MATH 112. Basic Mathematics I. (3 Credits)

Problem solving, real numbers, algebraic expressions, linear equations, systems of linear equations, proportions, geometry, graphs of linear functions, mathematics of finance.

MATH 113. Basic Mathematics II. (3 Credits)

The second part of a basic mathematics sequence. Sets, logic, probability and statistics. Prerequisite: MATH 112.

MATH 120. College Algebra. (3 Credits)

Functions and their graphs, transformation of functions, polynomial, rational, exponential and logarithmic functions, systems of equations; applications of these algebraic concepts to other disciplines.

MATH 121. Trigonometry. (3 Credits)

Trigonometric functions and their graphs, Trigonometric identities, inverse trigonometric functions, analytic trigonometry, and applications of trigonometry.

MATH 122. Finite Mathematics. (3 Credits)

Systems of linear equations and inequalities, introduction to matrices and linear programming, mathematics of finance, sets, counting and probability.

MATH 130. Number And Operations. (3 Credits)

ONLY for students seeking certification to reach PreK - 3/PreK - 6 Number systems and operations, elementary number theory, concepts of integers and rational number, proportions, computational algorithims, current techniques in a problem-solving environment. Including student investigations and hands-on activities.

MATH 131. Algebra And Functions. (3 Credits)

ONLY for students seeking certification to teach PreK - 3/PreK - 6 Basic algebraic operations, linear and quadratic equations, linear systems of equations and inequalities, algebraic functions in the context of modeling and various representations of functions (graphical, tabular, and symbolic). Will include student investigations and hands-on activities. Prerequisites: MATH 130.

MATH 150. Precalculus. (4 Credits)

Functions, Polynomial and rational functions, Inverse functions, exponential logarithmic functions, trigonometric functions and their inverses, transformations, polynomial division, roots of polynomials, partial fraction decomposition. Students successfully completing this course cannot take MATH 120 or MATH 121 for credit.

MATH 212. Business Calculus. (3 Credits)

Limits, continuity, derivatives and its applications in business, introduction to integrations. This course cannot be taken as a Mathematics elective by Mathematics majors. Prerequisites: MATH 120.

MATH 230. Geometry And Measurement. (3 Credits)

A basic study of properties and relationships of polygons and polyhedral, transformation geometry, coordinate geometry, construction, deductive and inductive reasoning, the processes of measurement through geometric investigations, and an introduction to non-Euclidean geometries. This course does not satisfy the requirements of MATH 340. ONLY for students seeking certification to reach PreK - 3/PreK - 6 Prerequisites: MATH 131.

MATH 260. Calculus I. (4 Credits)

Analytic geometry, limits, continuity, derivatives and its applications, introduction to integrations. Prerequisite: MATH 150 or MATH 121.

MATH 261. Calculus II. (4 Credits)

Techniques and applications of integrations, improper integrals, sequences and series, differentiation and integration of power series, Prerequisites: MATH 260.

MATH 280. Discrete Math Computer Science. (3 Credits)

Fundamental techniques in discrete mathematics for application in computer science. Sets, mathematical logic, proof techniques, relations, functions, mathematical induction, counting principle, and analysis of algorithms. Prerequisites: MATH 150.

MATH 284. Discrete Mathematics I. (3 Credits)

Logical statements, truth tables and logical equivalences, Boolean algebra, predicates and quantifies, proof techniques such as direct proof, by cases, by contraposition, and by contradiction, mathematical induction and recursion, proofs with sets and an introduction to counting. Prerequisite: MATH 150.

MATH 285. Discrete Mathematics II. (3 Credits)

Duality, mathematical induction and contradiction, recurrence relations, posets and sorting, vectors and matrices, planar and non-planar graphs, networks, error propagation, combinatorics, circuits, lattices, algebraic systems and machines, algorithms for flowcharting and programming. Prerequisite: MATH 284 Discrete Mathematics I or MATH 280 Discrete Mathematics for Computer Scientists.

