Mathematics

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Majors and Minors

Classes

MAT107 : College Algebra

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 MAT109. Not applicable to a major or minor in mathematics. Students with a grade of C or higher in MAT123 (or its equivalent) may not subsequently take MAT107 for credit.

Credit Hour(s)

3

Prerequisites

Math ACT subscore of 19 or permission of the mathematics coordinator.

MAT109 : Calculus for Business and the Social Sciences

An introductory survey of calculus, less theoretical in nature than MAT125. 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. Students with a grade of C or higher in MAT125 (or its equivalent) may not subsequently take this course for credit.

Credit Hour(s)

3

Prerequisites

Math ACT subscore of 22 or MAT107.

MAT111 : Elementary Probability and Statistics

An introductory study of statistics, including such topics as numerical and graphical descriptive statistics, sampling methods and design of studies and experiments, basic probability, the distribution of sampling statistics, and inferential procedures such as confidence intervals and tests of hypotheses. Not applicable to a major or minor in Mathematics.

Credit Hour(s)

3

Prerequisites

Math ACT subscore of 19 or permission of the mathematics coordinator.

MAT115 : Liberal Arts Mathematics

An introductory mathematics class with a focus on practical applications including but not limited to: money management, basic statistics, voting and social choice, and management science. Students with a grade of C or higher in MAT109 or MAT125 (or its equivalent) may not subsequently take this course for credit.  Not applicable to a major or minor in Mathematics.

Credit Hour(s)

3

MAT123 : Precalculus

A survey of algebraic and trigonometric techniques and functions designed to prepare students for the study of calculus. Topics include a review of algebra, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, and vectors. If time permits, systems of equations and conic sections will be introduced. Not applicable to a major or minor in mathematics.

Credit Hour(s)

3

Prerequisites

Math ACT subscore of 22 or consent of instructor.

MAT125 : Calculus I

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.

Credit Hour(s)

3

Prerequisites

a C or better in MAT123, or high school precalculus and knowledge of trigonometric functions.

MAT203 : Mathematics for Elementary Education I

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.

Credit Hour(s)

3

Prerequisites

Sophomore standing.

MAT204 : Mathematics for Elementary Education II

A continuation of MAT203. 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.

Credit Hour(s)

3

Prerequisites

MAT203.

MAT225 : Calculus II

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.

Credit Hour(s)

3

Prerequisites

MAT125 or the equivalent.

MAT301 : Discrete Mathematics

An introduction to fundamental theoretical concepts of mathematics. Topics include logic, techniques of proof, elementary set theory, mathematical induction, relations and functions, and counting techniques.

Credit Hour(s)

3

Corequisites

MAT225.

MAT303 : Fundamentals of Data Computing

This course focuses on data analysis in settings where the data is so large, dispersed or messy that machine-processing is required to gather, clean and transform it into forms suitable for analysis. We also study computer-based techniques for the analysis of such data, including machine data visualization and machine-learning. Finally we consider how the practice of reproducible research and the development of interactive web- based applications can enhance communication of the results of data analysis.

Credit Hour(s)

3

Prerequisites

MAT111 or CSC115 or PSY211 or permission of the instructor.

MAT310 : Linear Algebra

A theoretical study of systems of linear equations and vector spaces. Topics include matrix algebra, linear transformations, eigenvalues and eigenvectors, determinants, and linear programming.

Credit Hour(s)

3

Prerequisites

MAT225

MAT325 : Calculus III

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.

Credit Hour(s)

3

Prerequisites

MAT225.

MAT331 : Probability Theory

A study of chance phenomena and probability distributions, with selected applications. Topics include probability laws and elementary combinatorics, random variables, discrete and continuous probability distributions, joint distributions, and conditional probability.

Credit Hour(s)

3

Prerequisites

MAT225.

MAT335 : Advanced Geometry

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.

Credit Hour(s)

3

Prerequisites

MAT125 and 301.

MAT337 : Applied Statistical Models

A course on modeling in statistics, with a focus on applications. Topics include: basic model designs, geometric understanding of models and random vectors, interpretation of models and inference from them (confidence intervals and hypothesis testing), investigating causation, experiments.

Credit Hour(s)

3

Prerequisites

MAT225

MAT343 : Mathematical Modeling

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, and matrix modeling and Markov chains.

Credit Hour(s)

3

Prerequisites

MAT125 and CSC115.

MAT345 : Ordinary Differential Equations

A study of solution methods and applications of ordinary differential equations. Topics include first order equations, second and higher order linear equations, and linear systems. Additional topics are chosen from: the Laplace transform, power series techniques, Fourier series, nonlinear systems, calculus of variations. An introduction to partial differential equations may also be included.

Credit Hour(s)

3

Corequisites

MAT325.

MAT415 : Abstract Algebra

A theoretical development of basic algebraic structures, with an emphasis on group theory. Topics include cyclic groups, Lagrange’s Theorem, quotient groups, and homomorphisms. Rings, integral domains, and fields are introduced.

Credit Hour(s)

3

Prerequisites

MAT225 and 301.

MAT431 : Real Analysis I

A theoretical development of the elements of calculus. Topics include sequences, continuity, derivatives, and integrals of single-variable functions.

Credit Hour(s)

3

Prerequisites

MAT225 and 301.

MAT432 : Real Analysis II

A continuation of MAT431. Topics include integration theory, infinite series, and series and sequences of functions.

Credit Hour(s)

3

Prerequisites

MAT431.

MAT460 : Internship

Students may receive graduation credit for internships with appropriate disciplinary content that meet the faculty-approved criteria for academic internships. Such experiences include a significant reflective component and must be supervised by a full-time member of the Georgetown College faculty.

Credit Hour(s)

1 - 3

Prerequisites

Consent of the supervising instructor.