# Course Information | UMGC

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## Topics for Mathematical Literacy

#### MATH 105 | 3 Credits

Course Desc: (For students who do not need a college algebra, statistics, or higher-level mathematics course. Meets the general education requirement in mathematics.) An investigation of contemporary topics in mathematics. The aim is to apply mathematical processes to solve problems involving exponential and logarithmic modeling, personal finance, probability, basic logical thinking, and statistical reasoning.

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## College Algebra

#### MATH 107 | 3 Credits

Course Desc: (The first course in the two-course series MATH 107-MATH 108. An alternative to MATH 115). An introduction to equations and inequalities and a study of functions and their properties, including the development of graphing skills with polynomial, rational, exponential, and logarithmic functions. The objective is to apply appropriate technology and demonstrate fluency in the language of algebra; communicate mathematical ideas; perform operations on real numbers, complex numbers, and functions; solve equations and inequalities; analyze and graph circles and functions; and use mathematical modeling to translate, solve, and interpret applied problems. Technology is used for data modeling. Discussion also covers applications. Students may receive credit for only one of the following courses: MATH 107 or MATH 115.

## Trigonometry and Analytical Geometry

#### MATH 108 | 3 Credits

Course Desc: (The second course in the two-course series MATH 107¿MATH 108. An alternative to MATH 115.) Prerequisite: MATH 107. An introduction to trigonometric functions, identities, and equations and their applications. The goal is to demonstrate fluency in the language of trigonometry, analytic geometry, and selected mathematical topics; communicate mathematical ideas appropriately; apply and prove trigonometric identities; solve triangles and trigonometric equations; and perform vector operations. Discussion covers analytical geometry and conic sections, systems of linear equations, matrices, sequences, and series. Students may receive credit for only one of the following courses: MATH 108 or MATH 115.

## Pre-Calculus

#### MATH 115 | 3 Credits

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Course Desc: (Not open to students who have completed MATH 140 or any course for which MATH 140 is a prerequisite.) An explication of equations, functions, and graphs. The goal is to demonstrate fluency in pre-calculus; communicate mathematical ideas appropriately; solve equations and inequalities; analyze and graph functions; and use mathematical modeling to translate, solve, and interpret applied problems. Topics include polynomials, rational functions, exponential and logarithmic functions, trigonometry, and analytical geometry. Students may receive credit for only one of the following courses: MATH 107, MATH 108, or MATH 115.

## Calculus I

#### MATH 140 | 4 Credits

Course Desc: Prerequisite: MATH 108 or MATH 115. An introduction to calculus. The goal is to demonstrate fluency in the language of calculus; discuss mathematical ideas appropriately; and solve problems by identifying, representing, and modeling functional relationships. Topics include functions, the sketching of graphs of functions, limits, continuity, derivatives and applications of the derivative, definite and indefinite integrals, and calculation of area. Students may receive credit for only one of the following courses: MATH 130, MATH 131, or MATH 140.

## Calculus II

#### MATH 141 | 4 Credits

Course Desc: (A continuation of MATH 140.) Prerequisite: MATH 140. A study of integration and functions. The aim is to demonstrate fluency in the language of calculus; discuss mathematical ideas appropriately; model and solve problems using integrals and interpret the results; and use infinite series to approximate functions to model real-world scenarios. Focus is on techniques of integration, improper integrals, and applications of integration (such as volumes, work, arc length, and moments); inverse, exponential, and logarithmic functions; and sequences and series. Students may receive credit for only one of the following courses: MATH 131, MATH 132, or MATH 141.

## Calculus III

#### MATH 241 | 4 Credits

Course Desc: Prerequisite: MATH 141. An introduction to multivariable calculus. Exposition covers vectors and vector-valued functions; partial derivatives and applications of partial derivatives (such as tangent planes and Lagrangian multipliers); multiple integrals; volume; surface area; and the classical theorems of Green, Stokes, and Gauss. The objective is to use multivariate calculus to solve real-world problems.

## Differential Equations

#### MATH 246 | 3 Credits

Course Desc: Prerequisite: MATH 141 or MATH 132. An introduction to the basic methods of solving differential equations. The goal is to demonstrate fluency in the language of differential equations; communicate mathematical ideas; solve boundary-value problems for first- and second-order equations; and solve systems of linear differential equations. Topics include solutions of boundary-value problems for first- and second-order differential equations; solutions of systems of linear differential equations; series solutions, existence, and uniqueness; and formulation and solution of differential equations for physical systems.

## Concepts of Real Analysis I

#### MATH 301 | 3 Credits

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Course Desc: Prerequisite: MATH 141. A study of real analysis. The aim is to construct formal mathematical proofs and solve problems. Topics include sequences and series of numbers, continuity and differentiability of real-valued functions of one variable, the Riemann integral, sequences of functions, and power series. Students may receive credit for only one of the following courses: MATH 301 or MATH 410.

## Linear Algebra

#### MATH 340 | 4 Credits

Course Desc: Prerequisite: MATH 140. An examination of linear algebra. The aim is to demonstrate applications of various concepts in linear algebra. Topics include abstract vector spaces, linear transformations, algebra of matrices, determinants, similarity, eigenvalues and eigenvectors, and applications to systems of equations. Discussion also covers solutions of problems in physics, engineering, and the sciences. Students may receive credit for only one of the following courses: MATH 240, MATH 340, MATH 400, or MATH 461.

## Algebraic Structures

#### MATH 402 | 3 Credits

Course Desc: Prerequisite: MATH 141. An overview of algebraic structures. The aim is to construct mathematically correct and concise proofs. Set theory, techniques of proofs, and the application of those techniques are introduced. Topics include groups, subgroups, isomorphisms, rings, integral domains, and fields.

## Complex Analysis

#### MATH 463 | 3 Credits

Course Desc: Prerequisite: MATH 141. An overview of the theory and practice of complex variables to enrich the study of differential equations, real analysis, and numerical analysis. The aim is to use complex variables to analyze problem that have direct application to physical problems. Topics include complex numbers, functions, inverse functions, mappings, integrals, series, and poles in the complex numbers.

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