Course Code | Course Name | Course Content |
MATH 123
Must Course |
Discrete Mathematics | Propositional Logic, Predicates and Quantifiers, Techniques of Proofs, Set Theory, Induction and Recursion, The Basics of Countings, The Pigeonhole Principle, Permutations and Combinations, Recurrence Relations, Inclusion-Exclusion and its Applications, Relations: Equivalence Relations, Partial Orders, Total Orders, Zorn’s Lemma, Axiom of Choice and its Equivalences, Graphs |
MATH 124
Must Course |
Analytic Geometry | Cartesian Coordinates in the Plane, Review of Trigonometry, Polar Coordinates, Change of Coordinates, Vectors in the Plane, Cartesian Coordinates in 3-Space, Surfaces, Cylindrical and Spherical Coordinates, Conic Sections, Vectors in 3-Space |
MATH 151
Must Course |
Calculus I | Real numbers, intervals, absolute value, Inequalities, Graphs of Quadratic Equations, parabolas, Functions, Trigonometric functions, Transcendental functions, Limits and Continuity, Limits at infinity and infinite limits, Differentiation, chain rule, The Mean Value Theorem, implicit differentiation, Applications of Derivatives (Related rates, Indeterminate Forms and L’Hôpital’s Rule, Curve Sketching, Optimization), Integration, Fundamental Theorem of Calculus, Substitution, Integration by parts |
MATH 152
Must Course |
Calculus II | Applications of Integrals (Area, Volume, Arc length, Surface Area), Sequences and Series, Convergence Tests, Power Series, Infinite Products, Vectors, Planes and Lines, Functions of Several Variables, Limits and Continuity, Partial Derivatives, The Chain Rule, Gradients and Directional Derivative, Implicit Differentiation, Extreme Values, Lagrange Multipliers, Double Integrals, Triple Integrals, Line Integrals, Conservative Vector Fields, Divergence and Curl, Green’s Theorem, Stoke’s Theorem. |
MATH 223
Must Course |
Algebra I | Groups, Subgroups, Cyclic Groups, Generators of Groups, Groups of Permutations, Alternating Groups, Cosets, Theorem of Lagrange, Direct Products, Finitely Generated Abelian Groups, Homomorphisms, Isomorphisms, Factor Groups, Simple Groups, Group action on a set, Isomorphism Theorems, Sylow Theorems |
MATH 231
Must Course |
Linear Algebra I | Systems of Linear Equations, Row Echelon Form, Matrix Algebra, Elementary Matrices, Determinants, Vector Spaces, Linear Independence, Basis and Dimension, Row Space and Column Space, Null Spaces and Ranges, Linear Transformations, Similarity |
MATH 232
Must Course |
Linear Algebra II | Inner Product Spaces, Orthogonality, Orthonormal Sets, The Gram-Schmidt Orthogonalization Process, Eigenvalues and Eigenvectors, Diagonalization, Hermitian Matrices, Positive Matrices, Normal Matrices, Real Symmetric Matrices, Unitary and Orthogonal Matrices, Bilinear and Quadratic Forms, Canonical Forms, Decompositions. |
MATH 245
Must Course |
Differential Equations | Existence-uniqueness theorem of first order initial value problems. First order equations. Higher order linear ordinary differential equations. Constant coefficient equations. Reduction of order method, method of undetermined coefficients, method of variation of parameters. Riccati equations, Cauchy-Euler equations. Power series solutions. The Laplace transforms. Convolution integral. Solution of initial value problems using Laplace transform. Solution of systems of linear differential equations. |
MATH 251
Must Course |
Advanced Calculus I | The Real line and Euclidean space, The topology of Euclidean space (open sets, Interior of a set, closed sets, accumulation points, closure of a set, boundary of a set, sequences, completeness), Compact and Connected sets (compactness, the Heine-Borel theorem, Nested set property, Path-connected sets, connected sets), Continuous Mappings, Uniform, pointwise convergences, the Weierstrass M-test, Integration and differentiation of series, the space of continuous functions, the Arzela – Ascoli theorem. |
MATH 252
Must Course |
Advanced Calculus II | Continuous functions, the Arzela – Ascoli theorem, the contraction mapping, the Stone-Weierstrass theorem, Differentiable Mappings, Differentials of transformations, Matrix representation, Differentiable paths,The chain rule, Product rule and gradients, Higher derivatives, Maxima and Minima of the functions defined on R^n, The Inverse and Implicit Function Theorems, Lagrange Multipliers, Integration, Sets of measure zero, Improper Integrals, Fubini’s Theorem and the change of variables formula, Fourier Analysis, Inner Product Spaces, Orthogonal Families of Functions, Fourier Series. |
MATH 282
Must Course |
