Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH101

Analysis I

Fall

C

4+2

7

COURSE CONTENT

Sequences; Functions of one variable; Limit; Continuity; Derivative; Geometric and physical meanings of derivative; Extremes; Indeterminate forms in limits; Differential; Sketching curves.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH102

Analysis II

Spring

C

4+2

8

COURSE CONTENT

Indefinite and definite integrals of functions; Calculation of area, arc length, surface area and volume

with the help of Riemann integral; Improper integrals and convergence tests for improper integrals; Real valued series.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH103

Abstract Mathematics I

Fall

C

4+0+0

5

COURSE CONTENT

Propositions; Quantifiers; Proof methods; Sets and operations on sets; Relation; Function.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH104

Abstract Mathematics II

Spring

C

4+0+0

5

COURSE CONTENT

Operation and its properties; Cardinality of the sets; Finite, countable and uncountable sets; The construction of the number sets and algebraic operations on them; Summation and product notations.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH105

Analytic Geometry I

Fall

C

4+0+0

5

COURSE CONTENT

Vectors in plane; Coordinate systems in plane and in space; Line in plane; Vectors in space; Line in space; Coordinate systems in space; Plane in space

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH106

Analytic Geometry II

Spring

C

4+0+0

5

COURSE CONTENT

Conics; Analytical expression of conics; Elements of conics; Ellipse in plane; Circle in plane; Parabola in plane; Hyperbola in plane; Sphere surface; Cylinder surface; Cone surface; Ruled surfaces; Surfaces of revolution

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH201

Advanced Analysis I

Fall

C

4+2

7

COURSE CONTENT

Pointwise and uniform convergence in sequences and series of functions; Weierstrass M-test; Power series; Taylor series; Limit; Continuity and derivative of multivalued functions;, Partial derivatives; Maximum-minimum problems.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH202

Advanced Analysis II

Spring

C

4+2

7

COURSE CONTENT

Double integrals; Triple integrals; Spherical and cylindrical coordinates; Line integrals; Surface integrals; Fundamentals theorems and their applications of surface integrals

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH203

Linear Algebra I

Fall

C

4+0+0

6

COURSE CONTENT

Systems of linear equations; Matrices and special matrices; Echolon form; Solutions of systems of

linear equations; Determinants and their properties; Vector spaces; Subvector spaces; Vector space base and dimension

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH204

Linear Algebra II

Spring

C

4+0+0

6

COURSE CONTENT

Inner product spaces; Orthogonal complement; Linear transformations and their properties; Matrices of linear transformations; Rank and kernel of linear transformation; Eigenvalues and eigenvectors of matrices; Diagonalization of matrices

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH205

Topology I

Fall

C

4+0+0

6

COURSE CONTENT

The notions of metric and topology; Base for topology and subbase; The topological neighborhood system; Interior, exterior, boundary (or frontier) and closure of a set in a topological space;

Accumulation and isolated points of a set in a topological space; Continuity in topological spaces.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH206

Topology II

Spring

C

4+0+0

6

COURSE CONTENT

Homeomorphism; Separation axioms; Countable-separable spaces; Convergence in topological spaces; Product-quotient spaces; Compactness and connectedness in topological spaces.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH207

Introduction to Programming

Fall

C

3+0+0

3

COURSE CONTENT

Windows and their functions in the MATLAB/Octave programming software interface; Variable definitions and mathematical operations; Vectors and matrices; Conditional statements and loops; Functions and user-defined functions; Plotting graphs in two and three dimensions.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH208

Number Theory

Spring

C

3+0+0

4

COURSE CONTENT

Integers and their properties; Division algorithm; Base Arithmetic; Divisibility; GCD, LCM and applications; Linear Diophantine equations, Linear Diophantine equation systems, Arithmetic functions, Eulerin ϕ function, Möbius function, Congruence definition and properties, Congruence equations, Congruence applications,

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH209

Professional English I

Fall

C

2+1+0

4

COURSE CONTENT

Reel numbers; Cartesian coordinates; Functions; Basic concepts about limits and derivatives.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH213

Fuzzy Mathematics

Fall-Spring

S

3+0+0

4

COURSE CONTENT

Multi-valued logic; Classical sets; Fuzzy sets; Fuzzy set operations; Level sets of fuzzy sets; Fuzzy number and the extension principle; Arithmetic operations of fuzzy numbers; Fuzzy relations and their operations; Applications of fuzzy relations.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH214

Discrete Mathematics

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Algorithms; The growth of functions and complexity of algorithms; The basics of counting; The pigeonhole principle; Permutations and combinations; Binomial coefficients and identities; Generalized permutations and combinations; An introduction to discrete probability; Bayes theorem; Expected value and variance.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH217

Projective Geometry I

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Euclidean geometry; non-Euclidean geometries; Affine plane; Projective plane; Relationship between aaffine and projective plane; Other geometric structures

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH220

Symbolic Programming

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Limit, derivative and integral calculations and applications in symbolic programming packages in MATLAB/Octave programming software.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH224

Basic Combinatorics

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Mathematical induction and well-ordering; Recursive definitions and recursive algorithms; Solving linear recurrence relations; Divide-and-conquer algorithms and recurrence relations; Generating functions; Inclusion-exclusion; Finite-state machines with output and with no output.

