1. science
2. mathematics

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Opetussuunnitelma 2015 - 2016: kurssikuvaukset
Taso: DI- ja jatko-opintotasoiset kurssit
Laitos: Matematiikan ja systeemianalyysin laitos
Kielet: suomi, ruotsi, englanti
MS-E1000 Crystal Flowers in Halls of Mirrors: Mathematics meets Art and
Architecture (6-10 cr)
Responsible teacher: Kirsi Peltonen
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor of
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching Period: III-IV (Spring 2017), every other year
Workload: Contact teaching: 6h/week x 12 weeks=72h, independent study: 90h (projects
and reports)
Learning Outcomes: Students will learn to find connections between mathematics and
art and architecture. Real mathematics will be revealed through patterns, symmetries,
structures, shapes and beauty in such a way that will enable the student to view our
environment from a new perspective. By the end of the course, the students will be able
to distinguish aspects from their own fields which can be presented, considered and
developed using the language of modern mathematics.
Content:
During the course we will consider methods offered by various fields of mathematics
which meet the needs of art and architecture. Through concrete projects, we will find
phenomena and interpretations of these phenomena from both classical and modern
mathematics.
Possible topics from mathematics which may appear: Symmetries, systems of
proportions, projections and perspectives. Geometric inversion, conformality and more
general mapping classes. Tilings in the plane, polyhedrons and duality. Hopf fibration and
other structures. On different types of geometries: spherical, hyperbolic, geometry of
surfaces and minimal surfaces. Fractal geometry and dynamics. Kleinian groups, knot
theory and contact structures. We will also, depending on the interest of the students,
introduce artists and architects from different cultures: M.C. Escher, V. Vasarely, István
Orosz, Eero Saarinen, Islamic art, Celtic knots, Sangaku.
Assessment Methods and Criteria: There are no prerequisites from mathematics or art.
Students must participate in 80% of the contact teaching. The course consists of project
work completed in groups of at most six people at Aalto Design Factory. All steps of the
project: planning, implementation, written reports and presentations will have an impact
on grades. Individual input is also taken into account by reflections, portfolios, exercises
and essays. Optional forms of completing the course can be provided, if required. A
complete evaluation and monitoring of learning is performed during the course.
Study Material: To be determined at the beginning of the course.
Substitutes for Courses: Mat-1.3000 Kristallikukkia peilisaleissa: Matematiikka kohtaa
taiteen ja arkkitehtuurin
Grading Scale: 1-5
Language of Instruction: Finnish, English if needed
Further Information: At most 36 participants can be accepted. Tentatively 12 art
students, 12 architecture students and 12 others. No prerequisities from mathematics or
art. The course can be included for example in methodological studies and it is suitable at
every stage of studies and for students in every school.
MS-E1010 Tieteen filosofia (5 op)
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Vastuuopettaja: Ilpo Halonen
Kurssin taso: maisteriopinnot, jatko-opinnot
Opetusperiodi: I-II (syksy 2015), joka toinen vuosi
Työmäärä toteutustavoittain: 48 t (luennot), 56 t (luentojen kertaus), 26 t
(oheislukemisto)
Osaamistavoitteet: Opintojakson jälkeen opiskelija pystyy ymmärtämään ja arvioimaan
filosofista lähestymistapaa tieteeseen.
Sisältö: Tieteen ja tieteellisen ajattelun tunnuspiirteiden systemaattinen tarkastelu sekä
eri aikojen käsitykset tieteen tavoitteista, menetelmistä sekä tieteellisen tiedon luonteesta.
Tieteen ja tekniikan suhde eri aikoina. Matemaattisten ja fysikaalisten tieteiden perusteet,
tavoitteet ja menetelmät filosofisesta näkökulmasta. Myös historiallinen kehitys antiikin
ajattelijoista tieteiden vallankumoukseen ja edelleen nykypäivän keskeisiin näkemyksiin
asti. Logiikka ja argumentaatioteoria, tieteellinen päättely, sen luonne ja tavoitteet,
tieteellinen selittäminen ja kausaliteetin ongelmat. Tieteen etiikka ja tieteellinen
maailmankuva. Tiedon kasvuun ja tieteen kehitykseen liittyvät kysymykset.
Toteutus, työmuodot ja arvosteluperusteet: Kirjallinen tentti.
Oppimateriaali: Luentojen tiivistelmät ja tieto pakollisesta sekä suositeltavasta
oheiskirjallisuudesta julkaistaan kurssin MyCourses-sivuilla kurssin kuluessa.
Korvaavuudet: Mat-1.3013, Mat-1.3014, Mat-1.3015
Arvosteluasteikko: Hyväksytty/hylätty.
Opetuskieli: Suomi pääosin. Pyydettäessä suoritettavissa englanniksi.
Lisätietoja: [email protected]
MS-E1010 Vetenskapens filosofi (5 sp)
Ansvarig lärare: Ilpo Halonen
Kursens status:
Kursnivå: magisterstudier, fortbildningsstudier
Undervisningsperiod: I-II (hösten 2015), vartannat år
Arbetsmängd: 48 t (föreläsningar), 56 t (repetition av föreläsningar), 26 t (läsning av
annan litteratur)
Lärandemål: Opintojakson jälkeen opiskelija pystyy ymmärtämään ja arvioimaan
filosofista lähestymistapaa tieteeseen.
Innehåll:
n systematiskt behandling av de utmärkande dragen i vetenskapen och det
vetenskapliga tänkandet och uppfattningar under olika tidevarv om metoder och
målsättningar för vetenskapen och arten av vetenskaplig kunskap.
Grunder, målsättningar och metoder i de matematiska och fysikaliska vetenskaperna ur
en filosofisk synvinkel. Den historiksa utvecklingen från antikens tänkare till den
vetenskapliga revolutionen och vidare till centrala nutida åsikter. Logik och
argumentationsteori. Vetenskaplig slutledning, dess natur och
målsättningar. Vetenskapliga förklaringar och kausalitetsproblem. Vetenskapens etik
och den vetenskapliga världsbilden. Frågor som gäller kunskapstillväxten och
utvecklingen av vetenskapen.
Metoder, arbetssätt och bedömningsgrunder: Skriftlig tentamen.
Studiematerial: n sammanfattning av föreläsningar utges i kursens MyCourses-sidor på
finska.
Ersättande prestationer: Mat-1.3013, Mat-1.3014, Mat-1.3015
Bedömningsskala: Godkänt/Underkänt
Undervisningsspråk: Huvudsakligen på finska. Kan på begäran avläggas på engelska.
Tilläggsinformation: [email protected]
MS-E1010 Philosophy of Science (5 cr)
Responsible teacher: Ilpo Halonen
Status of the Course:
Level of the Course: master’s level, doctoral level
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Teaching Period: I-II (Autumn 2015), every other year
Workload: 48 hours (lectures), 56 t (repetition), 26 t (additional literature)
Learning Outcomes: Opintojakson jälkeen opiskelija pystyy ymmärtämään ja arvioimaan
filosofista lähestymistapaa tieteeseen.
Content: The course deals mainly the foundations, objectives, and the methods in the
mathematical and physical sciences from a philosophical point of view. The course
proceeds historically from the philosophers of antiquity to the scientific revolution and
from there to the essential modern philosophies. The characteristic features of science
and of scientific thinking are systematically treated as well as concepts about the
methods and the objectives of science and the nature of scientific knowledge during
different periods. Systematical consideration of science and scientific thinking and the
conceptions concerning objectives, methods and the nature of scientific knowledge
during different times. Foundations, objectives and methods of mathematical and physical
sciences from the philosophical point of view. The historical development from antiquity
through the scientific revolution until the main perspectives of modern times. The
scientific establishment of theories and concepts, scientific reasoning, its nature and
objectives, scientific explanation and causality, the ethics of science and questions
pertaining to the scientific world view, growth of knowledge and the development of
science.
Assessment Methods and Criteria: Written exam.
Study Material: A summary of the lectures in Finnish can be found on
the MyCourses pages during the course.
Substitutes for Courses: Mat-1.3013, Mat-1.3014, Mat-1.3015
Grading Scale: Pass/Fail
Language of Instruction: Primarily Finnish. Can be taken in English upon request.
Further Information: [email protected]
MS-E1011 Tieteen historia (5 op)
Vastuuopettaja: Ilpo Halonen
Kurssin taso: maisteriopinnot, jatko-opinnot
Opetusperiodi: I-II (syksy 2016), joka toinen vuosi
Työmäärä toteutustavoittain: 48 t (luennot), 56 t (luentojen kertaus), 26 t
(oheislukemisto)
Osaamistavoitteet: Opintojakson jälkeen opiskelija pystyy ymmärtämään ja arvioimaan,
miten tiede on eri aikoina vaikuttanut maailmankuvaan ja miten maailmankuva
(mahdollisesti) on vaikuttanut tieteeseen.
Sisältö: Valitut kohdat tiedehistoriasta antiikista uudelle ajalle asti. Asioiden
ymmärtäminen tieteen metodisen kehityksen ja tieteellisestä metodista esitettyjen
teorioiden kannalta. Järjestelmällisen tieteenharjoituksen synty Kreikassa, Aristoteleen
rooli filosofian ja tieteiden isänä, hänen teostensa asema keskiajan eurooppalaisissa
yliopistoissa. Luonnontieteen nousu 1600-luvulla, ns. “tieteen suuri vallankumous”.
Tämän vallankumouksen yhtenä tärkeänä teemana oli tähtitieteen kehitys. Em. kauden
keskeisten matemaattis-fysikaalisten keksintöjen takaa löytyvät hahmot: mm. Kopernikus,
Brahe, Kepler, Bacon, Galilei, Descartes, Newton ja Leibniz. Valittuja kohtia uudemmasta
tiedehistoriasta (mm. Einstein).
Toteutus, työmuodot ja arvosteluperusteet: Kirjallinen tentti.
Oppimateriaali:
Luentojen tiivistelmät ja tieto pakollisesta sekä suositeltavasta oheiskirjallisuudesta
julkaistaan kurssin Noppa-sivuilla kurssin kuluessa.
Substitutes for courses: Kurssin voi suorittaa myös pyydettäessä englanniksi
kirjallisuustentillä.
Korvaavuudet: Mat-1.3011, Mat-1.3012, Mat-1.3016
Arvosteluasteikko: Hyväksytty/hylätty.
Opetuskieli: Suomi pääosin. Pyydettäessä suoritettavissa englanniksi.
Lisätietoja: [email protected]
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MS-E1011 Vetenskapshistoria (5 sp)
Ansvarig lärare: Ilpo Halonen
Kursnivå: magisterstudier, fortbildningsstudier
Undervisningsperiod: I-II (hösten 2016), vartannat år
Arbetsmängd: 48 t (föreläsningar), 56 t (repetition av föreläsningar), 26 t (läsning av
annan litteratur)
Lärandemål: Kan förstå och bedöma hur vetenskapen under olika tider har påverkat
värdsbilden och hur världsbilden (eventuellt) har påverkat vetenskapen.
