Degree in Mathematics Course Descriptions1 at Manchester College
100 BASIC MATHEMATICS - 2 hours
A review of topics in arithmetic and elementary algebra. Topics include: fractions, decimals, proportions and percent, signed numbers, linear equations and inequalities, and exponents. Fall.
101 MATH FOR ELEMENTARY TEACHERS I - 3 hours
A course designed especially for the teacher of elementary school mathematics. Topics include: problem solving, sets, logic, functions, numeration systems, computational algorithms, rational and irrational numbers, and number theory. Prerequisite: placement. Fall.
102 MATH FOR ELEMENTARY TEACHERS II - 3 hours
Topics include: proportional reasoning, percent, descriptive statistics, probability, intuitive geometry, transformational geometry and measurement. Prerequisite: MATH 101 or consent of instructor. Spring. GE-D.
103 SURVEY OF MATHEMATICAL THOUGHT - 3 hours
A course designed to help students learn more about the contribution of mathematics to human culture. This course develops the capacity to engage in logical thinking and to analyze and communicate technical information. Fall. Spring. GE-D.
112 COLLEGE ALGEBRA - 3 hours
Topics include: exponents and radicals, factoring, linear and quadratic equations, linear inequalities, graphs and functions, polynomials, exponential and logarithmic functions, and systems of linear equations. Prerequisite: placement. Fall. January. Spring. GE-D.
120 PRECALCULUS - 3 hours
Topics include: graphs and functions, polynomials and their zeros, complex numbers, exponential and logarithmic functions, trigonometry (functions, graphs and identities) and applications. Prerequisite: MATH 112 or placement. Fall. January. Spring. GE-D.
121 CALCULUS I - 4 hours
An introduction to calculus including limits, continuity, derivatives and their applications, curve sketching, integrals and the Fundamental Theorem of Calculus. Trigonometric, exponential and logarithmic functions are included. Graphing calculators will be used. Prerequisite: MATH 120 or placement. Fall. Spring. GE-D.
122 CALCULUS II - 4 hours
Topics include: numerical integration, applications of integration, techniques of integration, inverse trigonometric functions, an introduction to differential equations, improper integrals, sequences and series and Taylor’s Theorem. A computer-algebra system will be used. Prerequisite: MATH 121. Fall. Spring.
130 DISCRETE MATHEMATICS - 4 hours
An introduction to discrete methods used in mathematics and computer science. Principal topics covered are: logic, sets, algorithms, number theory, reasoning and proof, recursion, combinatorics, relations and graph theory. Prerequisite: MATH 120 or consent of the instructor. Spring. GE-D
210 INTRODUCTION TO STATISTICS - 4 hours
An introduction to common statistical techniques used in business, social sciences and natural sciences. Course includes: graphic representation of data; sampling design; elementary probability; discrete and continuous random variables; binomial, uniform, normal, student’s t, and chi-squared distributions; linear regression; techniques for estimating and testing population means and proportions; and introduction to non-parametric tests. Students are introduced to a statistical software package during weekly lab sessions. As significant computer work is required, students are expected to possess computer skills comparable to CPTR 101 (i.e., familiarity with the campus network, the web, Windows and Windows applications.) Students are encouraged to take college algebra or have equivalent skills prior to enrolling. Fall. January. Spring. GE-D.
231 MULTIVARIABLE CALCULUS - 4 hours
Topics include: vector analysis in two-and three-dimensional spaces, polar and spherical coordinates, curves in space; multivariable functions and their derivatives, multiple integrals, line integrals, and Green’s and Stokes’ Theorems. Prerequisites: MATH 122, 251. Spring.
233 NUMERICAL ANALYSIS - 3 hours
A study of computational issues and methods used in applied mathematics and scientific computing. Topics include: computation errors; interpolation; convergence of numerical methods; approximate integration; numerical solution of ordinary differential equations; and numerical solution to systems of linear and non-linear equations. The course is oriented toward machine computation and involves programming of various solution techniques. Prerequisite: CPTR 105; MATH 121. Spring, odd years