### Faculty

Link to Department Personnel

Link to Profiles of Full-time Faculty

**Professors:** John P. Holcomb (Chairperson), Ching Lung Chang, Pratibha Ghatage, Gregory M. Lupton, Rasul A. Khan, Barbara Haas Margolius, John F. Oprea, Brian M. Scott, Sally SaiLai Shao, Chung-yi Suen, John J. Walsh; **Professors Emeriti:** Shih-Hung Chang, Thomas W. Hungerford, Keith M. Kendig, Sundaresan Kondagunta, Roger H. Marty, Allan J. Silberger, Sherwood D. Silliman, Chester W. Topp; **Associate Professors**: Peter Bubenik, Leah Gold, Luiz Felipe Martins, Carol Phillips-Bey, Ieda W. Rodrigues, Ivan Soprunov;** Associate Professors Emeriti:** Richard H. Black, Leonard F. Bruening, Paula C. Gnepp, David Herlacher, Arthur Lieberman, Shirley A. Lilge, Frank W. Lozier, Stewart M. Robinson; **Assistant Professors:** Ariadni Papana Dagiasis, Jonathan Scott, Partha Srinivasan, Yuping Wu; **Term Assistant Professor: **Linda Quinn; **Term Instructors:** Patricia Kan, Gregory LaPlaca, Antoinette Marquard.

### Course Descriptions

Students with credit in MTH 182, or in any mathematics course numbered above 220, may not register for a mathematics course numbered 168 or lower. A student who attempts to do so will be given a grade of W in the ineligible course. This rule takes precedence over the university regulations on repeated courses whenever both are applicable.

Placement Tests: All students must take the Mathematics Placement Examination before they will be permitted to register for mathematics courses numbered 115, 116, 117, 127, 147, 148, 167, 168, and 181, except for students who have passed the appropriate prerequisite course. Mandatory placement for these courses is in effect. Students are not permitted to register for a higher-level course than indicated by their placement exam score.

- Preparatory Courses
- Courses for Humanities, Business, Education, and Social Sciences
- Courses for Mathematics, Science, Engineering, Computer Science and Education Majors, and Statistics Minor

#### Preparatory Courses

A student who has been unconditionally admitted to the university should have already mastered the material in these courses. Credit earned in MTH 087 or MTH 088 does not count toward graduation.

** MTH 087 Basic Algebra (4-0-4).** MTH 087 begins with a pre-algebra review. It then proceeds to basic algebra topics such as linear equations and inequalities, rectangular coordinate system, graphs of linear equations, linear systems, polynomials, exponents, factoring, and quadratic equations with emphasis on graphing and applications through problem-solving. MTH 087 concludes with an introduction to statistics and probability. Pass/fail system of grading, but students receive modified letter grades: S(A), S(B), S(C), U(D), U(F). The letter grades in parentheses are not computed in the students' GPAs. No credit toward graduation. Return to top

** MTH 115 Applied Algebra (4-0-4).** Prerequisite: MTH 087 or MTH 088 or suitable placement-test score. Extension of basic algebra techniques, linear equations, and linear inequalities, an introduction to functions, roots, radicals, exponents, quadratic equations, solution of second degree equations and applications, and the analysis and solution of word problems. Return to top

#### Courses for Humanities, Business, Education, and Social Sciences

Any course in this section, except MTH 127, is suitable for meeting the requirement of the** GenEd**. Credit earned in these courses does not count toward the mathematics major.

** MTH 116 Foundations of Quantitative Literacy (4-0-4).** Prerequisite: a grade of SC or better in MTH 087 or suitable placement-exam score. Not open to students who have previously earned credit for MTH 119. This course is designed to develop quantitative reasoning skills as applied to personal and social issues. Students will learn mathematics and basic statistics needed for success in other college courses, advancement of one's career, and understanding of major issues in life. This course is for students not planning to major in a field requiring advanced mathematical skills. Return to top