Innehåll:
Valda delar av vetenskapshistorien från antiken till nya tiden. Förståelse av olika
fenomen med utgångspunkt i den metodiska utvecklingen av vetenskapen och de teorier
som framställts beträffande vetenskapliga metoder.
Uppkomsten av systematiska vetenskaper i Grekland, Aristoteles roll som filosofins och
vetenskapens fader, och hans verks ställning i de medeltida europeiska universiteten.
Den vetenskapliga uppgången under 1600-talet, “den stora vetenskapliga revolutionen”.
Ett viktigt tema i denna revolution var utvecklingen i astronomi. Bakom de centrala
matematisk-fysikaliska upptäckterna under perioden finns personer som t.ex. Kopernikus,
Brahe, Kepler, Bacon, Galilei, Descartes, Newton och Leibniz. Valda delar av nyare
vetenskapshistoria (bl.a. Einstein).
Metoder, arbetssätt och bedömningsgrunder: Skriftlig tentamen.
Studiematerial: En sammanfattning av föreläsningar utges i kursens MyCourses-sidor
på finska.
Ersättande prestationer: Kursen kan avläggas som självstudiekurs på engelska.
Bedömningsskala: Godkänt/Underkänt
Undervisningsspråk: Huvudsakligen på finska. Kan på begäran avläggas på engelska.
Tilläggsinformation: [email protected]
MS-E1011 History of Science (5 cr)
Responsible teacher: Ilpo Halonen
Level of the Course: master’s level, doctoral level
Teaching Period: I-II (Autumn 2016), every other year
Workload: 48 hours (lectures), 56 t (repetition), 26 t (additional literature)
Learning Outcomes: After the course the student can understand and evaluate, how
science has affected the world view and how the world view has (possibly) affected
science.
Content: The course examines the history of science by way of selected topics from
antiquity to the twentieth century. The emphasis is on the methodological development of
science and on the theories developed to deal with scientific method. Understanding the
material from the methodological development of science point of view. The rise of
systematic science in Greece. The role of Aristotle as the father of philosophy and
science, and the status of his works in medieval universities. The great scientific
advances made during the 17th century, often called “the great scientific revolution”, are
treated. An important theme in this revolution was the development of astronomy. Behind
the central mathematical-physical discoveries during the period were persons like
Kopernikus, Brahe, Kepler, Bacon, Galilei, Descartes, Newton and Leibniz. In addition the
course treats certain parts of more recent history of science (e.g. Einstein).
Assessment Methods and Criteria: Written exam.
Study Material: A summary of the lectures in Finnish can be found on the Noppa pages
during the course.
Substitutes for Courses: The course can be taken in English as a literature exam upon
request.
Grading Scale: Pass/Fail
Language of Instruction: Primarily Finnish. Can be taken in English upon request.
Further Information: [email protected]
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MS-E1050 Graph theory (5 cr)
Responsible teacher: Alexander Engström
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor of
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: I (Autumn)
Workload: Lectures and tutored problem solving 36h (3x2h/week, 6 weeks), self-study
about 100h.
Learning Outcomes: The students will after the course understand the basic invariants
of graphs and how they are related by regularity and structural graph theory.
Content: Basic properties as connectivity, planarity and minor containment both in the
deterministic and random setting. The Szemerédi regularity lemma, graph
homomorphisms and graph limits; the graph minor theorem and the strong perfect graph
theorem.
Study Material: Graph Theory, Diestel, 4th edition; Large Networks and Graph Limits,
Lovász.
Substitutes for Courses: Mat-1.3050
Prerequisites: Mathematical maturity comparable to a bachelor in computer science,
mathematics or operational research.
Evaluation: 1-5
Language of Instruction: English
MS-E1051 Combinatorics (5 cr)
Responsible teacher: Alexander Engström
Status of the Course: Major of Mathematics, Master’s Programme in Mathematics and
Operations Research, optional; master’s level Minor of Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: II (Autumn)
Workload: Lectures and tutored problem solving 36h (3x2h/week, 6 weeks), self-study
about 100h.
Learning Outcomes: The students will learn how to analyse combinatorial problems
using algebraic and analytic methods.
Content: Enumeration and generating functions; posets and their algebraic properties.
Study Material: Analytic Combinatorics, Flajolet and Sedgewick; Supplied lecture notes
on algebraic combinatorics.
Substitutes for Courses: MS-C1050
Prerequisites: Mathematical maturity comparable to a bachelor in computer science,
mathematics or operational research. Preferably some basic algebra and complex
analysis.
Evaluation: 1-5.
Language of Instruction: English
MS-E1059 Seminar on combinatorics (V) (V) (1-5 cr)
Responsible teacher: Alexander Engström
Status of the Course: Major of Mathematics, Master’s Programme in Mathematics and
Operations Research, optional
Level of the Course: master’s level, doctoral level
Teaching period: I-V (academic year)
Learning Outcomes: An overview of contemporary research trends in algebraic and
topological combinatorics and an understanding of the basic elements of a good math
talk.
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Content: Seminar talks and discussions.
Assessment Methods and Criteria: Active participation in seminars.
Course Homepage: http://math.aalto.fi/~alex/
Evaluation: pass/fail
Registration for Courses: Contact the teacher in charge.
Language of Instruction: English
MS-E1089 Seminar on Algebra, Number Theory, and Applications to
Communications and Computing V (V) (2 cr)
Responsible teacher: Camilla Hollanti
Teaching period: I-V (2015-2016)
Learning Outcomes: To get familiar with the research topics of algebra, number theory
and their applications.
Content: Research topics of algebra, number theory and their applications
Assessment Methods and Criteria: Attendance 6 times, including one presentation
Evaluation: Pass/fail
Language of Instruction: English
Further Information: http://math.aalto.fi/en/research/algnumb/seminar/
MS-E1110 Number theory (5 cr)
Responsible teacher: Camilla Hollanti
Status of the Course: Major in Applied Mathematics & Major in Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor in
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: II (Autumn).
Workload: 24+12 (4+2).
Learning Outcomes:
- The student understands the basic concepts of number theory and is able to solve
simple Diophantine equations and perform modular arithmetics.
- The student is familiar with some applications of number theory in cryptography.
Content: integer factorization, primes, pseudo primes, Diophantine equations, modular
arithmetics, squares and nonsquares in modular arithmetics, primititive roots, applications
to cryptography.
Assessment Methods and Criteria: Lectures, exercises, exam, essay.
Study Material: K. H. Rosen: Elementary number theory and its applications. 1993.
Substitutes for Courses: Mat-1.3111, MS-C1110.
Prerequisites: High school mathematics. MS-A040X OR MS-C1080 is recommended.
Evaluation: 1-5.
Language of Instruction: English
MS-E1111 Galois theory (5 cr)
Responsible teacher: Camilla Hollanti
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor of
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: IV (Spring 2016), every other year
Workload: 6 hours x 6 weeks
Content: To understand at an operative level the concepts of Galois extension and
Galois correspondence. Ability to solve equations with algebraic methods.
Assessment Methods and Criteria: Lectures, written exercises, possibility for an oral
exam if needed.
Study Material: Ian Stewart: Galois Theory, 3rd edition.
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Substitutes for Courses: Mat-1.3110
Prerequisites: MS-C1080 Algebran perusrakenteet or similar.
Evaluation: 1-5.
Language of Instruction: English
MS-E1280 Measure and integral (5 cr)
Responsible teacher: Juha Kinnunen
Status of the Course: Major of Mathematics, Master’s Programme in Mathematics and
Operations Research, optional; master’s level Minor of Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: II (Autumn)
Workload: lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks),
self-study ca 100h
Learning Outcomes: After this course you will know basic methods in measure and
integration theory.
Content: Outer measure (properties of measurable sets, characterizations of measurable
sets, Lebesgue outer measure), measurable functions (properties of measurable
functions, approximation by simple functions, Egoroff and Lusin theorems), integration
(construction and properties of integral, Lebesgue integral, convergence theorems),
Fubini’s theorem.
Assessment Methods and Criteria: Homework assignments and attendance (50%),
final exam (50%).
Study Material: All material is available at the course homepage.
Substitutes for Courses: MS-C1280.
Prerequisites: MS-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X, MS-C1540.
Evaluation: 1-5
Language of Instruction: English
MS-E1281 Real analysis (5 cr)
Responsible teacher: Juha Kinnunen
Status of the Course: Major of Mathematics, Master’s Programme in Mathematics and
Operations Research, optional; master’s level Minor of Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: IV (Spring 2016), every other year
Workload: 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca
100h
Learning Outcomes: After this course you will know how to apply real analysis
methods in research.
Content: Lebesgue spaces (Hölder’s and Minkowski’s inequalities, Riesz-Fischer
theorem, dual spaces and weak convergence), Hardy-Littlewood maximal function (Vitali
covering theorem, Marcinkiewicz interpolation theorem, maximal function theorem,
Lebesgue’s differentiation theorem), convolution approximations, differentiation of Radon
measures (Besicovitch covering theorem, Lebesgue points), Radon-Nikodym theorem,
Riesz representation theorem, weak convergence and compactness for Radon
measures, Sobolev spaces (Poincare and Sobolev inequalities).
Assessment Methods and Criteria: Homework assignments and attendance (100%).
Study Material: All material is available at the course homepage.
Substitutes for Courses: Mat-1.3283
Prerequisites: MS-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X, MS-C1280,
MS-C1350, MS-C1540.
Evaluation: 1-5
Language of Instruction: English
MS-E1289 Seminar on analysis and geometry (V) (V) (1-5 cr)
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Responsible teacher: Juha Kinnunen; Kirsi Peltonen
Status of the Course: Major of Mathematics, Master’s Programme in Mathematics and
Operations Research, optional; master’s level Minor of Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: I-V (academic year)
Learning Outcomes: This is a research seminar.
Content: We study the most recent methods and results in modern analysis and
geometry. The talks are related, for example, to differential geometry, geometric analysis,
harmonic analysis and partial differential equations.
Substitutes for Courses: Mat-1.3284
Evaluation: hyv · Opintojaksot
Language of Instruction: English
MS-E1460 Functional analysis (5 cr)
Responsible teacher: Ville Turunen
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor in
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: I (Autumn)
Workload: Lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6
weeks), self-study ca 100h.
Learning Outcomes: You will learn about norms and inner products in
infinite-dimensional vector spaces. Related to these structures, you will understand basic
properties of bounded linear operators and duality in Banach and Hilbert spaces, together
with diagonalization of compact self-adjoint operators.
Content: Bounded linear operators and functionals in Banach and Hilbert spaces,
elementary spectral theory (Riesz Compactness Theorem, Uniform Boundedness
Principle, Open Mapping and Closed Graph Theorems, Hahn-Banach Theorem, Riesz
Hilbert Space Representation and Hilbert-Schmidt Spectral Theorems).
Assessment Methods and Criteria: Weekly exercises (1/3) and an exam (2/3).
Alternatively, just exam (100%).
Study Material: Lecture notes (additional literature to be announced at the course
homepage).
Substitutes for Courses: Mat-1.3460 Principles of Functional Analysis.
