Course Descriptions
MAT 211 Calculus I (3 credits)
This course is designed to introduce the basics of calculus. Topics covered include: real number system and its algebraic and analytic properties, functions and graphs, limits and applications, derivatives and applications, and an introduction to integration and applications.
Prerequisite: Placement
MAT 203 Calculus II (3 credits)
This course continues what students learnt in MAT 211. Students will be trained to deal with study of functions, transcendental functions, integration concepts and applications. Students will use the basic techniques for integration to solve a variety of applications of integration. This course also will offer an introduction to the vector in two and three-dimension spaces (dot, cross product, etc.) and complex numbers.
Prerequisite: Placement or MAT 211
MAT 213 Calculus III (3 credits)
This advanced calculus course prepares students in theory and practice by building their abilities to define, model, and solve related problems in the following topics: functions of multiple variables, partial differentiation, Conic sections, Planes and surfaces, quadratic surfaces. sequences and series, and areas in polar coordinates, Double integrals. Special emphasis is also put on the applications. Use MATLAB in the previous subjects.
Prerequisite: Placement or MAT 203
MAT 225 Probability & Statistics for Science (3 credits)
Students from the sciences and engineering programs are introduced to the basics of probability and statistics concepts. Students will cover the concepts, applications and techniques to solve related problems. Contents include probability theory, laws, models, and applications, density functions, statistical analysis using Chi-square testing, t- and f- distributions, estimation, confidence limits, significance tests, and regression analysis.
Prerequisite: MAT 213
MAT 250 Discrete Mathematics (3 credits )
This course provides students with concepts and applications for professions that use university mathematics beyond the introductory level. Topics covered include: propositional logic, induction and recursion, number theory, set theory, relations and functions, graphs and trees, and permutations and combinations.
Prerequisite: Placement or MAT 203
MAT 290 Structure of Modern Geometry (3 credits)
The main goal of this course is for students to develop the structure of Euclidean and non-Euclidean geometries logically and apply the resulting theorems and formulas to address meaningful problems. Topics covered include: Models of geometric spaces, analytic geometry, Geometric Transformations, Euclidean plane geometry, Möbius geometry, Elliptic geometry, Absolute geometry, Projective geometry, axiom systems and non-Euclidean geometries.
Prerequisite: MAT 213.
MAT 320 Linear Algebra (3 credits)
This course acquaints students with the concepts, techniques, and solutions of linear equations and matrices, vector spaces, subspaces, linear independence, bases, dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, orthogonal matrices and diagonalization. Use MATLAB in the previous subjects.
Prerequisite: MAT 213
MAT 340 Differential Equations (3 credits)
This course is a cornerstone for engineering and sciences students. It provides the students with the concepts of Differential equations with its applications. Topics covered include: classification, fundamentals, use, solution techniques, and applications of equations of the first order and second order. Also, this course familiarizes students with Fourier series and Laplace transforms and their solutions and applications, Use MATLAB in the previous subjects.
Prerequisite: MAT 213
MAT 345 Calculus IV(3 credits)
This is a fourth semester calculus course. The course begins with triple integral in rectangular, cylindrical and spherical coordinates. Next, we study the calculus of vector fields: the various differential operators (grad, curl, div) that can be applied to a function or vector field, types of integrals of vector fields (line integrals, surface integrals, Parametric surfaces, Surface Area), and the fundamental theorems (Green, Stokes, divergence or Gauss) relating differentiation and integration of vector fields. The last part of the course is an introduction to the theory of functions of a complex variable. This theory is important in many applications of mathematics, physics, and engineering, and draws upon the material of the first two thirds of the course.
Prerequisite: MAT 340
MAT 350 Numerical Analysis (3 credits)
Students are introduced to the techniques, tools, and applications of numerical analysis methods. Topics include interpolation and approximation of functions; solution of algebraic equations; numerical differentiation and integration; numerical solutions of ordinary differential equations and boundary value problems; and computer implementation of algorithms. Use MATLAB in the previous subjects.
Prerequisite: MAT 320
MAT 355 Number Theory (3 credits)
This course is an introduction to the concepts and applications of number theory. Topics covered include: divisibility of integers, prime numbers and the fundamental theorem of arithmetic, linear congruence, the Chinese remainder theorem, Euler’s j-function, polynomial congruence’s, and primitive roots. Other topics may be included as a function of time availability for example, Diophantine equations, Mobius Inversion formula, Dirichlet’s theorem, continued fractions, Pell’s equation, Louisville’s theorem, algebraic and transcendental numbers.