** MTH 117 Mathematical Applications in the Real World (4-0-4).** Prerequisite: MTH 116 or MTH 119. Not open to students who have previously earned credit for MTH 118. This course continues the development of quantitative reasoning skills as started in MTH 116. Topics in this course include the mathematics in population growth models, architecture, art, music, and voting systems. This course is for students not planning to major in a field requiring advanced mathematical skills. Return to top

** MTH 127 Mathematics for Elementary School Teachers I (4-0-4).** Prerequisite: A grade of SC or better in MTH 087 or suitable placement-test score. Topics needed to teach elementary and middle school mathematics, including numeration systems and whole number arithmetic, integers and number theory, rational and real numbers, problem solving, and applications. Return to top

** MTH 128 Mathematics for Elementary School Teachers II (4-0-4). **Prerequisite: MTH 127. Inlcudes additional topics for the elementary curriculum, such as geometry, measurement, and applications. The course will incorporate the use of appropriate computer software for the elementary school classroom, such as LOGO and Cabri. Return to top

** MTH 129 Mathematics for Elementary School Teachers III (2-0-2).** Prerequisite: MTH 127. Includes additional topics for the elementary curriculum, such as probability and statistics. The course will incorporate the use of appropriate technology for the elementary school classroom such as the TI-73 calculator with the CBR and computer software Fathom and Excel. Return to top

** MTH 147 Statistical Concepts with Applications (4-0-4).** Prerequisite: A grade of SC or better in MTH 087 or suitable placement-test score. A first course in statistics that emphasizes statistical methodology as applied in the social and behavioral sciences, education, and business; topics include descriptive statistics, elementary probability, elementary sampling theory, estimation, hypothesis testing, regression and correlation. Return to top

** MTH 148 Mathematics for Business Majors I (4 – 0 – 4)***. [ Note: Course effective Fall 2010.]*

*Prerequisite:*a grade of SC or better in MTH 087 or suitable placement-exam score

*.*The topics for this course include equations of lines, graphs of functions, word problems, polynomial models, and mathematical applications. The course shows students how to use exponential and logarithmic functions to study mathematical finance applications such as simple interest, discount, compound interest, present and future values, annuities and amortization. The course also covers systems of linear equations, matrices, and linear programming using optimization such as the Simplex method. Return to top

**MTH 149 Mathematics for Business Majors II (4 – 0 – 4)**. *[ Note: Course effective Fall 2010 .]*

*Prerequisite:*a grade of C or better in MTH148

*.*The topics for this course include probability as it relates to computing empirical probability, conditional probability, and understanding independent events. Other topics include counting topics related to the multiplicative principle, permutations, and combinations. The course also includes material on the techniques of single and multivariate calculus that include methods and applications regarding rates of change, derivatives, anti-derivatives, integration, differential equations, partial derivatives and extrema of functions of several variables. Return to top

*[Note: The following sequence of courses, MTH151-156, is being phased out, to be replaced by a two-semester sequence MTH148-149 offered for the first time Fall 2010. MTH 151-156 will not be offered past Spring 2011.]*

**MTH 151 through MTH 156 Mathematical Concepts**. Each of these is a 1- or 2-credit course. Normally a student must register for MTH 151, 152, and 153, or for MTH 154, 155, and 156. One is taught at the beginning of the semester, one in the middle of the semester, and one at the end of the semester.

A graphing calculator is required for MTH 151 to 156. Consult the Mathematics Department for recommended models.

** MTH 151 Mathematical Concepts 1a (1-0-1)***. [Note: offered for the last time Summer 2010.]* Prerequisite: A grade of SC or better in MTH 087 or suitable placement-test score. Equations of lines, word problems, linear, polynomial and rational inequalities, graphs of functions, linear and quadratic functions, and their applications. Return to top

** MTH 152 Mathematical Concepts 1b (2-0-2)***. [Note: offered for the last time Fall 2010.]*Prerequisite: MTH 151. Systems of three or more linear equations, Gauss-Jordan elimination, matrix methods, linear programming. Return to top

** MTH 153 Mathematical Concepts 1c (1-0-1).*** [Note: offered for the last time Fall 2010.]* Prerequisite: MTH 152. Polynomial, exponential, and logarithmic functions and graphs, math of finance. Return to top