Course Code

Course Name

Semester

Course Type

(C/E)

T+P+L

(Hour/Week)

ECTS

MATH231

Fundamentals of Mathematics

Fall-Spring

C

3+0+0

4

COURSE CONTENT

Sets, numbers; Absolute value; Exponential and radical expressions; Functions; Equations; Inequality; Systems of equations; Trigonometry; Logarithm

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH301

Complex Analysis I

Fall

C

4+0

6

COURSE CONTENT

Algebraic; Geometric and topological properties of complex numbers; Complex sequences; Convergence of complex sequences; Analytic functions

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH302

Complex Analysis II

Spring

C

4+0

6

COURSE CONTENT

Elemantary functions and their derivatives; Cauchy-Rieamann equations; Harmonic functions; Complex curves; Complex integral; Cauchy-Goursat Theorem; Cauchy integral formula; Liouville Theorem and fundamental theorem of algebra; Taylor and Laurent series; Residues

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH303

Algebra I

Fall

C

4+0+0

6

COURSE CONTENT

Binary operations; groups, subgroups; Cyclic groups; Normal subgroups; Quotient groups; Direct product of groups; Group homomorphism and isomorphism; Conjugate classes; Sylow subgroups.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH304

Algebra II

Spring

C

4+0+0

6

COURSE CONTENT

Rings; subrings; Ideals; Quotient rings; Ring homomorphism and isomorphism; Polynomial rings; Unique factorization domain

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH305

Differential Equations I

Fall

C

4+0+0

4

COURSE CONTENT

Definitions and terminology; Initial value problems; First order differential equations; Solution curves and direction fields; Separable, linear, homogeneous and exact equations; Solutions by substitutions; Higher order differential equations; Theory of linear equations; Initial and boundary value problems; Homogeneous and nonhomogeneous equations; Reduction of order; Homogeneous linear equations with constant coefficients; Undetermined coefficients; Variation of parameters; Cauchy-Euler equations.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH306

Differential Equations II

Fall

C

4+0+0

4

COURSE CONTENT

Series solutions of linear ordinary differential equations; Solutions about ordinary and regular singular points; The Laplace transform; Properties of the Laplace transform and the inverse Laplace transform; The unit step function and the convolution; Solution of initial value problems by the Laplace transform; Systems of linear first-order differential equations; Theory of linear systems; Solution of homogeneous and nonhomogenous linear systems; Solution of the systems by the Laplace transform.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH307

Differential Geometry I

Fall

C

4+0+0

5

COURSE CONTENT

Affine space; Euclidean space; Manifold; Tangent vector; Tangent space; Vector field; Covariant derivative; Curves; Curve pairs

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH308

Differential Geometry II

Spring

C

4+0+0

5

COURSE CONTENT

Orientation on hypersurfaces; Shape operatör; Fundamental forms; Gaussian transformation; Gaussian curvature; Mean curvature; Geodesic curvature; Normal curvature; Some hypersurfaces

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH309

Numerical Analysis

Fall

E

3+0+0

4

COURSE CONTENT

Mathematical preliminaries on numerical calculations; Numerical solutions of nonlinear equations and systems of nonlinear equations; Numerical solution of systems of linear equations; Direct solution methods and iterative methods; Eigenvalue problem in matrices and numerical solution methods; Interpolation; Curve fitting; Numerical derivative and numerical integration.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH310

Applied Numerical Methods

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Solution of nonlinear equations using computer programs (programming software such as

MATLAB/Octave etc.) and numerical solution methods; Approximation to functions and interpolation; Numerical differentiation and integration.