Numerical Analysis | Roundoff errors, algorithms and convergence, bisection method, fixed point iteration, Newton’s method, error analysis, accelerating convergence. Interpolation and Lagrange polynomial, divided differences. Cubic splines. Numerical differentiation, Richardson’s extrapolation. Numerical integration, trapezoid, Simpson’s and Boole’s rules. Romberg integration, adaptive quadrature. Gaussian quadrature. Multiple integrals. |
MATH 311
Elective Course |
Calculus of Variations | Lagrange multipliers, Maxima and minima, the first variation. The Euler-Lagrange equations. Constraints. Natural and boundary conditions.Transversality conditions. The Hamiltonian formulation. |
MATH 315
Must Course |
Partial Differential Equations | First order equations; linear, quasilinear, and nonlinear equations; classification of second order linear partial differential equations; canonical forms; the Cauchy problem for the wave equation; Laplace and heat equations (Sturm-Liouville Problems) |
MATH 322
Elective Course |
Fuzzy Sets | The notion of membership, The concept of fuzzy subsets, Simple operations on fuzzy sets. Properties of the set of fuzzy subsets. Product and algebraic sum of two fuzzy subsets. Fuzzy graphs. Fuzzy relations. Properties of fuzzy binary relations. |
MATH 323
Must Course |
Algebra II | Rings, Fields, Integral Domains,Fermat’s and Euler’s Theorems, The Field of quotients of an integral domain, Rings of Polynomials, Factorization of Polynomials over a Field, Homomorphisms, Factor Rings, Prime Ideals, Maximal Ideals, Unique Factorization Domains, Euclidean Domains, Gaussian Integers, Field Extensions, Algebraic Extensions, Finite Fields. |
MATH 324
Must Course |
Introduction to Probability and Statistics | Statistical Inference, Sampling Procedures, Statistical Modeling, Graphical Methods, Data Description, Sample Spaces, Events, Algebra of Events, Probability of Events, Conditional Probability, Bayes’ Rule, Random Variables, Joint Random Variables, Mathematical Expectation, Variance, Covariance, Discrete Random Variables: Binomial, Hypergeometric, Negative Binomial, Geometric and Poison Distribution, Continuous Random Variables: Normal, Gamma and Exponential Distribution, Random Sampling, Sampling Distributions, Central Limit Theorem, t-Distribution, F-Distribution |
MATH 342
Must Course |
Applied Mathematics | Classification of Linear Integral Equations, Solution of an Integral Equation, Converting Volterra Equation to an ODE, Converting IVP to Volterra Equation, Converting BVP to Fredholm Equation, Fredholm Integral Equations, Volterra Integral Equations, Fredholm Integro-Differential Equations, Volterra Integro-Differential Equations, Real World Applications |
MATH 352
Must Course |
Complex Calculus | Complex numbers. Complex functions and linear mappings of regions. Limits and continuity. Branches of functions. Differentiable and analytic functions. Harmonic, Elementary functions. Contours and contour integrals. The Cauchy-Goursat theorem. Cauchy integral formula. Taylor and Laurent series representations. Singularities, zeros, and poles. The residue theorem and its applications to evaluation of trigonometric and improper integrals. The argument principle and Rouché’s theorem. |
MATH 366
Elective Course |
Elementary Number Theory | Divisibility. The linear Diophantine equation. Primes. Congruences. Euler, Fermat, Wilson, Lagrange and Chinese Remainder Theorems. Arithmetical functions. |
MATH 371
Elective Course |
Introduction to Fractional Differential Equations | Mittlag-Leffler Functions; Riemann-Liouville fractional integrals and derivatives; Caputo fractional derivatives; Grünwald-Letnikov fractional derivative; Riesz fractional integro-differentiation ordinary differential equations; fractional Laplace transform; Cauchy type problems. |
MATH 373
Elective Course |
History of Mathematics | The following periods of history of mathematics will be studied: Mathematical Periods, Egyptian and Babylonian Period (2000 B.C.- 500 B.C.) Greek Mathematics Period, (500 B.C- A.D.500) Hindu, Islamic and Period of Transmission (A.D.500-A.D.1700), Classic Period (A.D. 1700-A.D.1900) Modern Period (A.D.1900- present). |
MATH 381
Must Course |
Scientific Computation | Ordinary differential equations and initial value problems. Euler’s method. Higher order Taylor methods. Runge-Kutta methods. Error control, systems of ordinary differential equations and higher order equations. Linear systems of equations. Operations of linear algebra. Gaussian elimination. Pivoting strategies, LU factorization. Eigenvalues. Iterative methods of Gauss-Seidel and Jacobi. Applications with MATLAB. |