MATH 290. Foundations Of Mathematics. (3 Credits)

A study of the development of mathematical concepts and of the great mathematicians who introduced these concepts; development of integral and differential calculus, development of concepts in modern algebra and the use of rigorous set theory as the foundation for analysis, algebra and topology. Prerequisite: MATH 261 Calculus II or concurrent with MATH 261.

MATH 292. Introduction to Number Theory. (3 Credits)

Divisibility theory and prime numbers, Euclidean algorithm, unique factorization, congruences, linear Diophantine equations, and quadratic reciprocity. Prerequisites: MATH 150.

MATH 294. Mathematics of Finance I. (3 Credits)

Interest rates, accumulated and discount function, annuities, forborne and deferred, perpetuities, amortization. Prerequisite: MATH 261.

MATH 295. Mathematics Of Finance II. (3 Credits)

Financial markets and derivatives, hedging and arbitrage pricing. Binomial model. Introduction to stochastic processes and their calculus. The Black-Scholes equations and solutions. Models with continuous dividends. Prerequisite(s): MATH 294, STAT 330 or STAT 340.

MATH 298. Internship in Mathematics I. (1 Credit)

The internship allows students to obtain practical work experience related to mathematics under closely supervised conditions for approximately 45 clock hours. Students must complete a Memorandum of Agreement prior to commencing the internship. Course may be taken more than once for credit but no more than 3 times. Prerequisite: Junior standing and permission of department.

MATH 299. Introd Problem Solving Seminar. (3 Credits)

A seminar-based approach which examines areas including the appropriate uses of technology, cooperative learning projects, problem-solving, and mathematics content on the state mandated licensing examination for secondary mathematics. Mathematical topics will include algebra and number theory, measurement, trigonometry, functions, and calculus and basic probability theory. Prerequisite: MATH 261.

MATH 300. Foundation of Mathematics. (3 Credits)

Review of proof techniques and sets, functions and relations, posets, equivalence relations, quotient sets, cardinal numbers, recurrence relations, and introduction to graph theory. Prerequisite: MATH 280 or MATH 284.

MATH 317. Stochastic Processes. (3 Credits)

Conditional probability and conditional expectations, continuous and discrete time stochastic processes including random walks. Markov chains, Poissons process, Brownian motion, and Gaussian processes. Prerequisites: MATH 360, STAT 330 or STAT 340.

MATH 321. Combinatorics. (3 Credits)

Techniques for counting and enumeration including recurrence relations, binominal coefficients, the principle of inclusion and exclusion, graph theory, and networks. Prerequisites: MATH 280 or MATH 284.

MATH 325. Linear Algebra. (3 Credits)

Systems of linear equations, matrices, determinants, vector spaces, bases, dimensions, linear independence, eigenvalues and eigenvectors, and linear transformations. Prerequisite: MATH 260.

MATH 335. Mathematical Modeling. (3 Credits)

Formulation and analysis of mathematical models with applications to Biology, Finance, Engineering and other areas of science. Prerequisite: MATH 261.

MATH 340. Euclidean & Noneuclid Geomet I. (3 Credits)

A study of the foundations of Euclidean geometry including transformations deductive and inductive reasoning and an introduction to non-Euclidean geometries. Prerequisite: MATH 260.

MATH 341. Euclidean & Noneucl Geometr II. (3 Credits)

Euclidean geometry, logic and incidence geometry, Hilbert’s axioms, projective geometry, neutral geometry, parallel postulate - history and independence, Non-Euclidean geometry, geometric transformations, hyperbolic geometry and philosophical implications. Prerequisite: MATH 340.

MATH 348. Introduction to Game Theory. (3 Credits)

Introduction to game theory, the study of strategic behavior among parties having opposed, mixed or similar interests. Topics include social choice functions, May’s Theorem, Pareto and Condorcet criteria, Arrow’s Impossibility Theorem, zero-sum games, best responses and saddle points, mixed strategies, neutralizing strategies, bi-matrix games, solving 2-by-2 bi-matrix games, Nash equilibria, and the Prisoner’s Dilemma. Prerequisite: MATH 325.

MATH 350. Differential Equations. (3 Credits)

Introduction to differential equations, initial value problems, modeling and solutions of first-order differential equations, solutions of higher-order differential equations, boundary value problems, series solutions, Laplace transform. Prerequisite: MATH 261.

