# Course Descriptions

## MA 019W Quantitative Reasoning Workshop

This course is the workshop portion of MA 119 Math for Liberal Arts with Quantitative Reasoning Workshop, and must be taken concurrently with MA 119. The workshop provides a review of quantitative reasoning topics, including rate, ratio, and percents; perimeter, area, volume, and the units and conversion between units for those calculations; the mathematics of finance; linear models; visual representation of data; and estimation. This course is designed to help reduce students' mathematical anxiety and increase their confidence with mathematical applications. Credits for MA 019W may not be applied toward any degree. Corequisite: MA 119. (3)

## MA 094 Quantitative Reasoning

Provides a review of quantitative reasoning topics, including rate, ratios, and percents; perimeter, area, volume, and the units and conversion between units for those calculations; the mathematics of finance; linear models; visual representation of data; and estimation. This course is designed to help reduce students' mathematical anxiety and increase their confidence with mathematical applications. Intended as preparation for MA 121, MA 124, MA 127, and MA 132. Credits for MA 094 may not be applied toward any degree. Prerequisite: complete University's Directed Self-Placement process. (3)

## MA 095 Intermediate Algebra

This intermediate algebra course provides a review of topics, techniques, terminology, and applications of algebra. This course is intended as preparation for MA 151 and MA 171. Credits for MA 095 may not be applied toward any degree. Prerequisite: complete University's Directed Self-Placement process. (3)

## MA 119 Math for Liberal Arts with Quantitative Reasoning Workshop

This course is one part of a two-part module and must be taken concurrently with MA 019W Quantitative Reasoning Workshop. The course and its companion workshop review quantitative reasoning while presenting a survey of topics in college-level mathematics that develop critical thinking skills, flexibility of thought, appropriate problem-solving strategies, and the ability to express ideas in mathematical language. Strategies include modeling, using symmetry, algebra, logical reasoning, set theoretical analysis, detecting patterns, and making predictions. Emphasis is placed on developing skills in analysis, estimation, and verification. Prerequisite: complete University's Directed Self-Placement process. Corequisite: MA 019W. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 121 Math for Liberal Arts

A survey of topics in mathematics that develops critical thinking skills, flexibility of thought, appropriate problem-solving strategies, and the ability to express ideas in mathematical language. Strategies include modeling, symmetry, algebra, logical reasoning, set theoretic analysis, and probability. Emphasis is placed on developing skills in analysis, estimation, and verification. Prerequisite: complete University's Directed Self-Placement process, or a grade of C or better in MA 094 or MA 095. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 124 History of Mathematics

Further develops students' understanding of elementary mathematics using the history of the subject. Topics include numeration, computation, geometry, and the use of mathematics in problem solving. Offered spring semester only. Prerequisite: complete University's Directed Self-Placement process, or grade of C or better in MA 094 or MA 095. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 127 Applied Geometry

A survey of elementary geometrical topics stressing numerical relations rather than proofs. Emphasis is given to topics needed for design and for teacher preparation below the secondary level (proportion, area and volume, elementary trigonometry, symmetry). Prerequisite: complete University's Directed Self-Placement process, or a grade of C or better in MA 094 or MA 095. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 132 Statistical Analysis

An introduction to basic descriptive and inferential statistical procedures used in the analysis of data. Prerequisites: complete University's Directed Self-Placement process, or a grade of C or better in MA 094 or MA 095; placement into or completion of EN 101. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 151 Mathematical Methods for Business

This course uses Excel to apply mathematical analyses for data that reflects realistic business scenarios. Students will develop a deep understanding of linear models, including systems of linear equations and systems of linear inequalities. They will also be able to recognize, manipulate, and perform analyses involving polynomial and exponential functions. The course covers introductory probability, expected value, and regression. The mathematical concepts are applied to problems in break-even analysis, optimization, and decision analysis, with an eye to risk and sensitivity in model outcomes. Prerequisite: complete University's Directed Self Placement process, or a grade of C or better in MA 095. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 171 Calculus with Precalculus A

This is the first part of a year-long sequence that integrates the study of Precalculus with the study of Calculus. This first semester includes a review of functions, including polynomial and rational functions, limits, differentiation of algebraic functions, and applications of differentiation. Graphing calculators are used to explore properties of functions and to facilitate computations. Prerequisite: complete University's Directed Self-Placement process, or a grade of C or better in MA 095. Liberal Arts Core/University Requirements Designation: MT. (4)

