# Mathematics (MAT)

**Major**: 10 -12 courses. Completion of the calculus sequence (through MAT 122); a minimum of seven courses in Mathematics or Statistics numbered 202 or higher, at least four of which must be at the 300 level, and which include MAT 221, 236, 301, either 327 or 337, and completion of one of the 300-level two-course sequences (MAT 327-328, 337-338, or STA 347-348); CSC 151, 140; and STA 201 or 202 (if STA 348 is not one of the 300-level courses completed). The department recommends that CSC 140, which provides knowledge of a programming language, be acquired by the end of the sophomore year. The following courses cannot be used to satisfy requirements of the mathematics major: MAT 110, 280/380, 290/390, 511 and STA 280/380 and 290/390.

**Teaching Major**: Completion of the requirements for the Mathematics major with the additional stipulations that MAT 231 is required to be one of the seven upper-level courses and that the grade point average in all courses for the teaching major must be at least 2.5. In addition to the foregoing requirements, prospective teachers must also apply for admission to the Teacher Education Program (preferably at the start of their sophomore year) and complete coursework leading to secondary certification described under *Education*. Prospective teachers should request a current list of the specific course requirements from the Education Office. **No mathematics, statistics, or computer science courses required for the teaching major may be taken with the S/U option.**

**Second Teaching Area in Mathematics**: For information about a second teaching area in Mathematics, please consult the chair of the Education Department.

**Minor**: Minimum of six credits. Completion of the calculus sequence (through MAT 122); a minimum of three MAT or STA courses which include MAT 221, 301, and at least one other 300-level MAT or STA course; and CSC 151.

**110. On the Shoulders of Giants: Great Mathematical Ideas**

Investigation of a variety of great mathematical discoveries past and present. The ideas investigated will not require significant previous mathematical background, but will require the student to actively participate in the process of mathematical discovery. Only by doing mathematics can the creativity, beauty, and mathematical importance of these great ideas be understood. Specific content varies with the course instructor, but may include subjects such as knot theory, origami, game theory, the nature of infinity, or chaos and fractals. Prerequisite: two years of high school algebra. Recommended for non-mathematics majors. This course is not open to students who have completed MAT 120 or higher. This course does not count toward a mathematics major or minor. (Mathematics)

**119-120. Calculus of a Single Variable Part I & II**

Differential and integral calculus of functions of one real variable and analytic geometry of two variables. This course emphasizes review of precalculus material and is appropriate for students who feel they need more time in order to succeed in calculus. Prerequisite: three and one-half years of high school mathematics, including trigonometry. Unless a departmental exception is granted, this course combination must be taken in consecutive terms. This course is not open to students who have completed MAT 121 or higher. (Mathematics)

**121. Calculus of a Single Variable**

Differential and integral calculus of functions of one real variable and analytic geometry of two variables. Prerequisites: three and one-half years of high school mathematics, including trigonometry, in addition to an ACT Math score of 25 or above, or SAT Math score of 570 or above, or permission of instructor. This course is not open to students who have completed MAT 120. (Mathematics)

**122. Calculus of Several Variables**

Continuation of Calculus of a Single Variable, including further techniques of integration, vectors, and differential and integral calculus of several variables. Prerequisite: MAT 120 or 121.

**221. Linear Algebra**

Existence and uniqueness of solutions to linear systems. Linear transformations, linear independence, spanning vectors, vector spaces, basis and dimension, orthogonality, eigenvalues and eigenvectors. Students will be required to prepare written and oral presentations on a linear algebra application approved by the instructor. Prerequisites: either MAT 120 or 121 and either CSC 151 or MAT 122.

**231. Fundamentals of Geometries**

An examination of the assumptions inherent in the axiomatic structures of two-dimensional geometry through the parallel postulate and its alternatives. Additional topics may include projective geometries, finite geometries, coordinates and transformations, tilings, and higher-dimensional objects. Prerequisite: MAT 221. Alternate years. Not offered 2013-2014.

**234. Complex Variables**

Differential and integral calculus of functions of one complex variable. Analytic and harmonic functions, contour integration, Laurent series, residue theory, and conformal mapping. Prerequisite: MAT 122. Alternate years.

**236. Differential Equations**

This course is about how to predict the future. Mathematical modeling with differential equations, initial value problems and their approximate solutions, systems of differential equations, qualitative solutions, stability analysis and an introduction to chaos, and Laplace transforms. Prerequisites: MAT 122 and 221.

**255-260. Topics in Mathematics**

A topic of mathematics more computationally oriented than proof oriented. See *Topics Courses*. Prerequisite: MAT 122 and/or 221.

**301. Introduction to Proof: Number Theory**

An introduction–through the subject of number theory–to the ideas, logic, techniques, and reasoning used in writing a mathematical proof. Divisibility and factorization properties of integers, congruences, prime numbers, Diophantine equations, Fermat's Theorem, Wilson's Theorem, and Euler's Theorem, and applications. Prerequisites: CSC 151 and MAT 221.

**317. Mathematical Modeling**

An introduction to the process and techniques of modeling using tools from linear algebra, differential equations, and other mathematical disciplines. Appropriate mathematics and computational technology, including numerical methods, developed as needed. Models drawn from the physical sciences, life sciences, social sciences, and computing, with extensive use of case studies. Prerequisites: CSC 140 and MAT 236. Alternate years. Not offered 2013-2014.

**327- 328. Modern Algebra I & II**

Formal systems of algebra (groups, rings, integral domains, and fields) and their relations to other disciplines. Prerequisite: MAT 301. Alternate years.

**337-338. Analysis I & II**

Topics from the theory of functions of a real variable. First term will include limits and continuity, differentiation and theories of integration. Second term will extend these results to sequences and series of functions. The second term will include student reading projects and presentations on theory and/or applications related to analysis topics. Prerequisites: MAT 122 and 301. Alternate years. Not offered 2013-2014.

**355-360. Advanced Topics in Mathematics**

A proof-oriented topic in mathematics. See *Topics Courses*. Prerequisite: MAT 301.

**380. Internship**: see *Courses 280/380*.

**390. Individual Project**: see *Courses 290/390*.

**511. Extended Research in Mathematics** (1/4)

Developing and proving statements in an interesting area of mathematics which are original to the student. Must be taken over four consecutive terms. Prerequisites: CSC 151, MAT 122, a GPA in the department of 3.0 or higher, and permission of instructor. No more than one course credit of MAT 511 can be earned.