MATH 352. Intro to Mathematical Biology. (3 Credits)

This course is designed to develop mathematical models in biology and study the behavior of such models using numerical techniques and review the mathematical concepts behind many important biological principles. Topics will be drawn from conversation biology, genetics, and physiology. Mathematics and computational methods to be reviewed include functions in biology, difference and differential equations, integration as needed, probability, numerical matrix algebra and curve fitting software. Students can receive credit either for MATH 352 or BIOL 352 but not for both. Prerequisites: MATH 260 Calculus I, BIOL 120 Principles of Biology I and BIOL 121 Principles of Biology II, or consent of instructor.

MATH 355. Dynamical Systems & Chaos. (3 Credits)

Existence and uniqueness for solutions of ordinary differential equations and difference equations, linear systems, nonlinear systems, stability, periodic solutions, bifurcation theory. Prerequisite: MATH 350.

MATH 360. Calculus III. (4 Credits)

Polar coordinates, parametric equations, calculus of vector-valued functions, partial derivatives, multiple integrals, line and surface integrals, Lagrange multipliers, Curl and divergence, Green's and Stokes' Theorems. Applications. Prerequisite: MATH 261.

MATH 380. Seminar in Actuarial Science. (3 Credits)

Application of the fundamental probability tools to problems encountered in actuarial science. Risk management and insurance, corporate finance, price theory, actuarial models, loss models, simulation and survival models. Course serves as the capstone course in the Actuarial Science track. Co-requisite: MATH 295.

MATH 392. Introduction Linear Programmin. (3 Credits)

Introduction to operation research, modeling with linear programming, the simplex method and sensitivity analysis, duality, degeneracy, and applications. Prerequisite: MATH 260.

MATH 395. Math Problem Solving Seminar. (3 Credits)

A capstone course designed to examine the appropriate uses of technology, cooperative learning projects, problem-solving, mathematics content on the state mandated licensing examination for Secondary Mathematics, and presentations by experienced mathematics educators and business leaders. Mathematical topics include data analysis, probability, matrix algebra and discrete mathematics. Students must register and take the state mandated licensing examination for secondary mathematics as a requirement of the course. (May not be used as a mathematics elective). Prerequisite: Admitted to Teacher Education Candidacy and MATH 299, STAT 330 or STAT 340.

MATH 398. Internship in Mathematics II. (3 Credits)

The internship allows students to obtain practical work experience related to mathematics under closely supervised conditions for approximately 135 clock hours. Students must complete a Memorandum of Agreement prior to commencing the internship. Course may be taken more than once for credit but no more than two times. Prerequisite: Junior standing and permission of department.

MATH 400. Advanced Calculus I. (3 Credits)

Reinforcing proofs with sets and functions, cardinality of sets, axiom of completeness, basic topology of real numbers, sequences, subsequences and limit theorems, properties of continuous functions, differentiation. Prerequisite: MATH 300 Foundations of Mathematics.

MATH 401. Advanced Calculus II. (3 Credits)

Differentiability, Riemann integrals, Riemann-Stieljes, improper integrals, fundamental theorem of calculus, sequence and series of functions, convergence of series, uniform convergence, power series of functions. Prerequisite: MATH 400.

MATH 415. Matrix Theory. (3 Credits)

Matrix algebra, matrix factorization, vector and matrix norms, condition numbers, singular values, diagonalization and similar matrices, Jordan canonical form. Unitary and orthogonal transformations, and the eigenvalue problems. Prerequisite: MATH 325.

MATH 417. Numerical Linear Algebra. (3 Credits)

Numerical methods for solution of linear systems, perturbation theory and linear least square problem, QR factorization, conditioning and stability of linear systems, iterative methods for linear systems, symmetric eigenvalue problems and singular value decomposition, non-symmetric eigenvalue problems. Prerequisite: MATH 325.

MATH 425. Abstract Algebra I. (3 Credits)

Groups, subgroups, cyclic groups, groups of symmetries, permutation groups, alternating group, cosets, normal subgroups, Lagrange’s theorem, quotient groups, direct product of groups, group homeomorphisms and isomorphism. Prerequisite: MATH 300.

