negative Binomial Regression, Second Edition
Joseph M. Hilbe
Cambridge University Press, 2011, ISBN 9780511973420
http://dx.doi.org/10.1017/CBO9780511973420
How to speed up R code: an introduction
Nathan Uyttendaele (March 2015)
http://arxiv.org/abs/1503.00855
inside-R – A Community Site for R
http://www.inside-r.org/
Back to the Table of Contents
=======================================
Experimental Math and Math Computing ====
Also see:
MATLAB shelf in the Engineering section.
Experimental Mathematics in Action
David H. Bailey, Jonathan M. Borwein, Neil J. Calkin,
Roland Girgensohn, D. Russell Luke, and Victor H. Moll
2006 (preprint; published by AK Peters in 2007)
http://web.cs.dal.ca/~jborwein/Preprints/Books/EMA/ema.pdf
Website of David H. Bailey
http://www.davidhbailey.com/
Website of Jonathan Borwein
http://www.carma.newcastle.edu.au/jon/
CARMA – Priority Research Centre for Computer-Assisted
Research Mathematics and Its Applications,
University of Newcastle, NSW, Australia
http://www.carma.newcastle.edu.au/carmamembers.shtml
Experimental Mathematics (journal, Taylor & Francis)
http://www.tandfonline.com/loi/uexm20
OR
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=
Display&page=past&handle=euclid.em
The Linear Algebra Survival Guide:
Illustrated with Mathematica
Fred E. Szabo
Elsevier, 2015, ISBN 978-0-12-409520-5
http://www.sciencedirect.com/science/book/9780124095205
Modern Computer Algebra, Third Edition
Joachim von zur Gathen and Jurgen Gerhard
Cambridge University Press, 2013, ISBN 9781139856065
http://dx.doi.org/10.1017/CBO9781139856065
An Introduction to Modern Mathematical Computing:
With Maple
Jonathan M. Borwein and Matthew P. Skerritt
Springer, 2011, ISBN 978-1-4614-0122-3
http://dx.doi.org/10.1007/978-1-4614-0122-3
Calculus with Vectors
Jay S. Treiman
Springer, 2014, ISBN 978-3-319-09438-0
http://dx.doi.org/10.1007/978-3-319-09438-0
**** Maple ***
Computer Algebra Recipes:
An Introductory Guide to Mathematical Models of Science
Richard H. Enns and George C. McGuire
Springer, 2006, ISBN 978-0-387-31262-5
http://dx.doi.org/10.1007/0-387-31262-5
Modeling of Curves and Surfaces with MATLAB
Vladimir Rovenski
Springer, 2010, ISBN 978-0-387-71278-9
http://dx.doi.org/10.1007/978-0-387-71278-9
An Introduction to Modern Mathematical Computing:
With Mathematica
Jonathan M. Borwein and Matthew P. Skerritt
Springer, 2012, ISBN 978-1-4614-4253-0
http://dx.doi.org/10.1007/978-1-4614-4253-0
Programming with Mathematica: An Introduction
Paul Wellin
Cambridge University Press, 2013, ISBN 9780511972942
http://dx.doi.org/10.1017/CBO9780511972942
Mathematica in Action: Problem Solving Through
Visualization and Computation, Third Edition
Stan Wagon
Springer, 2010, ISBN 978-0-387-75477-2
http://dx.doi.org/10.1007/978-0-387-75477-2
Discovering Mathematics: A Problem-Solving Approach to
Mathematical Analysis with MATHEMATICA and Maple
Jiri Gregor and Jaroslav Tiser
Springer, 2011, ISBN 978-0-85729-064-9
http://dx.doi.org/10.1007/978-0-85729-064-9
Maple and Mathematica:
A Problem Solving Approach for Mathematics, Second Edition
Inna Shingareva and Carlos Lizarraga-Celaya
Springer, 2009, ISBN 978-3-211-99432-0
http://dx.doi.org/10.1007/978-3-211-99432-0
Sage – free open-source mathematics software system
http://www.sagemath.org/
Sage for Power Users
William Stein (2012)
http://wstein.org/books/sagebook/sagebook.pdf
Numerical Analysis Using Sage
George A. Anastassiou and Razvan A. Mezei
Springer, 2015, ISBN 978-3-319-16739-8
http://dx.doi.org/10.1007/978-3-319-16739-8
Algebra for Symbolic Computation
Antonio Machi
Springer, 2011, ISBN 978-88-470-2397-0
http://dx.doi.org/10.1007/978-88-470-2397-0
Back to the Table of Contents
=======================================
LaTeX ================================
Practical LaTeX
George Gratzer
Springer, 2014, ISBN 978-3-319-06425-3
http://dx.doi.org/10.1007/978-3-319-06425-3
More Math Into LaTeX, 4th Edition
George Gratzer
Springer, 2007, ISBN 978-0-387-68852-7
http://dx.doi.org/10.1007/978-0-387-68852-7
What Is New in LaTeX?
