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Mathematics
Dr. C. Taylor, chair; Dr. Lambright, Dr. Van Groningen
The program in mathematics has three major objectives: to provide the non-specialist with some understanding of the contributions of mathematics to cultural development; to offer students in natural, social, and behavioral sciences the mathematics necessary for understanding their own fields of interest; and to prepare mathematics majors for graduate study, for teaching at the secondary level, or for work in business and industry.
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Students considering careers in mathematics should realize that the emphasis in mathematics courses changes as progress is made through the undergraduate program. The early emphasis on problem solving is later subordinated to the task of formulating and dealing effectively with mathematical structures and abstract ideas.
Students who have pursued accelerated mathematics programs in high school may request advanced placement. Such requests should be made through correspondence with the department chair before registration. Credit, if granted for high school work in calculus or statistics, is through the Advanced Placement Program of the College Entrance Board. Consult with the chair of the Department of Mathematics or the Office of the University Registrar for details.
Students who plan to major in mathematics should consult the chair of the department as soon as possible. Students interested in actuarial science should consider the mathematics-finance major.
MATHEMATICS MAJOR, BACHELOR OF ARTS (30 hrs.) • MATH 2010, 2020, 3010, 3020, 4000 • One course numbered MATH 4010 or above • At least two additional courses numbered MATH 3100 or above • If necessary, remaining hours from additional MATH courses • MATH 1000, 1100, 1110, 1220, 1250, 1300, 1400, 4700 do not apply toward the major
MATHEMATICS MAJOR, BACHELOR OF SCIENCE (47 hrs.) • MATH 2010, 2020, 2200, 3010, 3020, 3300, 4000 • MATH 2120 or MATH 4010 • MATH 4100 or MATH 4200 • An additional 3 credit hours from MATH courses numbered 3100 or higher, excluding MATH 4700 • ENGR 2310 • CPSC 2320 • PHYS 2240 • An additional 4 credit hours from CHEM 2110 or above, PHYS 2250 or above, BIOL 2210 or above
MATHEMATICS-DECISION SCIENCE MAJOR, BACHELOR OF ARTS (53 hrs.) • MATH 2010, 2020, 2120, 3010, 3020, 3200, 4000, 4010 • One of MATH 3100, 3300, 3400 • BSNS 2710, 2810, 3240, 3510, 4110, 4330 • A 3-hour independent study course combining mathematics and decision science
MATHEMATICS-ECONOMICS MAJOR, BACHELOR OF ARTS (38 hrs.) • MATH 2010, 2020, 3010, 3020, 4000, 4010 • ECON 2010, 2020, 3020, 3410 • Remaining hours from additional upper-division MATH and ECON courses
MATHEMATICS-FINANCE MAJOR, BACHELOR OF ARTS (53 hrs.) • MATH 2010, 2020, 2120, 3010, 3020, 3400, 4000, 4010 • One of MATH 3100, 3200, 3300 • ACCT 2010 • BSNS 2510, 3350, 4150 • ECON 2010, 2020, 3410
MATHEMATICS TEACHING MAJOR, BACHELOR OF ARTS (40 hrs.) • MATH 2010, 2020, 2200, 2300, 3010, 3020, 4000, 4100, 4200 • MATH 2120 or 4010 • One course from MATH 3100, 3200, 3300, 3400 • MATH 4700 • In addition to these requirements, students pursuing a teaching major must also meet additional requirements listed in the Department of Teacher Education section of this catalog.
MATHEMATICS MINOR (16 hrs.) • MATH 2010, 2020 • Additional hours from MATH courses numbered 2120 or above
MATH COURSES
1000 Introductory Algebra 2 hrs. (2, 0)
Basic algebra course designed for students who need to meet the curricular mathematical proficiency requirement. Topics include whole numbers, fractions, decimals and percentages, ratios and proportions, polynomials, algebraic solutions of linear and quadratic equations, word problems, and systems of equations. Does not apply toward mathematics major or minor. PREREQUISITE: Placement by mathematics entrance examination. GRADE: CR/NC. OFFERED: Sem. I, II.
