FacebookUndergraduate Course Descriptions
107-3 Intermediate Algebra
Properties and operations of the number system. Elementary operations with polynomials and factoring. Elementary operations with algebraic fractions. Exponents, roots, and radicals. First and second-degree equations and inequalities. Functions and graphing. Systems of equations and inequalities. Exponential and logarithmic functions. This course does not satisfy the University Core Curriculum mathematics requirement and it does not count toward the 120 hours needed for graduation. Prerequisite: one year of high school algebra. Departmental Syllabus
NO CALCULATORS will be allowed for the final exam in Math 107. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam.
108-3 College Algebra
(Advanced University Core Curricu-lum course) The algebra of functions (polynomials, rational, exponential, logarithmic), graphing, conic sections, solving equations including systems. Credit is not given for both 108 and 111. Prerequisite: 107 or three years of college preparatory mathematics including Algebra I, Geometry and Algebra II with a C or better. New students must present satisfactory placement scores or obtain the permission of the department of mathematics. Departmental Syllabus
NO CALCULATORS will be allowed for the final exam in Math 108. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam.
109-3 Trigonometry and Analytic Geometry
(Advanced Uni-versity Core Curriculum course) Trigonometric and inverse trigonometric functions, complex numbers, conic sections, polar coordinates. Credit is not given for both 109 and 111. Prerequisite: 108 or equivalent with a grade of C or better. New students must present satisfactory placement score or obtain the permission of the Department of Mathematics. Satisfies University Core Curriculum Mathematics requirement in lieu of 110 or 113. Departmental Syllabus
ONLY an *approved scientific calculator will be permitted on the final examination for Math 109, 111, 139, 140, 150, and 250; however, calculators or computers with graphic, word-processing, symbolic manipulation or programming capabilities will not be allowed for this exam. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam. *"Approved scientific calculator" means TI-30.
110-3 Non-Technical Calculus (University Core Curriculum)
(University Core Curriculum) The elements of differentiation and integration. The emphasis is on the concepts and the power of the calculus rather than on technique. It is intended to provide an introduction to calculus for non-technical students. Does not count towards the major in mathematics. No credit hours may be applied to fulfillment of any degree requirements if there is prior credit in Mathematics 140, 141 or 150. Prerequisite: 3 years of college preparatory mathematics including algebra I, algebra II and geometry with C or better. Students must present satisfactory placement scores or obtain the permission of the Department of Mathematics. Departmental Syllabus
111-4 Precalculus
(Advanced University Core Curriculum course) An intensive review course in college algebra and trigonometry for students who plan to take Calculus I. The algebra of functions (polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric), graphing (polynomial, rational, exponential, logarithmic, and trigonometric function), analytic trigonometry and trigonometric identities, including the law of sines and the law of cosines, conic sections, complex numbers, polar coordinates, parametric equations. Not open to students with credit in 108 or 109. Prerequisite: Advanced Algebra and Trigonometry with C or better in high school and ACT math subscore of at least 24. Satisfies University Core Curriculum Mathematics requirement in lieu of 110 or 113. Departmental Syllabus
ONLY an *approved scientific calculator will be permitted on the final examination for Math 109, 111, 139, 140, 150, and 250; however, calculators or computers with graphic, word-processing, symbolic manipulation or programming capabilities will not be allowed for this exam. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam. *"Approved scientific calculator" means TI-30.