G. Gratzer
VII. The STIX Math Symbols
Notices of the AMS, Volume 62, Number 6 (June/July 2015)
http://dx.doi.org/10.1090/noti1261
VI. LaTeX on an iPad. Empire
Notices of the AMS, Volume 60, Number 4 (April 2013)
http://dx.doi.org/10.1090/noti963
V. LaTeX on an iPad. Foundation
Notices of the AMS, Volume 60, Number 3 (March 2013)
http://dx.doi.org/10.1090/noti957
IV. WYSIWYG LaTeX
Notices of the AMS, Volume 58, Number 6 (June/July 2011)
http://www.ams.org/notices/201106/rtx110600828p.pdf
III. Formatting References
Notices of the AMS, Volume 56, Number 8 (September 2009)
http://www.ams.org/notices/200908/rtx090800954p.pdf
II. TeX Implementations, Evolution or Revolution
Notices of the AMS, Volume 56, Number 5 (May 2009)
http://www.ams.org/notices/200905/rtx090500627p.pdf
I. Breaking Free
Notices of the AMS, Volume 56, Number 1 (January 2009)
http://www.ams.org/notices/200901/tx090100052p.pdf
LaTeX and Friends
M.R.C. van Dongen
Springer, 2012, ISBN 978-3-642-23816-1
http://dx.doi.org/10.1007/978-3-642-23816-1
Digital Typography Using LaTeX
Apostolos Syropoulos, Antonis Tsolomitis, and Nick Sofroniou
Springer, 2003, ISBN 978-0-387-22436-7
http://dx.doi.org/10.1007/b98959
Back to the Table of Contents
=======================================
People and Places ======================
Gnomes in the Fog:
The Reception of Brouwer’s Intuitionism in the 1920s
Dennis E. Hesseling
Springer, 2003, ISBN 978-3-0348-7989-7
http://dx.doi.org/10.1007/978-3-0348-7989-7
Kurt Godel and the Foundations of Mathematics:
Horizons of Truth
Matthias Baaz, Christos H. Papadimitriou, Hilary W. Putnam,
Dana S. Scott, and Charles L. Harper, Jr. (Editors)
Cambridge University Press, 2011, ISBN 9780511974236
http://dx.doi.org/10.1017/CBO9780511974236
Kurt Godel Centenary:
Lectures from the Institute for Advanced Study
http://www.youtube.com/watch?v=IvbnxT3VL1E
Bernhard Riemann 1826-1866 – Turning Points in the
Conception of Mathematics
Detlef Laugwitz
Springer, 2008, ISBN 978-0-8176-4777-3
http://dx.doi.org/10.1007/978-0-8176-4777-3
Gosta Mittag-Leffler: A Man of Conviction
Arild Stubhaug
Springer, 2010, ISBN 978-3-642-11672-8
http://dx.doi.org/10.1007/978-3-642-11672-8
Remembering Sofya Kovalevskaya
Michele Audin
Springer, 2011, ISBN 978-0-85729-929-1
http://dx.doi.org/10.1007/978-0-85729-929-1
Mathematical Lives – Protagonists of the Twentieth Century –
From Hilbert to Wiles
Claudio Bartocci, Renato Betti, Angelo Guerragio,
and Roberto Lucchetti (Editors)
Springer, 2011, ISBN 978-3-642-13606-1
http://dx.doi.org/10.1007/978-3-642-13606-1
Ernst Zermelo: An Approach to His Life and Work
Heinz-Dieter Ebbinghaus
Springer, 2007, 978-3-540-49553-6
http://dx.doi.org/10.1007/978-3-540-49553-6
Collected Works – Volume I – Set Theory, Miscellanea
Ernst Zermelo
