## Georgetown College

# Mathematics

*Dr. Homer White, Coordinator*

## Major

(B.A. degree) Thirty-three hours required. A minimum of thirty hours in Mathematics including MAT 125, 225, 325, 301, 310, 415, and 431. The remaining nine hours in Mathematics must be chosen from courses numbered above MAT 225. Allied course: CSC 115. (Secondary education mathematics majors are required to include MAT 331 and 335 in the major course selections. Total hours in Mathematics and Computer Science required: thirty-three)

(B.S. degree) Thirty-nine hours required. A minimum of thirty-six hours in Mathematics including MAT 125, 225, 301, 310, 325, 415, 431 and 432. The remaining twelve hours are to be chosen from courses numbered above 225, and nine hours must be chosen from MAT 331, 332, 343, 345, 405 or MAT/CSC 327. Allied course: CSC 115. (Secondary Education Mathematics majors are required to take MAT 331 and 335 in the major course selections. Total hours in Mathematics and Computer Science required: thirty-nine.)

## Minor

Eighteen hours required. A minimum of eighteen hours in Mathematics including MAT 125, 225 and 301. The remaining hours must be chosen from courses numbered above MAT 301.

## Notes

Students with strong backgrounds in mathematics will be placed at course levels commensurate with demonstrated ability. Students with a math subscore on the ACT of less than 19 (or its equivalent) must begin GSS 105 (or pass a by-pass exam or transfer an equivalent and previously approved course) no later than the third semester of full-time enrollment. Students must enroll in this course every semester until they have successfully completed the course with a grade of C or above; grading will be X or C or above. Students are not eligible for their Essential Proficiency math or computer science class until they have successfully completed GSS 105 or its equivalent. Drop slips must be approved by the Department Chair or the Mathematics Program Coordinator.

A prerequisite must be taken before the course; a co-requisite may be taken before or concurrently with a course.

## Courses

** 100. Mathematics & Computing. **(3 hours) A survey of computer science including some basic mathematical foundations of computing and a gentle introduction to computer programming. This is a Foundations and Core quantitative course especially for students other than mathematics or computer science majors and requires minimal math background. It can also be an informative gateway into a computer science major or minor for students with little prior exposure to computer programming or who are uncertain about whether they want to pursue computer science. Fall and Spring

** 107. College Algebra. **(3 hours) A survey of algebraic techniques and of functions. Topics include theory of equations and inequalities, graphs, transformations of functions, inverse functions, and exponential and logarithmic functions. Can be used as preparation for calculus. Not applicable to a major or minor in mathematics. Prerequisite: Math ACT subscore of 19, GSS 105, or bypass credit for GSS 105. Fall and Spring

** 109. Calculus for Business and the Social Sciences. ** (3 hours) An introductory survey of calculus, less theoretical in nature than MAT 125. Topics include derivatives of algebraic, exponential, and logarithmic functions, the definite integral, and applications to business and the social sciences. Not applicable to a major or minor in mathematics. Prerequisite: Math ACT subscore of 22 or MAT 107. Fall and Spring

** 111. Elementary Probability and Statistics. ** (3 hours) An introductory study of statistics and basic probability theory including such topics as frequency distributions, measures of central tendency, variation, the normal distribution and tests of hypotheses. Not applicable to a major or minor in mathematics. Prerequisite: ACT math subscore of 19, GSS 105, or bypass credit for GSS 105. Fall and Spring

**123. Precalculus.** (3 hours)Â A survey of algebraic and trigonometric techniques and functions designed to prepare students for the study of calculus.Â Topics include a review of algebra, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, and vectors.Â If time permits, systems of equations and conic sections will be introduced.Â Not applicable to a major or minor in mathematics. Â Prerequisite:Â Math ACT subscore of at least 22 or consent of instructor.Â Students with a grade of C or higher in MAT 123 (or its equivalent) may not subsequently take MAT 107 for credit. Fall

**125. Calculus I. ** (3 hours) A study of the derivative, its applications, and an introduction to the integral. Topics include limits, continuity, techniques of differentiation, optimization, the Fundamental Theorem of Calculus, and indefinite integrals. Prerequisite: MAT 107 or high school precalculus and knowledge of trigonometric functions. Fall and Spring

**170. Special Topics in Mathematics** (.5-3 hours) As needed

** 203. Mathematics for Elementary Education I. ** (3 hours) A detailed development of the mathematics taught in elementary school using a problem-solving approach. Topics include numeration, proportional reasoning, number theory, and, for whole numbers, fractions, and decimals, number sense and standard and non-standard algorithms. For elementary education majors only. Prerequisite: ACT math subscore of 19 or GSS105 or bypass credit for GSS105. Fall

** 204. Mathematics for Elementary Education II. **(3 hours) A continuation of MAT 203. A detailed development of the mathematics taught in elementary school using a problem-solving approach. Topics include further development of the real numbering system, informal geometry, probability and statistics. For elementary education majors only. Prerequisite: MAT 203. Spring

