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# Undergraduate Math Courses

In addition to the courses approved Foundational Math under the REAL Curriculum, we offer the following mathematics courses

**MATH 122 - Math Content for Teachers II **(R, GE)

Covers a variety of topics in geometry and basic algebra. The content of this course adheres to the NCTM Standards and the Virginia Standards of Learning where they can appropriately be applied. Will not satisfy requirements for a major in mathematics. Fomerly MATH 112. For more information, see MATH 122's detailed course description. (3 credits)

**MATH 126 - Business Calculus **(R, GE)

An introduction to calculus with particular emphasis on applications in business and economics. Topics include functions, limits and continuity, differentiation, exponential functions and logarithms, anti-derivatives and the integral. Students who wish to strengthen their mathematics skills before taking MATH 126 are advised to enroll in MATH 125. Will not satisfy requirements for a major in mathematics. Students who have received credit for MATH 151 may not also receive credit for MATH 126. For more information, see MATH 126's detailed course description. (3 credits)

Prerequisites: A grade of C or better in MATH 125 Precalculus I OR a score of 61 or greater on our math placement test ALEKS PPL

**MATH 132 - Honors Applications of Mathematics **(R, GE)

An introduction to the application of mathematical ideas for Honors students. Topics vary. This course can be taken more than once with different topics. For more information, see MATH 132's detailed course description. (3 credits)

**MATH 138 - Precalculus Function Analysis** (R, GE)

Basic concepts of functions and related real number algebra and graphing, especially polynomial, exponential and logarithmic functions; elements of trigonometry. Will not satisfy requirements for a major in mathematics. For more information, see MATH 138's detailed course description. (3 credits)

Prerequisites: A grade of C or better in MATH 125 Precalculus I OR a score of 61 or greater on our math placement test ALEKS PPL

**MATH 142 -- Discrete Mathematics**

Introduces the student to discrete structures and mathematical tools which are used to represent, analyze, and manipulate discrete objects. These include sets, functions, relations, graphs, combinatorics, discrete probability, recurrence relations, mathematical induction, symbolic logic, and graphs and trees. For more information, see MATH 142's detailed course description.

Prerequisites: Mathematics major or permission of instructor.

Offered: Every Spring (3 credits)

**MATH 160 -- Introductory Seminar in Mathematics**

Designed for students new to the mathematics major, this is a seminar course that will discuss various professional skills needed to succeed in the major and in a mathematical career. Topics may include: introduction to mathematics literature, discussions of career options, introduction to mathematics technology, and introductions to different topics in mathematics.Prerequisites: Mathematics major or permission of instructor. For more information, see MATH 160's detailed course description.

Offered: Every Fall (1 credit)

**MATH 168 - Calculus I with Integrated Precalculus I** (R, GE)

The sequence MATH 168:169 covers the topics covered in MATH 171 but also includes topics from algebra and trigonometry that MATH 171 assumes as prerequisite. MATH 168 covers limits and derivatives of algebraic functions and applications of the derivative, including curve sketching, velocity and acceleration, optimization, and related rates. Students may not receive credit for both MATH 168 and either MATH 171 or MATH 151. For more information, see MATH 168's detailed course description.

Prerequisites: A grade of C or better in MATH 125 Precalculus I OR a score of 61 or greater on our math placement test ALEKS PPL

**MATH 169 - Calculus I with Integrated Precalculus II **(R, GE)

The sequence MATH 168:169 covers the topics covered in MATH 171, but also includes topics from algebra and trigonometry that MATH 171 assumes as prerequisite. MATH 169 covers indefinite and definite integrals, the area of under a curve, and the Fundamental Theorem of Calculus. The course also covers limits, differentiation, and integration of exponential, logarithmic, and trigonometric functions, and l’Hôpital’s Rule. Students may not receive credit for both MATH 169 and either MATH 171 or MATH 151. For more information, see MATH 169's detailed course description.

Prerequisites: A grade of C or better in MATH 168. Students with credit for MATH 126 Business Calculus or another college level calculus course are encouraged to contact the Department of Mathematics and Statistics for permission. (3 credits)

**MATH 171 - Calculus and Analytic Geometry I **(R, GE)

This course lays the foundational concepts of calculus: the limit, differentiation, and integration. It includes techniques for finding limits, derivatives, and integrals of algebraic, exponential, logarithmic, trigonometric, and inverse functions. Applications of the derivative include curve sketching, velocity and acceleration, optimization, related rates, and l’Hôpital’s Rule. Integration includes the area under a curve and the Fundamental Theorem of Calculus. Students may not receive credit for both MATH 171 and the sequence MATH 168:169 and may not receive credit for both MATH 171 and MATH 151. For more information, see MATH 171's detailed course description.

Prerequisites for MATH 171 (4 credits)

**MATH 172 - Calculus and Analytic Geometry II **(R, GE)

This course covers applications of integration; techniques of integration; improper integrals; infinite sequences and series, including tests for convergence and power series representations of functions and Taylor’s Theorem; and calculus of parametric curves and polar coordinate systems. Students may not receive credit for both MATH 172 and either MATH 152 or MATH 251. For more information, see MATH 172's detailed course description.