Springer, 2010, ISBN 978-3-540-79384-7
http://dx.doi.org/10.1007/978-3-540-79384-7
The Map of My Life
Goro Shimura
Springer, 2008, ISBN 978-0-387-79715-1
http://dx.doi.org/10.1007/978-0-387-79715-1
Oscar Zariski (24 April 1899-4 July 1986)
Garrett Birkhoff
Proceedings of the American Philosophical Society
Volume 137, Number 2 (June 1993) Pages 306-320
http://www.jstor.org/stable/986739
The Unreal Life of Oscar Zariski
Carol Parikh
Springer, 2009, ISBN 978-0-387-09430-4
http://dx.doi.org/10.1007/978-0-387-09430-4
Claude Elwood Shannon, 30 April 1916 – 24 February 2001
Robert G. Gallagher
Proceedings of the American Philosophical Society
Volume 147, Number 2 (June 2003) Pages 187-191
http://www.jstor.org/stable/1558263
Kolmogorov’s Heritage in Mathematics
Eric Charpentier, Annick Lesne, and Nikolai K. Nikolski
(Editors)
Springer, 2007, ISBN 978-3-540-36351-4
http://dx.doi.org/10.1007/978-3-540-36351-4
Wikipedia:
http://en.wikipedia.org/wiki/Andrey_Kolmogorov
Selected Works of A. N. Kolmogorov, Volume I:
Mathematics and Mechanics
V. M. Tikhomirov (Editor)
Springer, 1991, ISBN 978-94-011-3030-1
http://dx.doi.org/10.1007/978-94-011-3030-1
Selected Works of A. N. Kolmogorov, Volume II:
Probability Theory and Mathematical Statistics
A.N. Shiryayev (Editor)
Springer, 1992, ISBN 978-94-011-2260-3
http://dx.doi.org/10.1007/978-94-011-2260-3
Selected Works of A. N. Kolmogorov, Volume III:
Information Theory and Theory of Algorithms
A.N. Shiryayev (Editor)
Springer, 1993, ISBN 978-94-017-2973-4
http://dx.doi.org/10.1007/978-94-017-2973-4
The Vexing Case of Igor Shafarevich, A Russian Political
Thinker
Krista Berglund
Springer, 2012, ISBN 978-3-0348-0215-4
http://dx.doi.org/10.1007/978-3-0348-0215-4
Wikipedia: http://en.wikipedia.org/wiki/Igor_Shafarevich
A Glimpse at Hilbert Space Operators:
Paul R. Halmos in Memoriam
Sheldon Axler, Peter Rosenthal, and Donald Sarason (Editors)
Birkhauser, 2010, ISBN 978-3-0346-0347-8
http://dx.doi.org/10.1007/978-3-0346-0347-8
Wikipedia:
http://en.wikipedia.org/wiki/Paul_Halmos
Random Curves: Journeys of a Mathematician
Neal Koblitz
Springer, 2008, ISBN 978-3-540-74078-0
http://dx.doi.org/10.1007/978-3-540-74078-0
Wikipedia: http://en.wikipedia.org/wiki/Neal_Koblitz
The Pleasures of Statistics:
The Autobiography of Frederick Mosteller
Frederick Mosteller
Springer, 2010, ISBN 978-0-387-77956-0
http://dx.doi.org/10.1007/978-0-387-77956-0
Wikipedia:
http://en.wikipedia.org/wiki/Frederick_Mosteller
Reminiscences of a Statistician: The Company I Kept
E. L. Lehman
Springer, 2007, ISBN 978-0-387-71597-1
http://dx.doi.org/10.1007/978-0-387-71597-1
An Accidental Statistician:
The Life and Memories of George E.P. Box
George E.P. Box
Wiley, 2013, ISBN 9781118514948
http://dx.doi.org/10.1002/9781118514948
