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 BSc Degree in Mathematics - Course Description

Degree Plan | Requirements | Course Descriptions

MATH 101Calculus I(4-0-4)
Limits and continuity of functions of a single variable. Differentiability. Techniques of differentiation. Implicit differentiation. Local extrema, first and second derivative tests for local extrema. Concavity and inflection points. Curve sketching. Applied extrema problems. The Mean Value Theorem and applications. 
PrerequisiteOne year preparatory mathematics or its equivalent
 

MATH 102Calculus II(4-0-4)
Definite and indefinite integrals of functions of a single variable. Fundamental Theorem of Calculus. Techniques of integration. Hyperbolic functions. Applications of the definite integral to area, volume, arc length and surface of revolution. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series. ​ ​
PrerequisiteMath 101
 
MATH 105Finite Mathematics(3-0-3)
Linear equations and inequalities. Systems of linear equations. Basic material on matrices. Elementary introduction to linear programming. Counting techniques. Permutations and combinations. Probability for finite sample space. Basic concepts in statistics. Topics in the mathematics of finance. ​ ​
PrerequisiteOne year preparatory mathematics or its equivalent
 
MATH 106Applied Calculus(3-0-3)
The derivative. Rules for differentiation. Derivative of logarithmic, exponential, and trigonometric functions. Differentials. Growth and decay models. Definite and indefinite integrals. Techniques of integration. Integrals involving logarithmic, exponential and trigonometric functions. Integration by tables. Area under a curve and between curves. Functions of several variables. Partial derivatives and their applications to optimization. ​ ​
PrerequisiteOne year preparatory mathematics or its equivalent
 
MATH 201Calculus III(3-0-3)
Definite and indefinite integrals of functions of a single variable. Fundamental Theorem of Calculus. Techniques of integration. Hyperbolic functions. Applications of the definite integral to area, volume, arc length and surface of revolution. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series. ​ ​
PrerequisiteMath 102
Math 202Elements of Differential Equations(3-0-3)
First order and first degree equations. The homogeneous differential equations with constant coefficients. The methods of undetermined coefficients, reduction of order, and variation of parameters. The Cauchy-Euler equation. Series solutions. Systems of linear differential equations. Applications to linear models of first and second order. ​ ​
PrerequisiteMath 102
 
Math 208Introduction to Differential Equations & Linear Algebra(3-0-3)

Systems of linear equations. Rank of matrices. Eigenvalues and eigenvectors. Vector spaces, subspaces, bases, dimensions. Invertible matrices. Similar matrices. Diagonalizable matrices. Block diagonal and Jordan forms. First order differential equations: separable and exact. The homogeneous differential equations with constant coefficients. Wronskian. Nonhomogeneous differential equations. Methods of undetermined coefficients and variation of parameters. Systems of differential equations. Non-homogeneous systems. Applications to linear models of first and second order.

Note: Not to be taken for credit with MATH 202 or MATH 225

PrerequisiteMath 102
 
MATH 210Introduction to Sets and Structures(3-0-3)

Elementary logic. Methods of proof. Set theory. Relations and functions. Finite and infinite sets. Equivalence relations and congruence. Divisibility and the fundamental theorem of arithmetic. Well-ordering and axiom of choice. Groups, subgroups, symmetric groups, cyclic groups and order of an element, isomorphisms, cosets and Lagrange's Theorem.

Note: Not to be taken for credit with ICS 253

PrerequisiteMath 102
 
MATH 225Introduction to Linear Algebra(3-0-3)
Matrices and systems of linear equations. Vector spaces and subspaces. Linear independence. Basis and dimension. Inner product spaces. The Gram-Schmidt process. Linear transformations. Determinants. Diagonalization. Real quadratic forms. Applications as mini Projects. ​ ​
PrerequisiteMath 102
MATH 302Engineering Mathematics(3-0-3)

Vector analysis including vector fields, gradient, divergence, curl, line and surface integrals, Gauss' and Stokes' theorems. Introduction to complex variables. Vector spaces and subspaces. Linear independence, basis and dimension. Solution of linear equations. Orthogonality. Eigenvalues and eigenvectors. Applications to systems of differential equations.