** MTH 154 Mathematical Concepts 2a (1-0-1).*** [Note: offered for the last time Summer 2010.]* Prerequisite: MTH 153. Intuitive differential calculus, derivatives, applications of derivatives. Return to top

** MTH 155 Mathematical Concepts 2b (2-0-2).*** [Note: offered for the last time Fall 2010.]*Prerequisite: MTH 154. Intuitive integral calculus, antiderivatives, the definite integral, applications, partial derivatives. Return to top

** MTH 156 Mathematical Concepts 2c (1-0-1).*** [Note: offered for the last time Fall 2010.]* Prerequisite: MTH 155. Probability, permutations, combinations, Bayes' Theorem. Return to top

#### Courses for Mathematics, Science, Engineering, Computer Science and Education Majors

##### Precalculus and First-Year Calculus Courses

The precalculus courses (MTH 167 and MTH 168) are designed for students who intend to take calculus (MTH 181) eventually and are not intended as general education courses. Depending on the placement-test score, a student starts with MTH 167 or with MTH 168. Credit earned in precalculus courses does not count toward the mathematics major.

A graphing calculator is required for MTH 167, 168, 181, and 182. Consult the Mathematics Department for recommended models.

** MTH 167 Precalculus Mathematics I (4-0-4).** Prerequisite: A grade of SC or better in MTH 115 or suitable placement-test score. Brief review of intermediate algebra techniques, rectangular coordinates, graphs of equations; also functions, lines, circles, detailed study of functions, and graphing techniques. *This course makes extensive use of the software ALEKS for computer assisted instruction, assessment, and testing. Some class meetings will be held in a computer laboratory setting and students are expected to use the software on a self-paced, out-of-class basis to supplement regular in-class meetings.* Return to top

** MTH 168 Precalculus Mathematics II (4-0-4).** Prerequisite: A grade of C or better in MTH 167or suitable placement-test score. Topics include functions, polynomial and rational functions, exponential, logarithmic, trigonometric, and inverse trigonometric functions. *This course makes extensive use of the software ALEKS for computer assisted instruction, assessment, and testing. Some class meetings will be held in a computer laboratory setting and students are expected to use the software on a self-paced, out-of-class basis to supplement regular in-class meetings.* Return to top

** MTH 181 Calculus I (4-0-4).** Prerequisite: A grade of C or better in MTH 168 or suitable placement-test score. Topics covered include limits, derivatives, continuity, applications of derivatives, antiderivatives and the definite integral. Graphing calculator required and used extensively.Return to top

**MTH 181H Honors Calculus I (4-0-4). ** Prerequisites: A grade of C or better in MTH 168 or suitable placement-test score, Honors standing or permission of university Honors Program. Topics to be covered include limits, derivatives, continuity, applications of the derivative, anti-derivatives and the definite integral. It covers the same basic topics as MTH 181, but with greater emphasis on rigorous treatment of the underlying mathematical ideas and real world applications. Course includes an introduction to the use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 182 Calculus II (4-0-4).** Prerequisite: A grade of C or better in MTH 181. Topics to be covered include applications of integration, techniques of integration, improper integrals, infinite series, power series, polar coordinates, conic sections, and vectors. Graphing calculator required and used extensively. Return to top

**MTH 182H Honors Calculus II (4-0-4).** Prerequisites: A grade of C or better in MTH 181H or suitable placement-test score, Honors standing or permission of university Honors Program. Topics to be covered include applications of integration, techniques of integration, improper integrals, infinite series, power series, polar coordinates, conic sections, and vectors. This course covers the same basic topics as MTH 182, but with greater emphasis on rigorous treatment of the underlying mathematical ideas and real world applications. Course includes an introduction to the use of a computer algebra system, such as Maple or MATLAB. Return to top

