MAT 102 – Topics in Mathematics
This course provides a general survey of mathematical topics that are useful in a variety of fields. Topics include: set theory, logical operators, topics in number theory, graph theory, Euler circuits, Hamiltonian circuits and search algorithms, voting methods, and topics in interest rate theory.
MAT 110 – Elementary Statistics
This course gives students a general overview of modern statistics. Topics include: organization of data; probability and probability distributions; measures of central tendency and variability; normal distributions; sampling; hypothesis testing; correlation and regression.
MAT 120 – Pre-Calculus Mathematics
This is a review of algebra and trigonometry intended to be taken before 131 or 125 by those students whose background in algebra and trigonometry is insufficient. The major emphasis is on the concept of functions. Elementary analytic geometry is discussed, along with algebra, composition of functions, inverse functions, trigonometry, and logarithmic and exponential functions.
MAT 125 – Calculus with Business/Economics Applications
Designed as a one-semester course for concentrators in business administration or economics, topics such as linear functions and models; matrices and matrix algebra; linear systems; functions and graphs; derivatives and integrals; and extremization are included. Partial differentiation also is introduced.
MAT 131 – Calculus and Analytic Geometry I
This course involves fundamental concepts of functions of one variable. Topics include: limits, continuity, differentiation, derivative applications, curve sketching, related rates, and maxima-minima problems. Introduction to indefinite and definite integration including the fundamental theorems, and numerical approximation techniques are also covered.
MAT 132 – Calculus and Analytic Geometry II
This course is a continuation of MAT 131. Topics include transcendental functions, applications of integration, including volume, surface area, arc length, and work. Also covered are integration techniques, indeterminate forms, improper integrals, sequences and series, and Taylor’s theorem.
Prerequisite: MAT 131 with a C- or better.
MAT 233 – Calculus and Analytic Geometry III
This course is a continuation of MAT 132. Topics include polar coordinates, parametric representation, vectors, analysis of functions of two or more variables, multiple integration, line and surface integrals, the divergence and Stokes’ Theorems.
Prerequisite: MAT 132
MAT 250 – Foundation of Mathematics
This is an introduction to abstract mathematics. Topics include symbolic logic, methods of proof (direct, contradiction, and induction), set theory, relations, functions, countable and uncountable sets.
Prerequisite: MAT 132 or permission of the department
MAT 300 – Discrete Mathematics
In this course students will study counting and finite structures. Topics from combinatorics include: permutations and combinations, binomial and multinomial coefficients, recursion, generating functions, and the twelvefold way. Topics from graph theory include graphs, trees, Eulerian and Hamiltonian cycles, planarity, and coloring. Additional topics may include but are not limited to Catalan numbers, Sterling numbers, partitions, Ramsey theory, Latin squares, design theory, and coding theory. Proof techniques, especially proof by induction, will be used throughout the course.
Prerequisite: MAT250 or permission of the department
MAT 310 – Probability and Mathematical Statistics
This course introduces probability and mathematical statistics at the level presupposing knowledge of calculus. Descriptive and inferential statistics are included, along with hypothesis testing, estimation and analysis of variance.
Prerequisite: MAT132 & 250 or permission of the department
MAT 320 – Linear Algebra
This is an introduction to matrix algebra, linear equations, linear independence, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and diagonalization.
Prerequisites: MAT 132 & 250 or permission of the department
MAT 325 – Abstract Algebra
This is an introduction to groups, rings, and fields, ideals, and polynomial rings.
Prerequisite: MAT 250 or permission of the department
MAT 334 – Differential Equations
This course is a study of solution techniques for ordinary differential equations. Topics include the principal types of equations of first and second order, linear equations with constant coefficient, higher order linear and non-linear equations, series solutions, operational methods, systems of equations and modeling problems. Runge- Kutta and other numerical approximation methods may be covered.
Prerequisite: MAT 233 & 320 or permission of the department
MAT 340 – Geometry
This course begins with a study of the most important ideas of Euclidean plane geometry, but also considers the historical significance of Euclid’s original postulates. Special attention is given to the notion of parallelism of lines and the resulting non-Euclidean geometries when the axiom of parallelism is altered. Differential geometry of curves and surfaces is also covered.
Prerequisites: MAT 233 & 250 or permission of the department
MAT 360 – Numerical Analysis
This is a study of numerical methods used in interpolation, differentiation and integration, solutions of equations and systems of equations, solutions of differential equations, fitting of empirical data and error estimation. Some computer or calculator programming will be employed and a basic level of programming is assumed. Applications are made to the sciences and engineering.
Prerequisite: MAT 233 & 250 or permission of the department
MAT 431 – Real Analysis
This course is designed to take a rigorous look at definitions, theorems and concepts taken from the foundational calculus courses. Rigorous treatment is given to topics such as continuity, mean-value theorems, analysis of functions of several variables, extremization and limits. Other topics include sequences, series, the Heine-Borel covering theorem and the Riemann Integral.
Prerequisites: MAT 233 & 250 or permission of the department
MAT 435 – Partial Differential Equations
Topics include: Orthogonal functions; Sturm-Liouville system; initial and boundary value problems; Fourier series; higher transcendental functions; separation-of-variables method; and other methods of solution of equations of mathematical physics.
Prerequisite: MAT 233, 250 & 334 or permission of the department
MAT 438 – Complex Analysis
This is an introduction to the theory of functions of a complex variable, including derivatives, integrals, Cauchy’s theorem, power series, theory of residues, and conformal mappings.
Prerequisite: MAT 233 & 250 or permission of the department
MAT 440 – Introduction to Topology
This course introduces definitions and properties of topological spaces, metric spaces, continuity, homeomorphisms, separation axioms, compactness, connectedness, and fundamental group.
Prerequisites: MAT 233 & 250 or permission of the department
MAT 480 – Advanced Topics in Mathematics
Designed to cover topics of interest that are not covered in other courses.
Prerequisites: Permission of the department
MAT 491 – Senior Seminar
A seminar in topics selected by the course instructor in which independent learning is stressed. The student will present both oral and written reports on the topics covered. Each student will select an additional topic with the approval of the instructor. The student is expected to present both oral and written reports on their topic of choice. This seminar is to be taken in the fall of the student’s senior year.
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