113-3 Introduction to Contemporary Mathematics (University Core Curriculum)
(University Core Curriculum) [IAI Course: M1 904] Elementary mathematical principles as they relate to a variety of applications in contemporary society. Exponential growth, probability, geometrical ideas and other topics. This course does not count towards the major in mathematics. Prerequisite: Mathematics 107 or 3 years of college preparatory high school mathematics including geometry and Algebra II. Students must present satisfactory placement scores or obtain the permission of the Department of Mathematics. Departmental Syllabus
120-3 Mathematics Content and Methods for Elementary School I (Same as Curriculum and Instruction 120)
Modern approaches to mathemat-ics instruction for the elementary grades. Mathematics content includes problem solving, intuitive set theory, development of whole numbers, integers and rational numbers and the fundamental arithmetic operations. Place value. Prime numbers and divisibility properties. Computation includes students’ informal mathematics, mental computation and estimation, algorithms and the appropriate use of calculators. Emphasis is placed throughout on reasoning, multiple representations of mathematical concepts, making connections and communication. Two hours lecture and two hours laboratory per week. Prerequisite: Three years of college preparatory mathematics including Algebra I, Algebra II and Geometry. Departmental Syllabus
125-4 Technical Mathematics with Applications
(Advanced University Core Curriculum course) Emphasizes the applications of algebra and trigonometry in technical fields. Topics in algebra include functions and graphs, systems of linear equations, quadratic equations, higher degree equations and variation. Topics in trigonometry include the trigonometric functions, laws of sines and cosines, complex numbers, exponential and logarithmic functions. Meets University Core Curriculum requirement in mathematics for Applied Sciences and Arts students. Enrollment restricted to students in the College of Ap-plied Sciences and Arts or permission of department. Prerequisite: Mathematics 107 or two years of high school algebra or equivalent, with a grade of C or better. Departmental Syllabus
139-3 Finite Mathematics
(Advanced University Core Curricu-lum course) Set concepts and operations, combinations, permutations, elementary probability theory including Bayes formula, linear systems of equations, matrix algebra, Gauss-Jordan row reduction, introduction to linear programming. This course does not count towards the major in mathematics. Prerequisite: MATH 108 (or equivalent) with a grade of C or better. New students must also present satisfactory placement scores or ob-tain the permission of the department of mathematics. Satisfies UCC Mathematics in lieu of 110 or 113. Departmental Syllabus
ONLY an *approved scientific calculator will be permitted on the final examination for Math 109, 111, 139, 140, 150, and 250; however, calculators or computers with graphic, word-processing, symbolic manipulation or programming capabilities will not be allowed for this exam. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam. *"Approved scientific calculator" means TI-30.
140-4 Short Course in Calculus
(Advanced University Core Curriculum course) Techniques of differentiation, increasing and decreasing functions, curve sketching, max-min problems in business and social science; partial derivatives, LaGrange multipliers, elementary techniques of integration. Credit hours for both 140 and 141 may not be applied to fulfillment of degree requirements. No credit hours for 140 may be applied to fulfillment of degree requirements if there is prior credit in 150. Does not count towards the major in mathematics. Prerequisite: MATH 108 (or equivalent) with a grade of C or better. New students must present satisfactory placement scores or obtain the permission of the department of mathematics. Satisfies University Core Curriculum Mathematics requirement in lieu of 110 or 113. Departmental Syllabus
ONLY an *approved scientific calculator will be permitted on the final examination for Math 109, 111, 139, 140, 150, and 250; however, calculators or computers with graphic, word-processing, symbolic manipulation or programming capabilities will not be allowed for this exam. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam. *"Approved scientific calculator" means TI-30.
141-3 Short Course in Calculus for Biological Sciences
(Advanced University Core Curriculum course) [IAI Course: M1 900] Basic techniques of differentiation and integration. Population and organism growth problems solved by using calculus. Translation of problems in the biological sciences into mathematical problems. Does not count towards the major in mathematics. Credit hours for both 140 and 141 may not be applied to fulfillment of degree requirements. No credit hours for 141 may be applied to fulfillment of degree requirements if there is prior credit in 150. Prerequisite: 111 or equivalent with grade of C or better. New students must present satisfactory placement scores or obtain the permission of the department of Mathematics. Satisfies University Core Curriculum Mathematics requirement in lieu of 110 or 113.
150-4 Calculus I
(Advanced University Core Curriculum course) [IAI Course: M1 900] Treatment of the major concepts and techniques of single-variable calculus, with careful statements but few proofs. Differential and integral calculus of the elementary functions with associated analytic geometry. If there is prior credit in 140 or 141 only 2 hours credit for 150 may be applied to graduation requirements. Prerequisite: 111 or equivalent with a grade of C or better. Students must present satisfactory placement scores or obtain the permission of the department of Mathematics. Satisfies University Core Curriculum Mathematics requirements in lieu of 110 or 113. Departmental Syllabus
ONLY an *approved scientific calculator will be permitted on the final examination for Math 109, 111, 139, 140, 150, and 250; however, calculators or computers with graphic, word-processing, symbolic manipulation or programming capabilities will not be allowed for this exam. The use of books, notes or other resource materials will not be permitted on the final examination. All cell phones prohibited during the final exam. *"Approved scientific calculator" means TI-30.
