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# Undergraduate Math Courses

In addition to the courses approved for the Core Curriculum, we offer the following mathematics courses

**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 212 -- Elementary and Middle School Mathematics for Social Analysis**

[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
**(Formerly MATH 135)

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: Mathematics major, Interdisciplinary Studies--Middle School Education major, Interdisciplinary Studies--Elementary Education major, or permission of instructor. It is recommended that Interdisciplinary Studies--Elementary Education majors take MATH 122 prior to MATH 135.

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 271 -- Calculus and Analytic Geometry III
**(Replaces MATH 252)

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

Offered: Every Fall (3 credits)

**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**

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, numerical methods for problems from linear algebra, interpolation, and solutions of non-linear equations. For more information, see MATH 434's detailed course description.

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

Offered: Every Fall (3 credits)

**MATH 435 -- Numerical Analysis II
**Numerical differentiation, numerical integration, and numerical methods for differential equations. 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

Offered: Spring, odd years (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

Offered: Fall, odd years (3 credits)

**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.