Note: Not to be taken for credit with MATH 225 or MATH 333

PrerequisiteMath 201
 
MATH 310Logic and Set Theory(3-0-3)
The Propositional Logic, First-order predicate calculus. Truth and Models. Soundness and Completeness for Propositional Logic. Deduction. Models of Theories. Interpretations. Soundness and Completeness Theorems for first-order logic. The Compactness Theorem. Nonstandard models. Naive Set Theory. Zermelo-Fraenkel Axioms. Wellorders and Ordinal Numbers. ON as a proper class. Arithmetic of Ordinals. Transfinite Induction and Recursion. Cardinality. Goodstein Sequences. ​ ​
PrerequisiteMATH 210 
 
MATH 315Development of Mathematics(3-0-3)

History of numeration: Egyptian, Babylonian, Hindu and Arabic contributions. Algebra: including the contributions of Al-Khwarizmi and Ibn Kura. Geometry: areas, approximation of , the work of Al-Toussi on Euclid's axioms. Analysis. The calculus: Newton, Leibniz, Gauss. The concept of limit: Cauchy, Laplace. An introduction to some famous old open

problems.

PrerequisiteMATH 102 or Math 106
 
MATH 323Modern Algebra I(3-0-3)
Review of basic group theory including Lagrange's Theorem. Normal subgroups, factor groups, homomorphisms, fundamental theorem of finite Abelian groups. Examples and basic properties, integral domains and fields, ideal and factor rings, homomorphisms. Polynomials, factorization of polynomials over a field, factor rings of polynomials over a field. Irreducibles and unique factorization, principal ideal domains. ​ ​
PrerequisiteMATH 210 or (ICS 253, ICS 254)
MATH 325Linear Algebra(3-0-3)
Theory of vector spaces and linear transformations. Direct sums. Inner product spaces. The dual space. Bilinear forms. Polynomials and matrices. Triangulation of matrices and linear transformations. Hamilton-Cayley theorem. ​ ​
PrerequisiteMath 225
 
MATH 333Methods of Applied Mathematics I(3-0-3)
Special functions. Bessel's functions and Legendre polynomials. Vector analysis including vector fields, divergence, curl, line and surface integrals, Green's, Gauss' and Stokes' theorems. Sturm-Liouville theory. Laplace transforms. Fourier series and transforms. Introduction to partial differential equations and boundary value problems in rectangular, cylindrical and spherical coordinates. ​ ​
PrerequisiteMath 201, MATH 202 or MATH 208
 
MATH 336Mathematical Models in Biology(3-0-3)
Growth models, Single species and interacting population dynamics. Dynamics of infectious diseases. Modeling enzyme dynamics. Some fatal diseases models. Programing software for numerical simulations. ​ ​
PrerequisiteMATH 202 or MATH 208
 
MATH 341Advanced Calculus I(3-0-3)
The real number system. Continuity and limits. Uniform continuity. Differentiability of functions of one variable. Definition, existence and properties of the Riemann integral. The fundamental theorem of calculus. Sequences and series of real numbers. ​ ​
PrerequisiteMath 210 or ICS 253
 
MATH 353Euclidean and Non-Euclidean Geometry(3-0-3)
Classical Euclidean and non-Euclidean geometries. Matrix representations of transformations in R3. Isometries. Transformation and symmetric groups. Similarity and affine transformations. ​ ​
PrerequisiteMath 210
MATH 371Introduction to Numerical Computing(2-2-3)

Floating-point arithmetic and error analysis. Solution of non-linear equations. Polynomial interpolation. Numerical integration and differentiation. Data fitting. Solution of linear algebraic systems. Initial and boundary value problems of ordinary differential equations; Using computer software as a computational platform.

Note: Not to be taken for credit with CISE 301

PrerequisiteMath 201
 
MATH 399Summer Training(0-0-2)
Students are required to spend one summer working in industry prior to the term in which they expect to graduate. Students are required to submit a report and make a presentation on their summer training experience and the knowledge gained. The student may do his summer training by doing research and other academic activities ​ ​
PrerequisiteENGL 214, Junior Standing, Approval of the Department
 

Math 405

Learning from Data

(3-0-3)

Basic vector and matrix operations, Factorizations, Basic Probability Theory, Inference, LeastSquare Estimation, Maximum Likelihood Estimation, Gradient Descent, Linear Regression and Neural Networks. ​ ​
PrerequisiteMATH 102 or MATH 106 and STAT 201 or 212, or 319 or ISE 205, and ICS 103
 
Math 423Modern Algebra II(3-0-3)
Finite and finitely generated Abelian groups. Solvable groups. Nilpotent groups. Sylow theorems. Factorization in integral domains. Principal ideal domains. Fields. Field extensions. Finite fields. An introduction to Galois theory. ​ ​
PrerequisiteMATH 323
 
MATH 424Applied Algebra(3-0-3)
Boolean algebras. Symmetry groups in three dimensions. Polya-Burnside method of enumeration. Monoids and machines. Introduction to automata theory. Error correcting codes. ​ ​
PrerequisiteMath 323
MATH 427Number Theory(3-0-3)
Divisibility and primes. Congruences. Positive roots. Quadratic reciprocity. Arithmetic functions. Diophantine equations. Applications (e.g. cryptography or rational approximations). ​ ​
PrerequisiteMATH 210 or Senior Standing
 
