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Professors: J. Barksdale, D. Biles, B. Brunson, C. Ernst, P. Hamburger, N. Iraniparast, B. Kessler Associate Professors: F. Atici, C. Edwards, L. Nguyen Assistant Professors: M. Autin, D. Benko, T. Bhattacharya, B. Csaba, M. Dunkum, Instructors: R. Ayers, J. Brantley, S. Britt*, L. Fitzpatrick*, T. Harris,
L. Rogers, J. Thornton, Mathematics courses at the University are designed with the interests and needs of varying groups of students in mind. Majors and minors are available to those planning to pursue careers in secondary education as well as to those whose preparation is being directed toward positions in business and industry or toward further work in mathematics at the graduate level. In addition, several courses are offered to meet the demands for the mathematical training of students whose major educational objectives are not directly related to mathematics. Mathematics majors are assigned advisors from among the departmental faculty and are required to consult with these advisors before each registration period. Majors are advised of the importance of selecting supporting courses from the area of computer science. When planning a program of study in this department, each student should be aware of the University’s academic requirements and regulations contained in this catalog in the chapter “Academic Information.” Specific attention should be given to the sub-sections in the chapter entitled (a) Academic Programs, (b) General Education Requirements, and (c) Academic Requirements and Regulations. Students should be aware that some academic programs may require additional scholastic regulations and standards not specified in the catalog. To obtain a copy of these regulations, students should contact the department head. Major in Mathematics A major in mathematics provides a bachelor of arts degree and requires either a minimum of 35 semester hours for a general major with a minor or second major (reference number 728) or a minimum of 48 semester hours for an extended major (reference number 528). Mathematics majors are required to complete CS 230 or CS 240. Both types of majors offer two options: (1) Major for Employment in Industry and/or Graduate Studies in Mathematics; (2) Major Certifiable for Teaching Secondary Level Mathematics. Option 1: Major for Employment in Industry and/or Graduate Studies in Mathematics (A) General Major (728): The student must complete a minimum of 35 hours of mathematics with a minor or second major giving a total of at least 54 hours (48 unduplicated) with the following requirements: MATH 126-227 (or 122-132-232), 307, 310, 317, 327, 498. · At least one of the sequences: MATH 317-417; 329-429; 331-435; 431-432; 431-450; ¸ At least 6 hours of 400-level mathematics other than MATH 475. Other acceptable courses for the general major are MATH 275 (up to 3 hours), 305, 315, 323, 329, 331, 398 (up to 3 hours), 405, 406, 415, 417, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours), and STAT 301. (B) Extended Major (528): The student must complete a minimum of 48 hours of mathematics with the following requirements: MATH 126-227 (or 122-132-232), 307, 310, 317, 327, 498. · At least one of the sequences: MATH 317-417; 329-429; 331-435; 431-432; 431-450; ¸ At least 12 hours of 400-level mathematics. Other acceptable courses for the extended major are MATH 275 (up to 3 hours), 305, 315, 323, 329, 331, 398 (up to 3 hours), 405, 406, 409, 415, 417, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours), and STAT 301. Option 2: Major Certifiable for Teaching Secondary Level Mathematics (A) General Certifiable Major (728): The student must complete a minimum of 35 hours of mathematics with a minor or second major giving a total of at least 54 hours (48 unduplicated) with the following requirements: MATH 126-227 (or 122-132-232), 307, 310, 317, 323, 327, 498; · At least 3 hours of 400-level mathematics other than MATH 475. Other acceptable courses for the general certifiable major are MATH 275 (up to 3 hours), 305, 315, 329, 331, 398 (up to 3 hours), 405, 406, 409, 415, 417, 421, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours). (B) Extended Certifiable Major (528): The student must complete a minimum of 48 hours of mathematics with the following requirements: MATH 126-227 (or 122-132-232), 307, 310, 317, 323, 327, 498; STAT 301. The student must complete these courses before the “professional semester.” · At least 9 hours of 400-level mathematics. Other acceptable courses for the extended certifiable major are MATH 275 (up to 3 hours), 305, 315, 329, 331, 398 (up to 3 hours), 405, 406, 409, 415, 417, 421, 423, 429, 431, 432, 435, 439, 450, 470, 475 (up to 6 hours). Minor in Mathematics