# Mathematics (MATH)

Humanities and Natural Sciences

MATH A092 Fundamentals of Algebra 3 crs.

This course is for those with one year of algebra, but who are not ready for MATH A115 or A118. Topics include arithmetic of signed numbers, polynomials, factoring, fractional and quadratic equations and applications. Credit from this course is not applicable to any degree program or to any math, Common Curriculum, or teacher certification requirement but will be added to normal total for student’s degree program. Students are assigned to this course based on placement test scores.

MATH A115 Introduction to Finite Mathematics 3 crs.

This course is designed to give social science and business students an introduction to the necessary analytic and quantitative tools in mathematics. Topics include elementary matrix theory and linear programming, life science models, and an introduction to probability.

MATH A116 Survey of Calculus 3 crs.

This course includes techniques in the calculus of algebraic, exponential, and logarithmic functions of one and two variables as met in the application fields of business, political science, and other social science fields.

MATH A117 Concepts in College Algebra 3 crs.

This course is designed to introduce the topics of college algebra. The course focuses on a conceptual understanding of the subject and includes a number of applications of algebra. Following a contemporary approach to mathematics education, this course includes exploration of real-world problems, group discussion of problems, and technological exploration of concepts with an emphasis on mathematical reasoning and communication.

MATH A118 Pre-calculus Mathematics 3 crs.

This course offers more preparation for those students who plan on taking calculus, but find themselves deficient in second-year high school algebra and trigonometry. Exponential, logarithmic, and trigonometric functions are included.

MATH A200 Introduction to Linear Algebra 3 crs.

This course is designed to introduce topics in matrix algebra for applications that are basic to future coursework. Vector spaces, determinants, matrices, linear transformations, and eigenvectors are included.

Prerequisite: high school Algebra II.

MATH A204 Discrete Math Structures 3 crs.

This is a course that bridges infinitesimal calculus and the world of sets, relations, digraphs, lattices, logic, etc. Topics include algebraic flow chart language, syntax and semantics, isomorphisms and invariants, directed graphs, Boolean algebra, permutations and cyclic groups, polish expressions, etc.

Prerequisite: high school Algebra II.

MATH A211 Introduction to Programming I 3 crs.

An introduction to concepts and terminology in programming. Topics include interface builders and problem solving techniques in various programming environments. Emphasis is placed on the basics of software design and on elementary applications to Mathematics and other disciplines.

Prerequisite: Placement in Math T122 or higher.

MATH A212 Introduction to Programming II 3 crs.

This is a continuation of MATH A211. Topics will include object-oriented programming, software development, and data structures such as stacks, queues, trees and lists. Further applications to Mathematics and other disciplines will be explored.

Prerequisite: Placement in Math T122 or higher.

MATH A241 Introduction to Probability and Statistics I 3 crs.

MATH A257 Calculus I 4 crs.

This is a beginning course in the calculus of one variable and analytic geometry. The concept of limits and their use in differential and integral calculus, max and min values of functions, and solving for areas and volumes are treated.

Prerequisites: high school algebra (two years), geometry, trigonometry.

MATH A258 Calculus II 4 crs.

Topics include the Mean Value Theorem and its applications, applications of the integral, transcendental functions, techniques of integration, sequences and series, and conic sections.

Prerequisite: MATH A257.

MATH A259 Calculus III 3 crs.

This course addresses the calculus of several variables and vector analysis. Topics include differentiation of vector valued functions, extreme values, Lagrange multipliers, multiple integration, line and surface integrals, and an introduction to vector fields.

Prerequisites: MATH A200, A258.

MATH A260 Statistical Inference for Scientists 3 crs.

This is a first course in statistical methods for science students. Emphasis centers on the practical application of statistical inference and estimation in the quest for scientific knowledge. Topics include exploratory data analysis, techniques for data collection, summarization, and presentation, graphical techniques and numerical measures, the role of the Normal distribution, regression and correlation analysis, confidence intervals, hypothesis testing, the analysis of variance, and distribution-free methods.

Prerequisites: MATH A257 or equivalent.

MATH A261 Statistical Inference for Scientists Lab 1 cr.

This is a first course in statistical methods for science students. Emphasis centers on the practical application of statistical inference and estimation in the quest for scientific knowledge. Topics include exploratory data analysis, techniques for data collection, summarization, and presentation, graphical techniques and numerical measures, the role of the Normal distribution, regression and correlation analysis, confidence intervals, hypothesis testing, the analysis of variance, and distribution-free methods.

Prerequisites: MATH A257 or equivalent.

MATH A271 Applied Scientific Computing 3 crs

This course introduces students to techniques and methods commonly used by scientists to analyze, build models, visualize and make decisions based on data collected in laboratory and field experiments. It emphasizes the interdisciplinary nature of scientific computing by applying the mathematical tools of statistics and numerical computations to hands on experiments from diverse areas of science.

Prerequisites: MATH A257 (MATH A211 recommended) or instructor permission.

MATH A310 Introduction to Differential Equations 3 crs.

Topics include fundamental methods of solving elementary differential equations. Includes exact solutions, series solutions, numerical solutions, solutions using Laplace transforms, and other topics.

Prerequisite: MATH A258.

MATH A320 Linear Algebra 3 crs.