Prerequisites: MS-A000X, MS-A010X, MS-C1540.
Evaluation: 1-5.
Language of Instruction: English.
MS-E1531 Differential geometry (5 cr)
Responsible teacher: Kirsi Peltonen
Status of the Course: Major of Mathematics, Master’s Programme in Mathematics and
Operations Research, optional; master’s level Minor of Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: III (Spring 2016), every other year
Workload: 36 + 18 (4 + 2)
Learning Outcomes: This course is an introduction to the basic machinery behind the
modern differential geometry: tensors, differential forms, smooth manifolds and vector
bundles. The geometries lying above these structures are involved in several applications
through mathematical analysis, physics, stochastics and statistical modells. The central
goal is to become familiar with this particular language of abstract mathematics that
opens the venue to apply geometric methods in different applications. A modern
viewpoint to some of the classical Riemann, Finsler or Kähler model geometries is served
in addition to the possibility to open the door to the beautiful worlds of contact and
symplectic geometry that are present in the most recent progress of geometrization of
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applications. The course provides basic skills to recognize geometric phenomena in
mathematical analysis and applications.
Content: Topics related to differential geometry varying from classical Riemannian
geometry to modern geometries. More specified topics will be announced later.
Assessment Methods and Criteria: Active participation in lectures and weekly
excercises. Individual research projects that are related to the topics of the course.
Always discuss beforehand with the lecturer before starting such a project. A traditional
exam is also possible.
Study Material: All material related to the course can be found from MyCourses pages of
the course. There is no special book the course is following but excellent treatments in
the spirit of the lectures are provided by:
- John M. Lee: Introduction to Smooth Manifolds, Springer
- John M. Lee: Riemannian Manifolds: An Introduction to Curvature, Springer.
Substitutes for Courses: Mat-1.3531
Prerequisites: MS-A210, MS-A310, MS-C1530, MS-C1540
Evaluation: 1-5
Language of Instruction: English
Further Information: The content of the course is part of a good mathematical
education, which should self-evidently belong to the curriculum of every math major
student. A highly open mind is necessary to gain the capability to apply methods provided
by differential geometry to other sciences. Suitable to everybody interested in
geometrization, especially those with a focus on fields in natural sciences where the
connection is most visible like in general relativity and electromagnetism. Other potential
fields are all sciences that make use of statistical or stochastic methods.
MS-E1600 Probability theory (5 cr)
Responsible teacher: Kalle Kytölä; Lasse Leskelä
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor of
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: III (Spring)
Workload: 2 x 2h lectures,1 x 2h exercises sessions
Learning Outcomes:
After completing the course, the participant
- Can compute the expected value of a random number as an integral with respect to a
probability measure
- Can compute probabilities related to independent random variables by using a product
measure
- Recognizes different types of convergence of a random sequence
- Can explain how and when a random sum can be approximated by a Gaussian
distribution
- Can represent conditional probabilities with respect to the information content of a
sigma-algebra
Content: - Random numbers, vectors, and sequences
- Integration with respect to a probability measure
- Stochastic independence and product measure
- Law of large numbers and the central limit theorem
- Conditional expectation with respect to a sigma-algebra
Study Material: TBA
Substitutes for Courses: Mat-1.3601
Prerequisites: Familiarity with continuous functions and open sets (e.g. MS-C1540
Euklidiset avaruudet)
Evaluation: 1-5
Language of Instruction: English
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MS-E1601 Brownian motion and stochastic analysis (5 cr)
Responsible teacher: Lasse Leskelä
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor of
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: II (Autumn 2015), every other year
Workload: - 2 x 2h lectures
- 1 x 2h exercises sessions
Learning Outcomes:
After completing the course the participant:
- Can compute probabilities and expectations related to Brownian motion
- Can define the stochastic integral
- Recognizes random processes which are integrable with respect to Brownian motion
- Can apply Itō’s formula to various functionals of Brownian motion
Content:
- Brownian motion
- Stochastic integral
- Itō’s formula and applications
Study Material: TBA
Substitutes for Courses: Mat-1.3602
Prerequisites: MS-E1600
Evaluation: hyv · Opintojaksot
Language of Instruction: English
MS-E1602 Large random systems (5 cr)
Responsible teacher: Kalle Kytölä
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional; master’s level Minor of
Mathematics, optional
Level of the Course: master’s level, doctoral level
Teaching period: IV (Spring 2016), every other year
Workload:
- 2 x 2h lectures
- 1 x 2h exercises sessions
Learning Outcomes:
After completing the course the participant is able to:
- Formulate mathematical models of various systems with a large number of interacting
random components
- Incorporate spacial structure and dynamics into probabilistic models
- Estimate the asymptotics of probabilities and expected values in models with a size
parameter
- Formulate qualitative phase transitions in stochastic models and recognize them
- Verify if a sequence of probability distributions on a metric space converges
Content:
Stochastic models with spatial and temporal structure
- 0-1 laws
- Large deviation estimates of rare events
- Phase transitions in stochastic models
- Convergence and tightness of probability measures
Study Material: TBA
Substitutes for Courses:
Prerequisites: MS-E1600
Evaluation: hyv · Opintojaksot
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Language of Instruction: English
MS-E1609 Seminar on stochastics and statistics (V) (V) (1-5 cr)
Responsible teacher: Sirkku Ilmonen; Kalle Kytölä; Lasse Leskelä
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional
Level of the Course: master’s level, doctoral level
Teaching period: I-V (academic year)
Evaluation: hyv · Opintojaksot
Language of Instruction: English
MS-E1651 Numerical matrix computations (5 cr)
Responsible teacher: Antti Hannukainen
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: I (Autumn)
Workload: 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca
100h
Learning Outcomes: Students learn to analyze and solve problems in linear algebra that
occur often in scientific computing, data fitting and optimization. The main focus is on
solution of linear systems, least squares problems and eigenvalue problems. After the
course, the students can choose the best solution method for each problem and have a
good understanding on issues related to numerical stability of the applied algorithms.
Content:
Matrix decompositions and their numerical computation, eigenvalue iterations, sparse
matrices, iterative solution of linear systems.
Assessment Methods and Criteria: weekly exercises (33.3%), an exam (66.6%)
Study Material: All essential material is included in the lecture notes that are available at
the course’s homepage.
Substitutes for Courses: Mat-1.3651
Prerequisites: MS-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X. The courses
MS- C1540 may also be useful.
Evaluation: 1-5
Language of Instruction: English
MS-E1652 Computational methods for differential equations (5 cr)
Responsible teacher: Nuutti Hyvönen
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: II (Autumn)
Workload: lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks),
self-study ca 100h
Learning Outcomes: You will familiarize yourself with the basic properties of initial value
problems for systems of ordinary differential equations. You will learn the fundamental
theory about linear multistep methods (definition, consistency, zero-stability,
convergence) and Runge-Kutta methods (definition, order conditions, convergence). You
will learn to identify a stiff system and to understand the difference between explicit and
implicit numerical schemes. You will understand the signifigance of absolute stability and
A-stability, and know how to examine the region of absolute stability for a given numerical
method. You will get to know the basic principles of the discrete Fourier transform. You
11
will familiarize yourself with simple parabolic and hyperpolic initial/boundary value
problems and learn how to discretize them with the help of difference schemes. You will
practice implementing the introduced methods numerically.
Content: Basic existence and uniqueness results for systems of ordinary differential
equations. Linear multistep methods and Runge-Kutta methods: stability, convergence
and numerical implementation. Discrete Fourier transform. Discretization of simple
initial/boundary value problems for parabolic and hyperbolic partial differential equations.
Assessment Methods and Criteria: Weekly exercises (33.3%) and an exam (66.7%).
Study Material: All essential material is included in the lecture notes that are available at
the course’s homepage.
Substitutes for Courses: Mat-1.3652.
Prerequisites: S-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X. The courses
MS-C1340, MS-C1350, MS-C1650, MS-E1651 may also be useful.
Evaluation: 1-5
Language of Instruction: English
MS-E1653 Finite element method (5 cr)
Responsible teacher: Antti Hannukainen
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: III-IV (Spring)
Workload: 48h (2x2h/week, 12 weeks), self-study ca 100h, project ca 20h
Learning Outcomes: Students learn to derive and analyze weak form of an elliptic partial
differential equation and to implement finite element solver in 2D. They will develop
understanding on the principles of the error analysis of the finite element method and
different factors affecting the accuracy of the solution.
Content: The topic of the course is solution of elliptic partial differential equation using
finite element method. Both algorithmic and theoretical aspects of the method are
covered.
Assessment Methods and Criteria: weekly exercises (50%), an exam (50%), project
(pass/fail)
Study Material: All essential material is included in the lecture notes that are available at
the course’s homepage.
Substitutes for Courses: MS-C1741
Prerequisites: MS-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X. The courses
MS-C1350, MS- C1540 may also be useful.
Evaluation: 1-5
Language of Instruction: English
MS-E1654 Computational inverse problems (5 cr)
Responsible teacher: Nuutti Hyvönen
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; Master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: IV (Spring)
Workload: lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks),
self-study ca 100h
Learning Outcomes: You will learn to identify an ill-posed inverse problem and to
understand the restrictions its nature imposes on the solution process. You will familiarize
yourself with several classical regularization methods for finding approximate solutions to
linear ill-posed problems. You will learn to formulate an inverse problem as a Bayesian
problem of statistical inference and to interpret the information contained in the resulting
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posterior probability distribution. You will learn to numerically implement the introduced
solution techniques.
Content: The course’s topic is computational methods for solving inverse problems
arising from practical applications. The course consists of two parts: the first three weeks
focus on classic regularization techniques, the latter three weeks discuss statistical
methods.
Assessment Methods and Criteria: weekly exercises (25%), a home exam (75%).
Study Material: All essential material is included in the lecture notes that are available at
the course’s homepage.
Substitutes for Courses: Mat-1.3626
Prerequisites: MS-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X. The courses
MS-C1340, MS-C1650, MS-E1460, MS-E1651, MS-E1652, MS-E2112 may also be
useful.
Evaluation: 1-5
Language of Instruction: English
MS-E1659 Seminar on applied mathematics (V) (V) (1-5 cr)
Responsible teacher: Nuutti Hyvönen; Antti Hannukainen
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional
Level of the Course: master’s level, doctoral level
Teaching period: I-V (academic year)
Learning Outcomes: An overview of research on applied mathematics and mechanics at
Aalto University and collaborating units.
Content: Seminar talks and discussion on current research topics in applied mathematics
and mechanics. The seminar usually convenes once a week during the academic year.
Assessment Methods and Criteria: A seminar talk and active participation.
Substitutes for Courses: Mat-1.3656, Mat-5.3753.
Prerequisites: MS-A000X, MS-A010X, MS-A020X, MS-A030X, MS-A050X. The courses
MS-C1340, MS-C1350, MS-C1650, MS-E1460, MS-E1651, MS-E1652, MS-E1653,
MS-E1654, MS-1740, MS-1741, MS-1742, MS-1743 may also be useful.
Evaluation: pass/fail
Registration for Courses: Contact the teachers in charge.
