MATHEMATICS (MATH)

Division of Natural Sciences and Mathematics

The Mathematics curriculum is designed to meet the undergraduate preparation of students who are seeking to: (1) pursue careers in industry as engineers, actuaries, statisticians or mathematicians; (2) enter graduate school in mathematics, statistics, engineering, computer science or operations research; or (3) teach mathematics on the elementary or secondary level.

Major Requirements

A major in mathematics consists of a minimum of 40 hours in mathematics as follows: twelve hours in calculus (MATH 206, 207, 208, 209); three hours in linear algebra (MATH 301); three hours in logic and set theory (MATH 303); three hours in computer programming (CS 111); three hours in modern algebra (MATH 341); three hours in analysis (MATH 411 or 412); one hour of seminar (MATH 420) and 12 additional hours in mathematics or computer science with at least three hours at the 300 level or above, at least three hours in the 400 level, and no more than three hours in computer science. The Mathematics faculty highly recommend PHY 101 and PHY 102 to meet the general education requirements for two lab sciences.

Minor Requirements

A minor in mathematics consists of 18 hours in mathematics as follows: six hours in calculus (MATH 206, 207); three hours in linear algebra (MATH 301); three hours in computer programming (CS 111); and two other mathematics courses. (See following note.)

MATH 100, MATH 101, MATH 103, MATH 105, MATH 200, MATH 202, MATH 308, and CS 101 cannot be counted toward major or minor in mathematics.

Teacher Education Program

Students majoring in mathematics who intend to pursue mathematics licensure must complete all requirements for the mathematics major. Additionally, some specific courses (MATH 236, MATH 302) must be taken. These can be included among the electives taken for the major.

Professional course requirements are as follows: EDU 200, EDU 200.1, EDU 200.3, *EDU 317, *EDU 317.1, EDU 325, EDU 375, *EDU 400, *EDU 494.3, *EDU 494, SPED 211.1, SPED 211 or SPED 253 or *SPED 367, PE 223, *MATH 302, *MATH 302.1, *MATH 308, *MATH 308.1, PSY 233 and *PSY 315.

The following courses, which may be taken as part of the general education requirements, are recommended: HIST 101 or 102; HIST 141 or 142; POL 201 or 202 or SOC 308; PHY 101 and 102; and two from the following: CIN 301, MUS 111, THE 106.

*Requires admission to Teacher Education

Students seeking teacher licensure must obtain at least a grade of C in each and all professional education and specialty area courses. No pass/fail grades will be accepted. Students are required to complete all professional/specialty courses prior to student teaching.

For information on additional teacher education requirements, procedures, and timelines, consult the section of the Catalog entitled Education, as well as the Teacher Education, Student Orientation, and Field Experiences Handbooks available from the social studies coordinator to the Teacher Education Program. Copies are also on reserve in the library. Students desiring SDPI licensure should be aware that graduation with licensure may require more than the minimum 124 semester hours.

Courses in Mathematics

MATH 100 Intermediate Algebra (3)

This course provides a smooth transition from arithmetic to the more abstract skills and reasoning abilities developed in a beginning algebra course. Basic concepts, integers and real numbers, radicals, solving equations and inequalities, exponents and polynomials, factoring, rational expressions, graphing linear equations/inequalities, quadratic equations. Technology will be used as an instructional tool in this course. This course does not count toward the general education requirement in mathematics. A student with credit for MATH 105 may not receive credit for MATH 100. Prerequisite: Placement by the department. Offered every semester.

MATH 101 Ideas in Mathematics (3)

This course provides students with an opportunity to explore mathematical ideas and develop quantitative reasoning and problem-solving skills. The content focuses on the historical development and contemporary applications of numeration and number theory, geometry, functions, statistics, and related topics. This course does not meet the prerequisite requirement for upper-level mathematics courses. Satisfies Natural Sciences/Mathematics General Education requirement. Offered at least one semester every year.

