Course Descriptions — Mathematics

MATH 005 — Algebra — 3 credits

A study of algebra including factoring, exponents, radicals, graphing, and linear and quadratic equations. Course is recommended for students who need MATH 106 but received a score below 10 on the DAT part of the Math Placement Test. Credits count only as free elective.

MATH 101 — (Q) Mathematics Discovery — 3 credits

Topics exploring various aspects of mathematical reasoning and modeling are selected to bring the excitement of contemporary mathematical thinking to the nonspecialist. Examples of topics covered in the past include fractal geometry, chaos theory, number theory, and non-Euclidean geometry. Not open to students with credit for or enrolled in any Mathematics course numbered above 101.

MATH 102 — (Q) Fundamentals of Numerical Mathematics — 3 credits

(Prerequisite: Not open to students with credit for, or enrolled in, MATH 103 or any mathematics course numbered above 105) A study of the fundamental elementary concepts underlying numbers and number systems and their applications. Topics covered include logic, sets, functions, the natural numbers, integers, rational numbers, real numbers, estimation, number theory, patterns, counting, and probability, in addition to other topics chosen by the instructor.

MATH 103 — (Q) Pre-Calculus Mathematics — 4 credits

An intensified course covering the topics of algebra, trigonometry, and analytic geometry. Not open to students with credit for or enrolled inWorld Languages and Culturesany calculus course.

MATH 105 — (Q) Fundamentals of Geometric Mathematics — 4 credits

(Prerequisite: Not open to students with credit for, or enrolled in, any other mathematics course numbered above 102) A study of the fundamental concepts underlying geometric mathematics and its applications. Topics include logic, sets, functions and relations, classical geometry, measurement, transformations, statistics, and analytic geometry and its relationship to algebra and functions, in addition to other topics chosen by the instructor.

MATH 106 — (Q) Quantitative Methods I — 3 credits

(Prerequisite: Math Placement DAT score of 10 or higher or chairperson’s permission) Topics from algebra including exponents, radicals, linear and quadratic equations, graphing, functions (including quadratic, exponential and logarithmic), and linear inequalities. Not open to students with credit for or enrolled in MATH 103.

MATH 107 — (Q) Quantitative Methods II — 3 credits

(Prerequisite: MATH 106, Math Placement PT score of 12 or higher, or chairperson’s permission) Topics from differential calculus including limits, derivatives, curve sketching, marginal cost functions, and maximum-minimum problems. Integration. Not open to students with credit for or enrolled in MATH 114.

MATH 108 — Quantitative Methods III — 3 credits

(Prerequisite: MATH 107 or 114) Topics from integral calculus including the definite and indefinite integral, techniques of integration, and multivariable calculus. Not open to students with credit for or enrolled in MATH 221.

MATH 114 — (Q) Calculus I — 4 credits

(Prerequisite: MATH 103 or equivalent) Topics from calculus and analytic geometry including limits, derivatives and their applications, integrals, and the Fundamental Theorem.

MATH 142 — (Q) Discrete Structures — 4 credits

A study of symbolic logic, sets, combinatorics, mathematical induction, recursion, graph theory, and trees. Intended for Mathematics, Computer Science, and Computer Information Systems majors, but open to other qualified students.

MATH 184-284-384-484 — Special Topics — 1-4 credits each

Topics, prerequisites, and amount of credit will be announced prior to preregistration.

MATH 204 — (Q) Special Topics of Statistics — 3 credits

Study of the computational aspects of statistics; hypothesis testing, goodness of fit; nonparametric tests; linear and quadratic regression, correlation and analysis of variance. Not open to students who have credit for or are enrolled in an equivalent statistics course.

MATH 221 — Calculus II — 4 credits

(Prerequisite: MATH 114) Topics from calculus and analytic geometry including applications of the definite integral, calculus of transcendental functions, methods of integration, improper integrals, sequences and series.

MATH 222 — Calculus III — 4 credits

(Prerequisite MATH 221) Topics from calculus and analytic geometry including parametric equations, vectors, space analytic geometry, partial derivatives and multiple integrals.

MATH 299 — (Q,W) Introduction to Mathematical Proof — 4 credits

(Prerequisite: MATH 221 or permission of the instructor). A writing-intensive introduction to the construction, analysis, and methods of mathematical proof. Topics include propositional and predicate logic, sets, relations, functions, recursion, mathematical induction, and counting arguments with the emphasis on writing an analyzing mathematical proofs about these topics.

MATH 310 — Applied Probability and Mathematical Statistics — 3 credits

(Prerequisite: MATH 221) Basic concepts of probability theory, random variables, distribution functions, multivariable distributions, sampling theory, estimation, confidence intervals, hypothesis testing, linear models and analysis of variance.