**208. Science Careers Seminar.** (3 hours) An interdisciplinary seminar in STEM (science, technology, engineering and mathematics) disciplines that will introduce students interested in scientific research to an array of professions and professionals in these fields. This introduction will emphasize comprehension and analysis of published scientific research and provide students with the opportunity to meet the science professional who produced the work. Prerequisites: One science or mathematics course for majors, sophomore or junior standing, and approval of the instructor. Fall

**225. Calculus II.** (3 hours) A continuation of the study of the integral and a study of infinite series. Topics include techniques of integration, applications of the definite integral, introduction to differential equations, tests for convergence of series, and power series. Prerequisite: MAT 125 or high school calculus. Fall and Spring

**301. Discrete Mathematics.** (3 hours) An introduction to fundamental theoretical concepts of mathematics and of mathematics in computer science. Topics include logic, techniques of proof, elementary set theory, mathematical induction, numeration systems, relations and functions, counting techniques, and Boolean algebra. Co-requisite: MAT 225 or CSC215. Fall and Spring

** 310. Linear Algebra. ** (3 hours) A theoretical study of systems of linear equations and vector spaces. Topics include matrix algebra, linear transformations, eigenvalues and eigenvectors, determinants, and linear programming. Prerequisites: MAT 225 and 301. Spring

** 325. Calculus III. ** (3 hours) A continuation of the study of single-variable calculus, and a study of multivariable calculus. Topics include parametric equations, polar coordinates, vectors and vector-valued functions, partial differentiation, Lagrange multipliers, double and triple integrals, and line integrals. Prerequisite: MAT 225. Fall

** 327. Introduction to Numerical Methods. ** (3 hours) An introduction to the analysis and implementation of numerical methods. Topics include number representation and errors, locating roots of equations, interpolation, numerical differentiation, numerical integration, numerical solution of linear systems of equations, approximation by spline functions, numerical solution of differential equations, and the method of least squares. Prerequisites: CSC 115 and MAT 301. Odd Springs

**331. Probability Theory. **(3 hours) A study of chance phenomena and probability distributions. Topics include probability laws and elementary combinatorics, random variables, mean and variance, discrete and continuous probability distributions, the Central Limit Theorem, and laws of large numbers. Prerequisite: MAT 225. Even Falls

**332. Mathematical Statistics. **(3 hours) A study of statistical methods and tests of hypotheses. Topics include estimation of parameters, test of hypotheses, linear regression, and analysis of variance. Prerequisite: MAT 331. Odd Springs

**335. Advanced Geometry.** (3 hours) A rigorous but non-axiomatic treatment of advanced geometry on the Euclidean plane, from two or more points of view. Possible viewpoints include synthetic geometry, vector geometry, and geometry using complex numbers. Usually additional topic(s) will be covered, with such topics typically being drawn from axiomatic development of elementary geometry, geometry in higher dimensions, non-Euclidean geometries, and historical studies, especially geometry in non-Western cultures. Prerequisites: MAT 125 and 301. Odd Falls

** 343. Mathematical Modeling. ** (3 hours) An introduction to the study of modeling real-world phenomena, with an emphasis on applications to science. Topics include modeling using difference equations and differential equations, simulation, matrix modeling and Markov chains, and dimensional analysis. Prerequisite: MAT 125 and CSC115. Odd Falls

** 345. Ordinary Differential Equations. **(3 hours) A study of solution methods and applications of differential equations. Topics include first order equations, higher order linear equations, the Laplace transform, and power series techniques. Corequisite: MAT 325. Spring

**405. Complex Analysis. **(3 hours) An introduction to the study of functions of one complex variable. Topics include the algebra of complex numbers, analytic functions, contour integrals, power series, the Residue Theorem, and conformal mappings. Corequisite: MAT 325. Odd Springs

**413. Number Theory and Cryptology.** (3 hours) A survey of topics in elementary number theory, with an emphasis on applications to cryptology. Topics include modular arithmetic, the Chinese Remainder Theorem, the Euler phi function, pseudoprimes, and various cyptosystems, including affine substitutions, the Vigenere square, and RSA. Prerequisite: MAT 301. Even Springs

** 415. Abstract Algebra. ** (3 hours) A theoretical development of basic algebraic structures, with an emphasis on group theory. Topics include cyclic groups, Lagrangeâ€™s Theorem, quotient groups, and homomorphisms. Rings, integral domains, and fields are introduced. Prerequisites: MAT 225 and 301. Even Falls

** 431. Real Analysis I. ** (3 hours) A theoretical development of the elements of calculus. Topics include sequences, continuity, derivatives and integrals of singlevariable functions. Prerequisites: MAT 225 and 301. Odd Falls

** 432. Real Analysis II. ** (3 hours) A continuation of MAT 431. Topics include integration theory, infinite series, and series and sequences of functions. Prerequisite: MAT 431. Even Springs

**440. Independent Study.** (1 to 3 hours) As needed

**470. Advanced Topics.** (0.5 to 3 hours)