MATH 103 Mathematics of Finance (3)

An introduction to the basic mathematics of finance. Topics covered are simple interest, bank discount, compound interest, annuities and applications of annuities. The course requires the purchase of a business calculator. This course does not meet the prerequisite requirement for upper-level mathematics courses. Prerequisite: High school Algebra I, MATH 100 or placement by the department. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every semester.

MATH 105 College Algebra (3)

This course is designed to provide a foundation for further study in mathematics at the 200 level. Content includes basic properties of real numbers; equations; exponents; rational expressions; problem solving; exponential and logarithmic functions; and other algebraic fundamentals. Prerequisite: MATH 100 with a grade of C or better or placement by department. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every semester.

MATH 200 Business Calculus (3)

This course is an emphasis on business applications with topics including limits, continuity, the derivative, graphing, tangents as slope functions and applicable related topics. Prerequisite: MATH 105 with a grade of C or higher or placement by the department. Students may receive credit for either MATH 200 or MATH 206, but not both. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every semester.

MATH 202 Trigonometry and Analytic Geometry (3)

This course is a study of analytic geometry and of particular classes of functions such as exponential, logarithmic and trigonometric. The analytic geometry component covers conic sections including parabolas, ellipses and hyperbolas. Emphasis will be on trigonometric functions, their graphs and applications. Prerequisite: MATH 105 with a grade of C or higher or proficiency in college algebra. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every Spring Semester.

MATH 205 Discrete Mathematics (3)

This course includes combinatorial methods (systematic counting techniques), graph theory, trees, codes, network flows, permutations and combinations, algorithmic thinking, game theory and decision theory. Prerequisite: MATH 105 with grade of C or higher. Satisfies Natural Sciences/Mathematics General Education requirement. Offered Fall Semesters, 2001 and 2003.

MATH 206 Calculus I (3)

This course covers limits, continuity, the derivative and its application, the differential and anti-differentiation. Prerequisite: MATH 202 with a grade of C or higher or placement by the department. Students may receive credit for either MATH 200 or MATH 206, but not both. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every Fall Semester.

MATH 207 Calculus II (3)

This is a continuation of Calculus I. It includes definite integrals, derivatives and integrals of logarithmic, exponential and trigonometric functions, hyperbolic functions and techniques of integration. Prerequisite: MATH 206 with a grade of C or higher. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every Spring Semester.

MATH 208 Calculus III (3)

This is a continuation of Calculus II. It covers indeterminate forms, Taylor's formula, infinite series, analytic geometry, polar coordinates, vectors, partial differentiation and multiple integrals. Satisfies Natural Sciences/Mathematics General Education requirement. Prerequisite: MATH 207 with a grade of C or higher. Offered every Fall Semester.

MATH 209 Vector Analysis (3)

The calculus of vector valued functions, including line and surface integrals, Green's, Gauss', and Stokes' theorems, and physical applications. Prerequisite: MATH 208 with a grade of C or higher. Offered every Spring Semester.

MATH 236 Statistics (3)

This is an introduction to elementary statistics. Topics include descriptive statistics, probability and probability distributions, binomial and normal distributions, confidence intervals, hypothesis testing and student's t and Chi square distributions. Prerequisite: MATH 105 with a grade of C or higher or placement by the department. Satisfies Natural Sciences/Mathematics General Education requirement. Offered every semester.

MATH 301 Linear Algebra (3)

This is an introductory course in linear algebra covering the following topics: systems of linear equations, matrices, vector spaces, linear transformation and eigenvalues. Prerequisite: MATH 206 with a grade of C or higher. Offered Fall Semesters, 2002 and 2004.

MATH 302 Geometry (3)

This course will include a brief history of geometry, including the development of non-Euclidean geometries, development of the basic concepts, definitions, constructions, measurements, and related topics. The fundamentals of Euclidean geometry, including work with congruence, similarity, area, volumes, surface areas, and angles will be included. Students will also apply coordinate and vector methods to geometric problems in two and three dimensions. An introduction to transformational geometry will also be provided. This course is required for teacher licensure in secondary mathematics and middle grades mathematics. Prerequisite: MATH 105 with a grade of C or higher. Offered Spring Semesters, 2002 and 2004.

