Program tanımları
Fen Bilimleri Enstitüsü
Matematik Programı Yüksek Lisans Dersleri
MODUL M1 COMPULSORY CORE COURSES (Zorunlu Çekirdek Dersleri)
MATH 511 Algebra I 3 Kredi
MATH 521 Analysis I 3 Kredi
MATH 531 Functional Logic I 3 Kredi
MATH 541 Computation Theory I 3 Kredi
MATH 551 Geometry I 3 Kredi
MATH 561 Topoloji I 3 Kredi
MODUL M2 ELECTIVE COURSES IN DEPTHNESS OF MATHEMATICS
(Matematikte Derinlik Seçmeli Dersleri)
MATH 512 Algebra II 3 Kredi
MATH 522 Analysis II 3 Kredi
MATH 532 Functional Logic II 3 Kredi
MATH 542 Computation Theory II 3 Kredi
MATH 552 Geometry II 3 Kredi
MATH 562 Topoloji II 3 Kredi
MODUL M2 ELECTIVE COURSES IN DEPTHNESS OF MATHEMATICS
(Matematikte Derinlik Seçmeli Dersleri)
MATH 513 Discrete Mathematics 3 Kredi
MATH 523 Differential Equations 3 Kredi
MATH 533 Rings and Modules 3 Kredi
MATH 543 Probability 3 Kredi
MATH 553 Automata Theory 3 Kredi
MATH 563 Linear Algebra 3 Kredi
MATH 574 Mathematics in Monetary The 3 Kredi
MATH 584 Mathematics in Economy 3 Kredi
MATH 594 Mathematics in the Management Science 3 Kredi
MODUL M4 THESISES
MATH 514 Graduation Report in Disciplines of Mathematics 3 Kredi
MATH 524 MS Thesis in Disciplines of Mathematics 9 Kredi
Matematik Yüksek Lisans Programındaki Ders İçerikleri ve Kitaplar:
MATH 511 Algebra I :
Number Theory, Group Theory, Ring Theory, Field Theory.
Ders Kitabı:Advanced Algebra, Joseph J. Rotman, ISBN: 0130878685 Publisher: Prentice Hall, Edition Number: 1
MATH 521 Analysis I :
1. Functions and Models. 2. Limits and Derivatives. 3. Differentiation Rules. 4. Applications of Differentiation. 5. Integrals. 6. Applications of Integration. 7. Techniques of Integration. 8. Further Applications of Integration. 9. Differential Equations. 10. Parametric Equations and Polar Coordinates. 11. Infinite Sequences and Series.
Ders Kitabı :Single Variable Calculus ,James Stewart ,ISBN: 0534393306 Pub. Date: December 2002 ,Publisher: Brooks/Cole ,Edition Description: 5th
MATH 531 Functional Logic I :
1. Introduction: Number Systems and Conversion. 2. Boolean Algebra. 3. Boolean Algebra (Continued). 4. Algebraic Simplification. 5. Applications of Boolean Algebra. 6. Karnaugh Maps. 7. Quine-Mccluskey Method. 8. Multi-Level Gate Networks: NAND and NOR Gates. 9. Multiple-Output Networks: Multiplexers, Decoders, Read-Only Memories, and Programmable Logic Arrays. 10. Combinational Network Design. 11. Flip-Flops. 12. Counters and Similar Networks. 13. Analysis of Clocked Sequential Networks.
Ders Kitabı : Fundamentals of Logic Design ,Charles H. Jr. H. Roth ISBN: 0534378048 ,Pub. Date: June 2003 ,Publisher: Brooks/Cole Edition Description: 5TH BK&CDR
MATH 541 Computation Theory I :
Automata and Languages, Regular Languages, Context-Free Languages, The Church-Turing Thesis, Decidability, Reducibility, Complexity Theory, Time Complexity, Space Complexity, Intractability, Advanced topics in complexity theory.
Ders Kitabı: Introduction to the Theory of Computation ,Michael Sipser ISBN: 053494728X , Pub. Date: December 1996,Publisher: Brooks/Cole Edition Number: 1
MATH 551 Geometry I(Analitic Geometri) :
1. Coordinate Systems, Line, Plane and Trigonometry. 2. Vectors in the Plane. 3. The Line and Plane Equations. 4. The Circle and Sphere Equations. 5. Conics and Conic Sections. 6. Transformation of Coordinates. 7. Curve Sketching. 8. Polar Coordinates and Parametric Equations. 9. Solid Analytic Geometry.