### Intermediate Courses

** MTH 201 Fucntions and Modeling (3-0-3). **Prerequisite: EUT 205. Enrollment is restricted to students seeking teaching licensure in the CSUTeach program. This course is designed to engage prospective secondary mathematics teachers in explorations and laboratory activities that will expand and strengthen knowledge and understanding of topics in the secondary mathematics curriculum. Connections between secondary and college mathematics will be illuminated; extensive use of technology will be integrated into solving non-routine problems and applying mathematics in real-world situations, which will be the primary focus. Explorations will involve the use of multiple representations, transformations, data analysis techniques (such as curve fitting) and interconnections among topics in algebra, analytic geometry, statistics, trigonometry, and calculus. No credit toward the mathematics major or minor. Return to top

** MTH 220 Introduction to Discrete Mathematics (4-0-4).** Prerequisites: A grade of C or better in one of MTH 149, 156 or 182. Topics include sets, relations, and functions; the concept of algorithm and mathematical induction and recursive definition. Applications of these fundamentals are chosen at the instructor's discretion from graph theory, Boolean algebra, lattice theory, finite-state automata, elementary grammars, and the theory of recurrence relations. Course includes an introduction to the use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 281 Multivariable Calculus (4-0-4).** Prerequisite: A grade of C or better in MTH 182. Topics include multivariate and vector calculus, three-dimensional analytic geometry, partial derivatives, multiple integrals, vector calculus, line integrals, Green's Theorem. Only 2 of the 4 credits may be counted toward graduation by students who have passed MTH 283. Course includes an introduction to the use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 283 Multivariable Calculus for Engineers (2-0-2).** Prerequisite: A grade of C or better in MTH 182. Multivariate calculus topics include three-dimensional analytic geometry, partial derivatives, and multiple integrals. Students who have passed MTH 281 may not register for MTH 283. A student who attempts to do so will be given a grade of W. Return to top

** MTH 284 Matrices for Engineers (2-0-2).** Prerequisite: A grade of C or better in MTH 182. Matrix algebra, topics include matrices and systems of linear equations, determinants, inverses, eigenvalues and eigenvectors. Students who have passed MTH 288 may not register for MTH 284. A student who attempts to do so will be given a grade of W. Return to top

** MTH 286 Introduction to Differential Equations (4-0-4).** Prerequisite: A grade of C or better in MTH 182. Topics include first-order differential equations, linear differential equations first order systems, Laplace transform techniques, and applications. Course also includes an introduction to the use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 288 Linear Algebra (4-0-4).** Prerequisite: A grade of C or better in MTH 182. Topics include systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors. Only two of the four credits may be counted toward graduation by students who have passed MTH 284. Course also includes an introduction to the use of a computer algebra system, such as Maple or MATLAB. Return to top

### Advanced Courses

** MTH 301 Introduction to Number Theory (4-0-4).** Prerequisite: A grade of C or better in at least one of the courses MTH 220, MTH 281, MTH 282, MTH 284, MTH 286, or MTH 288, or instructor permission. This course is an introduction to number theory and its applications. Topics covered include divisibility, greatest common divisor and Euclid’s algorithm, congruences the algebra of congruence classes, the theorems of Fermat and Euler, the Chinese Remainder Theorem, quadratic residues and primitive roots. Applications include cryptography, computer security, and coding theory. Return to top

** MTH 311 Numerical Analysis (4-0-4).** Prerequisites: MTH 284 or MTH 288, MTH 286, and a computer programming language. Course covers numerical methods for solving nonlinear equations, systems of linear equations, interpolation problems, integration problems, and differential equations. Return to top

** MTH 323 Statistical Methods (4-0-4).** Prerequisites: MTH 182 and a 200-level mathematics course. Course covers issues of data collection, graphical and numerical summary techniques, basic probability, discrete random variables, continuous random variables, central limit theorem, confidence intervals, hypothesis testing of a proportion, hypothesis testing of a mean, 2 sample hypothesis testing, chi square testing, regression. Appropriate statistical software used extensively. MTH 323 counts toward the statistics minor; one course from MTH 323 or MTH 347 counts toward the mathematics minor, but not both. Return to top