MATH 432Applied Matrix Theory(3-0-3)
Review of the theory of linear systems. Eigenvalues and eigenvectors. The Jordan canonical form. Bilinear and quadratic forms. Matrix analysis of differential equations. Variational principles and perturbation theory: the Courant minimax theorem, Weyl's inequalities, Gershgorin's theorem, perturbations of the spectrum, vector norms and related matrix norms, the condition number of a matrix. ​ ​
PrerequisiteMATH 208 or MATH 225 or MATH 302
 
MATH 433Methods of Applied Mathematics II(3-0-3)
Introduction to linear spaces and Hilbert spaces. Strong and weak convergence. Orthogonal and orthonormal systems. Integral Equations: Fredholm and Volterra equations. Green's Function: Idea of distributions, properties of Green's function and construction. Any one of the following topics: Asymptotic Methods: Laplace method, Steepest descent method, Perturbation Theory: regular and singular perturbations, Integral Transforms: Fourier, Laplace, Mellin and Hankel transforms. ​ ​
PrerequisiteMath 333
 
MATH 434Calculus of Variations and Optimal Control(3-0-3)
Introduction to the calculus of variations. Euler-Lagrange, Weierstrass, Legendre and Jacobi necessary conditions. Formulation of optimal control problems. Bolza, Mayer and Lagrange formulations. Variational approach to optimal control. Pontryagin maximum principle. ​ ​
PrerequisiteMath 202 or Math 208
 
MATH 435Ordinary Differential Equations(3-0-3)
First order scalar differential equations. Initial value problems. Existence, uniqueness, continuous dependence on initial data. Linear systems with constant coefficients. The exponential matrix. Asymptotic behavior of linear and almost linear systems. Two dimensional autonomous systems. Critical points and their classifications. Phase plane analysis. Introduction to the theory of Lyapunov stability. ​ ​
Prerequisite(Math 202, Math 225) or Math 208
MATH 436Discrete Models(3-0-3)
Difference equations and discrete dynamical systems, linear and nonlinear models, linear and nonlinear systems, stability and well-posedness, models and numerical experiments (from different fields of science and engineering). ​ ​
PrerequisiteMath 202 or Math 208
 
MATH 437Partial Differential Equations(3-0-3)
Systems of linear equations. Rank of matrices. Eigenvalues and eigenvectors. Vector spaces, subspaces, bases, dimensions. Invertible matrices. Similar matrices. Diagonalizable matrices. Block diagonal and Jordan forms. First order differential equations: separable and exact. The homogeneous differential equations with constant coefficients. Wronskian. Nonhomogeneous differential equations. Methods of undetermined coefficients and variation of parameters. Systems of differential equations. Non-homogeneous systems. ​ ​
PrerequisiteMath 333
 
MATH 441Advanced Calculus II(3-0-3)
Theory of sequences and series of functions. Real functions of several real variables: limit, continuity, differentiability. Taylor's theorem. Maxima and minima, Lagrange multipliers rule. Elementary notion of integration on RN. Change of variables in multiple integrals, Fubini's theorem. Implicit and inverse function theorems. Convergence and divergence of improper integrals- Differentiation under the integral sign. ​ ​
PrerequisiteMath 341
 
MATH 443Advanced Calculus III
Functions of bounded variation. The Riemann-Stieltjes integral. Implicit and inverse function theorems. Lagrange multipliers. Change of variables in multiple integrals. Vector functions and fields on Rn. Line and surface integrals. Green's theorem. Divergence theorem. Stokes' theorem. ​ ​
PrerequisiteMath 441
 
MATH 445Introduction to Complex Variables(3-0-3)
The theory of complex analytic functions, Cauchy's integral theorem, contour integrals, Laurent expansions, the residue theorem with applications, evaluation of improper real integrals and series, conformal mappings. ​ ​
PrerequisiteMath 201
MATH 451Differential Geometry(3-0-3)

Curves in 3-dimensional Euclidean space: the Frenet frame and formulae, curvature and torsion, natural equations. Surfaces in 3-dimensional Euclidean space: tangent plane, first fundamental form and isometries, second fundamental forms, normal and principal curvatures, Gaussian and mean curvatures, geodesics. Geometry of the sphere and the disc (with Poincare metric).

