Mathematics

Transfer credit - lower division elective.

Limits, continuity, differentiation, integration and applications of both differentiation and integration. Prerequisite: Passing score on the Mathematics Placement Exam on Math 1331 or the equivalent. Fall, Spring.

Transcendental functions, techniques of integration, applications of integration, parametric equations, polar coordinates, infinite sequences and series. Prerequisite: Grade of “C” or better in Math 1431. Fall, Spring.

This course is required of any student who fails the math placement exam and must be passed with a grade of 'C' or better to take any subsequent math course. Mathematics 1315 is especially designed to prepare a student for a subsequent mathematics course required by the university. This course does not satisfy the core requirement or credit requirements for graduation. Fall, Spring.

The application of common algebraic functions, including polynomial, exponential, logarithmic, and rational, to problems in business, economics, and the social sciences are addressed. The applications include mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value.

This course is an exploration of great ideas of mathematics. The course describes the nature of mathematics and provides insights into various strategies used by mathematicians in solving problems. The course emphasizes creative and effective thinking through an introductory examination of a wide variety of topics such as number theory, geometry, infinity, topology, chaos and fractals, and decision making. Prerequisite: Acceptance in the Mendenhall Summer Institute. Co-Requisite: ENGL 1311.

An integrated review course in pre–calculus algebra and trigonometry covering function concepts and symbols, rectangular coordinates, linear and quadratic functions, polynomial and rational functions, trigonometric functions, inequalities, systems of equations, complex numbers and analytic geometry.

Set theory, numerations systems, the system of whole numbers, integers and rational numbers. Does not satisfy the University core requirement in mathematics. Prerequisite: Department Consent. Fall.

Basic concepts of measurement, probability and statistics, logical thinking, problem solving, graphing and informal geometry. Does not satisfy the University core requirement in mathematics. Prerequisite: Department Consent. Spring.

Topics from contemporary mathematics, their development, applications and role in society. Some typical topics, to be chosen by the instructor, include graph theory, mathematical finance, critical path analysis, statistical inference, coding, game theory and symmetry. Applications are in the management, natural and social sciences.

Mathematics of finance, linear equations, inequalities and mathematical models with emphasis on applications.

An introduction to statistical reasoning focused on data collection, descriptive statistics, exploratory data analysis and simple linear regression. Other topics will include basic probability, normal distributions and fundamentals of hypothesis testing. This course is open only to students in the AAS-GENB program.

Topics covered will include numerical evaluation of logarithms and the use of methods for working with them, the interpretation and manipulation of numbers in scientific notation; trigonometric functions; the quantitative interpretation and generation of graphs; the evaluation of ratios of numbers with integer exponents; the simplification of rational expressions, and the use of percentages; estimation methods without the use of calculators; dimensional analysis; trigonometric functions. The course emphasizes creative and effective problem solving techniques in a real world context and an enhancement of mathematical skills leading to greater achievement in STEM (Science, Engineering, Technology and Mathematics) courses. Prerequisite: Acceptance in the Mendenhall Summer Institute. Co-requisite: UNIV 1201.

Limits, continuity, differentiation, integration and applications of both differentiation and integration.

Transcendental functions, techniques of integration, applications of integration, parametric equations, polar coordinates, infinite sequences and series. Prerequisite: Grade of “C” or better in MATH 1431.

Transfer credit - lower division core.

Provides students with the methods and logic to perform elementary statistical analysis used in clinical research including: descriptive meansures, probability, sampling, normal distribution, Student t and Chi squared distributions, estimation and hypothesis testing, analysis of variance, regression and correlation.

Students are introduced to the application of computers to engineering and scientific problems using modern computational packages and a high level programming language. Data representation, software design and utilization, structured programming and numerical algorithms are introduced through student programming projects. Prerequisite: MATH 1431. Fall.

Methods of proof (direct, contradiction, conditional, contraposition); valid and invalid arguments. Examples from set theory. Quantified statements and their arguments. Functions, indexed sets, set functions. Proofs in number theory, algebra, geometry and analysis. Proofs by induction. Equivalence and well–defined operations and functions. The axiomatic method. Prerequisite: MATH 1432 with a grade of 'C' or better.

Basic concepts, theory, methods, and applications of ordinary differential equations. Prerequisite: MATH 1432 with a grade of 'C' or better.

Provides students with the methods and logic to perform elementary statistical analysis used in clinical research including: Descriptive measures, probability, sampling, normal distribution, Student t and Chi squared distributions, estimation and hypothesis testing, analysis of variance, regression and correlation.

Vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, Green’s Theorem, curl and divergence, Stokes’ Theorem, The Divergence Theorem. Prerequisite: MATH 1432 with a grade of “C” or better.

Data collection and experimental design, descriptive statistics, confidence intervals, parametric and nonparametric one and two–sample hypothesis tests, analysis of variance, correlation, simple and multiple linear regression, chi–square tests. Not open to students with credit in MATH 3332 or MATH 3430. This course may not be used as part of the mathematics courses required of mathematics majors.

An introduction to quantitative and statistical analyses focusing on applications of algebraic and statistical methods. Topics to be covered include functions and graphs, break-even analysis, descriptive statistics, probability distributions, estimation, simple linear regression and basic hypothesis testing will be covered. This course may not be used as part of the mathematics courses required of mathematics majors.

A modern approach to the mathematics commonly taught to young children. Theoretic bases for computation and measurement are established. The geometric properties of shapes and solids are explored both visually and through computations. The basics of theoretical and empirical probability are developed using models and manipulatives. Additional topics such as problem solving algorithms, elementary logic and statistics are introduced. Prerequisites: successful completion of a University core mathematics course. Does not satisfy the University core requirements in mathematics.

