NIU Undergraduate Catalogue Excerpt

Disclaimer: Catalogues change annually; students need to be aware of which edition determines the requirements for them. What follows is from a recent edition; recent changes are not numerous but there have been some! In any case, it is one of the print editions of the undergraduate catalogue which will contain the definitive requirements for graduation for each student; this document is mainly advisory. For further assistance, contact an advisor within the department.

Department of Mathematical Sciences (MATH, STAT)

The Department of Mathematical Sciences offers the B.S. degree with a major in mathematical sciences with emphases in general mathematical sciences, applied mathematics, computational mathematics, probability and statistics, and mathematics education. Successful completion of the emphasis in mathematics education leads to certification to teach at the 6-12 grade levels.

The department also offers minors in mathematical sciences and in applied probability and statistics. These minors should be of interest to students majoring in the physical or social sciences or in business. In addition, the department offers an honors program in mathematical sciences and participates in the University Honors Program.

All students interested in the emphasis in probability and statistics or in actuarial sciences, a degree with honors in probability and statistics, or a minor in applied probability and statistics should contact the office of the Division of Statistics.

Several of the department's courses fulfill the university mathematics core competency requirement and others can be used by non-majors toward fulfilling the sciences and mathematics area requirement in the university's General Education Program. In addition, many of its courses are included as requirements for other programs.

Mathematical sciences majors are not permitted to count courses in computer science (CSCI) toward fulfilling general education area requirements.

For all majors in the department, the GPA in the major is calculated by using only those mathematical sciences courses numbered 229 or above which are available for credit toward the major.

Department Requirements

Students majoring or minoring in mathematical sciences must obtain a minimum GPA of 2.00 in those MATH/STAT courses applicable to that major or minor. Courses not applicable to the major or minor are identified in the course descriptions.

All majors are required to have a satisfactory portfolio of work done during their undergraduate studies on file in the Department of Mathematical Sciences. The contents of the portfolio are to be used to assess the department's program and are to be accumulated largely through course work assignments and examinations; students are expected to cooperate with instructors as these items are collected. In addition, each student must submit in his or her senior year a 250-300 word typed essay describing the student's experience in the major, including comments on the connections of mathematics with other disciplines. Details on the submission of materials and approval of the portfolio should be obtained from the student's adviser in the Department of Mathematical Sciences.

Mathematics Placement Examination Policy

Students planning to take MATH 110, MATH 155, MATH 206, MATH 210, MATH 211, or MATH 229 must take the Mathematics Placement Examination, so they may begin their mathematical studies at the appropriate level.

Proficiency Examination Policy

Ordinarily students will not be allowed to attempt a proficiency examination for a course if they have received credit for a higher numbered course (for exceptions, consult the department).

Major in Mathematical Sciences (B.S.)

Emphasis 1. General

Requirements in Department (40-41)

Two additional mathematical sciences courses numbered above MATH 333 (6-7)

Requirement outside Department (4)
Total Hours for Emphasis 1, General: 44-45
Recommendations

Emphasis 2. Applied Mathematics

Requirements in Department (40-41)

Two of the following (6)

MATH 420, Algebra I (3)

MATH 434, Numerical Linear Algebra (3)

MATH 435, Numerical Analysis (3)

MATH 438, Theory of Differential Equations (3)

MATH 440, Elements of Complex Analysis (3)

MATH 442, Elements of Partial Differential Equations (3)

MATH 444, Linear Programming and Network Flows (3)

STAT 470, Introduction to Probability Theory (3)

STAT 471, Probability Models and Applications (3)

One additional mathematical sciences course numbered above MATH 333 (3)

Requirement outside Department (4)

Total Hours for Emphasis 2, Applied Mathematics: 44-45
Special Requirement

Students in this emphasis are required to complete a minor selected with the approval of the department.