This second course expands on topics such as vector spaces, matrices, determinants, eigenvalues, linear functionals, bilinear forms, vector geometry, and their applications.

Prerequisite: MATH A200.

MATH A330 Theory of Numbers 3 crs.

Topics include divisibility, prime numbers, Euclidean algorithm, fundamental theorem of arithmetic, congruences, diophantine equations, and indices.

Prerequisite: permission of instructor.

MATH A340 Math Probability 3 crs.

This course introduces the theory of probability. Topics include combinatorial analysis, axioms of probability, discrete and continuous random variables, expectation, multivariate probability distributions, function of random variables, and basic limit theorems.

Prerequisite: MATH A310.

MATH A341 Statistics Theory and Methods 3 crs.

This course shows how statistics makes inferences about a population based on information from samples. Topics include estimation, hypothesis testing, linear models, and estimation by least squares. Experimental design, analysis of variance, analysis of enumerative data, and nonparametric statistics.

Prerequisites: MATH A340; permission of instructor.

MATH A345 Topics in Geometry 3 crs.

The course will include foundations of geometry, congruences, parallelism, similarities, measures, coordinate systems, axiom systems for the Euclidean, and projective planes.

Prerequisite: MATH A258.

MATH A350 Differential Equations 3 crs.

This course reviews and continues the introduction to ordinary differential equations met in MATH A310. Selected topics in partial differential equations and applications to various fields will be included.

Prerequisites: MATH A259, A310.

MATH A375 Computational Mathematics 3 crs

This course develops the computational procedures, which are fundamental to numeric applications.  The topics studied will be selected from but not limited to error analysis, numerical solutions of non-linear equations, systems of linear equations using direct and iterative methods, polynomial interpolation, quadrature, least squares curve fitting, and numerical solutions of ordinary differential equations.  This course will not count as a Mathematics elective for the Mathematics major.  It is a requirement for the Computational Science major and the Computational Science minor.

Prerequisites: MATH A211, A257 or instructor permission.

MATH A400 Abstract Algebra I 3 crs.

This is a general survey course in the concepts of algebra treating number systems, groups, rings, domains, fields, matrices over a field, elements of Galois theory, and canonical forms.

Prerequisite: MATH A200.

MATH A401 Abstract Algebra II 3 crs.

This course is a continuation of MATH A400.

Prerequisite: MATH A400.

MATH A410 Advanced Calculus I 3 crs.

This course offers a deeper look at analysis with special attention to linear methods as applied to the calculus of several variables. Topics include extrema, Jacobians, uniform continuity, line and surface integrals, differentials, integration theory, and series.

Prerequisites: MATH A259, A310.

MATH A411 Advanced Calculus II 3 crs.

This course is a continuation of MATH A410.

Prerequisite: MATH A410.

MATH A415 Complex Variables 3 crs.

This course studies the theory of analytic functions. Topics include Cauchy's integration theory, series representation, analytic continuation and conformal mappings.

Prerequisite: MATH A259, A310

MATH A425 General Topology 3 crs.

This course studies basic concepts from the topics of topological spaces, Hausdorff spaces, connectedness, metric spaces, continuous mappings, separability, compactness, and product spaces.

Prerequisite: permission of instructor.

MATH A430 Applied Math I 3 crs.

This course is designed to illustrate the application of mathematics to one or more fields by considering the aspects of model building and to further develop theory and techniques relevant to the needs of the field. Topics include partial differential equations, Eigen functions, Green’s functions, perturbation, and approximation methods.

Prerequisites: MATH A259, A310.

MATH A493 Directed Readings 3 crs.

MATH A495 Special Project arr.

This course focuses on the creative or productive efforts of one or more students. A special project is distinguished from a research project in its lack of the historical or experimental method and perspective characteristics of research.

MATH A496 Math Seminar 1 cr.

Topics from various branches of mathematics will be presented, discussed, and argued by the students. By invitation only.

MATH A498 Research Project arr.

The research project focuses on empirical or historical investigation, culminating in a written report.

MATH A499 Independent Study arr.

MATH H233 Honors Mathematics: Mathematics in Western Civilization 3 crs.

Common Curriculum: University Honors Program

The objective of this course is to present the development of mathematics in Western Civilization from a cultural, historical, and scientific perspective. The course material consists of important topics selected from the disciplines of number theory, logic, geometry, analysis, and probability theory. Not required of science or math majors.

MATH T122 Math Models 3 crs.

Common Curriculum: Introductory

This course will treat the concepts of model building, model types, model construction and analysis, and practical aspects of mathematical model usage. Applications of modeling techniques will be made to everyday experiences and to larger world problems such as demographics.

MATH Z132 Problem Solving in Ecology 3 crs.

Common Curriculum: Natural Sciences Modern

This course in environmental problem solving teaches students how to use relatively simple mathematical methods (often of the "back-of-the-envelope" type) to understand how planet Earth and its inhabitants interact. The problems will deal with issues such as pollution, the exhausting of fossil fuel resources, resources, and over-population.

MATH Z134 The Computer Impact 3 crs.

Common Curriculum: Natural Sciences Modern

This course provides students with the basic knowledge to understand computer information technology and, more importantly, to understand the impact of this technology and its ethical implications on the individual, organizations and society.