This course is an introduction to the rapidly developing science of complexity. It is a discussion of the tools—fractals, chaos, and self-organization—being refined for the purpose of understanding such things as the fractured and irregular structures of Nature, surprise and unpredictability, and the emergence of lifelike properties from inanimate matter. The theme of the course is that complexity can arise from simple origins, such as the repeated application of elementary processing rules. The course emphasizes the use of the computer for visualization. Practical application of these ideas in medicine and engineering will be discussed, as will examples of the connections between complexity in the sciences and that in the humanities and the arts.

Linear programming, matrices, sets and counting, Markov process, difference equations, and graphs. The course will emphasize developing, analyzing, and interpreting mathematical models.

This course is designed for students in the Elementary Education Certification Program and for students planning to complete the Secondary Education Certification Program in an area other than mathematics. The framework of the course consists of four themes: Number Systems and their Operations, Algebra and Functions, Geometry and Measurement, Data Analysis, Statistics, and Probability. Emphasis throughout is on reasoning and problem-solving using concepts and procedures from all four areas. Substantial amounts of both reading and writing will be required and students will be expected to demonstrate both orally and in writing a thorough understanding of the concepts and the ability to communicate this understanding to others.

Analytic geometry, the derivative and differential, elementary functions, limits, continuity, and applications. This course is part 1 (of 2) of a yearlong sequence in differential calculus. At the end of this two-course sequence, students will tackle all the topics above included in differential calculus. Completion of this year- long sequence is equivalent to completion of MAT 111: Differential Calculus. Please note, Pre-Calculus placement score must be less than 50 to take this course. Also note, MAT 106 and MAT 107 can be counted as a two-course quantitative sequence for distribution, but MAT 106 and 107 do not count as a quantitative course otherwise.

This course is the second semester of a year-long sequence in Differential Calculus. Topics in this course include trigonometry, derivatives of trigonometric functions, conic sections, implicit differentiation, and limits at infinity. The semester will conclude with the Fundamental Theorem of Calculus. Throughout the semester, students will work on a project involving Calculus, culminating in a final paper and a presentation. Completion of this year-long sequence is equivalent to completion of MAT 111: Differential Calculus. Also note, MAT 106 and MAT 107 can be counted as a two-course quantitative sequence for distribution, but MAT 106/107 does not count as a quantitative course otherwise.

Introduction to the appropriate methods for analyzing data and designing experiments. After a study of various measures of central tendency and dispersion, the course develops the basic principles of testing hypotheses, estimating parameters, and reaching decisions. Credit for MAT 109 will not be given if taken before or subsequently to BUS 109, PSY 209, or ECN 215.

Analytic geometry, the derivative and differential, elementary functions, limits, continuity, and applications. Prerequisite: It is strongly recommended that a student should have strong algebra and trigonometric skills before taking this course.

The indefinite integral, the definite integral, the fundamental theorem of the integral calculus, sequences, series, and applications. Prerequisite: MAT 111 or MAT 106-107 or permission of the instructor.

Vectors, partial derivatives, and multiple integrals for functions of several variables. Line and surface integrals. Prerequisite: MAT 112 or permission of the instructor.

A critical study of the basic concepts of geometry. This course begins with an axiomatic approach to Euclidean geometry which includes careful proofs of its principal theorems. The course will continue with an examination of various types of non-Euclidean geometries which may include spherical geometry, projective geometry, and/or hyperbolic geometry. Prerequisite: MAT 112 or permission of the instructor.

An introduction to logic, reasoning, and the discrete mathematical structures that are important in computer science. Topics include proposition logic, types of proof, induction and recursion, sets, combinatorics, functions, relations, and graphs.

This course serves as a focused introduction to programming for scientists and engineers. Topics include algorithm development, statistical tests, the fast Fourier transform (FFT), simulating the dynamics of systems represented by coupled ordinary differential equations (e.g. planetary motion via Runge-Kutta methods), numerical integration, root finding, fitting functions to experimental data, and the creation of publication-quality graphics. Students choose and complete an independent research project on a topic related to their major. This course enables students to integrate computation into advanced courses in theoretical and/or experimental science. Programming language: Python. Co-requisite: PHY 112.

An introduction to linear algebra balancing computation and the reading, understanding, and writing of mathematical proofs. A selection of topics from systems of linear equations, matrices, vector spaces, bases, dimension, linear transformations, determinants, eigenvalues, change of basis, matrix representations of linear transformations, matrix decompositions, and applications of linear algebra. It is recommended that students take MAT 240 before this course. Prerequisite: MAT 112 or permission of the instructor.

Elementary methods for the solution of ordinary differential equations, including the expansion of the solution in an infinite series. Prerequisite: MAT 210 or permission of the instructor.

Events and their probabilities, dependence, and independence. Bayes Theorem. Variates and expected values. Theorems of Bernoulli and De Moivre. Special distributions. Central limit theorem and applications. Prerequisite: Mathematics 112 or permission of the instructor.

Theory of functions of a complex variable, including applications to problems in the theory of functions of a real variable. Cauchy’s Integral Formula and its application to the calculus of residues. Prerequisite: Mathematics 210 or permission of the instructor.

Solution of equations and systems of equations by iteration and elimination, numerical differentiation and integration, assessment of accuracy, methods of interpolation and extrapolation. Prerequisite: Mathematics 210 or permission of the instructor.

Factorization of integers. Congruences and residue classes. Theorems of Euler, Fermat, Wilson, and Gauss. Primitive roots. Quadratic residues and the reciprocity theorem. Prerequisite: MAT 240.

Introduction to groups, rings and fields. Other topics may include integral domains, polynomial rings, and fields. Prerequisite: MAT 280 and mathematical maturity as demonstrated by the completion of MAT 240 or permission of the instructor.

A rigorous treatment of single-variable calculus. A selection of topics from the properties and the topology of the real numbers, sequences, series, continuity, differentiation, and Riemann integration. Prerequisite: MAT 210 and mathematical maturity as demonstrated by completion of one of MAT 240, or MAT 280, or permission of the instructor.

A continuation of Real Analysis II. Topics selected according to student and instructor interest. Topics could include analysis in metric spaces, analysis in n-dimensional space, Fourier analysis, functional analysis, measure theory, and Lebesgue integration. Suitable for engineers, chemists, physicists, economists, and mathematicians. Prerequisite: MAT 470

Open to mathematics majors only. Weekly meetings of the majors and faculty in the department are scheduled to provide information about careers, graduate school, thesis topics, and research areas, as well as to prepare each major to make presentations of problem solutions and to make the required presentation on the thesis. All junior mathematics majors are enrolled in the seminar and will receive a pass/fail grade at the end of the semester. Junior standing, and permission of the Department.

Open to mathematics majors only. Senior students will make a presentation of a preliminary outline of their capstone project in the fall semester and will present a report on the completed capstone project in the spring. All senior mathematics majors are enrolled in the seminar and will receive a pass/fail grade at the end of the semester. Prerequisite: Senior Standing, MAT 391/392 and permission of the Department.

Study of an area of mathematics not covered in other courses. Students are urged to suggest possible topics to the department as their interests and needs develop. Prerequisite: Permission of the instructor.