Ders Kitabı: Analytic Geometry ,Douglas F. Riddle, ISBN: 0534948545 Pub. Date: June 1996 ,Publisher: Brooks/Cole ,Edition Number: 6
MATH 561 Topoloji I (General Topology) :
1. Set Theory and Logic. 2. Topological Spaces and Continuous Functions. 3. Connectedness and Compactness. 4. Countability and Separation Axioms. 5. The Tychonoff Theorem. 6. Metrication Theorems and Paracompactness. 7. Complete Metric Spaces and Function Spaces. 8 .Baire Spaces
Ders Kitabı: Topology ,James R. Munkres, Munkres James,ISBN: 0131816292 Pub. Date: December 1999 ,Publisher: Prentice Hall ,Edition Description: 2ND
MATH 512 Algebra II :
Modules and Categories, Algebras, Advanced Linear Algebra, Homology.
Ders Kitabı: Advanced Algebra , Joseph J. Rotman, ISBN: 0130878685 Pub. Date: April 2002, Publisher: Prentice Hall ,Edition Number : 1
MATH 522 Analysis II :
12. Infinite Sequences and Series. 13. Vectors and the Geometry Of Space. 14. Vector Functions. 15. Partial Derivatives. 16. Multiple Integrals. 17. Vector Calculus. 18. Second-Order Differential Equations.
Ders Kitabı: Single Variable Calculus ,James Stewart ,ISBN: 0534393306 Pub. Date: December 2002 ,Publisher: Brooks/Cole ,Edition Description: 5TH
MATH 532 Functional Logic II :
14. Derivation of State Graphs and Tables. 15. Reduction of State Tables: State Assignment. 16. Sequential Network Design. 17. Iterative Networks. 18. MSI Integrated Circuits in Sequential Network Design. 19. Sequential Network Design with Programmable Logic Devices (PLDs). 20. Networks for Addition and Subtraction. 21. Networks for Arithmetic Operations. 22. State Machine Design with SM Charts. 23. Analysis of Asynchronous Sequential Networks. 24. Derivation and Reduction of Primitive Flow Tables. 25. State Assignment and Realization of Flow Tables. 26. Hazards. 27. Asynchronous Sequential Networks.
Ders Kitabı :Fundamentals of Logic Design ,Charles H. Jr. H. Roth ISBN: 0534378048 ,Pub. Date: June 2003 ,Publisher: Brooks/Cole , 5th ed.
MATH 542 Computation Theory II :
Formal Languages, Primitive Recursive Functions, Partial Recursive Functions, Turing Machines as Algorithms, Syntax, Semantics, Decision Problems, Free Schemas, Tree Schemas, Formalization in Predicate Calculus, Formalization of Properties of Flowchart Programs, Formalization of Properties of Flowchart Schemas, Translation Problems, Recursive Schemas. Functions and Functionals, Monotonic Functions, Continuous Functionals, Fixpoints of Functionals, Recursive Programs, Computation Rules, Fixpoint Computation Rules, Systems of Recursive Defintions, Verification Methods, Stepwise Computational, Complete Computational Induction, Fixpoint Induction, Structural Induction,
Ders Kitabı :Theory of Computation,Brainerd W. S., and Landweber, L. H. ISBN: 0471095850,Pub. Date: 1974, Publisher: John Wiley ,Edition Number: 1
MATH 552 Geometry II (Differential Geometry) :
1. Curves in R3: Frenet formulas and Fundamental Theorem. 2. Regular Surfaces. 3. Inverse Image of Regular Values. 4. Differentiable Functions on Surfaces. 5. Tangent Plane; the Differential of a Map, Vector Fields, the First Fundamental Form. 6. Gauss Map, Second Fundamental Form, Nnormal, Principal Curvatures, Principal and Asymptotic Directions. 7. Gauss Map in Local Coordinates. 8. Covariant Derivative. 9. Geodesics.
Ders Kitabı: Elementary Differential Geometry , Andrew Pressley,ISBN: 1852331526 Pub. Date: January 2001,Publisher: Springer-Verlag New York, LLC , 1st Ed.
MATH 562 Topology (Algebraic Topology) II:
9. The Fundamental Group. 10. Separation Theorems in the Plane. 11. The Seifert-van Kampen Theorem. 12. Classification of Surfaces. 13. Classification of Covering Spaces. 14. Applications to Group Theory. The Fundamental Group, Advanced Homology, Advanced Co homology, Advanced Homotopy Theory.
Ders Kitabı: Topology ,James R. Munkres, Munkres James, ISBN: 0131816292 Pub. Date: December 1999 ,Publisher: Prentice Hall ,Edition Description: 2ND
MATH 513 Discrete Mathematics : 1.Logic and Proofs. 2. The Language of Mathematics. 3. Algorithms. 4. Counting Methods. 5. Recurrence Relations. 6. Graph Theory. 7. Trees. 8. Network Models. 9. Boolean Algebras and Combinatorial Circuits. 10. Grammars, and Languages.
