Topics such as geometry, computing, algebra, number theory, history of mathematics, logic, probability, statistics, modeling and problem solving intended to give students insight into what mathematics is, what it attempts to accomplish and how mathematicians think. May be used for general education credit.
Applications and interpretation of numerical information in context. Selection and use of appropriate tools: scientific notation, percentages, descriptive summaries, absolute and relative changes, graphs, normal and exponential population models, and interpretations of bivariate models. Making informed decisions and effectively communicating them. Identifying limitations of information sources, assessing reasonableness of results, and basic concepts of confidence amid uncertainty. Not open to majors in mathematics or statistics. Not open to students who have previously earned credit in MATH 220 except with the consent of the department head. May be used for general education credit.
These courses, along with MATH 207, form a sequence that covers the topics of sets, logic, numeration systems, development of real numbers, number operations, number theory, geometry, measurement, algebra, functions, probability and data analysis. Sequence is required for early childhood, elementary or middle school teacher licensure. May be used for general education credit. Prerequisite for MATH 107: Sufficient score on the Mathematics Placement Exam or a grade of “C-“ or better in MATH 105. Prerequisite for MATH 108: MATH 107 with a grade of “C-” or better.
Algebraic, exponential, logarithmic and trigonometric functions; matrices and matrix solutions to systems of linear equations; vectors. Not open to students who have previously earned credit in MATH 155, 156, 205 or 235, except with the consent of the department head.
Polynomial, rational, exponential and logarithmic functions and applications, systems of equations and inequalities, sequences. Prerequisite: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or MATH 156. Not open to students who have previously earned credit in MATH 135, 156, 205, 231, 232 or 235.
Covers same topics as MATH 155. MATH 156 will meet five times a week for students requiring more instructional time. Prerequisites: Demonstration of proficiency in algebra at an intermediate level. A test is required to determine placement in MATH 155 or MATH 156. Not open to students who have previously earned credit in MATH 135, 155, 205, 231, 232 or 235.
Topics or projects in mathematics which are of interest to the lower-division student. May be repeated for credit when course content changes. Topics or projects selected may dictate prerequisites. Students should consult the instructor prior to enrolling for this course.
Review of fundamental mathematics required to be successful in MATH 205 or MATH 231, including graphs of functions, factoring, simplifying, solving equations and inequalities, and exponential/logarithmic/trigonometric functions. Self-paced study with required proctored tests. Students needing more instruction should register for MATH 155 instead. Corequisite: MATH 205 or MATH 231 with appropriate calculus placement score.
Topics from differential and integral calculus with applications to the social, behavioral or life sciences and business or management. Prerequisite: One of MATH 135, MATH 155, MATH 156 or sufficient score on the mathematics placement exam. Not open to mathematics or physics majors or to students who have already earned credit in MATH 232 or MATH 235. Not recommended for chemistry majors.
Topics from differential and integral calculus, including a laboratory component stressing data collection, data analysis, and applications to environmental issues. Prerequisite: Demonstration of strong preparation in algebra. Not open to mathematics or physics majors or to students who have already earned credit in MATH 205, MATH 231 or MATH 235. Not recommended for chemistry majors. Sufficient score on the Mathematics Placement Exam.
Topics from integral calculus with applications to the social, behavioral or life sciences and business or management. Prerequisite: MATH 205. Not open to mathematics or physics majors or to students who have already earned credit in MATH 236. Not recommended for chemistry majors.
A continuation of topics listed in the MATH 107-108 description will be covered. The MATH 107-108-207 sequence fulfills the requirements for licensure of prospective early childhood, elementary or middle school teachers. Prerequisite: “C-” or better in both MATH 107 and MATH 108.
Descriptive statistics, frequency distributions, sampling, estimation and testing of hypotheses, regression, correlation and an introduction to statistical analysis using computers. May be used for general education credit. Prerequisite: MATH 105 with a grade of “C-“ or better or sufficient score on the Mathematics Placement Exam.
An introduction to discrete mathematical structures including functions, relations, sets, logic, matrices, elementary number theory, proof techniques, basics of counting, graphic theory, discrete probability, digital logic, finite state machines, integer and floating point representations. Prerequisite for MATH/CS 227: MATH 155, MATH 156 or sufficient score on the Mathematics Placement Exam. Prerequisite for MATH/CS 228: MATH/CS 227.