MATH 320 — Chaos and Fractals — 3 credits

(Prerequisite: One math course beyond MATH 221 and one CMPS course or equivalent experience) Study of chaotic dynamical systems and fractal geometry. Topics from discrete dynamical systems theory include iteration, orbits, graphical analysis, fixed and periodic points, bifurcations, symbolic dynamics, Sarkovskii’s theorem, the Schwarzian derivative, and Newton’s method. Topics from fractal geometry include fractal, Hausdorff, and topological dimension, L-systems, Julia and Mandelbrot sets, iterated function systems, the collage theorem, and strange attractors.

MATH 325 — (W) History and Philosophy of Mathematics — 3 credits

(Prerequisite: MATH 222 and either MATH 142 or a math course numbered above 300 or instructor’s permission) A survey of major developments in mathematics from ancient through modern times. In addition to the mathematics, this course focuses on the context in which these results were discovered as well as the lives of the mathematicians. Topic may include development of numeral systems, Euclidean and non-Euclidean geometry, algebra, calculus, number theory, real analysis, logic and set theory. Offered fall of odd-numbered years only.

MATH 330 — Actuarial Mathematics — 3 credits

(Prerequisite: MATH 221) Theory of interest, accumulation and discount, present value, future value, annuities, perpetuities, amortizations, sinking funds, and yield rates.

MATH 341 — Differential Equations — 4 credits

(Prerequisite: MATH 222) Treatment of ordinary differential equations with applications. Topics include: first-order equations, first-order systems, linear and non-linear systems, numerical methods, and Laplace transforms. Computer-aided solutions will be used when appropriate.

MATH 345 — Geometry — 3 credits

(Prerequisite: MATH 299) Euclidean, non-Euclidean, and projective geometry. Transformations and invariants. Offered in the fall of even-numbered years only.

MATH 346 — Number Theory — 3 credits

(Prerequisite: MATH 299 or permission of instructor) Topics include divisibility, the Euclidean algorithm, linear diophantine equations, prime factorization, linear congruences, some special congruences, Wilson’s theorem, theorems of Fermat and Euler, Euler phi function and other multiplicative functions, and the Mobius Inversion Formula.

MATH 351 — Linear Algebra — 3 credits

(Prerequisite: MATH 221) Vector spaces, matrices, determinants, linear transformations, eigenvalues, eigenvectors, inner products, and orthogonality.

MATH 360 — Coding Theory — 3 credits

(Prerequisite: MATH 351) A study of algebraic coding theory. Topics include: linear codes, encoding and decoding, hamming, perfect, BCH cyclic and MDS codes, and applications to information theory.

MATH 361 — Numerical Analysis — 3 credits

(Prerequisites: MATH 222, MATH 351) Introductory numerical methods. Topics include: root finding, matrix factorizations, numerical linear algebra, polynomial interpolation, numerical integration, numerical solution of differential equations. Appropriate computation tools will be used.

MATH 410 — Introduction to Stochastic Processes — 3 credits

(Prerequisites: MATH 310, MATH 351) An introduction to stochastic processes studying Markov chains, stationary distributions, birth and death processes, pure jump processes, second order continuity, integration and differentiation, and stochastic differential equations.

MATH 446 — Real Analysis I — 3 credits

(Prerequisites: MATH 222, MATH 299) Topics include: the algebra and topology of the real numbers, functions, sequences of numbers, limits, continuity, absolute and uniform continuity, and differentiation.

MATH 447 — Real Analysis II — 3 credits

(Prerequisite: MATH 446) Selections from: integration theory, infinite series, sequences and infinite series of functions, and related topics.

MATH 448 — Modern Algebra I — 3 credits

(Prerequisites: MATH 299, MATH 351) Fundamental properties of groups, rings, polynomials, and homomorphisms.

MATH 449 — Modern Algebra II — 3 credits

(Prerequisite: MATH 448) Further study of algebraic structures.

MATH 460 — Topology — 3 credits

(Prerequisite: MATH 299) Topological spaces: connectedness, compactness, separation axioms, and metric spaces.

MATH 461 — Complex Variables — 3 credits

(Prerequisite: MATH 299 or permission of instructor) The theory of complex variables: the calculus of functions of complex variables, transformations, conformal mappings, residues and poles.

MATH 462 — Vector Calculus — 3 credits

(Prerequisites: MATH 222, MATH 351) The calculus of scalar and vector fields and of functions defined on paths or surfaces. Implicit Function, Green’s, Strokes, and Gauss’ Theorems. Applications.

MATH 463 — Topics in Biomathematics — 3 credits

(Prerequisites: MATH 341, MATH 351) A study of discrete and continuous mathematical models in biology. Topics include: population dynamics of single species and interacting species, infectious diseases, population genetics, and cell populations with tumor modeling.

MATH 493-494 — Undergraduate Mathematics Research — 6 credits

(Prerequisite: MATH 299) An introduction to mathematical research. Students will be required to investigate, present and write up the result of an undergraduate-level mathematical research project. Students will gain experience in researching the mathematical literature, investigating a mathematical problem, and learning how to write a mathematical paper. Students will be required to present their results in both oral and written form.