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220-3 Mathematics Content and Methods for Elementary School II (Same as Curriculum and Instruction 220)
Modern approaches to mathematics instruction for the elementary grades. Mathematics content focuses on rational and irrational numbers. Ordering of numbers. Decimal representations. Percents. Ratio and Proportion. Perimeter and area concepts. Pythagorean Theorem. Concept of square root and nth root. Exponent notation. Elementary geometry. Triangles, quadrilaterals, polygons, angles associated with a polygon. Reflectional and rotational symmetry. Congruence and Similarity. Tessellations. Transformations: translations, rotations, reflections. Measurement of perimeter, area, surface area, volume, mass, temperature. Conversion of measurements. Emphasis is placed throughout on reasoning, multiple representations of mathematical concepts, making connections and communication. Two hours lecture and two hours lab per week. Prerequisite: 120 or Curriculum and Instruction 120 or equivalent with a grade of C or better. Departmental Syllabus
221-3 Introduction to Linear Algebra
Vector spaces, linear functions, systems of equations, dimensions, determinants, eigenvalues, quadratic forms. Prerequisite: 150 with a grade of C or better. Departmental Syllabus
250-4 Calculus II
(Advanced University Core Curriculum course) [IAI Course: M1 900] Develops the techniques of single-variable calculus begun in Calculus I and extends the concepts of function, limit, derivative and integral to functions of more than one variable. The treatment is intuitive, as in Calculus I. Techniques of integration, introduction to multivariate calculus, elements of finite series. Prerequisite: 150 with a grade of C or better. Students must present satisfactory placement score or obtain the permission of the department. Satisfies University Core Curriculum Mathematics requirement in lieu of 110 or 113. Departmental Syllabus
251-3 Calculus III
(Advanced University Core Curriculum course) [IAI Course: M1 900] Further topics in calculus. Definite integrals over solid regions, applications of partial derivatives, vectors and vector operations, derivatives of vector functions, line integrals. Green’s theorem. Prerequisite: 250 with a grade of C or better. Satisfies University Core Curriculum Mathematics requirements in lieu of 110 or 113. Departmental Syllabus
257-1 to 12 Concurrent Work Experience
As an instructional aide, the student will do tutoring under the direction of an es-tablished teacher and under the supervision of a representative of the Department of Mathematics. Prerequisite: consent of de-partment. Mandatory Pass/Fail.
282-3 Introduction to Statistics
(Advanced University Core Curriculum course) [IAI Course: M1 902] Designed to introduce beginning students to basic concepts, techniques, and applications of statistics. Topics include the following: organization and display of data, measures of location and dispersion, elementary probability, statistical estimation, and parametric and nonparametric tests of hypotheses. Prerequisite: 108 or equivalent with a C or better. Satisfies University Core Curriculum Mathematics requirement in lieu of 110 or 113. Departmental Syllabus
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300I-3-History of Mathematics
(University Core Curriculum) This course examines how diverse cultures and history from the ancient past to the present have shaped the development of mathematical thought and how developing mathematical ideas have influenced history and society. Particular attention will be given to the evolution of the concepts of number and space; the emergence and applications of calculus, probability theory, non-Euclidean geometries and technology; and to the changes in the concept of mathematical rigor. Does not count towards the mathematics requirements of the mathematics major. Open to all students. Prerequisite: MATH 150.
302-3 Mathematical Communication and the Transition to Higher Mathematics
A course in communicating mathematical ideas with a special emphasis on reading, writing, and critiquing mathematical proofs. Topics covered include logic, proofs, set theory, relations, functions. Additional illustratory topics will be drawn from linear algebra, number theory, complex variables, and geometry. Prerequisite: Mathematics 221 and 250 with a grade of C or better. Departmental Syllabus
305-3 Introduction to Ordinary Differential Equations I
Solution techniques for differential equations with emphasis on second order equations, applications to physical sciences, series solutions. Prerequisite: 250 with a grade of C or better.