Language of Instruction: English
MS-E1740 Continuum mechanics 1 (5 cr)
Responsible teacher: Rolf Stenberg
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: I (Autumn)
Workload: 24 h (2x2h/week, 6weeks), exercises 12 h (1x2h/week, 6 weeks)
Learning Outcomes: You know the mathematical tools for modeling a continuum, i.e. a
solid or a fluid.
Content: Tensor calculus. The concepts of continuum mass and force. Kinematics.
Balance laws.
Assessment Methods and Criteria: Weekly exercises (1/3) and an exam (2/3).
Study Material: O. Gonzalez, A. Stuart. A first course in continuum
mechanics. Cambridge Texts in Applied Mathematics. Cambridge University Press,
Cambridge, 2008.
Substitutes for Courses: Mat-5.3740
Prerequisites: MS-A000X, MS-A010X,MS-A020X,MS-A030X
Evaluation: 1-5.
Language of Instruction: English
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MS-E1741 Continuum mechanics 2 (5 cr)
Responsible teacher: Rolf Stenberg
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: II (Autumn)
Workload: Lecture 24 h (2x2h/week, 6weeks), exercises 12 h (1x2h/week, 6 weeks)
Learning Outcomes: You are able to derive and analyze the main mathematical models
for fluids and solids.
Content: Constitutive laws. Inviscid fluids, Navier-Stokes equations. Linear and nonlinear
elasticity.
Assessment Methods and Criteria: Weekly exercises (1/3) and an exam (2/3).
Study Material: O. Gonzalez, A. Stuart. A first course in continuum
mechanics. Cambridge Texts in Applied Mathematics. Cambridge University Press,
Cambridge, 2008.
Substitutes for Courses: Mat-5.3740
Prerequisites: MS-E1740 Continuum mechanics 1.
Evaluation: 1-5.
Language of Instruction: English
MS-E1742 Computational mechanics 1 (5 cr)
Responsible teacher: Rolf Stenberg
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: IV (Spring)
Workload: 24 h (2x2h/week, 6weeks), exercises 12 h (1x2h/week, 6 weeks)
Learning Outcomes: You will learn how the finite element method is applied for
problems which are constrained minimization problems with a Lagrange multiplier.
Content: General variational problems. The finite element theory for approximating
saddle-point problems. Applications to Stokes equations.
Assessment Methods and Criteria: Weekly exercises (1/3) and an exam (2/3).
Study Material: Larson, Mats G.; Bengzon, Fredrik. The finite element method: theory,
implementation, and applications. Texts in Computational Science and Engineering, 10.
Springer, Heidelberg, 2013.
Substitutes for Courses: Mat-5.3750
Prerequisites: MS-E1653 Finite element method (5 cr).
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1743 Computational mechanics 2 (5 cr)
Responsible teacher: Rolf Stenberg
Status of the Course: Major of Applied Mathematics, Master’s Programme in
Mathematics and Operations Research, optional; master’s level Minor of Mathematics,
optional
Level of the Course: master’s level, doctoral level
Teaching period: V (Spring)
Workload: 24 h (2x2h/week, 6weeks), exercises 12 h (1x2h/week, 6 weeks)
Learning Outcomes: You will be able to apply the theory from MS-E1742 Computational
mechanics 1 to a variety of problems in continuum mechanics.
Content: Stabilized finite element methods; applications to the convection diffusion and
14
Stokes equations. Finite element methods in solid mechanics; the Timoshenko beam and
the Reissner-Mindlin plate model
Assessment Methods and Criteria: Weekly exercises (1/3) and an exam (2/3).
Study Material: Lecture notes.
Substitutes for Courses: Mat-5.3750
Prerequisites: MS-E1742
Evaluation: 1-5.
Language of Instruction: English
MS-E1980 Special assignment in mathematics (V) (V) (5-10 cr)
Responsible teacher: Nuutti Hyvönen
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional
Level of the Course: master’s level
Teaching period: I-V (academic year)
Workload: self-study ca 135h
Learning Outcomes: Understands the mathematics related to the assignment. Is able to
write a scientific report on the project.
Content: An individual research assignment or a literature survey.
Substitutes for Courses: Mat-1.3990, Mat-5.3751.
Evaluation: 1-5
Language of Instruction: English/Finnish/Swedish (to be agreed with the teacher)
Further Information: Before starting the special assignment, the topic must be agreed
with a member of the faculty at the Department of Mathematics and Systems Analysis.
MS-E1981 Individual studies in mathematics (V) (V) (1-10 cr)
Responsible teacher: Nuutti Hyvönen
Status of the Course: Major of Applied Mathematics & Major of Mathematics, Master’s
Programme in Mathematics and Operations Research, optional
Level of the Course: master’s level, doctoral level
Teaching period: I-V (academic year)
Content: Guest lectures, web-based teaching or other individual studies. The content
and scope must be settled with the teacher in charge.
Substitutes for Courses: Mat-1.2995, Mat-1.3980, Mat-1.3981
Evaluation: 1-5 or pass/fail
Language of Instruction: English/Finnish/Swedish (to be agreed with the teacher)
MS-E1990 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1991 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1992 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1993 Course with Varying Content V (V) (1-10 cr)
15
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1994 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1995 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1996 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1997 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1998 Course with Varying Content V (V) (1-10 cr)
Responsible teacher: Pekka Alestalo
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E1999 Matemaattiset ohjelmistot V (V) (1-5 op)
Vastuuopettaja: Heikki Apiola
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
Lisätietoja: Vaihtuvasisältöinen.
MS-E1999 Matematisk programvara V (V) (1-5 sp)
Ansvarig lärare: Heikki Apiola
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
Tilläggsinformation: Innehåll varieras.
MS-E1999 Mathematical software V (V) (1-5 cr)
Responsible teacher: Heikki Apiola
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
Further Information: Content varies.
MS-E2108 Systeemianalyysin erikoistyöt (V) (V) (5-8 op)
Vastuuopettaja: Enrico Bartolini; Harri Ehtamo; Raimo Hämäläinen; Ahti Salo; Kai
Virtanen
Kurssin taso: Maisteritaso
Opetusperiodi: I, II, III, IV, V
16
Työmäärä toteutustavoittain: Itsenäinen työskentely 130h
Osaamistavoitteet: Kirjallisen ja tieteellisen raportointitaidon kehittäminen.
Sisältö: Yksilöllinen itsenäinen tutkimustehtävä; aihe teollisuudesta, laboratoriosta tai
muualta korkeakoulusta. Tarkemmat ohjeet kurssin www-sivuilta.
Toteutus, työmuodot ja arvosteluperusteet: Työselostus
Korvaavuudet: Mat-2.4108 Sovelletun matematiikan erikoistyöt
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: sopimuksen mukaan
MS-E2108 Specialarbeten i systemanalys (V) (V) (5-8 sp)
Ansvarig lärare: Enrico Bartolini; Harri Ehtamo; Raimo Hämäläinen; Ahti Salo; Kai
Virtanen
Kursnivå: Magisternivå
Undervisningsperiod: I, II, III, IV, V
Arbetsmängd: Självständiga studier 130h
Lärandemål: Utveklandet av den skriftliga och vetenskapliga raporteringsförmoga.
Innehåll: En individuell forskningsuppgift. Temat från industrin, laboratoriet eller
högskolan. Ett huvudändåmål är utveckling av studentens skriftliga raporteringsförmåga.
Närmare uppgifter från kursen www-sidor.
Metoder, arbetssätt och bedömningsgrunder: Arbetsrapport
Ersättande prestationer: Mat-2.4108 Specialarbeten i systemanalys
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: enligt överenskommelse
MS-E2108 Independent research projects in systems analysis (V) (V) (5-8 cr)
Responsible teacher: Enrico Bartolini; Harri Ehtamo; Raimo Hämäläinen; Ahti Salo; Kai
Virtanen
Level of the Course: Master’s level
Teaching Period: I, II, III, IV, V (Autumn and Spring)
Workload: Autonomous studies 130h
Learning Outcomes: Written and scientific reporting skills.
Content: An individual research project; topics from industry or from research projects of
the laboratory. Students can also propose their own topics. The topics need to be
discussed and approved by one of the teachers. One of the main aims is to get
experience in writing a research report.
Assessment Methods and Criteria: Written report
Substitutes for Courses: Mat-2.4108 Independent research projects in systems analysis
Evaluation: 1-5 · Courses
Language of Instruction: To be agreed with the teacher
MS-E2112 Multivariate statistical analysis (5 cr)
Responsible teacher: Sirkku Ilmonen
Status of the Course: Major of Applied Mathematics & Major of Systems and Operations
Research, Master’s Programme in Mathematics and Operations Research, optional;
Minor of Systems and Operations Research, optional
Level of the Course: master’s level, doctoral level
Teaching period: III-IV (Spring)
Workload: Lectures 24h (2), Exercises 24h (2), Project work 40h, Other autonomous
studies 40h.
Learning Outcomes: This course is an introduction to multivariate statistical analysis.
The goal is to learn basics of common multivariate data analyzing techniques and to use
the methods in practice. Software R is used in the exercises of this course.
Content: Multivariate Location and Scatter, Principal Component Analysis (PCA),
Bivariate Correspondence Analysis, Multivariate Correspondence Analysis (MCA),
Canonical Correlation Analysis, Discriminant Analysis, Classification, Clustering.
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Assessment Methods and Criteria: Exam and compulsory project work.
Study Material: K. V. Mardia, J. T. Kent, J. M. Bibby: Multivariate Analysis, Academic
Press, London, 2003 (reprint of 1979) and lecture slides.
Substitutes for Courses: Mat-2.3112 Statistical Multivariate Methods P
Prerequisites: At least one statistics/probability course and one matrix algebra course.
Evaluation: 1-5
Language of Instruction: English
MS-E2113 Jonoteoria (3-6 op)
Vastuuopettaja: Harri Ehtamo
Kurssin taso: Maisteritaso
Opetusperiodi: Ei luennoida tänä lukuvuonna
Osaamistavoitteet: Johdatteleva kurssi jonoteoriaan.
Sisältö: Jonoilmiöiden tarkastelu stokastisena prosessina, ääretön tai äärellinen
käyttäjäjoukko, yksi tai useampi palveluyksikkö, jonokurit, prioriteetit, sisäkkäiset jonot,
jonojen käsittely Markov-prosesseina. Sovellutuksia palvelujärjestelmistä ja
tietoliikennetekniikan piiristä.
Korvaavuudet: Korvaa kurssin Mat-2.4113 Jonoteoria L Korvaava kurssi ELEC-E7450
Performance analysis
Esitiedot: 1. ja 2. vuoden matematiikka, MS-C2111 Stokastiset prosessit
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
MS-E2113 Köteori (3-6 sp)
Ansvarig lärare: Harri Ehtamo
Kursnivå: Magisternivå
Undervisningsperiod: Föreläses ej detta läsår
Lärandemål: Undervisa elementär köteori.