Emphasis 3. Computational Mathematics

Requirements in Department (40-42)

One of the following (3)

One additional course from CSCI 440 (4), CSCI 464 (4), and mathematical sciences (MATH/STAT) courses numbered above 333 (3-4)

Requirement outside Department (4)

CSCI 230, Computer Programming in FORTRAN (4)

Total Hours for Emphasis 3, Computational Mathematics: 44-46

Emphasis 4. Probability and Statistics

Requirements in Department (40-42)

Two of the following (6-7)

At least 3 additional credit hours from among the following courses (3-4)

Requirement outside Department (4)

CSCI 230, Computer Programming in FORTRAN (4)

Total Hours for Emphasis 4, Probability and Statistics: 44-45

Emphasis 5. Mathematics Education

Successful completion of the emphasis in mathematics education leads to certification to teach at the 6-12 grade levels. In addition to the course work and certification requirements in the Department of Mathematical Sciences, students must complete other course work and certification requirements outside the department. A minor which includes a teaching endorsement in a teaching area outside of mathematics is highly desirable to enhance placement opportunities. All students who wish to pursue the emphasis in mathematics education and to seek teacher certification should consult with an adviser in the Department of Mathematical Sciences before the end of the sophomore year. Transfer and postbaccalaureate students should see an adviser in the Department of Mathematical Sciences on arrival. Graduate students majoring in the mathematical sciences, graduate students majoring in secondary education, and students-at-large should consult the Graduate Catalog.

Requirements in Department (43)

One of the following (3)

One additional course from the following (3)

Special Departmental Requirements for Certification

1. Apply for admission to teacher certification in the Department of Mathematical Sciences. This is usually done three semesters prior to the semester of student teaching.

2. Pass the Basic Skills Test of the Illinois Certification Testing System in order to be formally admitted to the teacher certification program. This should be accomplished before taking MATH 412. An informational booklet about the test and registration materials for the test can be obtained from the Office of Testing Services.

3. Obtain departmental approval for admission to teacher certification. This is normally done through a conference with the coordinator of teacher certification in mathematics two semesters prior to the semester of student teaching.

4. Satisfy the minimum GPA requirements established by the department for the undergraduate emphasis in mathematics education: an overall GPA of 2.50, a GPA of 2.25 in all courses counted for credit toward the major, and a GPA of 2.25 in all courses counted for credit toward the major numbered above MATH 231.

Requirements outside Department (26-31)

Hours do not include general education requirements. The state of Illinois requires extensive work in general education for certification. In some cases these requirements exceed those required by the university for a baccalaureate degree. Therefore, students should consult with an adviser within the department as early as possible to ascertain all of the requirements.

The teacher certification requirements are the same for undergraduate mathematical sciences majors with an emphasis in mathematics education and for postbaccalaureate students seeking certification in mathematics without becoming a candidate for a degree. Admission to MATH 413, the student teaching course, is dependent upon the availability of resources.

For Illinois certification students must complete 100 clock hours of clinical experiences prior to student teaching. The requirement may be satisfied by completing the following sequence of courses.

Other Requirements

See "Teacher Certification Requirements."

Exit Examination

All students seeking certification must pass the Illinois certification examination. Information about this test may be obtained from the Office of Testing Services.

Degree with Honors

The Department of Mathematical Sciences offers the exceptional student an opportunity to earn a degree with honors in any of the five emphases. Any mathematical sciences student may become a candidate for an honors degree in mathematical sciences at the end of the sophomore year provided the student has a 3.00 or higher overall GPA and has a 3.50 or higher GPA in all mathematical sciences courses completed, including MATH 232 and MATH 240.

A student with these qualifications who wishes to become an honors degree candidate should go to the office of the Department of Mathematical Sciences (or, in the case of students in the emphasis in probability and statistics, to the office of the Division of Statistics) to fill out a candidacy form and be assigned an honors adviser. After the end of the sophomore year, a student showing exceptional talent may also become an honors degree candidate by obtaining consent.

Most 300-level and 400-level mathematical sciences courses may be taken as honors courses.

Requirements

Maintain a 3.00 or higher overall GPA.

Maintain a 3.50 or higher GPA for mathematical sciences courses numbered 300 and above.

Take at least four mathematical sciences honors courses numbered 300 or higher, which must include a two-course sequence of 400-level honors courses appropriate for the student's emphasis and approved by the honors degree adviser. The honors sequences from which a sequence appropriate for the student's emphasis may be chosen are MATH 420H-MATH 421H, MATH 420H-MATH 423H, MATH 430H-MATH 431H, MATH 434H-MATH 435H, STAT 470H-STAT 472H.

In one of the 400-level honors courses, prepare and submit an independent study paper on a suitable topic. The paper must be approved by the instructor of the course and by the honors degree adviser.