Back to the Table of Contents
=======================================
Ramanujan – Life and Work ==============
The Indian Mathematician Ramanujan
G. H. Hardy
The American Mathematical Monthly,
Volume 44, Number 3 (March 1937) Pages 137-155
http://www.jstor.org/stable/2301659
Documentary: Letters from an Indian Clerk
http://www.youtube.com/watch?v=OARGZ1xXCxs
Ramanujan: For Lowbrows
Bruce C. Berndt and S. Bhargava
The American Mathematical Monthly,
Volume 100, Number 7 (August-September 1993)
http://www.jstor.org/stable/2323885
Srinivasa Ramanujan: Going Strong at 125, Part I
Notices of the American Mathematical Society,
Volume 59, Number 11 (December 2012)
http://www.ams.org/notices/201211/index.html
Srinivasa Ramanujan: Going Strong at 125, Part II
Notices of the American Mathematical Society,
Volume 60, Number 1 (January 2013)
http://www.ams.org/notices/201301/index.html
Ramanujan’s Place in the World of Mathematics:
Essays Providing a Comparative Study
Krishnaswami Alladi
Springer, 2013, ISBN 978-81-322-0767-2
http://dx.doi.org/10.1007/978-81-322-0767-2
The Mathematical Legacy of Srinivasa Ramanujan
M. Ram Murty and V. Kumar Murty
Springer, 2013, ISN978-81-322-0770-2
http://dx.doi.org/10.1007/978-81-322-0770-2
Ramanujan’s Notebooks, Part I
Bruce C. Berndt
Springer, 1985, ISBN 978-1-4612-1088-7
http://dx.doi.org/10.1007/978-1-4612-1088-7
Ramanujan’s Notebooks, Part II
Bruce C. Berndt
Springer, 1989, ISBN 978-1-4612-4530-8
http://dx.doi.org/10.1007/978-1-4612-4530-8
Ramanujan’s Notebooks, Part III
Bruce C. Berndt
Springer, 1991, ISBN 978-1-4612-0965-2
http://dx.doi.org/10.1007/978-1-4612-0965-2
Ramanujan’s Notebooks, Part IV
Bruce C. Berndt
Springer, 1994, ISBN 978-1-4612-0879-2
http://dx.doi.org/10.1007/978-1-4612-0879-2
Ramanujan’s Notebooks, Part V
Bruce C. Berndt
Springer, 1998, ISBN 978-1-4612-1624-7
http://dx.doi.org/10.1007/978-1-4612-1624-7
Ramanujan’s Lost Notebook, Part I
George E. Andrews and Bruce C. Berndt
Springer, 2005, ISBN 978-0-387-28124-7
http://dx.doi.org/10.1007/0-387-28124-X
Ramanujan’s Lost Notebook, Part II
George E. Andrews and Bruce C. Berndt
Springer, 2009, ISBN 978-0-387-77766-5
http://dx.doi.org/10.1007/b13290
Ramanujan’s Lost Notebook, Part III
George E. Andrews and Bruce C. Berndt
Springer, 2012, ISBN 978-1-4614-3810-6
http://dx.doi.org/10.1007/978-1-4614-3810-6
Ramanujan’s Lost Notebook, Part IV
George E. Andrews and Bruce C. Berndt
Springer, 2013, ISBN 978-1-4614-4081-9
http://dx.doi.org/10.1007/978-1-4614-4081-9
Back to the Table of Contents
=======================================
Elements de Mathematique by N. Bourbaki ==
Theorie des Ensembles
Springer, 2006, ISBN 978-3-540-34035-5
http://dx.doi.org/10.1007/978-3-540-34035-5
Groupes et Algebres de Lie: Chapitre 1
Springer, 2007, ISBN 978-3-540-35337-9