MATH 386
Elective Course |
Introduction to Mathematical Modelling | Discrete dynamical systems. Optimization models and Linear Programming. Correlation and regression. Discrete and continuous probabilistic models. Predator-prey models, optimal harvesting, traffic flow. Verification and validation of models. |
MATH 402
Elective Course |
Dynamical Systems and Chaos | One dimensional maps. Fixed points and stability. Periodic points. Sensitive dependence on initial conditions. Chaos. Lyapunov exponents. Chaotic orbits. Fractals. Cantor set. Deterministic systems. Fractal dimensions. |
MATH 410
Elective Course |
Special Functions | Gamma function. Beta function. Bessel’s and generalized Bessel’s function. Orthogonal polynomials. Chebyshev, Legendre, Hermite, Laguere, Jacobi polynomials, Hypergeometric functions. |
MATH 414
Must Course |
Real Analysis | Sets of Measure zero, Borel sets, Measurable functions, Lebesgue integrals, Properties, Lebesgue integration for bounded measurable functions,Lebesgue integration for unbounded functions, the monotone and dominated convergence theorems, The L^p Spaces: Completeness and Approximation, the construction of the Lebesgue measure on R^d. |
MATH 417
Elective Course |
Introduction to Difference Equations | The difference calculus, first order equations, linear equations, equations with constant coefficients, equations with variable coefficients, undetermined coefficients method, variation of parameters method, the Z-transform, linear systems, stability theory. |
MATH 418
Elective Course |
Calculus on Time Scales | Basic Definitions, Differentiation, Integration, First Order Linear Equations, Second Order Linear Equations, Laplace Transform, Self-Adjoint Equations, Boundary Value Problems and Green’s Function, Eigenvalue Problems. |
MATH 427
Elective Course |
Introduction to Cryptography | History and overview of cryptography, The Basic Principles of Modern Cryptography, Private-Key Cryptography; One time pad and stream ciphers, Block ciphers, PRPs and PRFs, Attacks on block ciphers. Message Integrity; Collision resistant hashing, Authenticated encryption: security against active attacks. Public-Key Cryptography; Cryptography using arithmetic modulo primes, Public key encryption, Arithmetic modulo composites. Digital Signatures. |
MATH 428
Elective Course |
Introduction to Representation Theory | GroupRepresentations, FG-modules,GroupAlgebras, Maschke’sTheorem, Schur’sLemma, irreduciblemodulesandgroupalgebras, characters, charactertables. |
MATH 451
Must Course |
Topology | Topological. Spaces; definitions, bases and subbases; continuous closed and open functions; homeomorphisms; countability axioms; separation axioms; compactness; product and quotient topologies; connectedness; metric and normed spaces; function spaces, Ascoli’s theorem, compact open topology. |
MATH 452
Elective Course |
Functional Analysis | Metric Spaces, Completion of Metric Spaces, Normed Spaces, Finite Dimensional Normed Spaces, Bounded Linear operators, Linear Functional, Dual Space, Inner Product Spaces and Hilbert Spaces, Riesz Representation Theorem, Hilbert Adjoint Operator; Self-Adjoint, Unitary and Normal Operators; Hahn-Banach Theorem, Uniform Boundedness Principle, Strong and Weak Convergence. |
MATH 461
Must Course |
Mathematician’s Introduction to Modern Computer Science | The course covers a number of modern computer software technologies which have taken significant input from mathematicsThese technologies or applications range from explicit mathematical software such as Matlab, to the likes of web search, e-commerce and social networking. |
MATH 476
Must Course |
Differential Geometry | Curves in R^3, the local theory of curves parametrized by arc length, Frenet-Serret formulas,curvature and torsion. Regular surfaces, the tangent plane, the differential of a map, diffeomorphism, the first fundamental form, Gauss map, the second fundamental form, normal curvature, principal curvature, Gauss map in local coordinates. |
MATH 491
Must Course |
Graduation Project I | A practical / theoretical training in mathematics / modelling / computer / simulation. A report and presentation are required for the completion of the course. |
MATH 492
Must Course |
Graduation Project II | A practical / theoretical training in mathematics / modelling / computer / simulation. A report and presentation are required for the completion of the course. |
Undergraduate Course Descriptionswmultisite2017-06-23T00:22:48+03:00