Mathematics

Algebra and its Applications

Presents topics in algebra through traditional and applications-based methods. Topics include functions, exponents and scientific notation, linear, exponential, rational and quadratic functions and graphs, systems of equations, and quadratic and linear inequalities. Prerequisite: placement level C, MATH 005 with a grade of C or higher, or consent. Offered every semester.

Calculus with Precalculus, Part I

Students learn the basic tools of calculus, why they work, and how to apply them in various contexts. Symbolic, graphical, and numerical approaches are considered. Topics include limits, derivatives, and applications. Includes sufficient coverage of functions and trigonometry to support the study of calculus and of other sciences. The two-course sequence, MATH 135 and 136, is sufficient preparation for MATH 172 Calculus II. Prerequisite: placement level B, MATH 104 with a grade B or higher, or consent. Offered every fall.

Calculus with Precalculus, Part II

A continuation of MATH 135. Topics include applications of derivatives, the Riemann integral, and the Fundamental Theorem of Calculus. Includes sufficient instruction in advanced algebraic techniques to support the study of calculus. Prerequisite: MATH 135 with a grade of C- or higher or consent. Offered every spring.

Topics in Modern Mathematics

Exposes students to areas of modern mathematics. Topics vary but may include voting theory, game theory, mathematics and art, elementary number theory, graph theory and scheduling problems, management science, and others. Focus is on critical thinking skills, communicating mathematics orally and in writing, and applications to other disciplines. Prerequisite: placement level A or B. Offered every semester.

Precalculus with Trigonometry

Topics include algebra, the Binomial Theorem, functions, trigonometry, and the laws of sines and cosines. Function families, including polynomial, rational, exponential, logarithmic, and trigonometric functions, and their graphs will be analyzed. Trigonometric functions will be defined using right-triangle and circular definitions. Prerequisite: B Placement or MATH 104 (grade C or higher). Offered every semester.

Calculus I

Students learn the basic tools of calculus, why they work, and how to apply them in various contexts. Calculus I develops differential calculus through symbolic, graphical, and numerical approaches. Topics include differentiation of algebraic and transcendental functions, applications in modeling and optimization, the Fundamental Theorem of Calculus, and an introduction to differential equations. Prerequisite: placement level A or MATH 170 (grade C- or higher). Offered every semester.

Calculus II

A continuation of Calculus I. More advanced techniques are studied and used to solve quantitative problems in various contexts. Topics include integration techniques, applications of definite integration, polar coordinates, parametric equations, and sequences and series. Prerequisite: MATH 136 or 171 with a grade of C- or higher or consent. Offered every semester.

Foundations of Logic and Proof

Introduction to abstract mathematical thinking and logical reasoning skills needed in upper-level Math/CS courses. Topics include logic, argument, proofs, induction, sets, and abstract functions and relations. Emphasizes mathematical writing. Identical to CS 205. Prerequisite: MATH 217 with a grade of C- or higher or CS 212 with a grade of C or higher, or consent. Recommended spring of sophomore year. Offered every spring.

Introductory Statistics

Introduces students to learning from data. Topics include the basics of data production, data analysis, probability, Central Limit Theorem, and statistical inference. Statistical software is used for data management, calculation, and visualization. No previous knowledge of statistics is required. Students cannot receive credit for both MATH 210 and PSY 210. Prerequisites: sophomore status or higher, and placement level H, A, or B, or MATH 104 with a grade of C- or higher. Not appropriate for first-year students. Students must have a TI-83 or TI-84 graphing calculator. Offered every semester.

Linear Algebra

The study of vector spaces and linear equations in several variables. Topics include systems of linear equations, vector spaces, linear dependence of vectors, bases, dimension, linear transformations, matrices, determinants, and applications. Prerequisite: MATH 172 with a grade of C- or higher, or consent. Offered every fall.

Multivariable Calculus

Topics include functions of several variables, curves, surfaces, partial differentiation, multiple integrals, and vector analysis. Prerequisite: MATH 172 with a grade of C- or higher, or consent. Offered every spring.

Ordinary Differential Equations

Explores the theory and applications of ordinary differential equations and their solutions. Topics include linear and non-linear first order equations, higher order linear equations, series solutions, systems of linear differential equations, Laplace transforms, and numerical methods. Prerequisite: MATH 172 with a grade of C- or higher, or consent. Offered every fall.

Teaching Assistant Program for Math

Qualified students assist math instructors in teaching their classes. Enrollment is by invitation of the MATH/CS department. A student may enroll more than once but may apply no more than 3 semester hours earned in this manner toward graduation. May not be used to satisfy major or minor requirements in Mathematics. One semester is required for students seeking secondary education certification; however, the course is open to all students. Offered every semester.

