Course Descriptions for Mathematics

MTH001 Preparatory Mathematics for Engineers (3-2-4) Preparatory for MTH 103. Emphasizes the basic skills and techniques of algebra and trigonometry. Topics included are real and complex numbers, basic arithmetic, equations and inequalities, study of functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and introduction to limits. Prerequisite: Math Placement Test with grade less than D.

MTH002 Preparatory Business Mathematics (3-0-3) Preparatory for MTH 101 Mathematics for Business. Covers integers and variable expression, fractions, decimals and real numbers, basic algebraic operations, equations and inequalities, functions and graphs, polynomial and rational functions, and exponential and logarithmic functions.

MTH003 Preparatory Mathematics for Architects (3-0-3) Preparatory for MTH 111 Mathematics for Architects. Covers basic ideas and concepts of arithmetic, algebra, geometry and trigonometry and calculus applications needed for Architecture and Design.

MTH004 Pre-Calculus (3-0-3) Preparatory for MTH 103. Covers graphs and functions, exponential and logarithmic functions and their graphs, trigonometric functions of real numbers and angles, analytic trigonometry and introduction to limits. Prerequisite: Math Placement Test with grade D.

MTH100 Fundamentals of Logic and Geometry (3-0-3) Covers logic and set theory, geometry in the plane and space, and basic algebra. Topics include fundamentals of inductive and deductive reasoning; propositional and first order logic; sets, relations and functions; Euclidean and analytical geometries in two and three dimensions; and linear transformations and quadratic forms. Not open to Architecture, Architectural Studies, Engineering, Interior Design or Science students.

MTH101 Mathematics for Business I (3-0-3) Covers coordinate systems and graphs, matrices, linear systems and applications, elementary linear programming, set theory, counting techniques, permutations and combinations, introduction to probability, and the mathematics of finance. Emphasis is placed on techniques and applications. Not open to science or Engineering students. Prerequisite: MTH 002 or Math Placement Test or SAT II Math 1C test with score 600 and above.

MTH102 Mathematics for Business II (3-0-3) Covers the derivative, rules for differentiation and their applications, definite and indefinite integrals, methods of integration and applications, functions of more than one variable, partial differentiation and applications to optimization. Emphasis is placed on techniques and applications. Not open to Science or Engineering students. Prerequisite: MTH 101.

MTH103 Calculus I (3-1-3) Covers functions and limits, differentiation with applications including maxima and minima, related rates, linear approximations, Newton’s method, theory of integration with applications including areas, volumes, lengths, moments, center of mass and work. Prerequisite: MTH 001 or MTH 004 or Engineering Math Placement Test or SAT II Math 1C test with score 600 and above..

MTH104 Calculus II (3-1-3) Covers transcendental functions, exponential and logarithmic functions, trigonometric functions, techniques of integration, indeterminate forms, infinite series, power series, Talor series, parameterized curves, polar coordinates, integration in polar coordinates and complex numbers. Prerequisite: MTH 103.

MTH111 Mathematics for Architects (3-2-4) Introduces the topics of geometry and calculus needed for architecture. Reviews trigonometry, areas and volumes of elementary geometric figures, and the analytic geometry of lines, planes and vectors in two and three dimensions. Covers differential and integral calculus, including applications on optimization problems, and areas and volumes by integration. Prerequisite: MTH 001 or MTH 004 or MTH 003 or Math Placement Test or SAT II Math 1C test with score 600 and above.

MTH203 Calculus III (3-1-3) Covers calculus of functions of several variables, vectors and analytic geometry of three-dimensional space, partial derivatives, gradients, directional derivatives, maxima and minima, multiple integrals, line and surface integrals, Green’s theorem, divergence theorem and Stokes’ theorem. Prerequisite: MTH 104.

MTH205 Differential Equations (3-0-3) Covers mathematical formulation of ordinary differential equations, methods of solution and applications of first order and second order differential equations, power series solutions, solutions by Laplace transforms and solutions of first order linear systems. Prerequisite: MTH 104.

MTH213 Discrete Mathematics (Cross-listed with CMP 213). Logic, basic number theory, Graphs and trees, Math induction and recursion.

