# Course Descriptions - Math

**111 Mathematical Models for the Management Sciences**

Theory and applications of several mathematical models used in business and social sciences. Topics include matrices, linear programming, functions, limits and derivatives. (1 credit)

Lecture: 3 hrs/week (May not be taken if credit has been received for Mathematics 112 or 121).

**112 Concepts and Techniques of Calculus**

Primarily for students of biology, business, economics and the behavioral sciences. Topics include limits, differentiation and integration, maximum problems, numerous applications. (Credit cannot be received for both Mathematics 112 and 121, nor for both Mathematics 112 and Mathematics 118.) (1 credit)

Lecture: 3 hrs/week

**118 Differential Calculus ** An introduction to calculus, focusing on limits, derivatives, and the application of derivatives to real-world problems. Review of topics from precalculus and trigonometry are integrated throughout the calculus material. (Credit cannot be received for both Mathematics 112 and Mathematics 118.) (1 credit)

Lecture: 3 hrs/week.

**119 Integral Calculus **

An introduction to calculus focusing on the Fundamental Theorem of Calculus, development of definite and indefinite integrals, and applications of integration including area and volume. Review of topics of precalculus and trigonometry are integrated throughout the calculus material. (Credit cannot be received for both Mathematics 119 and Mathematics 121.) (1 credit)

Lecture: 3 hrs/week.

*Prerequisite: Mathematics 118*

**121 Calculus I**

The analysis of limits, derivatives, integrals and their applications for functions of one variable. (Credit cannot be received for both Mathematics 112 and 121, nor for both Mathematics 119 and Mathematics 121.) (1 credit)

Lecture: 3 hrs/week.*Prerequisite: Placement or permission.*

**122 Calculus II**

The analysis of integrals, sequences and series, parametric equations and their applications for functions of one variable. (1 credit)

Lecture: 3 hrs/week; Laboratory: 1.5 hrs/week*Prerequisite: Mathematics 119 or 121.*

**131 Discrete Mathematics**

An introduction to mathematical logic and proofs, with topics selected from set theory, number systems, formal logic, functions and relations, and graph theory. (1 credit)

Lecture: 3 hrs/week*Prerequisite: Mathematics 118 or 121.*

**201 Linear Algebra**

Linear equations, matrices, vector spaces, linear mappings, determinants, quadratic forms, geometric applications. (1 credit)*Prerequisite: Mathematics 122.*

**268 Combinatorics and Graph Theory**

An introduction to graph theory and combinatorics. Topics may include graph colorings, trees, matching problems, binomial and multinomial coefficients, and generating functions. An emphasis will be placed on mathematical exposition and formal arguments as the theory is developed. (1 credit)

Lecture: 3 hrs/week.* Prerequisite: Mathematics 131*

**271 ****Mathematical Problem Solving**

An introduction to mathematics as a problem-solving discipline. Includes the development of a small research project, and preparation for problem-solving mathematics competitions. (1/2 credit)

Lecture: 1.5 hrs/week.

*Pre-requisite: Mathematics 122.***278 Foundations of Geometry**A review of Euclidean geometry and an introduction to non-Euclidean geometries, with a special focus on the theoretical framework of various geometric systems. (1 credit)

**Lecture: 3 hrs/week.**

Prerequisite: Mathematics 131

Prerequisite: Mathematics 131

288 Special Topics in Mathematics

288 Special Topics in Mathematics

Special topics in Mathematics, focusing on building the mathematical and logical framework necessary for upper-level mathematics courses. (1 credit)

**Lecture: 3 hrs/week.**

*Prerequisite: Mathematics 131*

**This course provides an introduction to Operations Research: a mathematical approach to decision making based on optimization. Topics include the simplex method, sensitivity analysis, duality, transportation problems, and network models. (1 credit)**

**311 Operations Research**

**Lecture: 3 hrs/week.**

*Prerequisite*: Mathematics 201

**321 Vector Calculus**The analysis of functions of several variables, double and triple integrals, line integrals, vector fields and surface integrals. (1 credit)

Lecture: 3 hrs/week.

*Prerequisites: Mathematics 122.*

**331 Differential Equations**

Ordinary differential equations with applications. (1 credit)

Lecture: 3 hrs/week.*Prerequisite: Mathematics 201 or permission.*

** 332 Applied Differential Equations**Series solutions of differential equations. Bessel functions, Legendre polynomials, Fourier series, partial differential equations, boundary value problems. (1 credit)

Lecture: 3 hrs/week.

*Prerequisite: Mathematics 331.*

**342 Numerical Analysis**

Numerical integration and differentiation, numerical methods in linear algebra, interpolations; error analysis, stability and conditioning. (1 credit)

Lecture: 3 hrs/week.*Prerequisites: Mathematics 201, Mathematics 122, Computer Science 120.*

(Cross-listed as CPSC 342.)

**352 Complex Analysis**

The structure of the complex number system; analytic functions, conformal mappings and applications; the theory of complex integration. (1 credit)

Lecture: 3 hrs/week.*Prerequisite: Mathematics 122.*

**361 Abstract Algebra**

Axiomatic study of selected algebraic structures, including groups and rings. (1 credit)

Lecture: 3 hrs/week.*Prerequisites: Mathematics 131 and 201; students are strongly encouraged to have completed their Transitions Course requirement before enrolling in this course.*

**371 Topology**

Topological spaces, functions, mappings, connectedness, compactness, metric spaces. (1 credit)

Lecture: 3 hrs/week.*Prerequisites: Mathematics 131 and 201; students are strongly encouraged to have completed their Transitions Course requirement before enrolling in this course. *

**381 Real Analysis**

The structure of the real number system; selected topics from metric spaces, continuity, differentiation, integration, sequences and series. (1 credit)

Lecture: 3 hrs/week.*Prerequisites: Mathematics 131 and 201; students are strongly encouraged to have completed their Transitions Course requirement before enrolling in this course. *

**388 Topics in Mathematics**

Special topics in Mathematics. (1 credit)

Lecture: 3 hrs/week*Prerequisites: Mathematics 131 and 201 or permission.*(Offered on a rotating basis, not every year.)

**405, 406, 407 Independent Study and Research**

Selected topics in mathematics carried out under direction of a member of the department staff. (Enrollment with the approval of the department.) (1/2 credit, 1 credit, 1/2 credit)

**416 Internship**

Field placement providing practical experience and training in areas in which mathematics is applied. These areas may include industry, government agencies, educational institutions, insurance companies and a variety of private enterprises. (Permission of the department is required.) (1 credit)

**491 Math Seminar**

Advanced topics in pure and applied mathematics, presentation of math projects, topics in the history of math. (1 credit)

Lecture: 3 hrs/week*Prerequisite: Two of Mathematics 361, 371, or 381.*

**495, 496, 497 Honors Project**

A program of independent study culminating in a paper, artistic creation, or performance.*Prerequisite: To qualify for consideration to receive honors in the major, a student in his/her senior year or in the summer prior to the senior year, must work under the guidance of his/her committee. A written proposal and application must be approved by the committee and department. A minimum GPA of 3.4 in the major is required. 495 Honors Project is prerequisite for 497 Honors project.*(1/2 credit, 1 credit, 1/2 credit)

## Roanoke students use creativity, math and problem-solving skills to design optimal brownie pan

This year's team of Ed Hrinya, Jared Meadows and Kat Jansen received the second highest ranking of Meritorious, which placed them in the top 1 percent internationally in the Mathematical Competition in Modeling.