Prerequisite: MAT 250
MAT 360 Advance Linear Algebra with Applications (3 credits)
This is an advanced undergraduate course on linear algebra directed at students in the natural and social sciences and at engineering students. The emphasis in this course is both on theoretical considerations (with rigorous proofs of results) and on problem solving. Topics include vector spaces, linear transformations and matrix representation, spectral theory (both discrete and continuous), diagonalization of linear operators, inner products and duality, Hermitian (i.e., self-adjoint) and unitary operators, the Fourier transform, and applications to differential equations, probability theory, network analysis, and statistics.
Prerequisite: MAT 320 and MAT 340.
MAT 365 Mathematics as Problem Solving (3 credits )
This course will concentrate on solving, or attempting solve, mathematics problems. The emphasis is on exploration of various mathematics contexts to learn mathematics, to pose problems and problem extensions, to solve problems, and to communicate mathematical demonstrations. An introduction to the creative, inspirational, and playful side of mathematics exemplified in high quality middle school, high school, and undergraduate mathematics competitions and mathematical research. The problems will come from many sources and contexts. Discussion of heuristics, strategies, and methods of problem solving, and extensive practice in both group and individual problem solving. Communicating mathematics, reasoning and connections amongst topics in mathematics are emphasized.
Prerequisite: MAT 345 – MAT 360
MAT 370 Real Analysis (3 credits)
This course is an introduction to Analysis which, together with Algebra and Topology, form the central core of modern mathematics. Topics covered include: real number system, Euclidean spaces, metric spaces, calculus, sequences, series, continuity, derivatives, convergence and the concept of function that arose with the description of heat flow using Fourier series. Analysis is primarily concerned with infinite processes, the study of spaces and their geometry where these processes act and the application of differential and integral to problems that arise in geometry, partial differential equations, physics and probability.
Prerequisite: MAT 213
MAT 380: Partial Differential Equation (3 credits)
This course provides students with concepts and applications for the partial differential equations beyond the introductory level. Topic covered included: Basics concepts of PDEs, Partial differential equations as mathematical models in science (vibrating string, wave equations, Heat equations), Solutions of PDEs using Fourier series, Alembert solution of wave equation, Separable variable methods for solutions, Characteristics, Gibbs phenomenon, Sturm-Liouville Systems, Solutions of PDEs using Laplace transforms, pointwise and uniform convergence of sequences and series of functions.
Prerequisites: MAT 340.
MAT 400 Topology (3 credits)
A course designed to offer an introduction to topology. Students in this course are trained to understand and create theorem proofs. Topics covered include: topological space, separation and covering properties, and the topology of metric spaces.
Prerequisite: MAT 370
MAT 410 Functional Analysis (3 credits)
This course is designed to offer advanced topics in real analysis as continuity of MAT 370. Students are offered the opportunity to conduct a rigorous treatment of selected topics in real analysis, such as sequences of functions, Lebesgue integration, or multivariate integration and differential forms, Fubinis theorem, Limit of integrals. Emphasis is on topics like geometry and topology of Rn , Spaces of continuous functions, and Lp spaces.
Prerequisite: MAT 370 and MAT 400
MAT 420 Differential Calculus (3 credits)
An advanced course in Calculus. It covers: Differentiable mappings over an open in a normed vector space, The mean value theorem and its applications, primitives of regulated functions, and differentiation under summation sign, Local inversion theorem, Higher order derivatives and Taylor’s formula, Local and absolute extreme values, extreme values of implicit functions.
Prerequisite: MAT 370
MAT 425 Numerical Theory (3 credits)
This course continues the work in numerical analysis begin in MAT 345. It provides theoretical numerical analysis of the problems, Best approximation in the 1-norm and 2-norm, Weierstrass theorem, Equioscillation theorem, Chebyshev polynomials, Orthogonal polynomials, Numerical Integration, Interpolator rules, Romberg scheme, Gaussian quadrature. Numerical methods: one step methods and multistep methods, Euler’s method, Local truncation error, convergence, local error, Taylor series method, Runge-Kutta methods, Trapezium rule, Linear multistep methods and Absolute stability. Higher order systems. Insight into the previous algorithms will be given through MATLAB illustrations, but the course does not require any programming.
