Sets, relations, functions with particular attention to properties of algebraic, exponential, logarithmic functions, their graphs and applications in preparation for MATH 1212. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 1212 or above. Pre/co-requisites: Two years of secondary school algebra; one year of secondary school geometry.
Skills in working with numerical, algebraic, and trigonometric expressions are developed in preparation for MATH 1234. May not be taken for credit concurrently with, or following receipt of, credit for any mathematics course numbered MATH 1234 or above. Prerequisite: Two years of secondary school algebra; one year of secondary school geometry.
Introduction to mathematics of finite systems with applications, such as probability, statistics, graph theory, fair division and apportionment problems, voting systems. Prerequisites: Two years of secondary school algebra, MATH 1012, or MATH 1034.
Topics include geometry, measurement, probability, statistics, algebra, number theory, and problem solving to provide background for future instruction in elementary and middle school mathematics. Prerequisite: Three years of secondary school math.
Introduction to limits and differential/integral calculus with a wide variety of applications. Students interested in intensive use of mathematics should take MATH 1234. Credit not awarded for both MATH 1212 and MATH 1234 unless followed by MATH 1248. See MATH 1242. Prerequisite: C- or better in MATH 1012 or C- or better in MATH 1034, or a score of 61 or higher on the placement assessment.
Techniques and applications of integration. An introduction to multi-variable calculus: partial derivatives and double integrals. Prerequisite: MATH 1212 or MATH 1234.
Introduction to calculus of functions of one variable including: limits, continuity, techniques and applications of differentiation and integration. Credit not given for more than one course in the pair MATH 1212, MATH 1234 unless followed by MATH 1248 or MATH 1242. No credit following receipt of credit for MATH 1248 or above. Prerequisite: C- or better in MATH 1034 or a score of 76 or higher on the placement assessment.
Intended to make the transition from MATH 1212 to MATH 2248. Topics are similar to MATH 1248 but recognizing different backgrounds of students in MATH 1212 versus MATH 1234. Credit will not be given for both MATH 1248 and MATH 1242. No credit following receipt of credit for MATH 2248 or above. Prerequisite: B or better in MATH 1212, or B or better in MATH 1224.
Vectors and vector operations. Techniques and applications of integration. Polar coordinates, Taylor polynomials, sequences and series, power series. Credit will not be given for both MATH 1248 and MATH 1242. No credit following receipt of credit for MATH 2248 or above. Prerequisite: C- or better in MATH 1234.
Project-based course. Historical development of mathematical sciences emphasizing interrelations among them. Individual assignments correspond to background and interests of students. Prerequisite: Nine hours of college mathematics.
Emphasizing proofs, fundamental mathematical concepts and techniques are investigated within the context of number theory and other topics. Prerequisite: MATH 1234 or MATH 1242. Credit not given for more than one of MATH 2055 and CS 1640.
Algebraic concepts and relationships are explored and developed. Linear, quadratic, and exponential functions are featured. Credit not awarded for students majoring or minoring in Mathematics. Prerequisite: 3 credits of Math numbered MATH 1111 or above.
Vector-valued functions. Calculus of functions of several variables: partial derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes' and Green's theorems. Prerequisite: C- or better in MATH 1248 or MATH 1242.
Survey of the fundamental concepts of linear algebra necessary to describe the solution space of a linear differential equation and for solving systems of linear differential equations. Credit not awarded following receipt of credit for MATH 2522 or MATH 2544. Prerequisite: MATH 1234. Co-requisites: MATH 1248 or MATH 1242.
Vectors, matrices, linear independence, vector spaces (with focus on real n-space), determinants, linear transformations, eigenvalues and eigenvectors. Applications from engineering and the sciences incorporated through required computer assignments. Credit not given for both MATH 2522 and MATH 2544. Prerequisite: MATH 1248 or MATH 1242.
Vector spaces, linear independence, bases, linear transformations, matrices, determinants, change of basis characteristic equations, eigenvalues and eigenvectors, with applications. Emphasis on understanding and gaining facility with these concepts including proofs. Credit not given for both MATH 2522 and MATH 2544. Prerequisite: MATH 1248 or MATH 1242. Co-requisite: MATH 2248 or MATH 2055.
Introduction to basic combinatorial principles emphasizing problem-solving techniques. Enumeration, generating functions, Fibonacci numbers, pigeonhole principle, inclusion-exclusion, and graph theory. Prerequisites: MATH 2055 (preferred) or CS 1640.
Students will be introduced to the basic ideas and algebraic structures of interest theory, time-value of money, annuities, loans, bonds, cash-flows and portfolios. Prerequisites: MATH 1224, MATH 1248 or MATH 1242.
Differential equations, Laplace transforms, and systems of differential equations; brief introduction to Fourier series. Examples from engineering and physical sciences. Credit not granted for both MATH 3230 and MATH 3201. No credit for Mathematics majors. Prerequisite: MATH 2248. Co-requisites: Preferred: MATH 2522 or MATH 2544; or MATH 2500.
Solutions of linear ordinary differential equations, the Laplace transformation, and series solutions of differential equations. Prerequisite: MATH 2248. Corequisite: MATH 2522 or MATH 2544. Credit not granted for more than one of the courses MATH 3230 or MATH 3201.
Properties of the real numbers, basic topology of metric spaces, infinite sequences and series, continuity. Prerequisites: MATH 2468 or MATH 2551 or C- or better in MATH 2055; MATH 2248; MATH 2522 or MATH 2544.
Divisibility, prime numbers, Diophantine equations, congruence of numbers, and methods of solving congruences. A significant portion of the course devoted to individual and/or team projects. Prerequisites: MATH 2055 or CS 1640; MATH 2248, MATH 2522, or MATH 2544.
See Schedule of Courses for specific titles.
Program of reading and research culminating in written thesis and oral presentation. Honors notation appears on transcript and Commencement Program. Contact department chairperson for procedures.
Discrete and continuous dynamical systems, Julia sets, the Mandelbrot set, period doubling, renormalization, Henon map, phase plane analysis and Lorenz equations. Credit not awarded for both MATH 5766 and MATH 3766. Prerequisites: Graduate student or Instructor permission. Cross-listed with: CSYS 5766.
Research for the Master's Thesis.
Complex functions, differentiation and the Cauchy-Riemann equations, power and Laurent series, integration, calculus of residues, contour integration, isolated singularities, conformal mapping, harmonic functions. Prerequisite: Two semesters of real analysis required.
Topics will vary each semester and may include combinatorial designs, coding theory, topological graph theory, cryptography. Course is repeatable for credit. Prerequisite: MATH 3551 or MATH 5678.
Detailed exploration of distribution, transportation, small-world, scale-free, social, biological, organizational networks; generative mechanisms; measurement and statistics of network properties; network dynamics; contagion processes. Students from all disciplines welcomed. Pre/co-requisites: MATH 6701, CSYS 6701, calculus, and statistics required. Cross-listed with: CSYS 6713.
Research for the Doctoral Dissertation.
Graduate student work on individual or small team research projects under the supervision of a faculty member, for which credit is awarded. Offered at department discretion.