Courses in mathematics (designated MATH) may be applied as appropriate toward

- the general education requirement in mathematics (with the exception of MATH 009 and 012)
- electives

Beginning-level courses such as MATH 009 and 012 are designed to help students build confidence and skills in basic mathematics. Placement tests are required for enrollment in MATH 012, 106, 107 and recommended for enrollment in MATH 103. Due to their preparatory nature, the institutional credits earned for Math 009 and 012 do not apply toward a degree and will not transfer to other colleges and universities.

Based on the score that the student achieves on a UMGC placement exam, one or more of these courses serve as the student's prerequisite(s) for MATH 106 and MATH 107. These courses are listed on the student's transcript and the grades earned will be used in the calculation of the student's grade point average (GPA). Institutional credit does not apply toward the student's residency or degree requirements.

You are expected to own and use scientific calculators in all mathematics and statistics courses.

Degree-seeking students should complete the math general education requirement (or present the equivalent in transfer) during their first 18 credits of enrollment at UMGC.

## Introductory Algebra (3 Credits, MATH 009)

(Not open to students who have already successfully completed a higher-level mathematics course. Does not apply toward degree requirements. Yields institutional credit only.) A comprehensive review of real number properties and operations, including fractions, percentages, operations with signed numbers, and geometric formulas. The objective is to develop fluency in the language of introductory algebra; develop number sense and estimation skills; and use mathematical modeling to translate, solve, and interpret applied problems. Topics include linear equations and inequalities, equations of lines, graphs on number lines and rectangular coordinate systems, rules of exponents, and operations on polynomials. Students may receive credit for only one of the following courses: MATH 009, MATH 009M, or MATH 100.

## Intermediate Algebra (3 Credits, MATH 012)

(Not open to students who have already successfully completed a higher-level mathematics course. Does not apply toward degree requirements. Yields institutional credit only.) Prerequisite: MATH 009 or an appropriate result on the placement test. A study of problem-solving techniques in intermediate-level algebra. The goal is to demonstrate number sense and estimation skills; interpret mathematical ideas using appropriate terminology; manipulate, evaluate, and simplify real-number and algebraic expressions; and translate, solve, and interpret applied problems. Emphasis is on numbers and algebraic properties, graphing skills, and applications drawn from a variety of areas (such as finance, science, and the physical world). Topics include polynomials; factoring; exponents and their notation; rational expressions and equations; rational exponents and radical expressions; linear, quadratic, and other equations; and inequalities. Students may receive credit for only one of the following courses: MATH 012, MATH 101, MATH 101M, MATH 102, MATH 102M, MATH 199A, or MATH 199M.

## College Mathematics (3 Credits, MATH 103)

Prerequisite: MATH 012 or approval of the department. This course is not intended for students planning to take MATH 107 or higher-numbered mathematics courses and does not serve as a prerequisite for these courses. This course focuses on data driven applications and the development of critical thinking skills related to mathematics. Topics include problem solving, equations, inequalities, linear systems, graphs, functions, consumer mathematics, financial management, probability, and statistics.

## College Algebra (3 Credits, MATH 107)

(The first course in the two-course series MATH 107–108. An alternative to MATH 115). Prerequisite: MATH 012 or an appropriate result on the placement test. 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 (3 Credits, MATH 108)

(The second course in the two-course series MATH 107–108. An alternative to MATH 115.) Prerequisite: MATH 107 or an appropriate result on the placement test. 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.

## Calculus A (4 Credits, MATH 130)

Prerequisite: MATH 108, MATH 115, or an appropriate result on the placement test. An introduction to calculus. Topics include functions, continuity, derivatives, and applications of derivatives including maximum-minimum problems, related rates and graphs of functions. Students may receive credit for only one of the following courses: MATH 130, MATH 140, or MATH 220.

## Calculus B (4 Credits, MATH 131)

(A continuation of MATH 130.) Prerequisite: MATH 130. A study of definite and indefinite integrals. Topics include calculations of area between curves; applications of integrals (including volumes, arc length, surface, work, and moments; area in polar coordinates; exponential, logarithmic, inverse trigonometric, and hyperbolic functions; and integration by parts. Students may receive credit for only one of the following courses: MATH 131, MATH 140, MATH 141, MATH 220, or MATH 221.

## Calculus C (4 Credits, MATH 132)

(A continuation of MATH 131.) Prerequisite: MATH 131. Further study of integrals. Topics include techniques of integration (including parts, trigonometric substitution, and partial fractions); improper integrals; sequences and series (including convergence tests, Taylor polynomials, and Taylor's theorem); conic sections; and vectors (including dot and cross products). Students may receive credit for only one of the following courses: MATH 132, MATH 141, or MATH 221.

## Calculus I (4 Credits, MATH 140)

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 (4 Credits, MATH 141)

(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.