Prerequisites: A grade of C or better in MATH 171 or MATH 169. (4 credits)

**MATH 212 -- Elementary and Middle School Mathematics for Social Analysis **(R)

[Formerly MATH 312] The primary purpose of this course is to prepare future and current elementary and middle school teachers to critically analyze and explore the world using mathematics. Students will conduct meaningful and carefully reasoned real-world investigations and critiques using elementary and middle school mathematics and also communicate the results of these problem-posing and problem-solving investigations both orally and in writing. This course examines the interplay among mathematical topics and integrates mathematics across the curriculum. Students are introduced to the National Council of Teachers of Mathematics [NCTM] Standards and to the Virginia Standards of Learning. Mathematical content emphases are also based on the NCTM Standards and include topics in number and operations, algebraic thinking, geometry, measurement, and data analysis and probability. For more information, see MATH 212's detailed course description.

Prerequisites: MATH 121 and MATH 122

Offered: Every Fall and Spring (3 credits)

**MATH 235 -- Fundamentals of Geometry** (R, GE)

Introduces core concepts and principles of Euclidean geometry, with some attention also given to non-Euclidean geometry. Emphases are placed on the use of spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties from both formal and informal perspectives. Course content adheres to the National Council of Teachers of Mathematics *Standards* (2000) and the Virginia Standards of Learning where they can appropriately be applied. For more information, see MATH 235's detailed course description.

Prerequisites: Completion of any MATH course or a passing score on a placement test approved by the Department of Mathematics and Statistics It is recommended that Elementary Education majors take MATH 122 prior to MATH 235.

Offered: Every Fall (3 credits)

**MATH 260 -- Introductory Linear Algebra**

Matrix Operations, systems of linear equations, Gaussian elimination, determinants, basic properties of vector spaces, basis and orthogonality, and eigenvalues and eigenvectors. Calculators and computer software such as MATLAB will be used in this course. For more information, see MATH 260's detailed course description.

Offered: Every Fall and Spring (3 credits)

**MATH 261 -- Linear Algebra Computer Lab**

This course will reinforce and apply key concepts of MATH 260 Introductory Linear Algebra, specifically in situations where the problems are too large to do by hand and require use of a linear algebra software package such as Matlab. Topics include matrix and vector operations, solving large linear systems, least squares solutions, applications of linear algebra, and elementary computer programming concepts.

Offered: Every Fall and Spring (1 credit)

Pre- or correquisite: MATH 260

**MATH 271 -- Calculus and Analytic Geometry III **

This course extends the concepts of the limit, differentiation, and integration to vector-valued functions and to functions of several variables. This includes partial differentiation, iterated integrals, volume and surface area of three-dimensional regions, and optimization of functions or several variables. Students may not receive credit for both MATH 271 and MATH 252. For more information, see MATH 271's detailed course description.

Prerequisites: MATH 172

Offered: Every Fall and Spring. More information on the calculus sequence transition. (4 credits)

**MATH 280 -- Problem Solving**

A problem-based course requiring techniques from precalculus, geometry, first-year calculus, elementary linear algebra and basic statistics. For more information, see MATH 280's detailed course description.

Prerequisites: MATH 172 and MATH 260

**MATH 285 -- Topics in Mathematics
**Special topics in mathematics that are accessible to non-mathematics majors, as student and faculty interest demands. Syllabus is available each time the class is offered. Interested students should contact the department chairperson or the course instructor before registering. May be taken more than once for credit with a different topic. For more information, see MATH 285's detailed course description. (Variable credit)

**MATH 300 -- Mathematical Foundations**

A first course in the foundations of modern mathematics. The topics covered include sentential calculus, set theory, the number system, induction and recursion, functions and relations, and computation. The methods of proof and problem solving needed for upper-division coursework and the axiomatic basis of modern mathematics are emphasized throughout the course. For more information, see MATH 300's detailed course description.

Prerequisites: MATH 172 and MATH 260.

Offered: Every Fall and Spring (3 credits)

**MATH 321 -- History of Mathematics**

The pursuit of mathematics as a human endeavor, illustrating how mathematics has developed over the past 5000 years including the contributions of diverse cultures. This course will cover not only the evolution and historical perspective of the development of mathematics, but will include a study of the mathematics itself. For more information, see MATH 321's detailed course description.

Prerequisites: MATH 172

Offered: Every Spring (3 credits)

**MATH 325 -- Special Methods - Secondary Mathematics Education**

A special methods course in the teaching of mathematics at the secondary level. Will not satisfy the requirements for a major in mathematics except for those in the Bachelor of Science degree program pursuing certification to teach. Special emphasis will be placed on the role of technology in teaching, problem solving, and representation of mathematics concepts. For more information, see MATH 325's detailed course description.

Prerequisites: MATH 172, STAT 301

Offered: Every Spring (3 credits)

**MATH 335 -- Foundations of Geometry**

The course presents a formal axiomatic development of Euclidean geometry with an emphasis on valid arguments. Development of spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties from both formal and informal perspectives is an important part of the course. The content is presented as a sequence of theorems, each rigorously proven using axioms and earlier theorems. The goal is to develop students’ deeper understanding of geometric content and their ability to think critically. Some attention is also given to non-Euclidean geometry. For more information, see MATH 335's detailed course description.