This course may be paired with a current MATH course or taken with departmental approval. This course is not for credit. Prerequisite: Enrollment in paired MATH course or departmental approval.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

A rigorous treatment of calculus. Prerequisites: MATH 2340, 2431.

Basic concepts of statistics with emphasis on statistical inference. Sampling and experimentation, descriptive statistics, confidence intervals, probability, two–sample hypothesis tests for means and proportions, Chi–squared tests, linear and multiple regressions, analysis of variance. Not open to students with credit in MATH 2434 or 3430. This course may not be used as part of the upper–division mathematics courses required of mathematics majors.

Matrices, inverses, linear systems, determinants, eigenvalues, eigenvectors, vector spaces, linear transformations, inner product spaces, Fourier series and orthogonal bases. Prerequisite: MATH 1432.

An elementary introduction to the mathematical theory of probability for students of mathematics, engineering and the sciences (including the social sciences and management science). Topics include combinatorial analysis, axioms of probability, conditional probability and independence, and random variables. Prerequisite: MATH 1432.

A study of the foundations of Euclidean geometry; non–Euclidean geometry. Prerequisite: Successful completion of a University core mathematics course.

Numerical algorithms as applied to differential and integral calculus; stability and convergence of methods with error estimates. Prerequisites: COMSC 1450 and MATH 1431.

Continuation of Math 2343. Power series solutions of differential equations and Bessel functions, Fourier series and transforms, matrices, systems of differential equations, introduction to generalized functions. Recommended for students interested in applications of mathematics and engineering. Prerequisite: MATH 2343.

Evolution of mathematics from earliest to modern times. Major tends in mathematical thought, the interplay of mathematical and technological innovations, and the contributions of great mathematicians. Appropriate for prospective and in–service teachers. Prerequisite: Successful completion of a University core mathematics course.

Analysis topics chosen at the discretion of the instructor from logic, set theory, combinatorics, and graph theory. Methods of enumerative combinatorics: sum, product, and division rules, bijective and recursive techniques, inclusion and exclusion, generating functions, and the finite difference calculus. Advanced topics to be selected from the theory of partitions, Polya theory, designs, and codes, graphs and trees with applications including games of complete information. Combinatorial existence theorems, Ramsey’s theorem. Prerequisite: MATH 1431.

Data analytics is a process that turns data into usable information for answering questions. This course will introduce the process of acquiring, managing and analyzing data. Readily available real-world data sets will be analyzed using supervised and unsupervised learning methods. Prerequisite: MATH 2435, MATH 3332, MATH 3450 or PSYC 3433.

Appropriate visualizations of data are a key to revealing patterns and communicating important findings in research. This course will build on statistical and analytical thinking by emphasizing the role and use of visualizations in the analysis of data. Theories, techniques and software for managing, exploring, analyzing, displaying and communicating information about various types of data will be introduced. Visualizations will be produced using readily available real-world data sets. Prerequisites: MATH 2435, or MATH 3332, or MATH 3450, or PSYC 3433, or instructor approval.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Basic concepts leading to advanced applications in biostatistics. Topics include study design, data collection, descriptive statistics, probability and probability distributions, confidence intervals, hypothesis testing, power of statistical tests, and simple regression with an emphasis on applications in the biomedical sciences and biomedical research. Data will be analyzed using statistical software packages. Students may be required to register for MATH 1050 for this course.

Junior division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: Department Consent.

Written and oral analysis and presentations by students on topics from mathematics. Student research projects.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

Introduction to concepts and methods basic to real analysis. Topics such as the real number system, sequences, continuity, uniform continuity, differentiation, infinite series and integration. Prerequisite: Math 2341.

Continuation of Math 4331 covering such topics as uniform convergence and functions of several variables. Strongly recommended for students planning to enter graduate school or secondary teaching and those interested in applied mathematics. Prerequisite: MATH 4331.

The basics of point–set topology. Open and closed sets, limit points, topological spaces, countability, compactness, connectedness, metrics and metric topologies. Prerequisite: MATH 2431 and MATH 3334

Calculus of a function of a complex variable. Prerequisite: MATH 2431

Fundamental algebraic systems including groups, rings and fields. The structure of a system as a set with its operations and relationships between systems. Prerequisite: MATH 3360.

Direct products, Sylow theory, ideals, extensions of rings, factorization of ring elements, modules, and Galois theory. Prerequisite: MATH 4338.

Continuation of Math 2341. Linear transformations and similarity, eigenvalues and diagonalization, complex vector spaces, unitary and self–adjoing matrices, Spectral Theorem, Jordon canonical form. Selected topics in linear programming, convexity, numerical methods, and functional analysis. Prerequisites: MATH 3334.

Mathematical formulation of physical laws. Existence and uniqueness for Cauchy and Dirichlet problems; classification of equations; potential–theoretic methods; other topics at the discretion of the instructor. Recommended for students interested in applications of mathematics and engineering. Prerequisite: MATH 2343.

This course provides an introduction to developing mathematics models from real world situations through discussion of a series of examples, and hands-on exercises and projects that make use of a range of continuous and discrete mathematical tools.

Application and extension of Biostatistics I with a focus on advanced statistical concepts which recur in biomedical research literature; multiple regression, logistic regression and survival analysis. Other topics may include time series analysis and clinical trials. Practival experience with the widely used statistical research software package R. Emphasis on realistic data typically encountered in applications of biostatistics.

The student will work with faculty supervision and undertake a research project. The project will culminate in a tangible product such as a paper, a presentation or a research poster.

Advanced methods and/or applications of material learned in statistics courses. May be repeated for credit.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.

Student research on a selected problem in the field pursued under the guidance of an assigned member of the faculty. Prerequisite: consent of chair.

Upper–division treatment of selected topics of mutual interest to the faculty member and students. Prerequisite: consent of chair.