PrerequisiteMath 208 or MATH 225 or MATH 302
 
MATH 453Introduction to Topology(3-0-3)
Topological Spaces: Basis for a topology, The order topology. The subspace topology. Closed sets and limit points. Continuous functions. The product topology, The metric topology. Connected spaces. Compact spaces. Limit point compactness. The countability axioms. The separation axioms. Complete metric spaces. ​ ​
PrerequisiteMath 341
 
MATH 463Combinatorics(3-0-3)
Enumerative techniques, Recurrence relations, Generating functions, Principle of inclusionexclusion, Introduction to graph theory, selected topics (e.g. Ramsey Theory, Optimization in graphs and networks, Combinatorial designs, Probabilistic methods.) ​ ​
PrerequisiteMath 201
 
MATH 467Graph Theory
Graphs and digraphs. Degree sequences, paths, cycles, cut-vertices, and blocks. Eulerian graphs and digraphs. Trees, incidence matrix, cut-matrix, circuit matrix and adjacency matrix. Orthogonality relation. Decomposition, Euler formula, planar and nonplanar graphs. Menger's theorem. Hamiltonian graphs. ​ ​
PrerequisiteMath 208 or Math 225 Or Math 302
 
MATH 471Numerical Analysis I(3-0-3)
Floating-point, round-off analysis. Solution of linear algebraic systems: Gaussian elimination and LU decomposition, condition of a linear system, error analysis of Gaussian elimination, iterative improvement. Least squares and singular value decomposition. Matrix eigenvalue problems. ​ ​
PrerequisiteMath 371 or CISE 301
MATH 472Numerical Analysis II(3-0-3)
Approximation of functions: Polynomial interpolation, spline interpolation, least squares theory, adaptive approximation. Differentiation. Integration: basic and composite rules, Gaussian quadrature, Romberg integration, adaptive quadrature. Solution of ODEs: Euler, Taylor series and Runge-Kutta methods for IVPs, multistep methods for IVPs, systems of higher-order ODEs. Shooting, finite difference and collocation methods for BVPs. Stiff equations. ​ ​
PrerequisiteMath 371 or CISE 301
 
MATH 474Linear & Nonlinear Programming(3-0-3)
Formulation of linear programs. Basic properties of linear programs. The simplex method. Duality. Necessary and sufficient conditions for unconstrained problems. Minimization of convex functions. A method of solving unconstrained problems. Equality and inequality constrained optimization. The Lagrange multipliers theorem. The Kuhn-Tucker conditions. A method of solving constrained problems. ​ ​
PrerequisiteMath 201
 
MATH 475Wavelets and Applications(3-0-3)
Wavelets. Wavelet transforms. Multiresolution analysis. Discrete wavelet transform. Fast wavelet transform. Wavelet decomposition and reconstruction. Applications such as boundary value problems, data compression, etc. ​ ​
PrerequisiteMath 225 or MATH 302
 
MATH 477Foundation of Scientific Computing(3-0-3)
Concepts of numerical mathematics, approximation tools, system of equations, least squares, numerical differentiation and integration, quadrature on different geometries, Runge-Kutta and multistep methods for initial value problems, finite difference methods for initial and boundary value problems. Applications to steady-state and time-dependent problems.  ​
PrerequisiteMath 102
 
MATH 481Computational Inverse Problem(3-0-3)
Regression, Least squares, Maximum likelihood estimation, Rank deficiency, Ill-conditioning, Generalized and Truncated SVD solutions, regularizations (Tikohonov, spectral filtering), proximal and primal-dual iterative schemes, Nonlinear inverse (gradient-based and global optimization methods), OCCAM method. ​ ​
PrerequisiteMath 405 or consent of the instructor
MATH 490Seminar in Mathematics(1-0-1)
This course provides a forum for the exchange of mathematical ideas between faculty and students under the guidance of the course instructor. Students are expected to do research on a mathematical problem of their choice or the instructor's. The instructor arranges weekly presentations by himself, other faculty members and/or students, of lectures or discussions on topics or problems of general interest. The course culminates in the presentation by each student of at least one written report on a selected topic or problem, reflecting some independent work and evidence of familiarity with the mathematical literature. With the permission of the instructor, students may work with other faculty members in the preparation of written reports. ​ ​
PrerequisiteAny two of { Math 323, Math 333, Math 341, Math 371}
  
MATH 498Topics in Mathematics I(1-3, 0, 1-3)

Variable contents. Open for Senior students interested in studying an advanced topic in mathematics.

Note: May be repeatefor a maximum of three credit hours total.

PrerequisiteSenior Standing, Permission of the Department Chairman upon recommendation of the instructor
 
MATH 499Topics in Mathematics II(1-3, 0, 1-3)

Variable contents. Open for Senior students interested in studying an advanced topic in mathematics.

Note: May be repeated for a maximum of three credit hours total.

PrerequisiteSenior Standing, Permission of the Department Chairman upon recommendation of the instructor

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