Prerequisite: MATH 235

Offered: Every Spring (3 credits)

**MATH 346 -- Differential Equations **(R)

A study of techniques for solving differential equations, including first and second order equations and linear systems of equations; Laplace transform and numerical methods. Applications in the sciences will be considered. For more information, see MATH 346's detailed course description.

Prerequisites: MATH 260 and a C or better in MATH 172

Offered: Every Spring (3 credits)

**MATH 398 -- Mathematics Education Research Seminar I**

This course is the first of two seminar courses. The seminar is designed to engage mathematics majors in mathematics education research. The focus is on the literature review, which requires students to identify an area of study within mathematics education, to articulate their research purpose and create a research question. The literature review paper will be the capstone project in this course. For more information, see MATH 398's detailed course description.

Prerequisites: Junior standing and STAT 200 or STAT 301 or permission of instructor

Offered: Every Fall (1 credit)

**MATH 399 -- Mathematics Education Research Seminar II**

This course is the second of two seminar courses. This seminar is designed to further develop the mathematics majors as mathematics education researchers. The attention is placed on developing the prospectus for their study, in which the data collection phase can start in the latter part of the semester or during the summer. For more information, see MATH 399's detailed course description.

Prerequisites: MATH 398 or permission of instructor

Offered: Every Spring (1 credit)

**MATH 412 -- Theory of Numbers**

Study of divisibility, primes, congruences, diophantine equations and quadratic residues. For more information, see MATH 412's detailed course description.

Prerequisites: MATH 300

Offered: Every Spring (3 credits)

**MATH 423 -- Concepts of Abstract Alegbra
**A study of the structure of algebraic systems. For more information, see MATH 423's detailed course description.

Prerequisites: MATH 300

Offered: Every Fall (3 credits)

**MATH 428 -- Complex Varibles
**A study of elementary functions with complex domain and techniques of differentiation and integration of complex functions. For more information, see MATH 428's detailed course description.

Prerequisites: MATH 271

Offered: Spring, Even Years (3 credits)

**MATH 430 -- Advanced Calculus I
**A systematic modern approach to the differential and integral calculus of one and several variables, including standard theorems and analytical techniques of mathematical analysis. For more information, see MATH 430's detailed course description.

Prerequisites: MATH 271 and MATH 300

Offered: Every Fall (3 credits)

**MATH 431 -- Advanced Calculus II
**A systematic modern approach to the differential and integral calculus of one and several variables, including standard theorems and analytical techniques of mathematical analysis. For more information, see MATH 431's detailed course description.

Prerequisites: MATH 430

Offered: Every Spring (3 credits)

**MATH 434 -- Numerical Analysis I
**Introduction to scientific programming and numerical methods for nonlinear equations, linear algebra problems, interpolating data sets, numerical differentiation, and numberical integration. Both the implementation of the methods and the underlying analysis of how and why they work are considered. For more information, see MATH 434's detailed course description.

Prerequisites: MATH 260, MATH 261, MATH 271, and either ITEC 109 or 120

Offered: Every Fall (3 credits)

**MATH 435 -- Numerical Analysis II **(L)

Introduction to numerical methods for solving ordinary and partial differential equations and numerical optimization. Usage of these techniques in the context of applied mathematics is emphasized. For more information, see MATH 435's detailed course description.

Prerequisites: MATH 435

Pre- or corequisite: MATH 346

Offered: Every Spring (3 credits)

**MATH 441 - Topology
**An introduction to point-set topology, with emphasis on the study of functions and the real line. For more information, see MATH 441's detailed course description.

Prerequisites: MATH 300

(3 credits)

**MATH 460 -- Linear Algebra
**A study of the arithmetic, algebra and properties of vectors and matrices with applications to a variety of mathematical problems. Topics covered include Euclidean vector spaces, eigenvalues and eigenvectors, abstract vector spaces, linear transformations, change of basis and matrix normal forms. Applications these properties and techniques are applied to most or all of the following areas: stochastic processes, optimization, multi-variable calculus, and differential equations. For more information, see MATH 460's detailed course description.

Prerequisites: MATH 172, MATH 260

**MATH 480 -- Topics in Advanced Mathematics
**Special topics in mathematics, as student and faculty interest demands; syllabus is available each time the class is offered. Interested students should contact the department chairperson and the course instructor before registering. May be taken again for credit with a different topic. For more information, see MATH 480's detailed course description. (Variable credit)

**MATH 488 -- Final Honors Project
**A topic is to be explored determined by the student, the faculty member with whom the student works and the department. Topics may be chosen from the areas of analysis, algebra, topology or applied mathematics. In order to receive honors credit, a student must earn a grade of A or B for the final project. Course may not be repeated. For more information, see MATH 488's detailed course description. (3 credits)

**MATH 498 -- Independent Study**

For more information, see MATH 498's detailed course description.

**MATH 499 -- Internship in Mathematics**

For more information, see MATH 499's detailed course description.