** MTH 326 Numbers, Patterns and Operations for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. This course is an in-depth study of mathematical topics in middle school curricula in the area of numbers, patterns and operations. Topics include numeration concepts, concepts of measurement, study of rational and irrational numbers, proportionality, estimation and operations. No credit toward the mathematics major or minor. Return to top

** MTH 327 Algebra and Functions for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. This course emphasizes on algebra as a powerful symbolic language for studying patterns, relations, and variation; for solving linear and quadratic equations and inequalities; and for modeling real life situations. Emphasis is placed on variables and functions in symbolic and graphical forms, especially linear, quadratic, exponential, logarithmic, and inverse functions. Goals include developing deep understandings of these topics as appropriate for middle school teachers. No credit toward the mathematics major or minor. Return to top

** MTH 328 Measurement and Geometry of Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. This course is designed to increase the conceptual understanding of geometry for middle school teachers. Topics include dynamic geometry integrating use of computer software; basic geometry theorems and constructions; similarity, proportion, scaling, and geometric growth; tessellations; simple trigonometric relationships; van Hiele levels of geometric graphical representations; transformational geometry and analytic geometry. No credit toward the mathematics major or minor. Return to top

** MTH 329 Data Analysis and Probability for Middle School Teachers (4-0-4).** Prerequisite: Enrollment is restricted to students seeking middle childhood licensure with mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. An introduction to the concepts of calculus. Pictures and hands-on experiments are used to develop an overview of the big ideas and an appreciation of how calculus helps us understand the real world. Includes differentiation, integration, and applications of calculus to the real world. No credit toward the mathematics major or minor. Return to top

** MTH 330 Conversational Calculus for Middle School Teachers (4-0-4).** Prerequisite: MTH 327. Enrollment is restricted to students seeking middle-childhood licensurewith mathematics as one of their two areas of concentration or by permission of Mathematics Department chairperson. This course is an introduction to the concepts of calculus. Pictures and hands-on experiments are used to develop an overview of the big ideas and an appreciation of how calculus helps us understand the real world. It includes differentiation, integration and applications of calculus to the real world. No credit toward the mathematics major or minor. Return to top

** MTH 333 Geometry (4-0-4).** Prerequisite: MTH 284 or MTH 288. The main focus is on two-dimensional Euclidean geometry. Basic topics covered include congruence, parallelism, area, and similarity. These are discussed from the axiomatic point of view. Other topics include transformation geometry, non-Euclidean geometry, vectors in geometry and some three-dimensional Euclidean geometry. Many applications are given, such as analysis of repeating patterns, computer graphics, cartography, and robot arm motion. Dynamic geometry software, and physical models and manipulatives will be used. Return to top

** MTH 347 Applied Statistics (4-0-4).** Prerequisite: A grade of "C" or better in MTH 147, MTH 323, PSY 311, COM 303, ECN 322, ESC 310, OSM 201, PSC 351, SOC 353, SWK 305, or UST 404. Topics include simple linear regression, analysis of variance, nonparametric statistics, multiple and logistic regression, statistical process control, and basic time series analysis. This course emphasizes the applied nature of statistical analysis and require using a statistical analysis software package. It counts toward the statistics minor; no credit toward the mathematics major. One course from MTH 323 or MTH 347 counts toward the mathematics minor, but not both. Return to top

** MTH 358 Abstract Algebra (4-0-4).** Prerequisite: MTH 288 .This course is an introduction to modern abstract algebra, concentrating on the integers and number theory, rings, fields, polynomials, and applications of these concepts. It includes use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 386 Differential Equations (4-0-4).** Prerequisites: MTH 281 and MTH 288 or MTH 283 and MTH 284, and MTH 286. This course covers series solutions of second-order linear equations, qualitative behavior of linear and almost linear systems of first-order differential equations, boundary value problems, introduction to partial differential equations. Course includes use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 390 Foundations of Computing (3-0-3).** Prerequisites: MTH 181, 182, MTH 220, and CIS 335; Mathematics majors may substitute one mathematics course numbered 280 or above for CIS 335. Topics include sets, relations, regular languages, finite automata, context-free languages, pushdown automata, phrase-structure languages, Turing machines, Church's theory, recursion, computability, decidability, and computational complexity. It is cross-listed with CIS 490. Return to top