## MA 172 Calculus with Precalculus B

This is the second part of a year-long sequence that integrates the study of Precalculus with the study of Calculus. This second semester begins with an introduction to integration and continues to apply the study of differentiation and integration to exponential, logarithmic, and trigonometric functions. The course includes a careful look at integration using substitution and integration by parts. Graphing calculators are used to explore properties of functions and to facilitate computations. Completion of this course is equivalent to completion of MA 181. Prerequisite: a grade of C or better in MA 171. (4)

## MA 181 Calculus

Emphasizes separate visual, analytical, and numerical approaches to the fundamental ideas of elementary differential and integral calculus. Topics include differentiation and applications of the derivative, as well as a careful study of integration using substitution and integration by parts. Graphing calculators are used to explore properties of functions and to facilitate computations. Prerequisite: complete University's Directed Self-Placement process. Liberal Arts Core/University Requirements Designation: MT. (4)

## MA 200 Calculus of the Infinite

A continued study of differential and integral calculus of a single variable, with a focus on concepts in calculus considering infinite processes. Topics include the Riemann sum, areas and arc length in Cartesian and polar coordinates, volume of surfaces of revolution, improper integrals, and infinite sequences and series. Graphing calculators and computer algebra software are used to explore properties of functions and to facilitate computations. Offered spring semester, even-numbered years, only. Prerequisite: complete University's Directed Self-Placement process, or a grade of C or better in MA 172 or MA 181. Liberal Arts Core/University Requirements Designation: MT. (3).

## MA 210 Seminar with Introduction to Proofs through Discrete Math

This course introduces students to mathematical proofs through the topics of discrete mathematics, and simultaneously exposes students to careers and opportunities in mathematics. Additionally, there is a focus on written and oral presentation skills for mathematical topics. Offered fall semester only. (3)

## MA 215 Linear Algebra and Proof Techniques

An introduction to proof through the study of real vector spaces, linear transformations, matrices, determinants, eigenvalues, and eigenvectors. The course will be proof-based with an emphasis on concepts and logic. The course is offered spring semester, odd-numbered years, only. Prerequisites: a grade of C or better in MA 172 or MA 181 and MA 210 or instructor permission. (3)

## MA 218 Probability and Statistics

Introduction to probability theory and statistical inference with a focus on applications in life sciences. Includes probability laws, probability distributions, sampling methods, experimental design, descriptive statistics, confidence intervals, hypothesis testing, types of error, correlation and regression, and analysis of variance. Computer software for statistical computing is used to apply the concepts covered to realistic data sets from the biological and/or social sciences. Offered spring semester only. Prerequisite: a grade of C or better in MA 172 or MA 181. (3)

## MA 221 Multivariable Calculus

A study of multivariable calculus. Includes elementary three-dimensional geometry, vector-valued functions, partial differentiation, multiple integration, and computations using Green's and Stokes' theorems. Students are introduced to the appropriate use of computer algebra software to create three-dimensional graphs and to perform difficult numerical integration. Offered spring semester, odd-numbered years, only. Prerequisite: a grade of C or better in MA 172 or MA 181 or instructor permission. (4)

## MA 230 Scientific Computing

Introduces the use of computers in mathematics problem solving, including elementary numerical methods. Teaches programming fundamentals, including data and algorithm structure, and modular programming. Software vehicles include Excel, Mathematica, Matlab, and R. Offered fall semester, odd-numbered years, only. Prerequisite: a grade of C or better in MA 172 or MA 181. (3)

## MA 257 Introduction to Number Theory and Proof Techniques

An introduction to proof techniques using the many methods of proof that arise in number theory. This course takes a formal look at the properties of the integers and includes topics such as congruencies, quadratic reciprocity, and solution of Diophantine equations. Offered spring semester, even-numbered years, only. Prerequisite: a grade of C or better in MA 210. Liberal Arts Core/University Requirements Designation: DSINQ. (3)

## MA 260 Discrete Mathematics for Information Technology

Introduces basic discrete mathematical ideas, many of which were developed in the late 20th century to solve problems in computer science. Topics include elementary logic, Boolean algebras and combinatorial circuits, number systems, sets, counting, elementary probability, and an introduction to graphs and trees. Offered fall semester only. Prerequisite: a grade of C or better in a college-level mathematics course, complete University's Directed Self-Placement process with placement into MA 171 or MA 181, or permission of the instructor. Liberal Arts Core/University Requirements Designation: MT. (3)