Elementary foundations course for students preparing for elementary and middle school education. Includes deductive reasoning, the algebra of sets, numeration systems, properties of natural numbers, integers, rational numbers, real numbers, and data analysis. Does not apply toward mathematics major or minor. PREREQUISITE: Mathematics proficiency. OFFERED: Sem. I.
Includes point-set geometry, linear and angular measurement concepts, area and volume, transformational geometry, and probability. Designed particularly for elementary and middle school education majors. Does not apply toward mathematics major or minor. PREREQUISITE: Mathematics proficiency. OFFERED: Sem. II.
A course designed in order to fully prepare students for MATH 2010. Topics include right triangle trigonometry, trigonometric identities and equations, complex numbers, laws of sines and cosines, trigonometric, exponential, and logarithmic functions, analytic geometry, and conic sections. Does not apply toward mathematics major or minor. PREREQUISITE: Mathematics proficiency. OFFERED: Sem. I.
MATH (cont.)
1250 Explorations in Mathematics 3 hrs. (3, 0)
A course designed for students to explore different areas of college-level mathematics. Students will appreciate the relevance of mathematics through real-life applications. Emphasis will be placed on critical reasoning, problem solving, and the clear communication of mathematical ideas. Topics will be chosen from mathematics of finance, mathematical modeling, probability and statistics, voting theory, infinity, and logic. Does not apply toward mathematics major or minor. PREREQUISITE: Mathematics proficiency. OFFERED: With sufficient demand.
1300 Finite Mathematics 3 hrs. (3, 0)
Topics include introduction to counting techniques, probability, systems of linear equations and matrices, linear programming, Markov chains, and the mathematics of finance. Does not apply toward mathematics major or minor. PREREQUISITE: Mathematics proficiency. OFFERED: Sem. I, II.
1400 Applied Calculus 4 hrs. (4, 0)
Topics include functions, limits, derivatives, applications of derivatives, integration, and applications of integration. Functions considered are polynomial, rational, logarithmic, and exponential functions. Emphasis is on computational skill and problem solving. Applications are taken from management, life sciences, and social sciences. Does not apply toward mathematics major or minor. EXPECTATION: Two years of high school algebra. PREREQUISITE: Mathematics proficiency. Not open to students with a grade of C or better in MATH 2010 or its equivalent. OFFERED: With sufficient demand.
2010 Calculus I 4 hrs. (4, 0)
Introduction to plane analytic geometry, functions, limits, continuity, differentiation of algebraic and trigonometric functions, application of the derivative, and indefinite and definite integrals. EXPECTATION: Two years of high school algebra, plane geometry, and trigonometry, MATH 1220, or passing score on Calculus Readiness Exam. PREREQUISITE: Mathematics proficiency. OFFERED: Sem. I, II.
2020 Calculus II 4 hrs. (4, 0)
Continuation of MATH 2010. Attention given to methods of integration of algebraic and transcendental functions, curves given in polar coordinates, curves given by parametric equations, applications of integration, introduction to ordinary differential equations, and infinite sequences and series. PREREQUISITE: Grade of at least C- in MATH 2010. An appropriate AP score may waive the prerequisite; see department chair. OFFERED: Sem. II.
Descriptive statistics; binomial, normal, and chi-square distributions; sampling distributions; estimation; hypothesis testing; simple linear regression; and analysis of variance. EXPECTATION: Two years of high school algebra. OFFERED: Sem. II.
Topics include Boolean algebra, computer logic, relations and functions, logic and proof techniques, combinatorics, algebraic structures, and graph theory. PREREQUISITE: Mathematics proficiency. SAME AS: CPSC 2250. OFFERED: Sem. II.
2300 College Geometry 3 hrs. (3, 0)
Presents an axiomatic basis for Euclidean geometry and provides insight into the interdependence of various theorems and axioms. Topics include incidence and order properties, congruence, absolute and non-Euclidean geometry, the parallel postulate, and the real numbers and geometry. PREREQUISITE: MATH 2010. OFFERED: Sem. II, 2023-24.
