# Mathematics

*Associate Professor: M. Gregg
Assistant Professors: J. Smith, T. Sorenson*

The Mathematics curriculum is designed to provide for the educational needs of many students. For general education there are courses which develop basic competence in mathematical reasoning. More advanced courses furnish necessary mathematical background for a variety of majors. A major in Mathematics suits students intending to become mathematics teachers, planning to enter certain professions in business or industry, preparing for graduate study in mathematics or related areas, or simply wishing to support another major.

### Mathematics Major:

41 credit hours**Required Courses:** 33 credit hours

MATH 151 — Calculus I (4 cr)

MATH 152 — Calculus II (4 cr)

MATH 153 — Calculus III (3 cr)

MATH 200 — Foundations of Mathematics (3 cr)

MATH 220 — Linear Algebra (3 cr)

MATH 490 — Senior Seminar (1 cr)

*MATH 300-level — Elective courses (3 courses) 9 cr

**Two of the following courses: **

MATH 340 — Abstract Algebra (3 cr)

MATH 345 — Topology (3 cr)

MATH 350 — Real Analysis (3 cr)

MATH 355 — Complex Analysis (3 cr)

*May use the two courses not used for the elective area above.

**Required Supportive Courses:** 8 credit hours

COSC 210 — Computer Science I (4 cr)

PHYS 221 — General Physics I (4 cr)

### Mathematics Minor:

18 credit hours

MATH 152 — Calculus II (4 cr)

MATH 200-level — Elective (or higher) (3 cr)

*MATH — Elective courses (One COSC course allowed as a substitute) (11 cr)

### Mathematics Courses:

**MATH 110 — Structure of Mathematics** (3 credits)

Recommended for Elementary Education majors as a preliminary to MATH 113. An introduction to basic mathematical ideas including counting and measuring, calculation, symbol manipulation, algebra and logic. Topics are matched to the elementary school curriculum. The emphasis is on developing understanding, intuition, and imagination rather than rigidly following prescribed methods. Offered Every Semester.

**MATH 113 — Teaching Mathematics in Elementary and Middle School** (3 credits)

This course integrates study of theory, curriculum and pedagogy for teaching arithmetic in grades K-8. Topics include instructional methods in mathematical procedure and processes, technology in teaching and learning, lesson planning, teaching through problem-solving, formative and summative math assessments, local, state and national standards, and effective teacher discourse in the math classroom. This course is based on the recommendations of NCTM; namely that all children learn best by actively exploring and investigating math, that problem-solving, reasoning and communication are important goals of mathematics teaching and learning, and that all children have highly qualified teachers. Prerequisite: MATH 140 or higher and Admission to Teacher Education. Offered Every Semester.

**MATH 140 — Quantitative Reasoning** (Area 2.3) (3 credits)

For students with one or two years of high school algebra. This course is at the level of college algebra but is not focused on algebra. It stresses application of mathematics in careers of non-scientists and in the everyday lives of educated citizens, covering basic mathematics, logic, and problem solving in the context of real-world applications. Offered Every Semester.

**MATH 150 — Pre-Calculus** (Area 2.3) (4 credits)

Algebra review, functions and graphs, logarithmic and exponential functions, analytic geometry, trigonometric functions, trigonometric identities and equations, mathematical induction, complex numbers. Students completing this course are prepared to enter calculus. Offered Every Semester.

**MATH 151 — Calculus I** (Area 2.3) (4 credits)

Limits and continuity for functions of one real variable. Derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions. Applications of the derivative. Introduction to related numerical methods. Offered Every Semester.

**MATH 152 — Calculus II **(4 credits)

Techniques of integration, numerical integration, and applications of integrals. Infinite series including Taylor series. Introduction to differential equations. Calculus in polar coordinates. Offered Every Semester.

**MATH 153 — Calculus III **(3 credits)

The calculus of vector-valued functions, functions of several variables, and vector fields. Includes vector operations, equations of curves and surfaces in space, partial derivatives, multiple integrals, line integrals, surface integrals, and applications. Offered Every Spring Semester.