MATH 302.1 Fieldwork Component (1)

Required for all students seeking teacher licensure in mathematics. Prerequisite: Admission to Teacher Education. Offered Spring Semesters, 2002 and 2004.

Early fieldwork is a series of involved experiences sequentially planned to allow developmental opportunities for prospective teachers in actual classroom situations. Students are responsible for arranging their own transportation for assignments.

MATH 303 Logic and Set Theory (3)

This course will introduce elements of symbolic logic and Cantor's set theory, including relations, functions, bijections, cardinality and transfinite arithmetic. Required for major. Prerequisite: MATH 207 with a grade of C or higher. Offered Fall Semesters, 2002 and 2004.

MATH 305 Differential Equations (3)

This course provides an introduction to ordinary differential equations. Topics include first order equations, linear equations, linear systems, the Laplace transform, series techniques, and physical applications. Prerequisite: MATH 207 with a grade of C or higher. Offered Spring Semesters, 2003 and 2005.

MATH 308 Pedagogy of Mathematics (9-12) (3)

This course includes reading in historical background, curriculum and philosophy of mathematics education. The course provides secondary teachers with methods and materials for teaching in their respective areas. Prerequisite: Admission to Teacher Education. Offered Fall Semesters, 2001 and 2003.

MATH 308.1 Fieldwork Component (1)

Required for all students seeking teacher licensure in mathematics. For course description, see MATH 302.1. Prerequisite: Admission to Teacher Education. Offered Fall Semesters, 2002 and 2004.

MATH 336 Inferential Statistics (3)

This course is an introduction to inferential statistics with an emphasis on classical hypothesis testing. Tests involving the chi-square and F distribution are developed. Simple and multiple regression techniques are examined along with time series analysis and index numbers. Prerequisite: MATH 236 with a grade of C or higher or permission of the instructor. Offered periodically based upon student need.

MATH 341 Abstract Algebra (3)

The topics covered in this course include groups, subgroups, permutation groups, cyclic groups and homomorphisms. Prerequisite: MATH 301 and MATH 303 with a grade of C or higher. Offered Spring Semesters, 2003 and 2005.

MATH 350 Intermediate Special Topics in Mathematics (3)

This course will consider specialized topics in mathematics. Topics to be taught might include Graph theory, Number systems, Fractals, Inferential Statistics, Number theory. Satisfies Natural Sciences/Mathematics General Education requirement. Prerequisite: permission of the instructor. Offered periodically based upon student need.

MATH 411 Real Analysis (3)

This course covers bounded sets, sequences and series, convergence, metric spaces and continuity. Prerequisite: MATH 303 with a grade of C or higher. Offered Fall Semesters, 2001 and 2003.

MATH 412 Complex Analysis (3)

This course focuses on complex numbers, analytic functions of a complex variable, mappings and integration of complex functions, power series, residues and poles, and conformal mappings. Prerequisite: MATH 209 with a grade of C or higher. Offered Fall Semesters, 2002 and 2004.

MATH 414 General Topology (3)

This course is intended as an introduction to the theory of sets, relations, functions, finite and infinite sets, and other selected topics. Algebraic structure and topological properties of Euclidean Space and introduction to metric spaces will be included. Prerequisite: MATH 303 with a grade of C or higher or permission of the instructor. Offered periodically based upon student need.

MATH 420 Seminar (1)

This course is a capstone experience for mathematics majors and consists of presentative experiences on topics selected by the instructor. Competency in the course is demonstrated by successful collection, organization, and presentation of advanced mathematical topics. Required of all majors. Prerequisite: Junior standing. Offered every Fall Semester.

MATH 450 Special Topics in Mathematics (3)

This course will consider specialized topics in mathematics. Topics to be taught might include Partial Differential Equations, Numerical Analysis, Mathematical Models, and History of Mathematics. Prerequisite: Permission of the instructor. Offered periodically based upon student need.