Minor in Mathematical Sciences

Option 1. General (22-23)

At least two mathematical sciences courses chosen from STAT 350 or from MATH courses numbered above MATH 333. At least one of these must be numbered above MATH 419 (6-7).

Six or more semester hours in the minor must be taken at NIU.

1Students should consult with an adviser in the Department of Mathematical Sciences before enrolling in courses to fulfill this requirement.
2Undergraduates must consult with the Coordinator of Teacher Certification in Mathematics about admission to ILAS 210 at the beginning of the second semester
of their sophomore year. Postbaccalaureate students should consult with the Coordinator of Teacher Certification in Mathematics upon arrival.
3Students must consult with the Coordinator of Teacher Certification in Mathematics about admission to ILAS 300, ILAS 301, and MATH 401.
4If MATH 401 is not completed at the student teaching school, MATH 411, Secondary School Mathematics Clinical Experience (0) may be required.
5Students are normally admitted to MATH 413 only after satisfactory completion of MATH 412 at NIU and all other course work required for certification.

Option 2. Mathematics Education (29-31)

Provided that MATH 416 is not chosen as an elective, this option meets the minimal mathematics requirement for an endorsement to teach mathematics in grades 9-12 in Illinois. Provided that neither MATH 360 nor MATH 416 is chosen as an elective, and provided that the student also completes MATH 410, this option meets the minimal mathematics requirement for an endorsement to teach mathematics in grades 6-8 in Illinois. Students should contact the department for information about alternative ways of obtaining an endorsement which do not necessarily involve a minor.

Select from the following (7-9)

Six or more semester hours in the minor must be taken at NIU.

Minor in Applied Probability and Statistics (21-22)

Three of the following (9-10)

Six or more semester hours in the minor must be taken at NIU.


*Available for general education credit.


Course List

Note: Course listings manually updated March 2002; in case of errors or ambiguities, please note that the print edition of the Undergraduate Catalogue is definitive.

Mathematics (MATH)

101. CORE COMPETENCY IN MATHEMATICS (3). Mastery of elementary skills and facts, understanding of logically correct arguments, abstract thinking, and problem solving ability. Not intended as preparation for MATH 110 or for courses numbered above MATH 110. Not available for credit to students who have previously received credit with a grade of a C or better in a MATH course numbered above 110 except MATH 201. Not open for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: Intermediate algebra and geometry.

108. FUNDAMENTALS OF MATHEMATICS I (3). Designed for and restricted to first-semester freshmen, specially admitted students. Does not count as credit for graduation.

109. FUNDAMENTALS OF MATHEMATICS II (3). Designed for and restricted to first-year, specially admitted students. May be used to continue MATH 108. Does not count as credit for graduation. Used as preparation for MATH 101, MATH 110, MATH 201, or MATH 210.

110. COLLEGE ALGEBRA (3). Algebraic and exponential functions, basic linear algebra. Requires skills and knowledge of intermediate algebra and plane geometry. Does not count for credit toward the major or minor in mathematical sciences. Not open for credit to students having credit in MATH 155 or MATH 211 or MATH 229. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: Satisfactory performance on the Mathematics Placement Examination.

155. TRIGONOMETRY AND ELEMENTARY FUNCTIONS (3). Polynomials and rational functions, review of exponential and logarithmic functions, trigonometry, and complex numbers. Does not count for credit toward the major or minor in mathematical sciences. Not open for credit to students who have obtained a grade of C or better in MATH 229. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: MATH 110 or satisfactory performance on the Mathematics Placement Examination.

201. FOUNDATIONS OF ELEMENTARY SCHOOL MATHEMATICS (3). Introduction to sets, geometry, measurement, logic, structure of mathematical systems, and the real number system. Open for credit only
toward the majors in early childhood studies, elementary education, and special education. Does not count for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: One year of high school algebra and one year of high school geometry.

206. INTRODUCTORY DISCRETE MATHEMATICS (3). An introduction to sets, algorithms, induction, recursion, relations, graphs, trees, and algebraic structure, with applications, many of which are in computer science. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: MATH 110 or satisfactory performance on the Mathematics Placement Examination.