MATH 426. Abstract Algebra II. (3 Credits)

Rings, ring homeomorphisms, subrings, ideals, quotient rings, integral domains, polynomial extensions of rings, fields and field extensions. Prerequisite: MATH 425.

MATH 429. Approximation Theory. (3 Credits)

Best approximation in normal spaces, approximation by algebraic polynomials and Weierstrass theorem, trigonometric polynomials, uniform approximation by trigonometric polynomials, Chebyshev polynomials, characterization of the best approximation, and orthogonal polynomials. Prerequisite: MATH 400.

MATH 430. Optimizations Theory. (3 Credits)

Optimization fundamentals, unconstrained and constrained optimization. Lagrange multipliers, nonlinear programming algorithms and convex optimization. Prerequisite: MATH 360.

MATH 432. Complex Variables. (3 Credits)

Brief introduction of complex numbers and its properties, Elementary functions of Complex variable, Analytic functions and its basic properties, Contour integration, Cauchy’s Theorem and Integral formula, Maximum modulus principles, Series representation of analytic functions, Taylor's Theorem, Classification of singularities, Laurent series, Calculation of residues. Prerequisite: MATH 360, MATH 400.

MATH 445. Introduction to Topology. (3 Credits)

Metric spaces, topological spaces, separation of axioms, connectedness, compactness, homeomorphisms and product spaces. Prerequisite: MATH 400.

MATH 452. Numerical Analysis. (3 Credits)

Error analysis, iterative methods for solving equations in one variable including bisection, fixed-point, Newton's and secant iterations, interpolation and polynomial approximation, numerical differentiation and integration, solutions of differential equations. Prerequisite: MATH 350.

MATH 470. History Of Mathematics. (3 Credits)

An introduction to the chronological history of mathematics and the mathematics who made significant contributions from ancient to modern time. Emphases will be given to development of mathematics from the 19th century BC to the 20th century AD. Prerequisite: MATH 300.

MATH 473. Discrete Wavelet Transfor/Appl. (3 Credits)

Introduction to digital images, complex numbers and Fourier series, convolution and filters, the Haar wavelet transformation, Daubechies wavelet transformations, wavelet shrinkage.

MATH 475. Introd to Difference Equations. (3 Credits)

Dynamics of first-order differences equations, equilibrium points and their stability, periodic points, cycles and their stability, difference equations associated to differential equations, Euler’s method, differences calculus, linear differences equations, first and higher order, homogeneous with constant coefficients, non-homogeneous by the methods of undetermined coefficients, limiting behavior of solutions, nonlinear equations transformable to linear difference equations. Prerequisites: MATH 350.

MATH 490. Graph Theory. (3 Credits)

Basic definitions of graphs, Eulerian and Hamiltonian graphs, graph decompositions, matchings, trees, bipartite graphs, vertex colorings, network algorithms planar graphs, Kuratowski's theorem and the Four-color Theorem. Prerequisites: MATH 284 or MATH 280.

MATH 493. Topics in Mathematics. (3 Credits)

Topics in mathematics not covered in ordinary courses. The course may be repeated once for credit if content is different. Prerequisite: Consent of instructor.

MATH 495. Senior Project. (1-3 Credits)

Required of all senior mathematics majors. A capstone course designed to improve students’ research skills, students will work on a research project chosen by the faculty in consultation with the students, write a paper and make a presentation at the end of the semester. Prerequisite: Senior academic standing.

MATH 499. Gre Mathematics Review. (3 Credits)

Whole numbers, fractions, decimals, percent’s, signed numbers, averages and medians, powers, exponents and roots, algebraic expressions, equations, verbal problems, counting problems, ratio and proportions, sequence and progressions, inequalities, lines, polygons, tri-angles, quadrilaterals, circles, area and perimeter, coordinate geometry, tables, circle, line and bar graphs, cumulative graphs, analytical reasoning tactics, and logical reasoning tactics. A considerable part of the course will be devoted to practice tests similar to quantitative tests of GRE in order to develop the problem-solving and test-taking techniques required.