Innehåll: Köfenomen betraktade som stokastiska processer, oändligt eller ändligt många
kunder, en eller flere serviceenheter, ködisciplin, prioriteringar, inre köer, behandling av
köer som Markov-processer. Tillämpningar inom servicesystem och telekommunikation.
Ersättande prestationer: Mat-2.4113 Köteori Ersättande kurs ELEC-E7450
Performance analysis
Förkunskaper: 1. och 2. årets matematik, MS-C2111 Stokastiska processer
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
MS-E2113 Queuing Theory (3-6 cr)
Responsible teacher: Harri Ehtamo
Level of the Course: Master’s level
Teaching Period: Not lectured this academic year
Learning Outcomes: Introductory course to queueing theory.
Content: Queuing problems as stochastic processes, the problems including finite or
infinite set of users and servers, queuing disciplines, queues as Markov processes.
Applications include various serving systems, telecommunication systems etc.
Substitutes for Courses: Mat-2.4113 Queuing Theory Substitutive course ELEC-E7450
Performance analysis
Prerequisites: 1st and 2nd year math, MS-C2111 Stochastic Processes
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
MS-E2114 Investment science (5 cr)
Responsible teacher: Eeva Vilkkumaa
Status of the Course: Optional course of the Systems and Operations Research major.
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Optional course of the Systems and Operations Research minor.
Level of the Course: Master’s level
Teaching period: IV (Spring)
Workload: Lectures 24h (4)
Exercises 24h (4)
Assignment 25h
Autonomous studies 55h
Content: Instruments of investment science and finance, risk analysis, term structure of
interest rates, pricing of derivatives, optimization of investment portfolio return.
Assessment Methods and Criteria: Exam and assignments
Study Material: D.G. Luenberger: Investment Science, Oxford University Press, 1998.
Substitutes for Courses: Mat-2.3114 Investment science
Prerequisites: 1st and 2nd years math, applied probability
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2117 Riskianalyysi (5 op)
Vastuuopettaja: Ahti Salo
Kurssin asema: Systems and Operations Research -pääaineen valinnainen kurssi.
Systems and Operations Research ja Multi-Disciplinary Energy Studies -sivuaineiden
valinnainen kurssi.
Kurssin taso: Maisteritaso
Opetusperiodi: III - IV
Työmäärä toteutustavoittain: Luento-opetus 24h (2)
Laskuharjoitukset 24h (2)
Harjoitustyöt 20h
Itsenäinen työskentely 60h
Sisältö: Kurssi perehdyttää riskinalyysin keskeisimpiin menetelmiin ja antaa valmiudet
soveltaa niitä erilaisten teknis-taloudellisten järjestelmien riskitarkasteluissa (ml. riskien
tunnistaminen ja arviointi, riskienhallintatoimenpiteiden vertailu ja priorisointi,
riskiviestintä). Käsiteltäviä menetelmiä ovat muun muassa vikapuut, syy-seuraus-kaaviot
sekä todennäköisyyspohjainen turvallisuusanalyysi. Kurssilla perehdytään myös
todennäköisyyksien estimointiin sekä asiantuntija-arvioiden että tilastollisten menetelmien
pohjalta. Luennot ja laskuharjoitukset sisältävät riskianalyysien laatimista ja käyttöä
havainnollistavia esimerkkejä.
Toteutus, työmuodot ja arvosteluperusteet: Tentti ja harjoitustyöt
Oppimateriaali: M. Modarres: Risk Analysis in Engineering: Techniques, Tools and
Trends; Bilal M. Ayyub: Risk Analysis in Engineering and Economics
Korvaavuudet: Mat-2.3117 Riskianalyysi
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
MS-E2117 Riskanalys (5 sp)
Ansvarig lärare: Ahti Salo
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research. Valfri
kurs inom biämnen Systems and Operations Reserach och Multi-Disciplinary Energy
Studies.
Kursnivå: Magisternivå
Undervisningsperiod: III - IV
Arbetsmängd: Föreläsningar 24h (2)
Övningar 24h (2)
Studiearbeten 20h
Självständiga studier 60h
Innehåll: Introducering av de centrala modellerna och metoderna som används vid
riskanalys av olika system. Modeller för ekonomiska risker. Mer djupgående behandling
19
av risk- och osäkerhetsbegreppen samt presentation av konkreta tillämpningar inom
området.
Metoder, arbetssätt och bedömningsgrunder: Tentamen och övningsarbeten
Studiematerial: M. Modarres: Risk Analysis in Engineering: Techniques, Tools and
Trends; Bilal M. Ayyub: Risk Analysis in Engineering and Economics
Ersättande prestationer: Mat-2.3117 Riskanalys
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
MS-E2117 Risk Analysis (5 cr)
Responsible teacher: Ahti Salo
Status of the Course: Optional course of the Systems and Operations Research major.
Optional course of the minors Systems and Operations research and Multi-Disciplinary
Energy Studies.
Level of the Course: Master’s level
Teaching Period: III - IV (Spring)
Workload: Lectures 24h (2)
Exercises 24h (2)
Assignments 20h
Autonomous studies 60h
Content: The aim of the course is to introduce methods and models applied in the risk
analysis of various systems, including the models and approaches of economic risk
management. The course also provides a deeper view over concepts for handling risk
and uncertainty. Finally, practical examples on risk analyses are presented.
Assessment Methods and Criteria: Exam and assignments
Study Material: M. Modarres: Risk Analysis in Engineering: Techniques, Tools and
Trends; Bilal M. Ayyub: Risk Analysis in Engineering and Economics
Substitutes for Courses: Mat-2.3117 Risk Analysis
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
MS-E2129 Systeemien identifiointi (5 op)
Vastuuopettaja: Kai Virtanen
Kurssin asema: Systems and Operations Research -pääaineen valinnainen kurssi.
Systems and Operations Research -sivuaineen valinnainen kurssi.
Kurssin taso: Maisteritaso
Opetusperiodi: I - II
Työmäärä toteutustavoittain: Luento-opetus 24h (2)
Laskuharjoitukset 24h (2)
Harjoitustyöt 20h
Itsenäinen työskentely 60h
Osaamistavoitteet: Kurssi antaa perusvalmiudet dynaamisten systeemien
matemaattiseen mallintamiseen ja identifiointiin.
Sisältö: Dynaamisten järjestelmien siirtofunktio- ja tilaesitysmallit ja mallintaminen;
systeemiteoriaa. Dynaamisten järjestelmien identifiointi: epäparametriset menetelmät,
herätteet ja koesuunnittelu, mallirakenteet, ennustevirhemenetelmät, parametrien
estimointi, mallin rakenteen valinta, mallin validointi.
Toteutus, työmuodot ja arvosteluperusteet: Tentti, harjoitustyöt ja laskuharjoitukset.
Kaksi tenttitehtävää voi korvata harjoitustöillä ja kaksi tenttitehtävää voi korvata
aktiivisella osallistumisella laskuharjoituksiin.
Oppimateriaali: L. Ljung, T. Glad: Modeling of Dynamic Systems, Prentice Hall, 1994.
Saatavissa myös ruotsinkielisenä, kustantaja Studentlitteratur
Korvaavuudet: Mat-2.4129 Systeemien identifiointi
Esitiedot: MS-C2128 Ennustaminen ja aikasarja-analyysi
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
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MS-E2129 Systemidentifiering (5 sp)
Ansvarig lärare: Kai Virtanen
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research och
biämnet Systems and Operations Research.
Kursnivå: Magisternivå
Undervisningsperiod: I - II
Arbetsmängd: Föreläsningar 24h (2)
Övningar 24h (2)
Studiearbeten 20h
Självständiga studier 60h
Innehåll: Överförings- och tillståndsmodeller av dynamiska system, modellering;
systemteori. Identifiering av dynamiska system: oparametriska metoder, insignaler och
experimentplanering, modellstruktur, felpredikteringsmetoder, estimering av parameter,
val av modelstruktur, validering av modellen.
Metoder, arbetssätt och bedömningsgrunder: Tentamen, övningar och
övningsarbeten. Två examuppgifter kan ersätta med övningsarbeten och två
examuppgifter kan ersätta med övningar.
Studiematerial: L. Ljung, T. Glad: Modeling of Dynamic Systems, Prentice Hall, 1994.
Finns även på svenska, förläggare Studentlitteratur
Ersättande prestationer: Mat-2.4129 Systemidentifiering
Förkunskaper: MS-C2128 Prediktering och tidsserieanalys
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
MS-E2129 System Identification (5 cr)
Responsible teacher: Kai Virtanen
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching Period: I - II (Autumn)
Workload: Lectures 24h (2)
Exercises 24h (2)
Assignments 20h
Autonomous studies 60h
Content: Transfer function and state space models of dynamic systems, modeling;
systems theory. Identification of dynamic systems: nonparametric methods, inputs and
design of experiments, model structures, prediction error methods, estimation of
parameters, model structure selection, model validation.
Assessment Methods and Criteria: Exam and assignments. Two exercises in the exam
can be replaced by the assignments.
Study Material: L. Ljung, T. Glad: Modeling of Dynamic Systems, Prentice Hall, 1994.
Available in Swedish, publisher Studentlitteratur
Substitutes for Courses: Mat-2.4129 System identification
Prerequisites: MS-C2128 Prediction and Time Series Analysis
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
MS-E2130 Matemaattinen malliajattelu (3-6 op)
Vastuuopettaja: Kai Virtanen
Kurssin asema: Systems and Operations Research pääaineen ja sivuaineen valinnainen
kurssi.
Kurssin taso: Maisteritaso
Opetusperiodi: I - II
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Työmäärä toteutustavoittain: Itsenäinen työskentely 100h (viikottaiset verkkoluennot,
harjoitukset ja kommentoinnit)
Harjoitustyö 25h
Sisältö: Johdatus systeemiajatteluun ja matemaattisten mallien käyttöön eri alojen
sovellutuksissa. Mallin muodostaminen, differentiaali- ja differenssiyhtälömallit,
stokastiset mallit, optimointiin perustuva mallintaminen, dynaamisten järjestelmien
simulointi.
Toteutus, työmuodot ja arvosteluperusteet: Viikottaiset verkkoluennot,
harjoitustehtävät ja kommentoinnit sekä vapaaehtoinen harjoitustyö.
Oppimateriaali: S. Pohjolainen (toim.): Matemaattinen mallinnus, WSOYpro, 2010.
Lisälukemistona: F.R. Giordano, M.D. Weir, W.P. Fox: A First Course in Mathematical
Modeling, Brooks/Cole, 1997
Korvaavuudet: Mat-2.3130 Matemaattinen malliajattelu L
Esitiedot: 1. ja 2. vuoden matematiikka
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
Lisätietoja: Laajuus 4 op ja vapaaehtoisen harjoitustyön kanssa 5 op. Kurssi on
verkkopohjainen. Syksyllä järjestetään mallinnuksen peruskurssi ja sekä syksyllä että
keväällä vaihtuva-aiheisia jatkokursseja. Jatkokurssien suoritukset (3 op) kurssikoodilla
MS-E2195.
MS-E2130 Matematiskt modelltänkande (3-6 sp)
Ansvarig lärare: Kai Virtanen
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research och
biämnet Systems and Operations Research.