3010 Linear Algebra 4 hrs. (4, 0)
Introduction to algebra and geometry of R3 and its extension to Rn. Topics include vector spaces and linear transformations, systems of linear equations and their solutions, matrices and determinants, eigenvalues, eigenvectors. Applications of these topics will also be demonstrated. PREREQUISITE: Grade of at least C- in MATH 2010. OFFERED: Sem. I.
MATH (cont.)
3020 Calculus III 4 hrs. (4, 0)
Continuation of MATH 2020. Attention given to multi-dimensional calculus and its applications. Topics include partial differentiation, multiple integration, three-dimensional analytic geometry, and vector calculus. PREREQUISITE: MATH grade of at least C- in 2020, grade of at least C- in 3010. OFFERED: Sem. II.
3100 Differential Equations 3 hrs. (3, 0)
Methods of solving ordinary differential equations and their applications to life sciences, physics, and chemistry. Topics covered will include first and second order homogenous and nonhomogeneous equations, first order systems, Laplace transforms, series solutions, and an introduction to partial differential equations. PREREQUISITE: Grade of at least C- in MATH 2020. OFFERED: Sem. II.
3200 Mathematical Models 3 hrs. (3, 0)
Formation and study of mathematical models used in business, social, and biological sciences. Mathematical topics include N-person games, networks, Markov processes, application of graphs and digraphs, apportionment, and group decision-making. PREREQUISITE: Mathematics proficiency. OFFERED: Sem. II, 2022-23.
3300 Numerical Analysis 3 hrs. (3, 0)
Introduction to numerical algorithms fundamental to scientific and mathematical computer use. Includes root finding methods; polynomial interpolation; numerical integration and differentiation; matrix equations; numerical solutions to differential equations. PREREQUISITE: CPSC 1400, MATH 2020. SAME AS: CPSC 3300. OFFERED: Sem. I, 2023-24.
3400 Mathematics of Finance 3 hrs. (3, 0)
A course designed to introduce the fundamental concepts of financial mathematics with an emphasis on interest theory. Topics include mathematical foundations of the following: present and accumulated values, annuities, loans, bonds, financial markets, arbitrage, and financial derivatives. This course serves as a foundation for the second actuarial exam (FM/2). PREREQUISITE: MATH 2020. OFFERED: Sem. I, 2022-23.
4000 Problem Seminar 2 hrs. (2, 0)
Introduction to research techniques based on problems from parts of the regular curriculum such as calculus, linear algebra, probability, and statistics. Emphasis on problems from the required core of the curriculum — problems that are integrative in nature. This course applies to the liberal arts speaking-intensive requirement. PREREQUISITE: Senior standing. OFFERED: Sem. I.
4010 Mathematical Statistics 4 hrs. (4, 0)
Probability distributions, expectation, mean, variance, moment generating functions, special distributions, unbiasedness, maximum likelihood, confidence intervals, and hypothesis testing. PREREQUISITE: MATH 3010. OFFERED: Sem. I.
4100 Real Analysis 3 hrs. (3, 0)
Careful study of the real number system with attention given to the study of real-valued functions, metric spaces, sequences, continuity, differentiation, and integration. PREREQUISITE: MATH 3010. OFFERED: Sem. I, 2022-23.
4200 Abstract Algebra 3 hrs. (3, 0)
Consideration of fundamental concepts of modern algebra. Includes groups, rings, integral domains, and fields along with isomorphisms, homomorphisms, normal subgroups, and quotient groups. PREREQUISITE: MATH 3010. OFFERED: Sem. I, 2023-24.
4650 Independent Study 1-3 hrs. (arranged)
Selected topics in higher mathematics. Total combined credit from MATH 4650 and 4900 may not exceed 12 hours. CONSENT: Department chair.
4700 Methods in Teaching Mathematics
PREREQUISITE: MATH 3020. OFFERED: Sem. I.
2 hrs. (2, 0)
4900 Seminar 1-3 hrs. (arranged)
Seminars in algebra, analysis, topology, set theory, complex variables, non-Euclidean geometry, and applied mathematics. Total combined credit in MATH 4650 and 4900 may not exceed 12 hours. CONSENT: Department chair. OFFERED: With sufficient demand.