Degree in Mathematics Course Descriptions2 at Manchester College
240 MATHEMATICAL STATISTICS - 4 hours
Basic concepts of probability; expectation; variance, covariance, distribution functions; bivariate, marginal and conditional distributions. Treatment of experimental data; normal sampling theory; confidence intervals and test of hypotheses; introduction to regression and to analysis of variance. Prerequisite: MATH 122. Fall, odd years.
245 ORDINARY DIFFERENTIAL EQUATIONS - 3 hours
Topics include: classification of differential equations; methods of solving first order equations, second and higher order linear equations, and systems of linear equations; series solutions; and existence theorems. Prerequisite: MATH 122. Spring, even years.
251 LINEAR ALGEBRA I - 4 hours
Solution of linear systems, matrices and determinants, eigenvalues and eigenvectors, vector algebra, representation of lines and planes in Rn, linear transformations and mathematical models using matrix algebra. Prerequisites MATH 121, 130; or consent of the instructor. Fall.
303 MATH FOR ELEMENTARY TEACHERS III - 3 hours
The study of curriculum, methods, computer applications, materials and assessment for elementary school mathematics programs. Taken as part of the Elementary Methods Block, with field experiences a required component. Prerequisites: MATH 101, 102. Fall.
306 GEOMETRY - 3 hours
A study of the logical structure and content of both Euclidean and non-Euclidean geometries. The approach to Euclidean geometry is via Hilbert’s axioms. Prerequisite: MATH 251. Fall, even years.
330 OPERATIONS RESEARCH MODELS - 3 hours
Introduction to mathematical modeling processes; allocation models involving linear programming; simplex algorithm; dynamic programming; transportation models; network models; graph theory; Markov chain models; queuing theory and game theory. Prerequisite: MATH 130 or 251 or consent of instructor. January or spring, even years.
333 ALGEBRAIC STRUCTURES - 4 hours
Basic properties of groups, rings, factor groups, ideals, quotient rings, integral domains, fields, polynomials and elementary number theory. Prerequisite: MATH 251. Fall, odd years.
402 LINEAR ALGEBRA II - 3 hours
Numerical methods for solving linear systems, the four fundamental subspaces and applications, orthogonality and approximation, eigenvectors, eigenvalues, and diagonalization of matrices and applications. Prerequisite: MATH 251. Spring, odd years.
421 REAL ANALYSIS - 3 hours
Topics include: the completeness of the real number system; sequences and their limits; elementary point-set topology; and continuity and uniform continuity. The theory of series, the derivative and the Riemann integral will be treated as time permits. Prerequisites: MATH 130, 231. Fall, even years.
475 INTERNSHIP IN MATHEMATICS - 1-3 hours
Students work in business, industry, government or other agencies applying mathematical tools (e.g., probability, statistics, optimization) to real-world problems. Students are supervised by a professional with significant experience in such applications and also a faculty member. A written report describing the overall project and the student’s contribution will complete the course. Students must formally enroll in this course prior to beginning their work experience. Course may be repeated once for a maximum of four hours credit. Prerequisite: MATH 130, 122; permission of the department chair.
499 SENIOR PROJECT (W) - 1-3 hours
An in-depth study of some area of mathematics under the guidance of a primary and secondary faculty advisor. Students will write a thesis and give an oral presentation based on the thesis. Students will enroll either once or twice for a total of three hours credit. Prerequisite: ENG 111; permission of the department chair.
380 or 480 SPECIAL PROBLEMS - 1-4 hours
A student who has demonstrated ability to work independently may propose a course and pursue it with a qualified and willing professor. The department chair and the vice president and dean for academic affairs must also approve. A set of guidelines is available at the Office of the Registrar.
385 or 485 SEMINAR - 1-4 hours
An in-depth consideration of a significant scholarly problem or issue. Students pursue a supervised, independent inquiry on an aspect of the topic and exchange results through reports and discussions