Kursnivå: Magisternivå
Undervisningsperiod: I - II
Arbetsmängd: Självständiga studier 100h (web föreläsningar och övningar varje vecka)
Studiearbete 25h
Innehåll: Inledning till systemtänkande och användning av matematiska modeller vid
tillämpningar inom olika områden. Konstruktion av modeller, differential- och
differensekvationsmodeller, stokastik modeller, modellering baserad på optimering,
simulering av dynamiska system.
Metoder, arbetssätt och bedömningsgrunder: En nätföreläsning, övningar ch
kommenter per vecka, och övningsarbete.
Studiematerial: S. Pohjolainen: Matemaattinen mallinnus, WSOYpro, 2010.
Tilläggsmaterial: F.R. Giordano, M.D. Weir, W.P. Fox: A First Course in Mathematical
Modeling, Brooks/Cole, 1997
Ersättande prestationer: Mat-2.3130 Matematiskt modelltänkande
Förkunskaper: 1. och 2. årets matematik
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
Tilläggsinformation: Omfattning 4 sp och med frivilligt övningsarbete 5 sp. Kursen är
nätbaserad. På hösten arrangeras grundkurs i modellering och både på hösten och på
våren varierande fortsättningskurser. Fortsättningkurser (3 sp) avläggas under koden
MS-E2195.
MS-E2130 Mathematical Modelling (3-6 cr)
Responsible teacher: Kai Virtanen
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching Period: I - II (Autumn)
Workload: Autonomous studies 100h (weekly web lectures and assignments)
Assignment 25h
22
Content: An introduction to systems thinking and utilization of mathematical models in
different application areas. Construction of models, differential and difference equation
models, modeling based on optimization, simulation of dynamic systems.
Assessment Methods and Criteria: Weekly lectures, exercises and commentation in
Internet and assignment.
Study Material: S. Pohjolainen: Matemaattinen mallinnus, WSOYpro, 2010. Background
literature: F.R. Giordano, M.D. Weir, W.P. Fox: A First Course in Mathematical Modeling,
Brooks/Cole, 1997
Substitutes for Courses: Mat-2.3130 Mathematical Modelling
Prerequisites: 1st and 2nd year math
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
Further Information: 4 cr and with optional assignment 5 cr. Course will be held as an
Internet course. Basic course of modeling is held in autumn and various advanced
courses both in autumn and spring. The advanced courses (3 cr) are passed with course
code MS-E2195.
MS-E2133 Systems analysis laboratory II (5 cr)
Responsible teacher: Kai Virtanen
Status of the Course: Compulsory course of the Systems and Operations Research
major. Optional course of the Systems and Operations Research minor.
Level of the Course: Master’s level
Teaching period: I - II (Autumn)
Workload: Lectures 4h
Exercises 48h (4)
Autonomous studies 75h
Learning Outcomes: Get familiar with problem solving in operations research.
Content: Two fairly large assignments on the implementation and analysis of
mathematical models. The assignments deal with optimization and stabilization and
control of a large scale system.
Assessment Methods and Criteria: Assignments and written reports
Substitutes for Courses: Mat-2.4133 Systems analysis laboratory II
Prerequisites: MS-E2139 Nonlinear Programming, MS-E2148 Dynamic Optimization.
Taking the course simultaneously with MS-E2129 System Identification is recommended
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2134 Decision making and problem solving (5 cr)
Responsible teacher: Eeva Vilkkumaa
Status of the Course: Compulsory course of the Systems and Operations Research
major.
Level of the Course: Master’s level
Teaching period: I (Autumn)
Workload: Lectures 24h (4)
Exercises 24h (4)
Assignment 40h
Autonomous studies 40h
Learning Outcomes: After completing this course the student
1. knows the central concepts in decision analysis,
2. can structure and model problems with multiple attributes, decision dynamics and
uncertainty for aiding decision-making,
3. understands the assumptions underlying decision analytic models and why behavior of
real decision makers may differ from the behavior that these models would predict, and
4. knows how to use optimization methods in conjunction with decision analysis.
Content: Models for decision making: subjective values, multi-objective decision making
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and optimization, group decision making, decision under uncertainty, dynamics of
decision making.
Assessment Methods and Criteria: Exam and assignments
Study Material: Lecture slides and exercises are the primary course material. Additional
literature includes F. Eisenführ, M. Weber, T. Langer: Rational Decision-Making,
Springer, 2010, Clemen, R.T. (1996): Making Hard Decisions: An Introduction to Decision
Analysis, 2nd edition and French, S. (1988): Decision Theory: An Introduction to the
Mathematics of Rationality.
Substitutes for Courses: Mat-2.3134 Decision Making and Problem Solving P
Prerequisites: MS-C2105 Introduction to Optimization, applied probability
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2136 Special topics in decision making (V) (V) (3-6 cr)
Responsible teacher: Raimo Hämäläinen; Ahti Salo
Status of the Course: Optional course of the Systems and Operations Research major.
Optional course of the minors Systems and Operations Research and Multi-Disciplinary
Energy Studies.
Level of the Course: Master’s level
Teaching period: will be announced later
Content: Annually varying topics on decision making.
Substitutes for Courses: Mat-2.4136 Special Topics in Decision Making
Evaluation: 0-5 or pass/fail
Language of Instruction: English
MS-E2139 Nonlinear programming (5 cr)
Responsible teacher: Kimmo Berg
Status of the Course:
Alternative course of the Systems and Operations Research major.
Alternative course of the Systems and Operations Research minor (MSc).
Optional course of the Mathematics minor (MSc).
Level of the Course: Master’s level
Teaching period: II (Autumn)
Workload: Lectures 24h (4)
Exercises 24h (4)
Voluntary home exercises 15h
Autonomous studies 70h
Learning Outcomes: Present different convexity properties and concepts of convex
analysis. Interpret and explain the optimality conditions and use them to calculate optimal
solutions. Analyze different optimization algorithms and use them to solve optimization
problems.
Content: The first part of the course teaches the optimization theory: convexity,
necessary and sufficient optimality condition and their derivation, the interpretation of
Lagrange multipliers, and duality. The second part teaches numerical optimization:
unconstrained, convex, and constrained optimization. Applications from natural sciences,
engineering and economics.
Assessment Methods and Criteria: Exam. Extra points can be earned by doing
homework.
Study Material: M.S. Bazaraa, H.D. Sherali, C.M. Shetty: Nonlinear Programming,
Theory and Algorithms, Wiley and Sons 1993/2006. 2nd (blue or red) or 3rd (green)
edition is ok.
Substitutes for Courses: Mat-2.3139 Nonlinear Programming P
Prerequisites: 1st and 2nd year math
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
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MS-E2140 Linear programming (5 cr)
Responsible teacher: Enrico Bartolini
Status of the Course:
Alternative course of the Systems and Operations Research major.
Optional course of the Systems and Operations Research minor.
Level of the Course: Master’s level
Teaching period: I (Autumn)
Workload: Lectures 24h (4)
Exercises 24h (4)
Assignments 20h
Autonomous studies 60h
Learning Outcomes: After completing this course the student
1. can formulate a wide variety of optimization problems, which solutions can be used for
making better decisions (e.g. allocating resources, selecting routes and assigning tasks),
as (mixed integer) linear programming problems,
2. understands the theoretical foundation of the Simplex algorithm and duality, and knows
the special characteristics of network and integer programming problems, and
3. can solve (mixed integer) linear programming problems using optimization software.
Content: The simplex method, dual of the linear program, interior point algorithms,
integer programming. Applications to transportation problems, network problems and
production planning.
Assessment Methods and Criteria: Exam and assignments. Bonus points from home
work and exercise sessions
Study Material: D. Bertsimas, J.N. Tsitsiklis: Introduction to Linear Optimization, Athena
Scientific 1997
Substitutes for Courses: Mat-2.3140 Linear Programming P
Prerequisites: MS-C2105 Introduction to Optimization
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2142 Optimointiopin seminaari (V) (V) (5 op)
Vastuuopettaja: Enrico Bartolini; Raimo Hämäläinen; Ahti Salo; Kai Virtanen
Kurssin asema: Systems and Operations Research pää- ja sivuaineen valinnainen
kurssi.
Kurssin taso: Maisteritaso.
Opetusperiodi: mahdollisesta luennoinnista ilmoitetaan myöhemmin
Työmäärä toteutustavoittain: Seminaari 36h (3)
Itsenäinen työskentely 90h
Osaamistavoitteet: Syventää systeemi- ja operaatiotutkimuksen opintoja ja kehittää
valmiuksia hyvien seminaariesitysten pitämiseen.
Sisältö: Vaihtuva-alainen seminaari, joka voidaan suorittaa toistuvasti. Aihe ja
järjestäminen ilmoitetaan myöhemmin.
Toteutus, työmuodot ja arvosteluperusteet: toteutus: seminaari
työmuodot ja arvostelu: läsnäolo, esitelmät ja kotitehtävät
Korvaavuudet: Mat-2.4142 Optimointiopin seminaari L
Esitiedot: MS-C2105 Optimoinnin perusteet
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
MS-E2142 Seminarium i optimeringslära (V) (V) (5 sp)
Ansvarig lärare: Enrico Bartolini; Raimo Hämäläinen; Ahti Salo; Kai Virtanen
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research och
biämnet Systems and Operations Research.
25
Kursnivå: Magisternivå
Undervisningsperiod: meddelas senare
Arbetsmängd: Seminarium 36h (3)
Självständiga studier 90h
Lärandemål: Fördjupa studier i systems- och operationsforskning samt undervisa at ge
seminarieföredrag.
Innehåll: Varierar årligen. Möjlighet att delta flera gånger. Teman meddelas senare.
Metoder, arbetssätt och bedömningsgrunder: Seminarium, föredrag och hemuppgifter
Ersättande prestationer: Mat-2.4142 Seminarium i optimeringslära
Förkunskaper: MS-C2105 Grundkurs i optimering
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
MS-E2142 Seminar on Optimization (V) (V) (5 cr)
Responsible teacher: Enrico Bartolini; Raimo Hämäläinen; Ahti Salo; Kai Virtanen
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching Period: will be announced later
Workload: Seminar 36h (3)
Autonomous studies 90h
Learning Outcomes: Special topics in systems- and operation research. A special
emphasis is also on learning presentation skills.
Content: Varies yearly with a possibility to take part multiple times. The subject of the
seminar is announced later.
Assessment Methods and Criteria: Seminar, presentation and assignments
Substitutes for Courses: Mat-2.4142 Seminar on Optimization
Prerequisites: MS-C2105 Introduction to Optimization
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
MS-E2143 Network optimization (5 cr)
Responsible teacher: Enrico Bartolini
Level of the Course: Master’s level
Teaching period: Not lectured this academic year. Exam according to agreement
Workload: Autonomous studies
Learning Outcomes: An advanced course in optimization.
Content: Graphs and network flow formulations. Maximal flow, transportation,
assignment, and shortest path problems. Linear programming simplex algorithm, the
dual-, and primal-dual algorithm for network problem.
