# Mathematics Options

MATH 3107. Differential Equations (3-0-3) Prerequisites: MATH 1132 with a grade of "C" or better and MATH 2115 with a grade of "C" or better. Analytic, qualitative, and numerical techniques for ordinary differential equations. Eigenvalue method and matrix exponential for solving linear systems. Laplace transform methods. Use of appropriate software and technology.

MATH 4195. Undergraduate Research (3-0-3) Prerequisite: Math 3155 with a grade of "C" or better and consent of the Department Chair. Student selection of a research topic, completion of a written research proposal, and in association with a faculty mentor, the execution of the research plan. Each student will prepare both written and oral presentations of the work, and where appropriate, students will be encouraged to make presentations at regional or professional meetings, or submit work to a journal for publication. (Course fee required.)

MATH 5114. Set Theory (3-0-3) Prerequisite: MATH 1132 with a grade of "C" or better. This course is an introduction to intuitive set theory. Topics include sets, operations for sets, relations, equivalence relations, functions, ordering relations, natural numbers, cardinal numbers, and countable sets. Emphasis will be placed on the extension of the natural numbers to the real numbers. This includes Cantor's definition of the real numbers and a detailed study of the properties of the real numbers.

MATH 5116. Number Theory (3-0-3) Prerequisite: MATH 3155 with a grade of "C" or better. Congruences, algebraic number fields, and prime number theorems.

MATH 5125. Discrete Mathematics (3-0-3) Prerequisites: MATH 1132 with a grade of "C" or better or MATH 2125 with a grade of "C" or better. Topics include enumeration, relations, graphs, trees, and modeling computation.

MATH 5165. Numerical Analysis (3-0-3) Prerequisites: MATH 3155 with a grade of "C" or better and MATH 1165 with a grade of "C" or better. Use of computers to solve mathematical problems. Topics may include root finding, interpolation, numerical differentiation and integration, solutions to initial value problems in ordinary differential equations. Error analysis. Use of appropriate software and technology.

MATH 5555. Selected Topics in Mathematics (3-0-3) Prerequisite: MATH 3155 with a grade of "C" or better. Topics for this course will vary. May be repeated for credit with consent of the advisor and if topics are different.