http://dx.doi.org/10.1007/978-3-540-35337-9
Groupes et Algebres de Lie: Chapitre 4 a 6
Springer, 2007, ISBN 978-3-540-34491-9
http://dx.doi.org/10.1007/978-3-540-34491-9
Elements d’histoire des mathematiques
Springer, 2007, ISBN 978-3-540-33981-6
http://dx.doi.org/10.1007/978-3-540-33981-6
Back to the Table of Contents
=======================================
Mathematical Fun ======================
Crafting Conundrums:
Puzzles and Patterns for the Bead Crochet Artist
Ellie Baker and Susan Goldstine
CRC Press, 2014, ISBN 978-1-4665-8849-3
http://dx.doi.org/10.1201/b17578
Flexagons Inside Out
Les Pook
Cambridge University Press, 2003, ISBN 9780511543302
http://dx.doi.org/10.1017/CBO9780511543302
Serious Fun with Flexagons: A Compendium and Guide
Les Pook
Springer, 2009, ISBN 978-90-481-2503-6
http://dx.doi.org/10.1007/978-90-481-2503-6
Manifold Mirrors:
The Crossing Paths of the Arts and Mathematics
Felipe Cucker
Cambridge University Press, 2013, ISBN 9781139014632
http://dx.doi.org/10.1017/CBO9781139014632
A Mathematical Tapestry:
Demonstrating the Beautiful Unity of Mathematics
Peter Hilton and Jean Pedersen
Cambridge University Press, 2010, ISBN 9780511777004
http://dx.doi.org/10.1017/CBO9780511777004
Dicing with Death: Chance, Risk and Health
Stephen Senn
Cambridge University Press, 2003, ISBN 9780511543319
http://dx.doi.org/10.1017/CBO9780511543319
Fallacies in Mathematics
E. A. Maxwell
Cambridge University Press, 1959, ISBN 9780511569739
http://dx.doi.org/10.1017/CBO9780511569739
Insights into Game Theory:
An Alternative Mathematical Experience
Ein-Ya Gura and Michael Maschler
Cambridge University Press, 2008, ISBN 9780511754229
http://dx.doi.org/10.1017/CBO9780511754326
Social Choice and the Mathematics of Manipulation
Alan D. Taylor
Cambridge University Press, 2005, ISBN 9780511614316
http://dx.doi.org/10.1017/CBO9780511614316
Naïve Decision Making: Mathematics Applied to the Social
World
T. W. Korner
Cambridge University Press, 2008, ISBN 9780511755439
http://dx.doi.org/10.1017/CBO9780511755439
Back to the Table of Contents
=======================================
Legal Matters ==========================
Patenting mathematical algorithms: What’s the harm? –
A thought experiment in algebra
Pal B. de Laat
International Review of Law and Economics, Volume 20 (2000)
http://dx.doi.org/10.1016/S0144-8188(00)00031-4
Patent Strategy:
For Researchers and Research Managers, Third Edition
H. Jackson Knight
Wiley, 2013, ISBN 9781118314289
http://dx.doi.org/10.1002/9781118314289
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Reference Material =====================
Computational Statistics: Concepts and Methods,
Handbook of; Second Edition
James E. Gentle, Wolfgang Karl Hardle, and Yuichi Mori
(Editors)