Assessment Methods and Criteria: Homework exercises from the course book.
Study Material: D. Bertsekas: Network Optimization, Athena Scientific, 1998.
Substitutes for Courses: Mat-2.4143 Network Optimization P
Prerequisites: MS-C2105 Introduction to Optimization or MS-E2140 Linear Programming
Evaluation: pass/fail
Language of Instruction: English
MS-E2144 Optimoinnin matemaattinen teoria (V) (V) (3-6 op)
Vastuuopettaja: Kimmo Berg
Kurssin taso: Maisteritaso
Opetusperiodi: Ei luennoida tänä lukuvuonna
Sisältö: Vuosittain vaihtuva-aiheinen optimoinnin teorian jotain osa-aluetta, kuten
konveksi optimointi tai funktionaalien optimointi, käsittelevä opintojakso.
Toteutus, työmuodot ja arvosteluperusteet: Tentti
26
Korvaavuudet: Mat-2.4144 Optimoinnin matemaattinen teoria L
Esitiedot: MS-E2139 Nonlinear programming tai MS-E2140 Linear programming tai
MS-E2148 Dynamic optimization
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
MS-E2144 Matematisk optimeringsteori (V) (V) (3-6 sp)
Ansvarig lärare: Kimmo Berg
Kursnivå: Magisternivå
Undervisningsperiod: Föreläses ej detta läsår
Innehåll: Årligen varierande tema som behandlar något delområde inom optimering
Metoder, arbetssätt och bedömningsgrunder: Tentamen
Ersättande prestationer: Mat-2.4144 Matematisk optimeringsteori
Förkunskaper: MS-E2139 Nonlinear programming eller MS-E2140 Linear programming
eller MS-E2148 Dynamic optimization
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
MS-E2144 Optimization Theory (V) (V) (3-6 cr)
Responsible teacher: Kimmo Berg
Level of the Course: Master’s level
Teaching Period: not given this academic year
Content: Annually changing topic of some of the mainstream themes in optimization
Assessment Methods and Criteria: Exam
Substitutes for Courses: Mat-2.4144 Optimization Theory
Prerequisites: MS-E2139 Nonlinear Programming or MS-E2140 Linear Programming or
MS-E2148 Dynamic optimization
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
MS-E2146 Integer programming (5 cr)
Responsible teacher: Enrico Bartolini
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching period: IV (Spring)
Workload: Lectures 24h (4)
Exercises 24h (4)
Home exercises 20h
Assignment 20h
Autonomous studies 40h
Learning Outcomes: Be able to formulate a wide variety of optimization problems in
integer and binary variables. Explain, interpret, and compare the most important families
of algorithms in the general case and in special cases. Discuss the concept of complexity
theory and relate it with the topics of the course.
Content: Optimization problems including integer variables together with most common
algorithms: branch and bound, cutting plane, dynamic programming, approximation and
heuristics. Complexity analysis. Dual problem and its relation to the network problem.
Lagrangian relaxation. Column generation algorithms.
Assessment Methods and Criteria: Exam, assignment and home exercises
Study Material: Laurence A. Wolsey: Integer Programming, Wiley-Interscience
Publication, 1998.
Substitutes for Courses: Mat-2.4146 Integer Programming P
Prerequisites: MS-E2140 Linear Programming
27
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2148 Dynamic optimization (5 cr)
Responsible teacher: Kimmo Berg
Status of the Course: Compulsory course of the Systems and Operations Research
major. Optional course of the Systems and Operations Research minor.
Level of the Course: Master’s level
Teaching period: III (Spring)
Workload: Lectures 24h (4)
Exercises 24h (4)
Voluntary home exercises 15h
Autonomous studies 65h
Learning Outcomes: The students learn
1. the basic notions and classes of dynamic optimization problems,
2. to build and solve dynamic optimization models.
Content: Optimization methods for dynamic systems: dynamic programming, calculus of
variations, maximum principle, numerical solution methods. Application examples on
engineering, economics and biology.
Assessment Methods and Criteria: Exam. Bonus points from home work and exercise
sessions
Study Material: D.E. Kirk: Optimal Control Theory; M.I. Kamien, N.L. Schwarz: Dynamic
Optimization - the Calculus of Variations and Optimal Control in Economics and
Management; D.P. Bertsekas: Dynamic Programming and Optimal Control, vols I and II;
lecture notes
Substitutes for Courses: Mat-2.3148 Dynamic optimization
Prerequisites: 1st and 2nd years math
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2152 Peliteoria (V) (V) (5 op)
Vastuuopettaja: Harri Ehtamo
Kurssin asema: Systems and Operations Research pää- ja sivuaineen valinnainen
kurssi.
Kurssin taso: Maisteritaso
Opetusperiodi: I-II
Työmäärä toteutustavoittain: Luento-opetus 24h (2)
Laskuharjoitukset 24h (2)
Vapaaehtoiset kotitehtävät 15h
Itsenäinen työskentely 65h
Osaamistavoitteet: Johdatteleva kurssi peliteoriaan
Sisältö: Strategisen muodon pelit ja Nashin tasapaino; toistetut pelit ja folkteoreemat;
laajennetun muodon pelit ja osapelitäydellisyys; epätäydellinen informaatio ja Bayesin
pelit; Nashin tasapainon evoluutiobiologinen tulkinta.
Toteutus, työmuodot ja arvosteluperusteet: Tentti. Lisäpisteitä kotitehtävistä saa
yhden tenttitehtävän verran.
Oppimateriaali: R. Gibbons: A Primer in Game Theory, Prentice Hall, 1992.
Korvaavuudet: Mat-2.3152 Peliteoria L
Esitiedot: MS-C2105 Optimoinnin perusteet, todennäköisyyslaskenta
Arvosteluasteikko: 1-5 · Opintojaksot
Opetuskieli: suomi
MS-E2152 Spelteori (V) (V) (5 sp)
Ansvarig lärare: Harri Ehtamo
28
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research och
biämnet Systems and Operations Research.
Kursnivå: Magisternivå
Undervisningsperiod: I-II
Arbetsmängd: Föreläsningar 24h (2)
Övningar 24h (2)
Frivilliga hemuppgifter 15h
Självständiga studier 65h
Lärandemål: Undervisa elementär spelteori
Innehåll: Strategiska spel och Nash-jävikt; repeterade spel och folkteorem; utvidgade
spel och delspelperfektionen; ofullständigt information och Bayes spel; blandad strategi,
vetande och jämvikt; evolutiobiologisk interpretation av Nash-jämvikt.
Metoder, arbetssätt och bedömningsgrunder: Tentamen. Extrapoäng av
hemuppgifter, circa en examuppgift
Studiematerial: R. Gibbons: A Primer in Game Theory, Prentice Hall, 1992.
Ersättande prestationer: Mat-2.3152 Spelteori
Förkunskaper: MS-C2105 Grundkurs i optimering, tillämpad sannolikhetskalkyl
Bedömningsskala: 1-5 · Studieperioder
Undervisningsspråk: finska
MS-E2152 Game Theory (V) (V) (5 cr)
Responsible teacher: Harri Ehtamo
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching Period: I-II
Workload: Lectures 24h (2)
Exercises 24h (2)
Voluntary assignments 15h
Autonomous studies 65h
Learning Outcomes: Introductory course to game theory
Content: Strategic form games and Nash equilibrium; repeated games and folk
theorems; extensive form games and subgame perfectness; incomplete information and
Bayesian games; evolutionbiological interpretation of game theory.
Assessment Methods and Criteria: Exam. Bonus points from home work
Study Material: R. Gibbons: A Primer in Game Theory, Prentice Hall, 1992.
Substitutes for Courses: Mat-2.3152 Game Theory
Prerequisites: MS-C2105 Introduction to Optimization, applied probability
Evaluation: 1-5 · Courses
Language of Instruction: Finnish
MS-E2153 Multiple criteria optimization (3-6 cr)
Responsible teacher: Matteo Brunelli
Level of the Course: Master’s level
Teaching period: I, II, III, IV, V (Autumn and Spring)
Workload: Autonomous studies 75h
Learning Outcomes: To familiarize the students with multi-criteria optimization
Content: One and multi-objective decision making, utility function, Pareto-optimality,
theory of vector maximization, goal programming, interactive algorithms. Applications.
Assessment Methods and Criteria: Home assignments
Study Material: K.M. Miettinen: Nonlinear Multiobjective Optimization, Kluwer 1999
Substitutes for Courses: Mat-2.4153 Multiple Criteria Optimization P
Prerequisites: MS-C2105 Introduction to Optimization or MS-E2139 Nonlinear
Programming or MS-E2140 Linear Programming
Evaluation: 1-5 · Opintojaksot
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Language of Instruction: English
Further Information: 3 cr. Course is taken as an independent study, see the course web
site for instructions
MS-E2170 Simulation (V) (V) (5 cr)
Responsible teacher: Joona Tuovinen; Kai Virtanen
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching period: IV (Spring)
Workload: Lectures 20h (4)
Exercises 10h (2)
Demo 3h
Autonomous studies, including project 80h
Learning Outcomes:
The course has two alternative topics. Spring 2016 will be on topic I.
Topic I: The course gives basic skills for analysis of queuing phenomena through
discrete-event system simulation.
Topic II: The course’s objective is to provide capabilities to identify, model and
understand a variety of economic, organizational and socio-technical systems. After the
course, students will recognize principles of systems thinking and are able to apply them
to study the system of interest. Students will also be able to construct a system dynamics
simulation model for problem solving.
Content:
The topic of the course varies. The course has two alternative topics at the moment.
Topic I: Simulation of systems including discrete events and queues: random number
generation, construction of a model, input models, output data analysis, model validation.
Topic II: During the course, we will discuss the analysis and control of dynamic system,
model building and validation. We will also go through the basics of Vensim-software and
present some practical applications.
Assessment Methods and Criteria: Assignments and a case study
Study Material: Topic I: Law, A.M. ja W.D. Kelton, Simulation Modeling and analysis,
McGraw-Hill, 2002. Topic II: Sterman J.D., Business Dynamics: Systems Thinking and
Modeling for a Complex World, McGraw-Hill.
Substitutes for Courses: Mat-2.3170 Simulation
Prerequisites: 1st and 2nd year math courses
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2174 Computational methods in operations research (V) (V) (3-6 cr)
Responsible teacher: Enrico Bartolini
Level of the Course: Master’s level
Teaching period: V (Spring)
Workload: Lectures 20h (4)
Exercises 20h (4)
Home exercises 20h
Assignments 40h
Autonomous studies 25h
Learning Outcomes: Give students basic skills to implement mathematical algorithms to
solve different problems.
Content: Column generation and stabilization, Benders and Lagrangian decomposition,
branch-and-price, cutting planes with branch-and-price systems, metaheuristics.
Applications in vehicle routing and transportation problems.
Assessment Methods and Criteria: Exam, assignments and home exercises
Substitutes for Courses: Mat-2.4174 Programming of Mathematical Algorithms P
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Prerequisites: MS-E2140 Linear Programming, MS-E2146 Integer programming
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
Further Information: 5 cr. From master to graduate students who know the basics of
programming (preferrably Java, Fortran, C or C++).