210. FINITE MATHEMATICS (3). An introduction to mathematical topics with applications to business, social science, and other fields. Includes such topics as functions and graphs, matrix algebra and solutions of systems of linear equations, inequalities and linear programming, elementary combinatorics, and probability. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: One year of high school algebra, one year of high school geometry, and satisfactory performance on the Mathematics Placement Examination or MATH 110.

211. CALCULUS FOR BUSINESS AND SOCIAL SCIENCE (3). An elementary treatment of topics from differential and integral calculus, with applications in social science and business. Except with departmental approval students may not receive credit for both MATH 211 and MATH 229. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: MATH 110 with a grade of C or better, or satisfactory performance on the Mathematics Placement Examination.

229. CALCULUS I (4). A first course in calculus. Except with departmental approval, students may not receive credit for both MATH 211 and MATH 229. PRQ: MATH 155 or satisfactory performance on the Mathematics Placement Examination.

230. CALCULUS II (4). Continuation of MATH 229. Techniques of integration and applications of integrals, transcendental functions, and applications of series. PRQ: MATH 229 with a grade of C or better.

232. CALCULUS III (4). Continuation of MATH 230. Multivariable and vector calculus. PRQ: MATH 230 with a grade of C or better.

240. LINEAR ALGEBRA AND APPLICATIONS (4). Matrix algebra and solutions of systems of linear equations, matrix inversion, determinants. Vector spaces, linear dependence, basis and dimension, subspaces. Inner products, Gram-Schmidt process. Linear transformations, matrices of a linear transformation. Eigenvalues and eigenvectors. Some numerical methods for linear systems -- Gaussian elimination with partial pivoting, the iterative Jacobi and Gauss-Seidel methods. Applications. PRQ: MATH 232.

280. INTRODUCTION TO MATHEMATICAL REASONING (3). An introduction to the idea of mathematical proof. Emphasis on improving students' ability to construct, explain, and justify mathematical arguments. Assists in the transition from the calculus sequence to more abstract, proof-oriented courses. PRQ: MATH 230.

297. DIRECTED STUDY (1-3). Selected readings to supplement lower-division mathematical sciences courses. May be repeated to a maximum of 6 semester hours. PRQ: Consent of department.

302. INTRODUCTION TO GEOMETRY (3). Basic concepts in plane and solid geometry, measurement, congruence and similarity, constructions, coordinate geometry, transformations and tessellations, topology, and selected topics. Not used in major or minor GPA calculations for mathematical sciences majors or minors. PRQ: MATH 229 or consent of department.

303. INTRODUCTION TO NUMBER THEORY (3). Problem solving, methods of proof, divisibility, primes, congruences, Diophantine equations, integer sequences, number-theoretic functions, and selected topics. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: MATH 229 or consent of department.

304. HISTORY OF MATHEMATICS THROUGH THE 17TH CENTURY (3). Mathematical developments from the ancients through the 17th century. Emphasis on the development of an interrelationship among special topics from arithmetic, algebra, geometry and calculus, across different cultures and through time. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: MATH 229 or consent of department.

334. FOUNDATIONS OF APPLIED MATHEMATICS (4). Solution techniques for ordinary differential equations. Topics include hyperbolic functions, Laplace transforms, Fourier series, partial differential equations, and special functions. Not open for credit to students who have received credit for MATH 336. PRQ: MATH 232.

336. ORDINARY DIFFERENTIAL EQUATIONS (3). Rudiments of the theory of ordinary differential equations and techniques of solution. Applications. Not available for credit to students who have received credit for MATH 334. PRQ: MATH 230.

339. ENGINEERING MATHEMATICS I (3). Constrained extrema, Lagrange multipliers. Calculus of variations. Fourier series. Introduction to partial differential equations and integral transforms. Multiple integrals. Line and surface integrals. Vector analysis. Functions of a complex variable. Applications. PRQ: ELE 210, MEE 211, MATH 232, and MATH 336.

353. GEOMETRY (3). The study and development of geometric axiomatic systems. Topics selected from Hilbert's axioms for Euclidean geometry; projective, affine and Euclidean spaces over real vector spaces; convexity. Primarily intended for students preparing to teach mathematics. PRQ: MATH 240 or consent of department.

360. MODEL BUILDING IN APPLIED MATHEMATICS (3). An introduction to the formulation, analysis and interpretation of mathematical models in the study of selected problems in the natural sciences, the social sciences, and management science. Not open for credit to students having credit in MATH or STAT courses numbered 420 or above, except by consent of department. PRQ: MATH 230.