Springer, 2012, ISBN 978-3-642-21550-6
http://dx.doi.org/10.1007/978-3-642-21551-3
Continued Fractions for Special Functions, Handbook of
Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk,
Haakon Waadeland, and William B. Jones
Springer, 2008, ISBN 978-1-4020-6949-9
http://dx.doi.org/10.1007/978-1-4020-6949-9
Geomathematics, Handbook of
Willi Freeden, M. Zuhair Nashed, and Thomas Sonar
(Editors)
Springer, Live Reference – Constantly updated,
ISBN 978-3-642-27793-1
http://dx.doi.org/10.1007/978-3-642-27793-1
Mathematics, Handbook of; Sixth Edition
I. N. Bronshtein, K. A. Semendyayev, Gerhard Musiol,
and Heiner Muhlig
Springer, 2015, ISBN 978-3-662-46221-8
http://dx.doi.org/10.1007/978-3-662-46221-8
Operator Theory
Daniel Alpay (Editor)
Springer, Live Reference – Constantly updated,
ISBN 978-3-0348-0692-3
http://dx.doi.org/10.1007/978-3-0348-0692-3
Statistical Sciences, Encyclopedia of
Samuel Kotz, Campbell B. Read, N. Balakrishnan,
and Brani Vidakovic (Editors)
Wiley, 1999-present, ISBN 9780471667193
http://dx.doi.org/10.1002/0471667196
http://projecteuclid.org/euclid.ss/1177012021
Statistical Science, International Encyclopedia of
Miodrag Lovric (Editor)
Springer, 2011 ISBN 978-3-642-04898-2
http://dx.doi.org/10.1007/978-3-642-04898-2
Statistics, The Concise Encyclopedia of
Yadolah Dodge
Springer, 2008, ISBN 978-0-387-32833-1
http://dx.doi.org/10.1007/978-0-387-32833-1
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Additional Web Resources ===============
MacTutor History of Mathematics Archive
School of Mathematics and Statistics
University of St Andrews, Scotland
http://www-history.mcs.st-and.ac.uk/
Reprints in Theory and Applications of Categories
http://www.tac.mta.ca/tac/reprints/
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Online Publications – Directly =============
Theory and Applications of Categories
http://www.tac.mta.ca/tac/index.html
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=======================================
Odds & Ends ===========================
Introduction to Neutrosophic Statistics
Florentin Smarandache (2014)
http://arxiv.org/abs/1406.2000
Smarandache Notions Journal (plus a lot more)
http://fs.gallup.unm.edu/
Two Millennia of Mathematics: From Archimedes to Gauss
George M. Phillips
Springer, 2000, ISBN 978-1-4612-1180-8
http://dx.doi.org/10.1007/978-1-4612-1180-8
Mathematical Intuition: Poincare, Polya, Dewey
Reuben Hersh
http://dx.doi.org/10.1007/978-0-8176-8394-8_2
The Courant-Friedrichs-Lewy (CFL) Condition:
80 Years After Its Discovery
Carlos A. de Moura and Carlos S. Kubrusly (Editors)
Springer, 2013, ISBN 978-0-8176-8394-8
http://dx.doi.org/10.1007/978-0-8176-8394-8
Theory of Transformation Groups I:
General Properties of Continuous transformation Groups.