MS-E2177 Operaatiotutkimuksen projektityöseminaari (V) (V) (5 op)
Vastuuopettaja: Ahti Salo
Kurssin asema: Systems and Operations Research -pää- ja sivuaineiden valinnainen
kurssi.
Kurssin taso: Maisteritaso
Opetusperiodi: III - IV
Työmäärä toteutustavoittain: Luento-opetus 14h
Projektityö 115h (170h projektipäällikkö)
Osaamistavoitteet: Harjaannuttaa opiskelijat projektiluontoiseen operaatiotutkimuksen
mallien ja menetelmien soveltamiseen.
Sisältö: Ryhmätyöskentelyä eri aiheita käsittelevien teknis-taloudellisten projektien
puitteissa. Mallien rakentaminen ja soveltaminen, projektien suunnittelu, toteutus ja
raportointi. Opintoretkiä yrityksiin ja tutkimuslaitoksiin.
Toteutus, työmuodot ja arvosteluperusteet: Osallistuminen seminaariin ja projektityöt
Oppimateriaali: Luentokalvot
Korvaavuudet: Mat-2.4177 Operaatiotutkimuksen projektityöseminaari L
Esitiedot: MS-C2105 Optimoinnin perusteet sekä todennäköisyyslaskenta
Arvosteluasteikko: hyväksytty/hylätty
Opetuskieli: suomi
Lisätietoja: Laajuus 5 op, projektipäällikölle 7 op. Rajoitettu osallistujamäärä, lähinnä
systeemi- ja operaatiotutkimuksen pääaineopiskelijoille
MS-E2177 Projektarbetsseminarium i operationsanalys (V) (V) (5 sp)
Ansvarig lärare: Ahti Salo
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research och
biämnet Systems and Operations Research.
Kursnivå: Magisternivå
Undervisningsperiod: III - IV
Arbetsmängd: Föreläsningar 14h
Projektsarbete 115h (170h projektledare)
Lärandemål: Att rutinera studeranden för att tillämpa operationsforsknings modeller och
metoder i arbeten av projektnatur.
Innehåll: Arbete i grupp övas inom ramen för teknisk-ekonomiska projekt. Konstruktion
och tillämpning av modeller, planering och utförande av projekt. Studie-excursioner till
företag och forskningsanstalter.
Metoder, arbetssätt och bedömningsgrunder: Närvaro på seminaren och
projectarbete
Studiematerial: Föreläsningtransparents
Ersättande prestationer: Mat-2.4177 Projektarbetsseminarium i operationsanalys
Förkunskaper: MS-C2105 Grundkurs i optimering samt tillämpad sannolikhetskalkyl
Bedömningsskala: godkänd/underkänd
Undervisningsspråk: finska
Tilläggsinformation: Omfattning 5 sp, för projektledare 7 sp. Begränsat antal deltagare,
främst för huvudämnestuderande
MS-E2177 Seminar on Case Studies in Operations Research (V) (V) (5 cr)
Responsible teacher: Ahti Salo
Status of the Course: Optional course of the Systems and Operations Research major
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and minor.
Level of the Course: Master’s level
Teaching Period: III - IV (Spring)
Workload: Lectures 14h
Project work 115h (170h project leader)
Learning Outcomes: To equip students with skills needed in project-oriented application
of methods and models of operations research.
Content: Teamwork is practiced in the context of techno-economic projects. Building and
application of models. Project planning, execution and reporting. Excursions to
companies and research organizations.
Assessment Methods and Criteria: Participation in seminar and project work
Study Material: Lecture slides
Substitutes for Courses: Mat-2.4177 Seminar on Case Studies in Operations Reserach
Prerequisites: MS-C2105 Introduction to Optimization and applied probability
Grading Scale: pass/fail
Language of Instruction: Finnish
Further Information: 5 cr, for project leader 7 cr. Restricted number of participants,
mainly for students majoring in Systems and operations research
MS-E2191 Graduate seminar on operations research (V) (V) (5 cr)
Responsible teacher: Harri Ehtamo
Status of the Course: Optional course of the Systems and Operations Research major.
Level of the Course: Master’s level
Teaching period: Not organized this academic year
Learning Outcomes: Seminar on topics of current interest in systems and operations
research, mainly for postgraduate but also for undergraduate students.
Content: The course can be taken repeatedly. The topic varies annually and is
announced separately in the beginning of the term.
Assessment Methods and Criteria: Seminar, presentation, and homework exercises
Substitutes for Courses: Mat-2.4191 Graduate seminar on operations research
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2192 Systems research seminar (V) (V) (1-6 cr)
Responsible teacher: Raimo Hämäläinen
Level of the Course: Master’s level
Teaching period: The arrangement will be announced later
Content: Presentations on new topics and problems in systems analysis, decision
making and risk management given by participants and visitors.
Substitutes for Courses: Mat-2.4192 Systems Research Seminar P
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2193 Independent studies in systems analysis (V) (V) (1-9 cr)
Responsible teacher: Enrico Bartolini; Harri Ehtamo; Raimo Hämäläinen; Ahti Salo; Kai
Virtanen
Level of the Course: Master’s level
Teaching period: I - II, III - V (Autumn and Spring)
Learning Outcomes: The course makes it possible to take courses from other
universities.
Content: Independent studies or supplementing normal course offerings. Credit by
agreement.
Substitutes for Courses: Mat-2.4193 Independent Studies in Systems Analysis and
Applied Mathematics P
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Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2194 Research course in systems science (V) (V) (1-6 cr)
Responsible teacher: Raimo Hämäläinen; Ahti Salo
Level of the Course: Master’s level
Teaching period: I, II, III, IV, V (Autumn and Spring)
Content: Advanced graduate course on topics of current interest in systems research
given mainly by visitors. The description of courses offered each year can be found at the
homepage.
Substitutes for Courses: Mat-2.4194 Research Course in Systems Science P
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
Further Information: Credit can also be earned by individual agreement by taking
courses offered by the Doctoral Education Network in Systems Analysis, Decision Making
and Risk Management, see http://sal.aalto.fi/en/gradschool/courses/
MS-E2195 Web-based courses in systems analysis (V) (V) (1-6 cr)
Responsible teacher: Kimmo Berg; Matteo Brunelli; Kai Virtanen
Status of the Course: Optional course of the Systems and Operations Research minor.
Level of the Course: Master’s level
Teaching period: I - II, III - V (Autumn and Spring)
Content: Independent studies with web-based teaching material produced by the
Systems Analysis Laboratory and selected foreign universities. See the available courses
at the web pages
Assessment Methods and Criteria: Exam or homework
Substitutes for Courses: Mat-2.4195 Web-based courses in systems analysis
Evaluation: 1-5 · Opintojaksot
Language of Instruction: English
MS-E2198 Luovan ongelmanratkaisun seminaari (V) (V) (5-8 op)
Vastuuopettaja: Raimo Hämäläinen; Esa Saarinen
Kurssin asema: Systems and Operations Research -pää- ja sivuaineiden valinnainen
kurssi.
Kurssin taso: Maisteritaso
Opetusperiodi: I - II
Työmäärä toteutustavoittain: Seminaari 33h (3)
Esitelmä 10h
Itsenäinen työskentely 85h
Osaamistavoitteet: Kurssin tavoitteena on laajentaa ja moniulotteistaa osallistujien
ajattelua ja kirjallista ilmaisua, antaa työvälineitä henkilökohtaisen henkisen muutoksen
hallintaan, itsensä tuntemiseen ja luovaan vuorovaikutukseen sekä lisätä systeemiälyä
koskevaa ymmärrystä.
Sisältö: Perus- sekä jatko-opiskelijoille tarkoitettu vaihtuvasisältöinen seminaari, jossa
paneudutaan luovan ongelmanratkaisun kysymyksiin eri metodisilla lähestymistavoilla.
Toteutus, työmuodot ja arvosteluperusteet: Esitelmä, aktiivinen osallistuminen ja
kirjalliset työt
Korvaavuudet: Mat-2.4198 Luovan ongelmanratkaisun seminaari L
Esitiedot: MS-C2197 Filosofia ja systeemiajattelu
Arvosteluasteikko: hyväksytty/hylätty
Opetuskieli: suomi
Lisätietoja: Vaihtuvasisältöinen. Kurssi voidaan suorittaa myös koodilla TU-E3130.
Esitietona MS-C2197 Filosofia ja systeemiajattelu. Osallistujamäärä on rajoitettu ja
kurssilaisten valintamenettely ilmoitetaan esitietokurssin suorittaneille sähköpostitse.
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MS-E2198 Seminarium i kreativ problemlösning (V) (V) (5-8 sp)
Ansvarig lärare: Raimo Hämäläinen; Esa Saarinen
Kursens status: Valfri kurs inom huvudämnet Systems and Operations Research och
biämnet Systems and Operations Research.
Kursnivå: Magisternivå
Undervisningsperiod: I - II
Arbetsmängd: Seminaari 33h (3)
Föredrag 10h
Självständiga studier 85h
Lärandemål: Målet med kursen är att utvidga och göra mera mångsidigt deltagarnas
tänkande och skriftligt uttryck, ge verktyg för personlig växt, självkännedom och kreativ
interaktion, och öka förståelse av systemintelligens.
Innehåll: Seminarium för grund- och fortsättningsstuderande. Betoning på frågor i kreativ
problemlösning och relevanta metoder för dessa.
Metoder, arbetssätt och bedömningsgrunder: Föredrag, aktivt deltagande och essä.
Ersättande prestationer: Mat-2.4198 Seminarium i kreativ problemlösning
Förkunskaper: MS-C2197 Filosofi och systemtänkande
Bedömningsskala: godkänd/underkänd
Undervisningsspråk: finska
Tilläggsinformation: Innehåll varieras. Kursen kan ocskå avläggas under koden
TU-E3130. Registrering är begränsad.
MS-E2198 Seminar of Creative Problem Solving (V) (V) (5-8 cr)
Responsible teacher: Raimo Hämäläinen; Esa Saarinen
Status of the Course: Optional course of the Systems and Operations Research major
and minor.
Level of the Course: Master’s level
Teaching Period: I - II (Autumn)
Workload: Seminar 33h (3)
Presentation 10h
Autonomous studies 85h
Learning Outcomes: The aim of the course is to expand and deepen participant’s
thinking and capabilities for written expression. It provides tools for participant’s mental
growth and change management, improving self-knowledge and abilities for creative
interaction, and brings about understanding regarding systems intelligence.
Content: The course is arranged for undergraduate and graduate students, and the
contents vary yearly. Themes deal with creative problem solving and systems
intelligence.
Assessment Methods and Criteria: Presentation, active participation and written
assignments.
Substitutes for Courses: Mat-2.4198 Seminar of Creative Problem Solving
Prerequisites: MS-C2197 Philosophy and Systems Thinking
Grading Scale: pass/fail
Language of Instruction: Finnish
Further Information: Content varies. The course can also be passed with course code
TU-E3130. Registration is restricted.
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