380. ELEMENTARY COMBINATORICS (3). Permutations, combinations, generating functions, Dirichlet principle, Ramsey's theorem, principle of inclusion-exclusion. Graphs, trees, circuits, Latin squares. PRQ: MATH 230.

401. CLINICAL SECONDARY SCHOOL EXPERIENCE IN MATHEMATICS (1-2). A discipline-based clinical experience for students seeking initial secondary certification in mathematics. Includes observations, evaluation, methods, and problems practicum as a part of a minimum of 40 clock hours of supervised and formally evaluated experiences in the particular setting likely for the student teaching experience. S/U grading. PRQ: Consent of department.

402. METHODS OF INSTRUCTION IN THE MATHEMATICS CURRICULUM FOR GRADES K-9 (3). Crosslisted as CIEE 402X. Methods, techniques, materials, curricular issues, learning theories, and research utilized in the teaching of elementary school mathematics. Attention given to the teaching of exceptional students and to planning for multicultural learning situations. Intended for students in education. Accepted for credit as an elementary mathematics methods course, but not as an upper-division mathematical content course. Not open for credit toward the major or minor in mathematical sciences. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: MATH 201 with a grade of C or better and junior standing or consent of department.

410. METHODS OF INSTRUCTION IN THE MATHEMATICS CURRICULUM FOR THE MIDDLE SCHOOL (3). Objectives, problems, strategies, and trends in teaching middle school and junior high school mathematics. Applications of learning theory and research focusing on remediation, presentation of new concepts, the needs of exceptional students, planning for multicultural settings, and the use of manipulatives. Accepted for credit as a middle school mathematics methods course, but not as an upper-division mathematical content course. Accepted as mathematical sciences credit only for those preparing to teach. Not used in major or minor GPA calculations for mathematical sciences majors or minors. PRQ: For those seeking or holding elementary education certification, MATH 229 and MATH 402; for those seeking or holding secondary education certification, MATH 229.

411. SECONDARY SCHOOL MATHEMATICS CLINICAL EXPERIENCE (0). Fifteen clock hours of pre-student teaching clinical experience. PRQ: Consent of department.

412. METHODS OF INSTRUCTION IN THE MATHEMATICS CURRICULUM FOR GRADES 6-12 (3). Objectives and organization of the curriculum and instructional materials for mathematics programs for grades 6-12 with attention to methods of instruction, the needs of exceptional students, reading techniques in mathematics, and planning for multicultural learning situations. Accepted for credit toward the major or minor only for those preparing to teach. Accepted for credit as a methods course for grades 6-12, but not as an upper-division mathematical content course. Not used in major or minor GPA calculation except for mathematics education majors and minors. CRQ: MATH 353 and consent of department.

413. STUDENT TEACHING (SECONDARY) IN MATHEMATICS (7-12). Student teaching for 10 weeks or for one semester. Assignments to be arranged with the Office of Teacher Certification in the College of Liberal Arts and Sciences after approval by the Department of Mathematical Sciences. Not available for credit in the major. See "Teacher Certification Requirements." PRQ: MATH 412 and consent of department.

416. TOPICS IN MATHEMATICS FOR TEACHERS (3). Selected topics in mathematical sciences. This course is intended primarily for students preparing to teach mathematics in the secondary school. Not used in major or minor GPA calculation except for Emphasis 5 majors and Option 3 minors. PRQ: MATH 240 and consent of department.

420. ALGEBRA I (3). Introduction to group theory. Properties of the integers, functions, and equivalence relations. A concrete approach to cyclic groups and permutations groups; isomorphisms and the theorems of Lagrange and Cayley. PRQ: MATH 240.

421. ALGEBRA II (3). A continuation of MATH 420. Homomorphisms and factor groups; introduction to commutative rings, with emphasis on polynomial rings; and fields, and algebraic extensions. Applications to classical geometric problems. PRQ: MATH 420.

423. LINEAR AND MULTILINEAR ALGEBRA (3). The general theory of vector spaces, linear transformations, and matrices. Topics selected from determinants, tensor products, canonical forms, and bilinear and quadratic forms. PRQ: MATH 240 and MATH 420, or consent of department.