Prerequisite: MAT 350
MAT 430 Vector and Tensor Analysis (3 credits)
This course is useful for those students intending to study higher level of mathematics in the physics and engineering majors. Topics include: vector algebra and calculus, integral theorems, general coordinates, invariance, tensor analysis, and perhaps an introduction to differential geometry.
Prerequisite: MAT 345
MAT 455 Abstract Algebra (3 credits)
A course designed to provide students with knowledge and understanding of partitions and equivalence relations; properties of integers, groups, subgroups, normal subgroup and factor group, fundamental homomorphism theorem for groups, isomorphism theorems; rings, fields and Cayley's theorem.
Prerequisite: MAT 250
MAT 460 Complex Analysis (3 credits)
An advanced course in mathematics. It covers De Moivre's theorem, analytic functions of complex variables, harmonic functions, multiple - valued functions, contour integration, the Jordan curve theorem, the Cauchy Integral theorem, Taylor series, Laurent series, residues and poles, and conformal mappings.
Prerequisite: MAT 213
MAT 470 Modern Geometry (3 credits)
This course is designed to teach students deal with the geometries of the Euclidean plane, the sphere and the projective plane. Topics include congruence, isometries, affine transformations, Desargue's Theorem and Pappus Theorem.
Prerequisites:
MAT 490 Special Topics in Mathematics (1-3 credits)
Students are assigned a reading program or development of an assigned mathematical problem.
Prerequisite: Consent of Advisor
MAT 492 Special Topics in Undergraduate Research (1-3 credits)
Students apply supervised literature investigations of mathematical problems of contemporary interest.
Prerequisite: Consent of Advisor
MAT 497 Practical Training (3 credits)
Students in their junior year are required to work on part time or full time basis in order to experiment with and practice what they learned in class. A student presents a formal report by the end of this training period then he/she makes a public presentation exposing his/her experience.
Prerequisite: Consent of Advisor
MAT 499 Capstone Project (3 credits)
Students will utilize the blue prints prepared in the curriculum to deal with Mathematics Problems not encountered in regular course of study. It integrates and synthesizes concepts in Mathematics theory with applications. Topics include open-ended analysis of data, review of research literature on current techniques and practice of Mathematics and Applied Mathematics, development of mathematics communication skills and the use of computational tools in data analysis. Students are expected to introduce the method in a presentation and to prepare a comprehensive, professional report detailing the selected method and its application to a real problem.
Prerequisite: Consent of Advisor
PHY 210 Physics I (3 credits)
Introduction to mechanics. Topics covered include vectors, statics, uniform accelerated motion, energy, momentum, uniform circular motion, elasticity and simple harmonic motion. This course emphasizes the development of quantitative concepts and problem solving skills for students needing a broad background in physics as part of their preparation in other major programs.
Prerequisite: Placement or MAT 211, ENG 201
PHY 220 Physics II (3 credits)
This course provides students with the principles and applications of electricity, magnetism, light, sound, atomic physics, and nuclear physics. Topics covered include: wave motion, sound, electric field, electric potential, direct current circuits, electrochemistry, the magnetic field, electromagnetic function, flux and electromotive force.
Prerequisite: PHY 210
STA 220 Probability and Statistics for Science I (3 credits)
Students from the science and engineering programs are introduced to the basics of probability and statistics concepts. This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab, R, or other is used for data analysis and statistical applications.
Prerequisite: MAT 213
STA 230 Probability and Statistics for Science II (3 credits)
This course covers basic statistical concepts to analyze and synthesize data. Topics covered include: sampling theory, hypothesis testing, confidence intervals, point estimation, and simple correlation, non-parametric testing methods, analysis of variance and covariance, and linear regression. The statistical software package Minitab, R, or other will be used for data analysis and statistical applications.
Prerequisite: STA 220
STA 410 Mathematical Statistics I (3 credits)
This course offers students the skills to study statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. This course provides a brief review of basic probability concepts and distribution theory. It covers mathematical properties of distributions needed for statistical inference.
Prerequisite: STA 230
STA 420 Mathematical Statistics II (3 credits)
This course is a continuation of STA 410 covering classical and Bayesian methods in estimation theory, chi-square test, Nyman-Pearson lemma, mathematical justification of standard test procedures, sufficient statistics, and further topics in statistical inference.
Prerequisite: STA 410