Ders Kitabı :Discrete Mathematics ,Richard Johnsonbaugh,ISBN: 0131176862 Pub. Date: August 2004 ,Publisher: Prentice Hall ,Edition Number: 6
MATH 523 Differential Equations :
First Order Differential Equations, Second Order Linear Equations, Higher Order Linear Equations, Series Solutions of Second Order Linear Equations, The Laplace Transform. Systems of First Order Linear Equations, Numerical Methods, Nonlinear Differential Equations and Stability, Partial Differential Equations and Fourier Series, Boundary Value Problems.
Ders Kitabı:Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima ,ISBN: 0471433381 Pub. Date: April 2004 ,Publisher: Wiley, John & Sons, Incorporated ,8th ed.
MATH 533 Rings and Modules Modules :
Free Modules, Injective Modules, Tensor Products, Certain Important Algebras, Simple Modules and Primitive Rings, The Jacobson Radical, Sub direct Product Decompositions, Primes and Semi primes, Projective Modules and More on Wedderburn Theorems, Direct Sum Decompositions, Simple Algebras, Hereditary Rings. Free and Projective Modules, Module Constructions, Categories and Functors, Module Categories, Flat Modules, Purity.
Ders Kitabı:Modules and Rings ,John Dauns,ISBN: 0521462584 Pub. Date: October 1994 ,Publisher: Cambridge University Press
MATH 543 Probability :
An Introduction to Measure Theory, Kolmogorov Axioms, Independence, Random Variables, Expectation, Modes of Convergence for Sequences of Random Variables, Moments of a Random Variable, Generating Functions, Characteristic Functions, Product Measures and Joint Probability, Distribution Laws, Conditional Expectations, Strong and Weak Law of Large Numbers, Convergence Theorems for Probability Measures, Central Limit Theorems.
Ders Kitabı:First Course in Probability ,Sheldon Ross ,ISBN: 0130338516 Pub. Date: August 2001,Publisher: Prentice Hall ,Edition Description: 6TH
MATH 553 Automata Theory :
Group-matrix Type Automata, General Automata, Classes of Automata as Posets, Languages and Operations, Shuffle Closed Languages, Insertions and Deletions, Shuffles and Scattered Deletions, Directable Automata.
Ders Kitabı:Algebraic Automata Theory ,M. Holcombe, W. M. Holcombe, Bela Bollobas (Editor) ,ISBN: 0521604923 ,Pub. Date: June 2004 ,Publisher: Cambridge University Press
MATH 563 Linear Algebra :
Linear Equations, Matrix Algebra, Determinants. Vector Spaces, Eigenvalues and Eigenvectors, Orthogonality and Least-Squares, Symmetric Matrices and Quadratic Forms.
Ders Kitabı:Linear Algebra with Applications ,,Otto Bretscher ,ISBN: 0131453343 Pub. Date: June 2004 ,Publisher: Prentice Hall ,Edition Number: 3
MATH 573 Mathematics for Finance :
1 A Simple Market Model, 2 Risk-Free Assets, 3 Risky Assets, 4 Discrete Time Market Models, 5 Portfolio Management, 6 Forward and Futures Contracts, 7 Options: General Properties, 8 Option Pricing, 9 Financial Engineering, 10 Variable Interest Rates, 11 Stochastic Interest.
Ders Kitabı :Mathematics for Finance: First Steps ,Marek Capinski, Tomasz Zastawniak, ISBN: 1852333308 ,Pub. Date: July 2003, Publisher: Springer-Verlag New York, LLC
MATH 583 Mathematics for Economies and Business :
Functions in Economics, 2 Equations in Economics, 3 Macroeconomic Models, 4 Changes, Rates, Finance and Series, 5 Differentiation in Economics, 6 Maximum and Minimum Values, 7 Further Rules of Differentiation, 8 Partial Differentiation in Economics, 9 Constrained Maxima and Minima, 10 Integration in Economics.
Ders Kitabı: Mathematics for Economies and Business: An Interactive Introduction Jean Soper ,ISBN: 0631207813 ,Pub. Date: December 1998 ,Publisher: Blackwell Publishers
MATH 514 Graduation Project of Master Science in Mathematics (MS in Mathematics) : The Graduation Projectof Master of Science in Mathematics is a written report on individual research with a clear academic character. The Graduation Project is written independently by the student under supervision of a member of the academic staff. The general aim of the Graduation Project is that students display adequate knowledge, understanding, and ability in the field of study to successfully participate in academic discussions, and contribute to these with their own research. The thesis will be written in the language of instruction of the program.
MATH 524 Thesis of Master Science in Mathematics
The thesis Master Science in Mathematics is a written report on individual research with a clear academic character. The thesis is written independently by the student under supervision of a member of the academic staff. The general aim of the thesis is that students display adequate knowledge, understanding, and ability in the field of study to successfully participate in academic discussions, and contribute to these with their own research. The thesis will be written in the language of instruction of the Thesis of Master Science in Mathematics Program