Course Code

Course Name

Semester

Course

Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH311

Vector Analysis I

Fall-Spring

C

3+0+0

6

COURSE CONTENT

Differential and integral of vector valued functions; Surface integrals; Vector fields; Integrals of vector fields

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH313

Kinematics

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Dual numbers; Ring of dual numbers; Matrix representation of dual numbers; Dual vectors; Dual vector spaces; E-study transformation; Theory of quaternions

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH314

Transformations and Geometries

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Transformations; Transformation groups; Classification of geometries using transformations; Types of motion in the plane; Similarity transformations

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH315

Introduction To Coding Theory

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Basic assumptions, correcting and detecting error patterns, finding the most likely codeword transmitted, error-detecting codes and error-correcting codes; Linear codes, generating and parity check matrices; Some bounds for codes, perfect codes; Hamming codes, the extended Golay code, Reed-Muller (RM) codes.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Wee k)

ECTS

MATH316

Spectral Theory I

Fall-Spring

E

2+0+0

4

COURSE CONTENT

Introduction to spectral theory; Linear operators; Boundary conditions and definition of Sturm- Liouville operators; Lagrange identity; Positive, symetric and selfadjoint Sturm-Liouville operators; Eigenvalues and eigenfunctions of selfadjoint operators; Examples of eigenvalues and eigenfunctions; Finding the solutions of Sturm-Liouville equation; Getting the solutions by

consecutive approximation; Asymptotics of functions; Obtaining the asymptotics of the solutions of Sturm-Liouville equations; Getting the asymphtotics of eigenvalues; Calculating the asymphtotics of eigenfunctions.

Course Code

Course Name

Semester

Course

Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH317

Fourier Analysis

Fall-Spring

C

3+0+0

6

COURSE CONTENT

Fourier series; Fourier integra; Derivatives of Fourier mappings

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH318

Preparing Scientific Documents

Fall-Spring

E

2+0+0

4

COURSE CONTENT

Latex document structure; Mathematical expressions; Graphs and tables; References and tagging; Bibliography management.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH321

Introduction To Crytography

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Encryption schemes, symmetric-key encryption; Fiestal ciphers and DES; Algorithms, complexitiy, and modular arithmetic, quadratic residues, primality testing, factoring and square roots, discrete logarithms; One-way and hash functions, RSA, ElGamal, cryptographic protocols.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Wee k)

ECTS

MATH322

Scattering Theory I

Fall-Spring

E

2+0+0

4

COURSE CONTENT

L1 and L2 spaces; Parameter dependent integrals; Fourier transform and its properties; Examples of Fourier transforms; Asymptotic equalities; Jost solution and its properties; Asymptotics of the Jost solution with respect to x and 𝜆 variables; Jost function and its zeros; Scattering function; Scattering data and its properties.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH323

Introduction To Graph Theory

Fall-Spring

E

3+0+0

4

COURSE CONTENT

Graph terminology, representing graphs and graph isomorphism; Directed graphs; Trees and characterizations of trees, spanning trees, optimization and trees; Matchings and covers.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH324

Metric Spaces I

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Sets and functions; Absolute value and some inequalities; Convergence and continuity in real numbers; Metric spaces; Normed spaces; Convergence in metric spaces; Topological analysis of metric spaces.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH325

Metric Spaces II

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Covergence and completeness in metric spaces; Banach Fixed-point Theorem; Continuity and compactness in metric spaces.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH401

Introduction to Funtional Analysis

Fall

C

4+0

6

COURSE CONTENT

Metric spaces; Normed spaces; Linear and bounded operators; Hahn Banach theorem; Banach Steinhauss theorem; Open mapping and closed graph theorem.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH402

Graduation Exercise

Bahar

C

2+0+0

6

COURSE CONTENT

Scientific research; Scientific ethics; Literature review; Classification of resources.

Course Code

Course Name

Semester

Course

Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH403

Theory of Complex Functions

Fall-Spring

C

3+0+0

6

COURSE CONTENT

Linear and non-linear complex mappings; Conform mappings; Analytical functions; Argument theorem and related results; Riemann surfaces

Course Code

Course Name

Semester

Course Type

(C/E)

T+P+L

(Hour/Week)

ECTS

MATH404

Functional Analysis

Fall-Spring

C

3+0+0

6

COURSE CONTENT

Hilbert spaces; Compact operators; Adjoint; Self-adjoint operators; Volterra operators

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH405

Partial Differential Equations

Fall

E

3+0+0

6

COURSE CONTENT

Basic concepts and classification of partial differential equations; First order partial differential equations; Types and normal forms of second order linear differential equations; Hyperbolic, parabolic and elliptic equations; Method of separation of variables; Fourier series; Solution of one-dimensional heat and wave equations.