## MA 309 Mathematics Seminar

This weekly seminar is intended for mathematics majors, and encouraged for mathematics minors. Includes lectures on mathematical topics or careers in mathematics. Students will plan and give at least one large presentation, and they will partner with other students for smaller presentations. The large presentation must be researched using articles supported by MathSciNet investigations. Offered fall semester only. Prerequisite: MA 210 or permission of the instructor. (1)

## MA 325 Differential Equations

Provides students with a first look at Ordinary Differential Equations that focuses on concepts rather than techniques, and equally addresses qualitative, numeric, and analytic approaches to this subject. Students must work intelligently with a computer algebra system to analyze various differential equations and models that arise in the course. Topics include basic modeling, slope fields, bifurcations, some standard forms of differential equations, numerical methods, properties of linear systems, and the analysis of nonlinear systems. Offered fall semester, even-numbered years, only. Prerequisite: a grade of C or better in MA 172 or MA 181. Liberal Arts Core/University Requirements Designation: DSINQ. (3)

## MA 385 Approaches to Teaching Secondary Mathematics

Prepares the student to teach mathematics at the secondary level by integrating content mastery with effective pedagogical strategies. Field experience: 20 hours. Prerequisites: ED 200, ED 327, and PSY 110. (3)

## MA 400 Internship

Students register for an internship with a cooperating employer in the Washington metropolitan area. The experience is monitored by a supervising professor and a representative of the cooperating firm. Students completing requirements for mathematics teaching certification fulfill internship requirements through student teaching. Prerequisite: junior status. Liberal Arts Core/University Requirements Designation: EXP. (3-6)

## MA 409 Mathematics Seminar

This weekly seminar is intended for mathematics majors and encouraged for mathematics minors. Includes lectures on mathematical topics or careers in mathematics. Students will be expected to be a senior partner with other seminar participants preparing smaller investigations, and will give a larger presentation explaining an approved mathematical topic from a refereed mathematics journal. Offered fall semester only. Prerequisite: MA 309 or permission of the instructor. (1)

## MA 418 Stochastic Modeling

A survey of real-world phenomena that are modeled using statistical methods. Topics include decision analysis (tables, trees, and utility theory; applications of Bayes Theorem; forecasting; regression; Markov chains; and game simulations. Offered spring semester, even numbered years only. Prerequisite: a grade of C or better in MA 218. (3)

## MA 420 Abstract Algebra

An introduction to abstract reasoning in mathematics in the context of algebraic structures such as rings, fields, and groups. Offered fall semester, even-numbered years, only. Prerequisite: a grade of C or better in MA 215 or MA 257. Liberal Arts Core/University Requirements Designation: DSINQ, WI. (3)

## MA 421 Project

This course is for the independent study of a particular area of mathematics under the direction of a faculty member. Prerequisite: approval of department chair. (1-3)

## MA 425 Introduction to Real Analysis

An introduction to proof techniques using the many methods of proof that arise in the study of number systems and in continuous mathematics, with emphasis on proofs of calculus. Offered fall semester, odd numbered years only. Prerequisite: a grade of C or better in MA 200 and MA 215 or MA 257. Liberal Arts Core/University Requirements Designation: DSINQ, WI. (3)

## MA 427 Euclidean and Non-Euclidean Geometries

A study of plane geometry based on Euclid's axioms, both with and without the parallel postulate. Includes formal study of the consequences of these axioms and algebraic models of both Euclidean and non-Euclidean systems. Offered fall semester, odd-numbered years, only. Prerequisite: a grade of C or better in MA 215 or MA 257. (3)

## MA 433 Research

A student in this course will conduct collaborative research (scholarly work leading to new knowledge) under the direction of a faculty member. Prerequisites: application and approval of department chair. Liberal Arts Core/University Requirements Designation: EXP. (1-6)

## MA 440 Topics in Mathematics

This course is intended as an opportunity to offer an elective topic of interest for mathematics majors. Topics may be chosen from Complex Analysis, Logic, Topology, Mathematical Modeling, Combinatorics, Graph Theory, and Theory of Computation. Prerequisites: a grade of C or better in MA 200 and MA 210. (3)