430. ADVANCED CALCULUS I (3). A re-examination of the calculus of functions of one variable: convergence, continuity, differentiation, the mean-value theorem, and the Riemann integral. PRQ: MATH 232 and MATH 240, or MATH 334.

431. ADVANCED CALCULUS II (3). Further study of sequences and series of functions; functions of several variables. PRQ: MATH 430.

432. ADVANCED CALCULUS III (3). Line and surface integrals, the Riemann-Stieltjes integral, gamma and beta functions, and Fourier series and integrals. Applications to probability theory and mathematical physics. PRQ: MATH 431 or both MATH 334 and PHYS 385.

434. NUMERICAL LINEAR ALGEBRA (3). Crosslisted as CSCI 434X. Roundoff errors and computer arithmetic. Direct and iterative methods for solving linear systems; norms and condition numbers, iterative refinement. Linear least squares problems: the normal equations and QR approach for overdetermined systems. Numerical methods for eigenvalues: an introduction to the QR iteration. The course makes extensive use of computers. PRQ: MATH 232, MATH 240, and either CSCI 230 or approved equivalent.

435. NUMERICAL ANALYSIS (3). Crosslisted as CSCI 435X. Polynomial interpolation, numerical solutions of nonlinear equations, least squares approximation by polynomials, orthogonal polynomials, economization of power series. Numerical integration including quadrature formulae, adaptive quadrature, composite quadrature formulae, and Romberg integration. Numerical methods for initial value problems including Taylor series methods, Runge-Kutta methods, and multistep methods. The course makes extensive use of computers. PRQ: MATH 232, MATH 240, and either CSCI 230 or approved equivalent.

438. THEORY OF DIFFERENTIAL EQUATIONS (3). Topics include linear systems, existence and uniqueness of solutions, nonlinear equations, and stability. PRQ: MATH 232, MATH 240, and either MATH 334 or MATH 336, or consent of department.

439. ENGINEERING MATHEMATICS II (3). Green's functions and integral transform solutions of partial differential equations. Coordinate transformations and tensor analysis. Gamma, beta and error functions. Elliptic functions. Asymptotic series. Series solutions of ordinary and partial differential equations. Orthogonal expansions. Probability. Numerical methods. PRQ: MATH 339 with a grade of C or better.

440. ELEMENTS OF COMPLEX ANALYSIS (3). A beginning course in complex analysis emphasizing the applications of complex function theory. PRQ: MATH 232 and MATH 240, or MATH 334, or equivalent.

442. ELEMENTS OF PARTIAL DIFFERENTIAL EQUATIONS (3). An introduction to partial differential equations emphasizing constructive methods of solution for the wave equation, heat equation, and the Laplace and Poisson equations. Separation of variables, Fourier series, Fourier integral, method of characteristics, maximum principles, Green's functions, eigenfunction expansions, and the Laplace and Fourier transforms. PRQ: Either MATH 334, or MATH 232 and MATH 336.

444. LINEAR PROGRAMMING AND NETWORK FLOWS (3). An introduction to linear programming, network flows, and applications. PRQ: MATH 240 or consent of department.

450. INTRODUCTION TO TOPOLOGY (3). The basic notions of metric and topological spaces; additional topics from combinatorial and algebraic topology may be included. PRQ: MATH 430.

456. LINEAR GEOMETRY (3). A treatment of affine and related geometries using the techniques of linear algebra. PRQ: MATH 420.

460. MODELING DYNAMICAL SYSTEMS (3). This course involves students in the process of translating some questions about the observed world into mathematical form, combining formal reasoning with intuitive insights. Phenomena susceptible to formulation in terms of difference equations and various kinds of differential equations are investigated. The concepts of equilibrium, stability, bifurcation, limit cycles, and chaos are illustrated. PRQ: MATH 232, and MATH 240, and MATH 336. PHYS 250A, and PHYS 251A, or consent of department.

480. NUMBER THEORY (3). Divisibility, primes, congruences, quadratic reciprocity, Diophantine equations, continued fractions, and selected topics. PRQ: MATH 420 or consent of department.

490X. TOPICS IN COMPUTER SCIENCE (3). Crosslisted as CSCI 490.

A. Algorithms
C. Automata, Computability, and Formal Languages

Selected topics from major areas in computer science. May be repeated when subject varies. PRQ: Senior standing and consent of department.