**MATH 200 — Foundations of Mathematics** (3 credits)

Bridges the gap between computational, algorithmic mathematics courses and more abstract, theoretical courses. Emphasizes the structure of modern mathematics: axioms, postulates, definitions, examples conjectures, counterexamples, theorems, and proofs. Builds skill in reading and writing proofs. Includes careful treatment of sets, functions, relations, cardinality, and construction of the integers, and the rational, real, and complex number systems. Prerequisite: MATH 152; Offered Every Fall Semester.

**MATH 220 — Linear Algebra** (3 credits)

Vector spaces, linear independence, basis and dimension, linear mappings, matrices, linear equations, determinants, Eigen values, and quadratic forms. Prerequisite: MATH 152; Offered Every Spring Semester.

**MATH 310 — Differential Equations** (3 credits)

Methods of solving first and second order differential equations, applications, systems of equations, series solutions, existence theorems, numerical methods, and partial differential equations. Prerequisite: MATH 152; Offered Every Fall Semester.

**MATH 315 — Probability and Statistics** (3 credits)

Probability as a mathematical system, random variables and their distributions, limit theorems, statistical inference, estimation, decision theory and testing hypotheses. Prerequisite: MATH 152; Offered Every Fall Semester.

**MATH 320 — Discrete Structures **(3 credits)

Topics to be selected from counting techniques, mathematical logic, set theory, data structures, graph theory, trees, directed graphs, algebraic structures, Boolean algebra, lattices, and optimization of discrete processes. Prerequisites: MATH 151 and COSC 210; Offered Every Spring Semester.

**MATH 330 — History of Mathematics** (W - Area 2.1B) (3 credits)

The history of mathematics from ancient to modern times. The mathematicians, their times, their problems, and their tools. Major emphasis on the development of geometry, algebra, and calculus. Prerequisite: MATH 200; Offered Interim, Odd Years.

**MATH 335 — Modern Geometry** (3 credits)

A review of Euclidean geometry, an examination of deficiencies in Euclidean geometry, and an introduction to non-Euclidean geometrics. Axiomatic structure and methods of proof are emphasized. Prerequisite: MATH 200; Offered Interim, Even Years.

**MATH 340 — Abstract Algebra **(3 credits)

A survey of the classical algebraic structures taking an axiomatic approach. Deals with the theory of groups and rings and associated structures, including subgroups, factor groups, direct sums of groups or rings, quotient rings, polynomial rings, ideals, and fields. Prerequisite: MATH 200 and 220; Offered Fall Semester, Even Years.

**MATH 345 — Topology **(3 credits)

An introduction to topological structures from point-set, differential, algebraic, and combinatorial points of view. Topics include continuity, connectedness, compactness, separation, dimension, homeomorphism, homology, homotopy, and classification of surfaces. Prerequisite: MATH 200 and 220; Offered Spring Semester, Odd Years.

**MATH 350 — Real Analysis** (3 credits)

This course develops the logical foundations underlying the calculus of real-valued functions of a single real variable. Topics include limits, continuity, uniform continuity, derivatives and integrals, sequences and series of numbers and functions, convergence, and uniform convergence. Prerequisite: MATH 200 and 220; Offered Fall Semester, Odd Years.

**MATH 355 — Complex Analysis **(3 credits)

A study of the concepts of calculus for functions with domain and range in the complex numbers. The concepts are limits, continuity, derivatives, integrals, sequences, and series. Topics include Cauchy-Riemann equations, analytic functions, contour integrals, Cauchy integral formulas, Taylor and Laurent series, and special functions. Prerequisite: MATH 200 and 220; Offered Spring Semester, Even Years.

**MATH 197, 297, 397 — Topics in Mathematics **(2-4 credits)

**MATH 199, 299, 399 — Independent Study** (2-4 credits)

**MATH 490 — Senior Seminar** (1 credit)

This course reviews and correlates the courses in the mathematics major. Each student is responsible for preparing the review of one area. Students also read papers from contemporary mathematics journals and present them to the class. The course uses the ETS mathematics major exam. Prerequisite: MATH 200 and 220; Offered Every Spring Semester.