University:Al-Nahrain University College: Science Department:Mathematics and Computer applications Lecturer name:Dr. Ahlam J. Khaleel Course Instructor E_mail Title Course Code Course Description Learning Outcome Stage: Third Academic Status:Assistant Professor Dr. Ahlam Jameel Khaleel [email protected] Abstract Algebra (I) MATH 312 Abstract Algebra (I) is an overview of some of the seminal achievements in group theory from ancient to modern times. Topics include definitions and properties of group theory, Cyclic subgroup, normal subgroup, Quotient group , Homomorphism's, Fundamental theorems, Jordan Holder theorem and its applications. 1- Definitions and Examples of Groups. 2- Certain Elementary Theorems on Groups. 3- Two Important Groups. 4- Subgroups. 5- Certain Elementary Theorems on Subgroups. 6- Cyclic Subgroups. 7- Product of Subgroups. Textbook Introduction to Modern Abstract Algebra, B. Burton , 1967 References )1( باسل الهاشمي. عادل غسان و د. تأليف د/مقدمة حىل نظرية الزمر (2) Theory of groups by Macdonald, 1965. (3) Introduction to Modern Abstract Algebra, B. Burton ,1985 Course Assessment General Notes Term Tests 30 Laboratory Quizzes Assignments 0 5 5 Final Exam 60 1- The time offered for the subject was not enough to cover the materials of the first course because many holidays were given during this course. 2- The students has shown a satisfactory performance and achievements during this course. Course weekly Outline week 1 Topics Covered Definitions and Examples of Groups 2 Certain Elementary Theorems on Groups 3 Certain Elementary Theorems on Groups 4 Certain Elementary Theorems on Groups 5 Certain Elementary Theorems on Groups 6 7 8 9 10 Two Important Groups Two Important Groups Two Important Groups Subgroups Certain Elementary Theorems on Subgroups Certain Elementary Theorems on Subgroups Certain Elementary Theorems on Subgroups Cyclic Subgroups Order of a Finite Group and Order of an Element Group Product of Subgroups 11 12 13 14 15 Instructor Signature: Dr. Ahlam Jameel Khaleel University: AL-Nahrain College: Sciences Computer Applications Stage: Forth year Lecturer name: IBTISAM KAMIL HANAN Department: Mathematics and Academic Status: Lucterer IBTISAM KAMIL HANAN Course Instructor E_mail [email protected] Title Complex Analysis I Course Coordinator Course Description Learning Outcome Textbook MATH 411 and Studying field, sequences, functions, series of complex numbers and integrals of complex functions Theory of pure mathematics Complex Variables and Applications, by Ruel V. Chirchill References Course Assessment Term Tests 40% General Notes none Laboratory - Quizzes - Assignments - Final Exam 60% Course weekly Outline week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Topics Covered Addition and multiplication of complex numbers, complex conjugate, absolute value of complex numbers The space of complex numbers Definition of connected space, polar form De Mover's theorem, Euler formula The n-th root of complex number Definition of path, path wise connected Simply connected paths Convergent sequence, Cauchy sequence Completeness of the space of complex numbers Definitions: domain, limit, continuous, derivative, analytic functions Cauchy-Riemann equations Harmonic functions and harmonic conjugate functions Exponential functions, Logarithmic functions, Trigonometric functions and Hyperbolic functions Smooth path, contour path The line integral, Cauchy-Goursat theorem Instructor Signature: IBTISAM KAMIL HANAN Lab. Experiment Assignments University: alnahrain & comp. app. College: science Stage: fourth Lecturer name: Iman Abdulwahab Hussain Course Instructor E_mail Title Course Code Course Description Learning Outcome Textbook Department: math. Academic Status: Ass. Lucterer Iman Abdulwahab Hussain Imanbs76_math @yahoo.com Topology I MATH 415 The aim of this courses is to provide a fundamental of general topology Study the theory of topology by using the set theory An introduction to general topology, by Paul E. Long An introduction to general topology, by Paul E. Long References Course Assessment General Notes General topology schaum’s out line series Term Laboratory Quizzes Assignments Final Exam Tests 40% 60% Course weekly Outline week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Topics Covered Lab. Experiment Assignments Definition of topological space Open and closed set Usual & cofinite topology Limit point & derived set Interior and boundary points Closure of sets Holiday Basis and local basis First exam Sub basis Sub spaces Continuous mappings Open & closed mapping Second exam Homeomorphism Instructor Signature: Iman Abdulwahab Hussain University: alnahrain mathematics & comp. app. College: science Stage: third Lecturer name: Salam Adel Ahmed Course Instructor E_mail Title Course Coordinator Department: Academic Status: Ass. lecturer Salam Adel Ahmed [email protected] Applied mathematics MATH 316 Course Description Solution of order differential equations by series method , special functions, Fourier series and transform Learning Outcome Solution of ordinary differential equation with variable coefficients, fourier series ,special type of functions Textbook References Course Assessment General Notes Fourier series and boundary value problems Elementary differential equation, by E. D. Rainville and P. E. Bedeint طرق في الرياضيات التطبيقية تاليف دز باسل يعقوب يوسف Term Tests Laboratory Quizzes Assignments Final Exam 40 - - - 60 none Course weekly Outline week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Topics Covered Power series solution Ordinary points and singular points and solution near an ordinary point Regular singular points and indicial equation Indicial equation with difference of roots nonintegral Indicial equation with equal roots Indicial equation with difference of roots a positive integer nonlogarithmic case Holiday First Exam. Indicial equation with difference of roots a positive integer logarithmic case & Fourier series Determination of the coefficients of the fourier series Fourier sine & cosine series Fourier transform & Gamma function Second Exam. Beta function Euler equation Legender Equation Instructor Signature: Salam Adel Ahmed Lab. Experiment Assignments
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