A Contemporary Approach and Translation
Sophus Lie
Springer, 2015, ISBN 978-3-662-46211-9
http://dx.doi.org/10.1007/978-3-662-46211-9
Elliptic Tales: Curves, Counting, and Number Theory
Avner Ash and Robert Gross
Princeton University Press, 2012, ISBN 978-1-4008-4171-4
http://www.degruyter.com/viewbooktoc/product/452369
In Pursuit of the Travelling Salesman:
Mathematics at the Limits of Computation
William J. Cook
Princeton University Press, 2011, ISBN 978-1-4008-3959-9
http://www.degruyter.com/viewbooktoc/product/452549
The Elementary Theory of Groups:
A Guide through the Proofs of the Tarski Conjectures
Benjamin Fine, Anthony Gaglione, Alexei Myashnikov,
Gerhard Rosenberger, and Dennis Spellman
Walter de Gruyter, 2014, ISBN 978-3-11-034203-1
http://www.degruyter.com/viewbooktoc/product/247008
The History of Approximation Theory: From Euler to Bernstein
Karl-Georg Steffens
Springer, 2006, ISB8 978-0-8176-4475-8
http://dx.doi.org/10.1007/0-8176-4475-X
Approximation Theory: From Taylor Polynomials to Wavelets
Ole Christensen and Khadija L. Christensen
Springer, 2005, ISBN 978-0-8176-4448-2
http://dx.doi.org/10.1007/978-0-8176-4448-2
Mathematics of Approximation
Johan de Villiers
Springer, 2012, ISBN 978-94-91216-50-3
http://dx.doi.org/10.2991/978-94-91216-50-3
Tauberian Theory: A Century of Developments
Jacob Korevaar
Springer, 2004, ISBN 978-3-662-10225-1
http://dx.doi.org/10.1007/978-3-662-10225-1
Spatial Mathematics: Theory and Practice through Mapping
Sandra Lach Arlinghaus and Joseph J. Kerski
CRC Press, 2014, ISBN 978-1-4665-0533-9
http://dx.doi.org/10.1201/b15049
Inside Interesting Integrals
Paul J. Nahin
Springer, 2015, ISBN 978-1-4939-1277-3
http://dx.doi.org/10.1007/978-1-4939-1277-3
Divide-and-Conquer:
A Proportional, Minimal-Envy Cake-Cutting Algorithm
Steven J. Brams, Michael A. Jones, and Christian Klamler
SIAM Review, Volume 53, Number 2 (2011)
http://dx.doi.org/10.1137/080729475
The Mereon Matrix: Unity, Perspective and Paradox
Lynnclaire Dennis, Jytte Brender McNair,
and Louis H. Kauffman (Editors)
Elsevier, 2013, ISBN 978-0-12-404613-9
http://www.sciencedirect.com/science/book/9780124046139
Programming for Mathematicians
Raymond Seroul
Springer, 2000, ISBN 978-3-642-57129-9
http://dx.doi.org/10.1007/978-3-642-57129-9
The Nonlinear World:
Conceptual Analysis and Phenomenology
Yoshitsugu Oono
Springer, 2013, ISBN 978-4-431-54029-8
http://dx.doi.org/10.1007/978-4-431-54029-8
Quantum Theory for Mathematicians
Brian C. Hall
Springer, 2013, ISBN 978-1-4614-7116-5
http://dx.doi.org/10.1007/978-1-4614-7116-5
The Mathematical Language of Quantum Theory:
From Uncertainty to Entanglement
Teiko Heinosaari and Mario Ziman
Cambridge University Press, 2012, ISBN 9781139031103
http://dx.doi.org/10.1017/CBO9781139031103
Vladimir I. Arnold – Collected Works, Volume II:
Hydrodynamics, Bifurcation Theory, and Algebraic Geometry
1965-1972
Springer, 2014, ISBN 978-3-642-31031-7
http://dx.doi.org/10.1007/978-3-642-31031-7
Home Page of Terence Tao (Analysis Group, UCLA)
http://www.math.ucla.edu/~tao/
The Personal Pages of Jonathan Borwein
http://www.carma.newcastle.edu.au/~jb616
Squaring.Net
Stuart Anderson
http://www.squaring.net/
Indiscrete Thoughts
Gian-Carlo Rota
Springer, 2008, ISBN 978-0-8176-4781-0
http://dx.doi.org/10.1007/978-0-8176-4781-0
Undergraduate Math Journal
Rose-Hulman Institute of Technology
http://www.rose-hulman.edu/mathjournal/index.php
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