# Mathematics and Computer Systems

### Mathematics Major

The Mathematics Major prepares students for careers in secondary mathematics education and for further graduate study in mathematics, statistics, and related disciplines. It also combines well as a secondary major with any area, especially science, business,computer systems, and intelligence studies.

After completion of the bachelor's degree in mathematics, students interested in secondary education may enroll in the one-year Master of Science: Pedagogy and Practice program here at the University and earn a master's degree along with teaching certification.

(Click course titles to show/hide course descriptions.)

This is the initial course in a sequence of courses on the fundamental ideas of the calculus of one variable. It is here that truly significant applications of mathematics begin. Topics included are functions, continuity, limits, derivatives, maxima and minima and antiderivatives. Projects may be assigned requiring the students to use a Symbolic Computer Algebra System. Satisfies either the common or distribution core requirements in mathematics. Offered Fall and Winter terms. 4 credits.

Any student who has completed Calculus I should take Calculus II to obtain a complete study of the calculus of one variable. Topics included are the integral antiderivatives, the Fundamental Theorem, volume, length of an arc, surface area, average value, moments, integration techniques, series, sequences. Projects may be assigned requiring the students to use a Symbolic Computer Algebra System. Satisfies the distribution core requirement in mathematics. Prequisite: MATH 170. 4 credits.

This course is an introduction to the algebra and geometry of Euclidean 3-space and its extensions to Euclidean N-Space. Topics included are systems of linear equations, determinants, vectors, bases, linear transformations and matrices. 3 credits.

This is an introduction to the calculus of several variables. Topics selected from polar coordinates, functions of several variables, partial derivatives, multiple integrals, line integrals, surface integrals, Green's theorem and Stokes' Theorem. Prequisites: MATH 150, MATH 171. 4 credits.

An introduction to the basic mathematical content of ordinary differential equations and their applications. This will include analytical, qualitative, and numerical methods for ordinary differential equations. Topics include first- order and second-order equations and applications, systems of differential equations, and matrix methods for linear systems. Prequisites: MATH 150, And, MATH 171, Or Department Permission. 3 credits.

Emphasis is given to geometry, uses of geometry in various mathematical subjects, historical aspects of geometry and mathematics, and mathematical curricular developments. The following topics are integrated into the course: Euclidean and non-Euclidean geometry, historical and cultural significance of mathematics, and mathematical software products. Prequisites: MATH 150, MATH 171. 3 credits.

This course will teach the student how to use programming skills together with mathematical software to efficiently solve a variety of problems. The primary programming language will be using the MATLAB environment. This approach will prepare the student for occasions where programming is required as well as the ability to utilize software packages such as MATLAB. A secondary objective is learning to use the markup language LaTeX. Having a laptop computer is not required but may be of great benefit for this course. Prequisites: MATH 150, MATH 233, MIS 126, or approved programming language. 3 credits.

This course is designed to facilitate the mathematics student’s transition to courses requiring a higher level of mathematical maturity. Emphasis will be on the reading and writing of proofs, and on communicating mathematically—both orally and in writing. Topics will include logic, set theory, functions, relations, and number theory. Prequisites: MATH 150, MATH 171. 3 credits.

The underlying theme consists of looking at the structure of mathematical systems primarily as related to certain operations. Topics included are logic and sets, relations, equivalence relations and partitions, number theory (the integers), groups, subgroups,isomorphisms, homomorphisms, rings, fields. Prequisites: MATH 150, MATH 233, MATH 265. 3 credits.

An introduction to statistical concepts and techniques with emphasis on the underlying probability theoretical basis. Topics included are sums of random variables; moment generating functions; sampling distributions; F- and t- distributions; chi-square; point estimation; interval estimation; testing hypotheses, theory, and application; regression and correlation; analysis of variance. Prequisites: MATH 150, MATH 233. 3 credits.

This course introduces the fundamental concepts of a function of a real variable from a rigorous point of view. Topics included are completion of the rational numbers, theory of continuous functions, theory of differentiation, theory of the Riemann integral, sequences, series. Prequisites: MATH 150, MATH 233, MATH 265. 3 credits.

Mathematics majors must also take two Mathematical Topics courses (Math 400), for a total of 13 courses.