Course Code

Course Name

Semester

Course

Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH406

Real Analysis

Fall-Spring

C

3+0+0

6

COURSE CONTENT

Set classes; Measure function; Measurable set and measurable function; Lebesgue integrals; Lp spaces

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH407

Applied Mathematics

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Linear equation systems and operator method; Eigenvalue problems; Sturm-Liouville systems; Eigenfunctions, and orthogonal function spaces; Eigenfunction expansions; Mean convergence; Completeness; Parseval`s identity; Adjoint forms and Lagrange identity; Singular (irregular) Sturm- Liouville systems; Oscillatory solutions; Sturm separation and comparison theorems

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH409

Nonlinear Dynamical Systems

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Fixed points and stability analysis of one-dimensional models; Bifurcation and bifurcation types; Solutions of two-dimensional linear systems and classification of fixed points; Analysis of phase planes of two-dimensional nonlinear systems.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH410

Cyclic Linear Codes

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Cyclic codes, generating and parity check matrices for cyclic codes; Finite fields, minimal polynomials; Cyclic Hamming codes, BCH codes, Reed-Solomon codes, Burst error-correcting codes; Berlekamp- Massey algorithm.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH411

Module Theory

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Module definition and module examples; Submodules; Finite generated modules; Cyclic modules; Simple modules; Module homomorphisms; Module isomorphism theorems; Torsional modules; Quotient modules; Orthogonal sums of modules; Complete sequences (short complete sequences, fragmented complete sequences); Free modules and vector spaces.

Course Code

Course Name

Semester

Course

Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH412

Elliptic Functions and Integrals

Fall-Spring

C

3+0+0

6

COURSE CONTENT

Elliptic functions; Derivatives; Integrals and graphs of elliptic functions

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH413

Numerical Solutions Of Ordinary Differential Equations

Fall

E

3+0+0

6

COURSE CONTENT

Initial value problems; Difference equations; Stability, consistency and convergence analysis; Runge- Kutta methods; Extrapolation method; Stability analysis; Stiff systems; Adaptive methods; Multi-step methods; General linear multi-step methods; Predictor-corrector methods; Hybrid methods; Numerical solution methods for boundary value problems.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH415

Graph Theory

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Cuts and connectivity, k-connected graphs; Vertex colorings and upper bounds, structures of k- chromatic graphs, counting proper colorings; Embeddings and Euler`s formula, characterization of planar graphs, parameters of planarity; Line graphs and edge-colorings, Hamilton cycles.

Course Code

Course Name

Course Name

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH416

Spectral Theory II

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Periodic and antiperiodic Sturm-Liouville operators; Lagrange formula for periodic and antiperiodic Sturm-Liouville operators; Examples of finding eigenvalues and eigenfunctions; Asymptotics of the eigenvalues and eigenfunctions of periodic and antiperiodic operators; Singular Sturm-Liouville operator; General eigenvalue problems; Multiple of eigenvalues; Integral representation of the Jost solution and its asymptotics; Jost function and its properties; Resolvent operator; Examples of resolvent operator; Continuous spectrum; Zeros of Jost function and discrete spectrum.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH416

Field Extensions

Fall-Spring

S

3+0+0

6

COURSE CONTENT

Vector spaces and linear transformations; Field extensions; Algebraic extensions; Decomposition fields; Field isomorphisms and extensions; Separability; Finite extensions; Galois Theory; Galois group of polynomials; Solutions of polynomial equations

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH417

Manifolds I

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Euclidean space; Topological concepts; Differentiability in Rⁿ; Introduction to the concept of manifolds; Topological manifolds; Differentiable manifolds; Differentiable manifold examples; Smooth functions on manifolds; Smooth functions between manifolds; Diffeomorphisms; Partial derivatives; Inverse function theorem

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH418

Manifolds II

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Submanifolds; Submanifold examples; Curves on manifolds; Darboux frame; Vector bundles; Tangent vectors and tangent space on manifolds; Vector field on manifolds; Dual vector field; Derivative transformation; Pull-back transformation; Exterior derivative, inner derivative and Lie derivative; Distributions and integral manifolds; Riemann manifolds

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH420

Mathematical Biology

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Applications of difference equations and differential equations in biology; Stability, stability analysis and applications; Bifurcations, bifurcation theory and applications.

Course Code

Course Name

Course Name

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH422

Scattering Theory II

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Vector valued L1 and L2 spaces; Asymptotic equalities for vector valued functions; Dirac system; Jost solutions of Dirac system; Integral representation for Jost solution; Asymtotics of Jost solution; Scattering function of Dirac system and its properties; Scattering matrix of Dirac system and its properties; Sturm-Lioville equation on the whole real axis.

Course Code

Course Name

Semester

Course Type (C/E)

T+P+L

(Hour/Week)

ECTS

MATH423

Introduction to Geometric Topology

Fall-Spring

E

3+0+0

6

COURSE CONTENT

Product and quotient spaces; n-dimensional usual topological space; Surfaces; Connected sum; Classification of surfaces and some invariants; Graphs and trees; Simplicial complexes.