MTH221 Linear Algebra (3-0-3) Includes systems of linear equation, algebra of matrices, linear transformations, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, diagonalization and orthogonality, special matrices and applications. The use of computer software is essential. Prerequisite: MTH 104.

MTH320 Modern Algebra with applications(3-0-3): Covers Boolean algebra, groups, subgroups, cyclic groups, Lagrange’s Theorem , quotient groups, direct product of finite groups, rings, and in particular, finite fields. Applications: Circuits , Machines, Coding and decoding.

MTH325 Coding Theory (3-0-3) Introduces coding theory, linear codes, Hamming codes, Hamming distances, Hamming weights, probability, Shannon’s theorem, dual codes, weight distribution of linear codes, cyclic codes, BCH codes, convolutional codes, encoding and decoding. Prerequisite/concurrent: MTH 221

MTH341 Computational Methods (3-0-3) (Cross-listed with CMP 341). Introduces the fundamentals of numerical algorithms and their application for scientific computing. Includes topics such as error analysis, root finding, interpolation and function approximations, integration and differentiation, optimization techniques and linear programming. Prerequisite/concurrent: MTH 221.

MTH342 Numerical Linear Algebra (3-0-3) Covers direct and iterative methods for solving general and special systems of linear equations; includes LU and Choleski decomposition, nested dissection, Jacobi, Gauss-Seidel, successive overrelaxation, alternating directions and conjugate gradient methods. Also covers singular value decomposition and iterative methods for algebraic eigenvalue problem. Prerequisite: MTH 221.

MTH351 Methods of Applied Mathematics (3-0-3) Covers Fourier series, special functions, calculus of variation, curvilinear coordinates, integral transforms and integral equations. Real-world problems are used to introduce, motivate and illustrate concepts. Prerequisite/concurrent: MTH 205.

MTH360 Probability and Stochastic Processes (3-0-3) (Cross-listed as STA 360 or ELE 360 or COE 360). Covers set theory, preliminaries of probability theory and random variables, stochastic processes, Markov chains, examples of continuous time Markov chains and applications to systems. Prerequisite: MTH 221, and NGN 111 or STA 201.

MTH382 Linear Programming and Optimization (3-0-3) Introduces optimization theory and methods, nonlinear unconstrained optimization, linear programming, sensitivity analysis, various algorithms and search methods for optimization and their analysis. Examples from various disciplines are given. Prerequisite: MTH 221.

MTH412 Complex Variables (3-0-3) Studies functions of a complex variable, algebra of complex numbers, elementary functions with their mapping properties, analytic functions, power series, integration, Cauchy’s Theorem, Laurent series and residue calculus, elementary conformal mappings and boundary value problems. Prerequisite: MTH 203.

MTH418 Graph Theory (3-0-3) Covers graphs and subgraphs, connected and disconnected graphs, matrices, trees and girth, planar and nonplanar graphs, graph embeddings, connectivity and edge connectivity, Hamiltonian graphs, matchings, factorization and coverings, networks, and applications to science and engineering. Prerequisite: MTH 213 and CMP 213.

MTH432 Partial Differential Equations (3-0-3) Covers mathematical formulations and solutions of partial differential equations of physical problems, including the wave, heat and Laplace’s equation. The mathematical tools include Fourier transform, Fourier series and Laplace transform. Prerequisite: MTH 205.

MTH441 Numerical Solutions of Ordinary Differential Equations (3-0-3) Covers theory of numerical techniques for linear and nonlinear initial, boundary-value and eigenvalue problems, stiff equations and multiple time scales. The analysis of the numerical techniques focuses on consistency, accuracy, stability, stiffness, numerical efficiency, etc. Prerequisite: CMP 341 or MTH 341 or MTH 342.

MTH442 Numerical Solutions of Partial Differential Equations (3-0-3) Covers computationally efficient schemes for solving PDE numerically: finite difference schemes, stability and convergence of finite difference schemes. Introduces finite element methods. Prerequisite: MTH 441.

MTH494 Topics in Mathematics (3-0-3) Topics of current interest in mathematics not covered in existing courses. May be repeated under a different subtitle. Prerequisite: senior standing.

MTH496 Independent Study (1 to 4 credits) A theoretical or practical project initiated by an individual student and conducted under faculty supervision beyond what is offered in existing courses. Prerequisite: junior standing and approval of advisor.