A minor in mathematics (reference number 417) requires a minimum of 18/21 semester hours. The program offers two options: (1) Minor for Employment in Industry and/or Graduate Studies in Mathematics. (2) Minor Certifiable for Teaching Secondary Level Mathematics. The student who elects a minor in mathematics (either option) must complete the following courses: the sequence MATH 126, 227 or the sequence MATH 122, 132, 232; and MATH 307. Option 1: Minor for Employment in Industry The student who elects a minor in mathematics but does not plan to teach is provided a noncertifiable minor that requires at least eighteen semester hours of mathematics. In addition to the foundational sequence (MATH 126, 227, 307*) this student is required to select two courses from MATH 305, 310, 317, 327, 329, 331, or STAT 301**. * Students majoring in engineering may replace MATH 307 with MATH 350. Option 2: Minor Certifiable for Teaching Secondary Mathematics The student who elects a minor in mathematics certifiable for secondary education is required to complete at least twenty-one semester hours of mathematics. In addition to the foundational sequence (MATH 126, 227, 307) this student is required to complete the following: Both MATH 310 Grades K-5 Certification All students seeking grades K-5 certification must satisfy the general education requirement in mathematics prior to enrolling in the required courses: MATH 211 and MATH 212. Middle School Certification in Mathematics Students seeking middle school certification for teaching mathematics must choose one of the following options: (1) two teaching fields from English/communication, mathematics, science and social studies; or (2) a single concentrated teaching field in mathematics or science. For option 1 (two fields) students must complete the following courses (to total at least 25 hours): a. MATH 116 or MATH 118, MATH 119 or MATH 126 The following sequencing of mathematics courses is recommended for students seeking middle grades certification in mathematics (two fields). Fall Spring Freshman year MATH 116 or 118 MATH 119 or 126 Sophomore year MATH 211 MATH 212 Junior year MATH 403 MATH 411 and MGE 477 Senior year MATH 203 Student Teaching Note: A student with appropriate high school mathematics preparation and a math ACT score of 27 or greater may choose to begin with MATH 126 or Math 119. If a student’s initial course is MATH 119 or 126, MATH 409 or 413 should be selected to complete the hour requirement. Also, if a student expects to study calculus beyond that for middle school preparation, MATH 126 should be selected. For option 2 (one field) students must complete the following courses (to total at least 30 hours): a. MATH 117 or MATH 118, MATH 122, 132 or MATH 126, 227 Fall Spring Freshman year MATH 117 or 118 MATH 122 or 126, MATH 211 Sophomore year MATH 132 or 227, MATH 203 or STAT 301, MATH 307 Junior year MATH 403 or MATH 411 and MGE 477 Senior year MATH 409 Student Teaching Note: If a student begins his or her college mathematics courses at a level higher than indicated in item a, the department may grant permission to substitute higher level mathematics courses. Graduate Degree Programs The Department of mathematics offers graduate courses for the master of science in mathematics. Mathematics coursework is also provided for those seeking graduate degrees in elementary or middle grades education. Several assistantships are available for qualified graduate students. For further information select this Graduate Studies Hyperlink or contact the Division of Graduate Studies. Courses of Instruction Note: Any course approved for general education credit is designated to the right of the title. For details refer to the section of the catalog titled “General Education Requirements.” (Courses numbered below 122 are not applicable toward a major or minor.) A student who has earned credit for the listed course with a grade of “C” or better may not subsequently receive credit for the courses following in parentheses: MATH 116 (Math 096); MATH 117 (Math 096 and 116); MATH 118 (Math 096, 116, and 117); MATH 119 (MATH 096, 116, and 118); MATH 122 (MATH 096, 116, and 118); MATH 126 (MATH 096, 116, 117, 118, 119, and 122); MATH 203 (MATH 096, 116, and 118); MATH 227 (MATH 096, 116, 117, 118, 119, 122, 126, 132, and 232); MATH 310 (MATH 109); MATH 329 (MATH 109 and 203); STAT 301 (MATH 109 and 203). * These courses fulfill the Mathematics (Category D-II) general education requirement. MATH 096 Intermediate Algebra 4 hours For those students needing algebra who do not have the prerequisites for MATH 116 or 118. Topics include functions, graphs, and fundamental concepts of algebra. Credit for MATH 096 is not applicable toward a baccalaureate degree.