MATH 231 and MATH 232 form a sequence that combines first-semester calculus with algebra and trigonometry. The sequence is designed for students whose pre-calculus skills are not strong enough for MATH 235. Calculus material in MATH 231 includes limits and derivatives of algebraic functions and their applications. May be used for general education credit. Prerequisite: MATH 155, MATH 156 or sufficient score on the Mathematics Placement Exam. MATH 231-232 together are equivalent to MATH 235 for all prerequisites. Not open to students who have already earned credit in MATH 235.
A continuation of MATH 231. Calculus topics include limits and derivatives of transcendental functions, the theory of integration and basic integration techniques. Prerequisite: MATH 231 with a grade of “C-” or better. MATH 231-232 together are equivalent to MATH 235 for all prerequisites. Not open to students who have already earned credit in MATH 235.
Differential and integral calculus of functions of one variable. Sequences and infinite series. MATH 235 may be used for general education credit. Prerequisite for MATH 235: Sufficient score on the Mathematics Placement Exam. Prerequisite for MATH 236: MATH 232 or MATH 235 with grade of “C-” or better. MATH 235 is not open to students who have already earned credit in MATH 232.
Vectors. Multivariate calculus. Prerequisite: MATH 236 with grade of “C-” or better.
Matrices; determinants; vector spaces; linear transformations; eigenvalues and eigenvectors; separable, exact and linear differential equations; and systems of linear differential equations. Prerequisite: MATH 236. Not open to students with credit in MATH 300 or MATH 336 without departmental permission.
Logic, set theory, relations and functions, mathematical induction and equivalent forms, recurrence relations, and counting techniques. Prerequisite or corequisite: MATH 236.
Programming in a high-level computer language. Applications of numerical algorithms to problems basic to areas such as mathematics, the sciences and economics and finance. Prerequisite: MATH 236 or corequisite MATH 236 and consent of instructor. This course is not open to students who have previously earned credit in MATH/CS 448.
Introduces the student to the application of vector calculus to the description of fluids. The Euler equation, viscosity and the Navier-Stokes equation will be covered. Prerequisites: MATH 237 and PHYS 260.
An introduction to the applications of vector and tensor calculus to the description of continua, with emphasis on the mechanics of solids. Topics will include deformation, motion, stress, conservation laws, and constitutive equations.
Topics include experimental and survey design, distributions, variation, chance, sampling variation, computer simulation, bootstrapping, estimation and hypothesis testing using real data generated from classroom experiments and large databases. Prerequisite: MATH 206, MATH 236 or permission of the instructor. Not open to students who have already earned credit in MATH 220 or MATH 318.
Students pursue research in a selected area of mathematics and/or statistics. Student must make arrangements with a supervising instructor prior to registration. Course may be repeated.
Vector spaces, linear transformations, matrices, determinants, systems of linear equations, and eigenvalues and eigenvectors. Prerequisite: MATH 236. Not open for credit to students with credit in MATH 238.
Descriptive statistics, measures of central tendency and dispersion, correlation, probability, probability distributions and statistical inference. Prerequisite: “C-” or better in MATH 107, MATH 108 and MATH 207.
Use of statistical software to manage, process and analyze data. Writing of statistical programs to perform simulation experiments. A student may not earn credit in both MATH 280 and MATH 309. Prerequisite: MATH 220 or MATH 318 or equivalent.
Properties of integers and prime numbers, divisibility, congruence, residues and selected topics. Prerequisite: MATH 245 or consent of the instructor.
A development of the real number system through a systematic approach to the natural numbers, integers, rationals and irrationals. Prerequisite: MATH 245 or consent of the instructor.
Descriptive statistics, counting, probability axioms, discrete and continuous univariate random variables, expected values of random variables and sums of independent random variables, sampling distributions and the Central Limit Theorem, single and two sample inference for proportions and means, chi-square test of independence, simple linear regression, and correlation. Prerequisite: MATH 236.
Introduction to basic concepts in statistics with applications of statistical techniques including estimation, test of hypothesis, analysis of variance and topics in experimental design. Prerequisite: MATH 220 or MATH 318 or equivalent.
Methods of analyzing data from non-normal populations including binomial tests, contingency tables, use of ranks, Kolmogorov-Smirnov type statistics and selected topics. Prerequisite: MATH 220 or MATH 318 or equivalent.
Theory and practice of sampling including stratified random samples, discussion of simple random samples, cluster sampling, estimating sample size, ratio estimates, subsampling, two-state sampling and analysis of sampling error. Prerequisite: MATH 220 or MATH 318 or equivalent.
Uses and concepts of probability and sampling procedures. Acceptance sampling by attributes and variables, Shewhart concepts of process control, control chart process capability studies, reliability and life testing. Design of sampling plans. Prerequisite: MATH 318.