492. SCHOOL MATHEMATICS (1-6).

A. Elementary School
B. Junior High-Middle School
C. Secondary School

Intensive study of selected mathematical topics in curriculum and instruction as they relate to the teaching of mathematics. Not open for credit toward the major or minor in mathematical sciences. Course may be repeated to a maximum of 12 semester hours as topic changes. PRQ: Consent of department.

496. SEMINAR IN COMPUTATIONAL MATHEMATICS (3). Builds on the required courses in the computational mathematics emphasis to give the student in-depth experience doing projects. PRQ: Consent of department.

497. UNDERGRADUATE READINGS IN MATHEMATICS (1-3). Selected readings from mathematical literature. May be repeated to a maximum of 6 semester hours. PRQ: Consent of department.

Statistics (STAT)

208. BASIC STATISTICS (3). A general course designed to provide students with an understanding of reasoning involved in the statistician's approach to a variety of problems. Not open for credit toward the major or minor in mathematical sciences. Not open for credit to students who have credit in an upper-division statistics course or in OMIS 324 or UBUS 223. Not used in major or minor GPA calculation for mathematical sciences majors or minors. PRQ: 1-1/2 years of high school algebra and one year of high school geometry, or equivalent.

301. ELEMENTARY STATISTICS (4). An introduction to basic concepts in statistical methods including probability, theoretical and empirical distributions, estimation, tests of hypotheses, linear regression and correlation, and single classification analysis of variance procedures. Not available for credit toward the major in mathematical sciences. Not used in major GPA calculation for mathematical sciences majors. PRQ: MATH 206 or MATH 210 or MATH 211 or MATH 229.

350. INTRODUCTION TO PROBABILITY AND STATISTICS (3). An introduction to the basic ideas and fundamental laws of probability including sample spaces, events, independence, random variables, special probability distributions and elementary statistical inference. PRQ: MATH 230.

470. INTRODUCTION TO PROBABILITY THEORY (3). The mathematical study of probability including probability spaces, random variables, discrete, continuous, mixed probability distributions, moment generating functions, multivariate distributions, conditional probability, conditional expectation, special distributions, laws of large numbers, and central limit theorem. PRQ: MATH 232 and MATH 240, or consent of division.

471. PROBABILITY MODELS AND APPLICATIONS (3). An introduction to elementary stochastic processes and their applications to various phenomena in engineering, management science, the physical and social sciences, and operations research. PRQ: STAT 470.

472. INTRODUCTION TO MATHEMATICAL STATISTICS (3). An introductory study of mathematical statistics including distributions of functions of random variables, interval estimation, sufficiency, completeness, point estimation, statistical hypotheses, analysis of variance, and the multivariate normal distribution. PRQ: STAT 470.

473. STATISTICAL METHODS AND MODELS I (3). A first course in statistical methods and models including exploratory data analysis and graphical techniques, regression analysis, experimental design and basic sampling techniques. Extensive use of statistical computer packages. PRQ: MATH 211 and STAT 301, or STAT 350, or consent of division. CRQ: STAT 473A.

473A. STATISTICAL COMPUTING PACKAGES (1). Introduction to statistical computing with the aid of software packages. Data entry, transformations, simple plots, summary statistics, and statistical procedures. No previous computer experience is required. PRQ: MATH 211 and STAT 301, or STAT 350, or consent of division. CRQ: STAT 473 or consent of division.

474. STATISTICAL METHODS AND MODELS II (3). Continuation of STAT 473. Topics include cluster sampling, two-level factorial experiments, confounding and fractional replications, analysis of discrete data, an introduction to time series analysis, control charts for quality, and productivity analysis. PRQ: STAT 473 or consent of division.

478. STATISTICAL METHODS OF FORECASTING (3). Introduction to forecasting including use of regression in forecasting; removal and estimation of trend and seasonality; exponential smoothing; stochastic time series models; stochastic difference equations; autoregressive, moving average, and mixed models; model identification and estimation; diagnostic checking; and the use of time series models in forecasting. PRQ: STAT 473 or consent of division.

493. SPECIAL TOPICS IN STATISTICS (1-3). Discussion and study of readings on topics of special interest to undergraduate statistics/probability students. May be repeated to a maximum of 6 semester hours. PRQ: Consent of division.

Mathematical Sciences Faculty