*MATH 109 General Mathematics 3 hours GEN ED D-II Terminal course for non‑science majors suggested for the student who has satisfactorily completed minimum high school mathematics requirements and needs no further work in algebra. Topics include sets, introduction to probability and statistics, geometry, and consumer mathematics. *MATH 116 College Algebra 3 hours GEN ED D-II Graphing and problem solving are integrated throughout the study of polynomial, absolute value, rational, radical, exponential, and logarithmic functions. (Graphing calculator required.) *MATH 117 Trigonometry 3 hours gen ed D-II Unit circle; trigonometric functions and graphs; trigonometric identities and equations; right triangle trigonometry; laws of sines and cosines; DeMoivre’s Theorem; vectors and applications of trigonometry. (Graphing calculator required.) *MATH 118 College Algebra and Trigonometry 5 hours GEN ED D-II Real number system, algebraic manipulations, and solutions of equations and inequalities, absolute value, exponential and logarithmic functions, trigonometry, systems of equations, complex numbers. (Graphing calculator required.) *MATH 119 Fundamentals of Calculus 4 hours GEN ED D-II An introduction to calculus designed for non‑science and non‑technical majors. Applications are directed toward the management sciences and related areas. Not accepted for credit toward a mathematics major or minor. (Graphing calculator required.) *MATH 122 Calculus of a Single Variable I 3 hours GEN ED D-II Introductory analytic geometry and differential calculus. First course of a three-course sequence presenting a unified development of analytical geometry, differential and integral calculus, and series. (Graphing calculator required.) *MATH 126 Calculus and Analytic Geometry I 4.5 hours GEN ED D-II This is the first of a sequence of courses which present a unified treatment of plane and solid analytic geometry and differential and integral calculus. (Graphing calculator required.) MATH 132 Calculus of a Single Variable II 3 hours Integral calculus. Second course of a three-course sequence presenting a unified development of analytical geometry, differential and integral calculus, and series. MATH 175 University Experience – Mathematics 2 hours Transition to university experience. Topics include study skills, critical thinking skills, library education, exploration of majors and careers, degree programs, campus resources and personal development. Specific degree requirements for a major in mathematics and career opportunities in mathematics are also discussed.
*MATH 203 Statistics 3 hours GEN ED D-II Introduction to elementary probability theory. The analysis of data by means of frequency distributions and the statistics which describe them. The binomial and normal probability distributions. Statistical inference. Emphasis is on applied real world problems. Not accepted for credit toward a mathematics major or minor. MATH 211 Mathematics for Elementary Teachers I 3 hours Elementary work with relations, systems of numeration, number systems, and number theory. MATH 212 Mathematics for Elementary Teachers II 3 hours Construction geometry, motion geometry, nonmetric geometry, measurement including the metric system, and introductions to computers, probability, and statistics. MATH 213 Laboratory for Mathematics for Elementary Teachers I 1 hour Hands-on laboratory, using manipulatives and problem-solving techniques to strengthen mathematical vocabularies and deepen understanding of topics from MATH 211. MATH 214 Laboratory for Mathematics for Elementary Teachers II 1 hour Hands-on laboratory, using manipulatives and problem-solving techniques to strengthen mathematical vocabularies and deepen understanding of topics from MATH 212. MATH 227 Calculus and Analytic Geometry II 4.5 hours The continuation of MATH 126. MATH 232 Calculus of a Single Variable III 3 hours Sequences, series, parametric equations and polar coordinates, applications using technology. Third course of a three-course sequence presenting a unified development of analytical geometry, differential and integral calculus, and series. MATH 275 Introductory Topics in Mathematics 1-3 hours Varied topics selected to give students an early introduction to interesting mathematical problems or applications not found in the foundation sequence. MATH 295 Introduction to Research Methodology 1 hour To familiarize Ogden Research Scholars and other interested students with the fundamentals of choosing a research topic, performing a bibliographical search on a subject, classification of instruments, data taking, data reduction, professional ethics and related topics. The common points of research methodology in the different scientific areas will be emphasized, with examples drawn from various disciplines. Computers will be utilized. (Course does not count toward any major or minor.)
MATH 305 Introduction to Mathematical Modeling 3 hours Theory and computer implementation of mathematical models. Deterministic, stochastic, discrete, continuous, and matrix models. Introduction to advanced topics such as linear algebra, differential and difference equations, probability, stochastic processes, and dynamical systems. MATH 307 Introduction to Linear Algebra 3 hours Systems of linear equations, matrix algebra, vector spaces, inner product spaces, linear transformations, eigenvectors, quadratic forms. MATH 310 Introduction to Discrete Mathematics 3 hours Introduction to discrete topics. Development of skills in abstraction and generalization. Set theory, functions and relations, mathematical induction, elementary propositional logic, quantification, truth tables, validity; counting techniques, pigeonhole principle, permutations and combinations; recurrence relations and generating functions; elementary graph theory, isomorphisms, trees. MATH 315 Theory of Numbers 3 hours A study of the arithmetic of the integers, divisibility, prime numbers, factorization, diophantine equations, congruences, quadratic residues. MATH 317 Introduction to Algebraic Systems 3 hours Introduction to groups, rings, polynomial rings, integral domains, and fields. MATH 323 Geometry I 3 hours Beginning with a re-examination of elementary Euclidean geometry, the course includes a study of absolute plane geometry and the parallel postulate, which leads to an axiomatic treatment of hyperbolic geometry and related topics. MATH 327 Multivariable Calculus 4 hours Topics in real-valued functions of several variables including directional derivatives, implicit functions, gradient, Taylor’s Theorem, maxima, minima, and Lagrange multipliers. Differential calculus of vector-valued functions including chain rule and Inverse Function Theorem. Multiple integrals, line integrals, surface integrals, Stokes’ and Green’s Theorems. MATH 329 Probability and Statistics I 3 hours Axioms and laws of probability; discrete and continuous probability distributions; multivariate distributions; random variables; expectation; moment generating functions; Central Limit Theorem. MATH 331 Differential Equations 3 hours Methods of solution of differential equations, existence and nature of solutions, systems of differential equations, applications, and numerical solutions. MATH 350 Advanced Engineering Mathematics 3 HOURS Special topics in Laplace transforms, linear algebra and complex analysis. Designed for engineering students. MATH 398 Seminar 1 hour (May be repeated for up to a total of 3 hours credit.) Students will read and present papers that have appeared in (or have been accepted by) mathematical journals. Topics covered will be determined by areas of interest of the respective students.