** MTH 396 Junior Seminar (2-0-2).** Prerequisites: MTH 182; three of MTH 220, MTH 281, MTH 286 and MTH 288, all grade "C" or better; or departmental approval. Weekly meetings introduce students to a wide range of mathematical topics and also include workshops on various aspects of writing cogent and well-formulated technical reports in mathematics. A focus throughout the semester will be on appreciating the historical development of mathematical topics encountered throughout the undergraduate curriculum. A primary goal of this course is to prepare the student for MTH 496 Senior Project. Successful completion of the course requires the student having an approved topic and supervisor for MTH 496. Return to top

** MTH 401 Mathematical Modeling (4-0-4).** Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above (MTH 301 recommended). Topics include deterministic and probabilistic models chosen from the areas of linear optimization, Markov chains, game theory, graphs and networks, axiom systems, growth processes, and queuing systems. This course includes the use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 415 Real Analysis (4-0-4).**Prerequisite: A grade of C or better in MTH 281 or MTH 283, a grade of C or better in at least one mathematics course numbered 300 or above, or permission of instructor. This course gives a rigorous introduction to the real numbers. Topics include sequences and series, basic topology of the real numbers, functional limits and continuity, the derivative, sequences and series of functions, the Riemann integral, and metric spaces. The major application is Fourier series. Return to top

** MTH 416 Complex Analyses (4-0-4).** Prerequisite: A grade of C or better in MTH 281 or MTH 283, a grade of C or better in at least one mathematics course numbered 300 or above or permission of instructor. This course deals with the fundamentals of complex analysis, including basic properties of complex numbers, analytic functions, harmonic functions, integration, Taylor and Laurent series, residue calculus, conformal mapping, and their applications. Return to top

** MTH 420 Combinatorial Mathematics (4-0-4). **Prerequisite: At least one mathematics course numbered 300 or above. This course is a survey of combinatorial methods, including binomial coefficients and other special numbers, recurrence relations, calculus of finite differences, and generating functions, emphasizing exact evaluation of combinatorial sums in closed form. The course includes use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 421 Time Series Analysis (4-0-4).** Prerequisite: MTH 347 with a grade of “C” or better or permission of instructor. The course covers techniques of modeling data that are collected sequentially. Topics include a review of basic ideas of modeling a continuous variable, time series regression, autocorrelation, decomposition methods, exponential smoothing, ARMA (Autoregressive Moving Average) models, and ARIMA (Autoregressive Integrated Moving Average) models. The course uses a statistical programming language. Data from a variety of fields will be studied. Counts toward the statistics minor; does not count toward the minor, B.A., or B.S. in Mathematics. Return to top

** MTH 424 Probability Theory and Applications (4-0-4).** Prerequisites: MTH 281 or MTH 283, MTH 284 or MTH 288, and a 300-level mathematics course. This course covers general probability (set functions, basic axioms, independence); Bayes' theorem; univariate probability distributions (probabilities, moments, variance, mode, percentiles, transformations); multivariate probability distributions (central limit theorem, joint conditional and marginal distributions - probabilities, moments, variance, covariance); discrete and continuous time Markov chains; and selected applications. Course makes extensive use of appropriate software. Return to top

** MTH 431 Categorical Data Analysis (4-0-4).**Prerequisite: MTH 347 with a grade of “C” or better or permission of instructor. The course covers techniques of modeling data for data that are categorical rather than continuous in nature. Topics include joint, marginal, and conditional probabilities, relative risk, odds ratios, generalized linear models, logistic regression, multi-category logit models, and loglinear models. The course utilizes data examples from the fields of biology, medicine, health, epidemiology, environmental science, and psychology; it uses a statistical programming language and counts toward the statistics minor; it does not count toward the minor, B.A. or B.S. in Mathematics. Return to top