Exact inference for population proportions, comparison of population proportions for independent and dependent samples, two and three-way contingency tables, Chi-square tests of independence and homogeneity, Chi-square goodness-of-fit tests and Poisson and logistic regression. Prerequisite: MATH 220 or MATH 318 or equivalent.
Regression and exponential smoothing methods for forecasting nonseasonal and seasonal time series, stochastic processes, Box-Jenkins’ autoregressive and moving average models. Prerequisites: MATH 238 or MATH 300; and MATH 318.
Development of techniques for obtaining, analyzing and graphing solutions to differential equations, with emphasis on first and second order equations. Prerequisite: MATH 236. Not open for credit to students with credit in MATH 238.
Laplace transforms, power series and their application to differential equations. Vector differential and integral calculus; parametric curves; coordinate systems; line, surface and volume integrals; and gradient, divergence and curl including the theorems of Green, Stokes and Gauss. Prerequisites: MATH 237; and MATH 238 or MATH 336.
Linear and nonlinear optimization with an emphasis on applications in the sciences, economics and social sciences. Techniques studied include the simplex, Newton and Lagrange methods and Kuhn-Tucker theory. Software packages will be used to implement these methods. Prerequisites: MATH 237; and MATH 238 or MATH 300 or consent of instructor.
Introductory study of nonlinear dynamics and chaos intended primarily for upper-level undergraduates in science and mathematics. Topics include stability, bifurcations, phase portraits, strange attractors, fractals and selected applications of nonlinear dynamics in pure and applied science. Computers may be utilized for simulations and graphics. Prerequisites: MATH 238 or (MATH 300 and MATH 336); and MATH 248.
Introduction to dynamical models (discrete and continuous time) applied to biology. Tools of mathematical analysis from linear and nonlinear dynamics will be taught, including stability analysis of equilibria, as well as appropriate use of software packages. Emphasis will be on model development and interpretation in the context of applications, including effective written and oral presentation. Prerequisites: MATH 232 or MATH 235 or equivalent.
Graphs and their applications. Possible topics include trees, Euler paths and Hamiltonian circuits, planar graphs, digraphs, adjacency matrices, connectivity and coloring problems. Prerequisite: MATH 245 or consent of instructor.
This course discusses the role of statistics in biological research and interpretation of biological phenomena. The course will cover topics of sampling, correlation, regression analysis, tests of hypotheses, commonly observed distributions in natural populations, nonparametric tests, goodness-of-fit tests and ANOVA. In order to fully comprehend the statistical analysis of those publications, students will review approximately half a dozen publications from different fields of biology. Prerequisite: MATH 220 or MATH 318 or equivalent.
Introduction to algebraic properties of complex numbers, analytic functions, harmonic functions, mappings of elementary functions, contour integration, series, residues, and poles and conformal mappings. Emphasis on computations and applications to fluid and heat flow. Prerequisite: MATH 237.
Development and applications of mathematical models and computer simulations to investigate problems in solid mechanics, with emphasis on numerical solution of associated boundary value problems. Prerequisite: MATH/PHYS 266, MATH 238, and MATH 248, or consent of instructor.
This course represents an introduction to sound, hearing, and vibration. Architectural, biological and environmental acoustics will also be discussed. Students will develop an ability to use mathematical models and experimental techniques to study problems in acoustics and to transfer this knowledge to analogous situations. They will also develop an ability to conduct a semester–long research or expository project and present it in written and oral form to an audience of peers. Prerequisite: MATH 236 or permission of instructor.
An overview of the role of mathematical concepts in financial applications. Topics include continuous time finance, optimization, numerical analysis and applications in asset pricing. Prerequisites: MATH 237 and FIN 380.
A quantitative treatment of the theory and method of financial securities pricing to include an examination of closed form pricing models such as the Black-Scholes and its various derivatives as well as numerical solution techniques such as binomial methods. Prerequisite: MATH/FIN 395.
Limits, continuity, differentiation, sequences, series, integration and selected topics. Prerequisite for MATH 410: MATH 238 or MATH 300; and MATH 245 or consent of the instructor. Prerequisite for MATH 411: MATH 410.
Topics in the history of mathematics spanning ancient times to the present. Prerequisite: MATH 245 or consent of the instructor.
Multivariate statistical methods with applications. Topics include canonical correlation, clustering, discriminant analysis, factor analysis, multivariate analysis of variance, multiple regression, multidimensional scaling and principal component analysis. Prerequisites: MATH 300 or MATH 238; and MATH 321 or MATH 322.