MATH 403 Geometry For Elementary and Middle School Teachers 3 hours Both formal and informal methods are used to explain the basic concepts of Euclidean geometry. Emphasis is given to the investigative approach, organizational skills, and problem solving. MATH 405 Numerical Analysis I (CS 405) 3 hours Computer arithmetic, roots of equations, polynomial approximation and interpolation, numerical differentiation and integration. Computer solutions of problems will be required. MATH 406 Numerical Analysis II 3 hours The solution of linear systems by direct and iterative methods, matrix inversion, the calculation of eigenvalues and eigenvectors of matrices. Initial and boundary value problems in ordinary differential equations. Computer solution of problems will be required. MATH 409 History of Mathematics 3 hours History of mathematics from ancient times through the development of calculus, with emphasis on famous problems. Provides knowledge and appreciation useful in the classroom. This course cannot be accepted as part of the 35-hour requirement for the non-certifiable mathematics major. Term papers will be required. MATH 411 Problem Solving for Elementary and Middle School Teachers 3 hours Integrates concepts developed in algebra, geometry, logic, statistics, probability, and elementary number theory. Students are encouraged to use problem-solving strategies, models, and technologies, and to create problems of their own. MATH 413 Algebra and Technology for Middle Grades Teachers 3 hours The use of graphing calculators and computer software to explore algebraic ideas including patterns, functions, equations, inequalities, linear programming, curve fitting, and practical applications of algebra and technology. MATH 415 Algebra and Number Theory 3 hours An integrated survey of modern algebra and number theory. Topics include number systems, divisibility, congruences, groups and their application to number theory. MATH 417 Algebraic Systems 3 hours Theory of groups. MATH 421 Problem Solving for Secondary Teachers 3 hours Utilizes various techniques and technology to solve mathematical problems. Integrates concepts from algebra, geometry, trigonometry, probability, statistics, number theory, discrete mathematics, linear algebra, and calculus. MATH 423 Geometry II 3 hours An axiomatic development of hyperbolic geometry based on the hyperbolic parallel postulate and the absolute geometry developed in MATH 323, including an emphasis on contrasts with Euclidean geometry. MATH 429 Probability and Statistics II 3 hours Multivariate probability distributions; sampling distributions, statistical inference; point and interval estimation, properties of estimators; hypothesis testing; regression and correlation; analysis of variance; non-parametric methods. MATH 431 Intermediate Analysis I 3 hours Topics chosen from cardinality, limits, continuity, elementary topological concepts, sequences and series, differentiation and integration, elementary functional analysis. MATH 432 Intermediate Analysis II 3 hours Continuation of MATH 431. MATH 435 Partial Differential Equations 3 hours Equations of first and second order; elliptic, hyperbolic and parabolic equations; Sturm-Liouville theory; applications to equations of mathematical physics using separation of variables and Fourier series. MATH 439 Topology 3 hours Topological spaces, mappings, separation axioms, compactness, connectedness, arcwise connectedness, metric spaces. MATH 450 Complex Variables 3 hours Complex number plane, analytic functions of a complex variable, integration, power series, calculus of residues, conformal representation, applications of analytic function theory. MATH 470 Introduction to Operations Research 3 hours Principles and techniques of operations research including linear programming, integer programming, quality theory, sensitivity analysis, and dynamic programming. MATH 475 Selected Topics in Mathematics 1-3 hours A consideration of special topics to acquaint the advanced undergraduate student with significant problems and developments of current interest in mathematics. Topics may vary each semester offered. MATH 498 senior seminar 1 hour Students will study articles in current mathematical journals or undertake independent investigations in mathematics. Written and oral presentations are required. STATISTICS STAT 301 Introductory Probability and Applied Statistics 3 hours A calculus-based introduction to applied statistics, with emphasis on analysis of real data. Curve fitting, probability models, estimation and testing for means and proportions, quality control; use of computers for data analysis and simulation. |
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