** MTH 434 Differential Geometry (4-0-4).** Prerequisites: MTH 281 or MTH 283, MTH 286, and at least one mathematics course numbered 300 or above. This course focuses on the calculus, linear algebra, and geometry of curves and surfaces, as well as applications to engineering and science. Material covered includes the curvature and torsion of curves, Gaussian and mean curvatures of surfaces, minimal surfaces, geodesics, holonomy, and the Gauss-Bonnet theorem. Optional material includes applications of the calculus of variations to geometry and of minimal surface theory to soap film formation. The course makes extensive use of a computer algebra system, such as Maple. Return to top

**MTH 435 Statistical Consulting (4-0-4).**Prerequisite: MTH 347 with a grade of “C” or better, senior standing, or permission of instructor. This course assigns students to work in consulting teams with university or community partners on real-world case studies of statistical methods learned in previous courses. Students prepare written reports and oral presentations that discuss the findings of the analysis. In addition, students learn data manipulation and graphics skills involving the SAS and R software packages. The course counts toward statistics minor; does not count toward the minor, BA, or BS in Mathematics. Return to top

** MTH 482 Topics in Number Theory (4-0-4)**. Prerequisite: A grade of C or better in a course of level 300 or above in one of the following disciplines, MTH, CIS, EEC, EET, ESC; or instructor permission. This course presents advanced topics in number theory. Topics may include primality testing, prime number generation, integer factorization, discrete logarithms, elliptic curves and advanced cryptographic protocols, and other topics chosen by the instructor. Return to top

** MTH 487 Dynamical Systems (4-0-4).** Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above. Topics include systems of differential equations, local and global behavior of a vector field in the plane, discrete dynamical systems, structural stability, the Poincare-Bendixon theorem, bifurcations, chaos, and strange attractors. The course includes use of a computer algebra system, such as Maple or MATLAB. Return to top

** MTH 491 Financial Mathematics (4-0-4).** Prerequisites: MTH 281 or 283, or permission of the instructor. This course covers basic mathematical interest theory and time value of money, annuities, loan repayment, bonds, equations of value and yield rates, interest rate sensitivity, stocks and financial markets, arbitrage, term structure of interest rates and derivatives. It is designed to prepare students for the SOA Exam FM/CAS Exam 2 (Financial Mathematics Exam). Return to top

** MTH 493 Special Topics in Mathematics (4-0-4). **Prerequisite: At least one mathematics course numbered 300 or above, or permission of instructor. This is a detailed study of a selected topic in advanced mathematics. The topic will vary, depending on instructor. It may be taken for credit more than once, but no single topic may be repeated. Please consult the Mathematics Department for current information. Return to top

** MTH 493H Special Topics in Mathematics Honors (4-0-4).** Prerequisites: At least one mathematics course at the 300 level or above, plus approval of the Department Honors Liaison Officer. This is a detailed study of a selected topic in advanced mathematics. Topics will vary, depending on instructor. This course may be taken for credit more than once, but no single topic may be repeated. It demands mathematical rigor to a degree beyond regular mathematics courses. In addition, students play a more active role in the discovery and exploration of mathematical truth. Consult the Mathematics Department for current information. Return to top

** MTH 496 Senior Project (4-0-4).** Prerequisites: MTH 396 (grade of S) and at least two other mathematics courses numbered 300 or above, or departmental approval. Prerequisite or co-requisite: At least one other mathematics course numbered 400 or above, or departmental approval. Working individually with a faculty supervisor, each student will read papers in technical journals, make an oral presentation, and write a technical report. Return to top

** MTH 496H Honors Project (4-0-4)**. Prerequisites: At least two mathematics courses numbered 300 or above, plus approval of the Department Honors Liaison Officer. Students will work individually with a mathematics faculty investigating a mathematical or statistical topic of mutual interest. Students will be required to read articles assigned by the faculty member. A student's work will consist of a written pre-proposal, and a final paper complete with Abstract, Introduction, Methods, Results, Discussion, and References. In addition, students will give an oral presentation of their work to department faculty and students. Return to top

** MTH 497 Readings in Mathematics (1 to 4 credits).** Prerequisite: Departmental approval. Topics studied under supervision of an adviser. Return to top