Statistical Models

A course in applied data analysis. Emphasizes construction of models for authentic data sets. Statistical software is used extensively for analyzing real data sets from various contexts. Topics include parametric and non-parametric tests, simple and multiple regression, and ANOVA. Prerequisites: ENG 105 with a grade of C or higher, MATH 172 with a grade C or higher, and MATH 210 with a grade C or higher, or consent. Offered spring of even-numbered years.

Probability

Approaches probability as a discipline with applications throughout mathematics and the sciences. Topics include classical and axiomatic probability, random variables, common distributions, density functions, expectation, conditional probability, independence, the Law of Large Numbers, and the Central Limit Theorem. Prerequisite: MATH 273 with a grade of C- or higher, or consent. Offered fall of odd-numbered years.

Algebraic Structures I

An introduction to algebraic structures. Topics include homomorphisms and isomorphisms, equivalence classes, and quotient structures. Prerequisites: MATH/CS 205 with a grade of C- or higher and MATH 217 with a grade of C- or higher. Offered every fall.

Theory of Elementary Mathematics I

Develops a professional knowledge of the mathematics generally taught in elementary schools (K-6). Part I focuses on number systems, arithmetic, number theory and algebraic concepts. Does not count as an elective for any mathematics major. Prerequisites: Any credit-bearing Mathematics course, junior/senior status, and admission to the program for Elementary or Special Education Teacher Certification. Offered every fall.

Theory of Elementary Mathematics II

Develops a professional knowledge of the mathematics generally taught in elementary schools (K6). Part II focuses on geometry, probability, and statistics. Does not count as an elective in any mathematics major. Prerequisite: MATH 325 (grade of C or higher). Offered every spring.

Number Theory

An introduction to the study of the set of natural numbers. Topics may include linear congruence, greatest common divisor, Euler's totient function, Chinese Remainder Theorem, Fermat's Little Theorem, Wilson's Theorem, Legendre symbol, and quadratic reciprocity. Prerequisite: ENG 105 with a grade of C or higher and MATH/CS 205 with a grade of C- or higher, or consent. Offered fall of odd-numbered years.

Modern Geometries

Explores Euclidean and non-Euclidean geometries and the cultural impact of non-Euclidean geometries. Topics may include geodesics, plane geometry, non-Euclidean geometries, finite geometries, complex numbers, and geometric transformations. Prerequisite: MATH/CS 205 with a grade of C- or higher, MATH 217 with a grade of C- or higher, or consent. Offered spring of odd-numbered years.

Numerical Methods

Examines methods used in solving numerical problems with the aid of a computer. Topics include floating-point arithmetic, interpolation, integration, roots of non-linear equations, ordinary differential equations, and systems of linear equations. Identical to CS 350. Students enrolled in the pre-engineering program with ODU cannot receive credit for this course and the cross-registered courses MAE 340 or CEE 305. Prerequisites: MATH 172 with a grade of C- or higher and CS 212 with a grade of C- or higher, or consent. Offered spring of even-numbered years.

Real Analysis

A theoretical treatment of continuity and real-valued functions. Topics may include sequences, series, limits, the derivative, and the integral. Prerequisite: MATH/CS 205 with a grade of C- or higher and MATH 217 with a grade of C- or higher. Offered fall of even-numbered years.

Advanced Topics in Mathematics

Explores an area of mathematics which is not otherwise included in the curriculum. Students may repeat the course for credit as the topic varies. Prerequisite: MATH 217 with a grade of C- or higher and consent. Offered intermittently.

Mathematical Models

An introduction to mathematical models and sensitivity analysis. Emphasizes construction of models for real world applications in a variety of areas. Mathematical software is used extensively for problem solving. Topics include optimization models, linear and discrete programming, dynamic models, and probability models. Prerequisites: ENG 105 with a grade of C or higher, MATH 217 with a grade of C- or higher, and MATH 273 with a grade of C- or higher. Offered fall of even-numbered years.

Algebraic Structures II

A continuation of Algebraic Structures I. Prerequisite: MATH 319 with a grade of C- or higher. Offered spring of even-numbered years.

Internship in Mathematics

An intensive mathematics project conducted in a professional setting. Pass/Fail grading. Prerequisites: junior/senior status, cumulative GPA of at least 2.5, and consent. Offered intermittently.

Mathematics Senior Seminar

Students read and discuss current journal articles in mathematics. Topics vary and may include problem solving. Pass/fail grading. Prerequisite: declared Mathematics major and senior status, or consent. Offered every spring.

Research in Mathematics

Offers students the opportunity to conduct original scientific research in an area of interest. Students work closely with one or more members of the natural science faculty to develop and conduct a research project, then present their findings orally during the semester's undergraduate research symposium and as a formal research paper. Students are encouraged to present their findings at a conference. Prerequisite: junior/senior status and a major in Mathematics, prior approval by the project advisor, and consent of the instructor. Students may enroll for 2 or 4 hours in a given semester. May be repeated for a maximum total of 8 semester hours. Identical to BIO 489, CHEM 489, CS 489, and EES 489. Offered intermittently.