Sequences and classes of random variables. Applications to physical, biological, social and management sciences. Topics include Markov chains, branching processes, the Poisson process, queuing systems and renewal processes. Prerequisites: MATH 238 or MATH 300; and MATH 318.
Development and use of probability and statistics for strategic decision making with applications. Topics include decision flow diagrams, analysis of risk and risk aversion, utility theory, Bayesian statistical methods, the economics of sampling, sensitivity analysis and collective decision making. Prerequisite: MATH 318.
Derivations and proofs of probability theorems, discrete and continuous univariate and multivariate random variables, conditional distributions, mathematical expectations, functions of random variables, moment generating functions, properties and derivation of estimators including the method of moments and maximum likelihood estimation. Prerequisite: MATH 318.
Limiting distributions, sampling theory and distributions, theory and applications of estimation and hypothesis testing. Prerequisite: MATH 426.
Training and experience in statistical consulting emphasizing oral and written communication, interview, report-writing and presentation skills. Participate in significant cross disciplinary consulting project that will require meeting with the client, creating reports summarizing the clients’ problem and an analysis performed by the students, and explanation of results using language that can be understood by the client. Students are required to meet with clients outside of class meeting times. Prerequisite or corequisite: MATH 322. Prerequisite: MATH 318, MATH 321, at least junior status, or permission of instructor.
Experience in the design, data collection and analysis for a survey or experiment. Prerequisite: Consent of instructor.
A proof-based linear algebra course covering such topics as vector spaces, linear transformations and matrices, eigenvalues and eigenvectors, inner product spaces, and canonical forms. Prerequisites: MATH 245 and either MATH 238 or MATH 300.
Elementary applied partial differential equations, the heat equation, Laplace’s equation, the wave equation; Fourier series and boundary value problems. Both theory and problem-solving will be included. Prerequisite: MATH 238 or MATH 336.
Analysis of qualitative properties and dynamics of linear and non-linear ordinary differential equations, including topics such as existence, uniqueness, phase portraits, stability and chaos, with applications to the sciences. Prerequisites: MATH 238 or (MATH 300 and MATH 336); and MATH 245 or MATH 440 or permission of the instructor.
Study and analysis of algorithms used to solve nonlinear equations and systems of linear and nonlinear equations. Iterative methods for matrices and Newton-type methods. Numerical differential and integral calculus. Programming using a high-level language and/or software packages. Prerequisites: MATH 237, MATH 238 or MATH 300; and MATH 248.
Study and analysis of numerical techniques to solve ordinary and partial differential equations, including Euler, Runge-Kutta, Picard, finite-difference and finite-element methods. Programming using a high-level language and/or software packages. Prerequisite: MATH 237, MATH 238 or MATH 336, and MATH 248.
An introduction to the analysis, design and theory of algorithms. Algorithms studied will be selected from searching, sorting and graph theory. Included are elements of counting, recurrence relations, direct and indirect proofs, recursion, complexity classes, language theory, decidability and undecidability. Prerequisites: MATH/CS 228 and CS 240.
Theory and application of contingency mathematics in the areas of life and health insurance and of annuities from both a probabilistic and deterministic approach. This class, together with MATH/FIN 466, helps students prepare for the professional actuarial examinations. Prerequisite: MATH/FIN 395 or consent of the instructor. Prerequisite or corequisite: MATH 426.
A continuation of MATH/FIN 465. Additional coverage of contingency mathematics in the areas of life and health insurance, annuities, pensions and risk theory from both probabilistic and deterministic approaches. The two-course sequence helps to prepare the student for the professional actuarial examinations. Prerequisite: MATH/FIN 465. Prerequisite or corequisite: MATH 427.
This course is a mathematics capstone course primarily for math majors with secondary education minors. It covers a variety of topics, each designed to develop the interconnectedness of advanced mathematics to the secondary curriculum. Prerequisite or corequisite: MATH 318, MATH 410, MATH 430, and MATH 475.
Origin and development of Euclidean and other geometries including axiomatic systems, mathematical proof and special topics from incidence geometry. Prerequisite: MATH 245 or consent of instructor.
Topics in advanced mathematics or statistics which are not covered in the regularly offered courses. Offered only with approval of the department head; may be repeated for credit when course content changes. Prerequisites: Consent of the instructor.
Students pursue advanced research in a selected area of mathematics and/or statistics. Student must make arrangements with a supervising instructor prior to registration. Offered only with consent of the department head. Repeatable up to 6 credits.
Three-semester sequence (parts A, B and C with 1-4 credits each) totaling 6 credits. Two-three-one credit sequence is recommended. Prerequisite: Consent of SHP supervisor.
Print Version of Catalog