311-4 Teaching of Secondary Mathematics
The nature and objectives of the secondary mathematics curriculum. Particular attention is given to the means of introducing new ideas into the high school program. For students preparing to be certified teachers of secondary mathematics. Three lectures and two laboratory hours per week. Does not count toward a mathematics major in the College of Liberal Arts or in the College of the Science. Prerequisite: 319, 335 and EDUC 313. Departmental Syllabus
318-2 An Introduction to Mathematics Software
This course is an introduction to the use of Maple, a modern computer algebra system, as a computational and experimental tool in mathematics. The preparation of reports using text, graphics and mathematics is emphasized. Topics will include: solving equations, plotting techniques, special packages, programming with Maple V. Prerequisite: 150 with B or better or 250 with C or better.
319-3 Introduction to Abstract Algebra
Basic properties of groups and rings: Binary operations, groups, subgroups, permutations, cyclic groups, isomorphisms, Cayley’s theorem, direct products, cosets, normal subgroups, factor groups, homomorphisms, rings, integral domains. Prerequisite: 221; plus for secondary education majors, 302.
321-3 Mathematics Content and Methods for Elementary School III (Same as Curriculum and Instruction 321)
Modern approaches to mathematics instruction for the elementary grades. Mathematics content focuses on: straight-edge and compass constructions. Justification and proof of geometric properties. Three-dimensional geometry. Coordinate geometry. Transformations expressed in coordinate notation. Analysis of linear relationships geometrically and algebraically. Modeling various “real-world” situations by linear equations and inequalities. Setting up and solving equations and inequalities. Exploration of statistical data. Representation of data, interpretation of data, misrepresentation of data. Introduction to the fundamental ideas of statistics; measures of spread and central tendency. Introduction to the fundamental concepts of probability. Counting techniques needed for calcu-lating probabilities. Dependent and independent events. Conditional probability. Odds, expected value. Simulation. Emphasis is placed throughout on reasoning, multiple representations of mathematical concepts, making connections and communication. Two hours lecture and two hours lab per week. Prerequisite: 220, Curriculum and Instruction 220 or equivalent with a grade of C or better. Departmental Syllabus
322-3 Mathematics Content and Methods for Elementary School IV (Same as Curriculum and Instruction 322)
Modern approaches to mathematics instruction for the elementary grades. Mathematics content focuses on: algebra and algebraic thinking, geometry, relations and functions and their applications to real-life problems. Emphasis is placed throughout on reasoning, multiple representations of mathematical concepts, making connections and communication. Two hours lecture and two hours laboratory per week. Prerequisite: 321, Curriculum and Instruction 321 with a grade of C or better. Departmental Syllabus
335-3 Concepts of Geometry
Introduction to the foundations of Euclidean and non-Euclidean geometry with an emphasis on axiom systems, models, and counterexamples. Topics include metric geometry, betweenness, plane separation, congruence, absolute plane geometry, the critical function, and parallelism. Prerequisite: 221 or 250; for secondary education majors concurrent enrollment in Mathematics 302 is highly recommended.
349-3 Introduction to Discrete Mathematics
Numbers, sets, relations and functions; elementary enumeration; introduction to graph theory; logic, partially ordered sets and Boolean algebra; mathematical induction; recurrence relations. Prerequisite: 221.
352-3 Theory of Calculus
An introduction to understanding and writing proofs in mathematical analysis, through a careful study of limits, continuity, the derivative, and the integral. Prerequisite: 221, 250; plus for secondary education majors, 302.
380-3 Elements of Probability
Probability as a mathematical system. Axioms, permutations and combinations, random variables, generating functions, limit theorems, and Monte Carlo procedure. Prerequisite: 250 and Computer Science 202.
390-3 to 6 Topics in Contemporary Mathematics
Content will vary according to the instructor. The seminar will introduce students to new and developing areas of mathematics, such as Chaos, Fractals, Algorithms, Fourier Analysis, Difference Equa-tions, etc. Prerequisite: intended for students who have com-pleted Mathematics 150, 221, 250 and either 251 or 305. Other prerequisites may apply. May be repeated as topics vary.
Content will vary according to the instructor. The seminar will introduce students to new and developing areas of mathematics, such as Chaos, Fractals, Algorithms, Fourier Analysis, Difference Equations, etc. Prerequisite: intended for students who have completed Mathematics 150, 221, 250 and either 251 or 305. Other prerequisites may apply. May be repeated as topics vary.
395-1 to 6 Readings in Mathematics
Supervised reading in selected subjects. Prerequisite: 3.00 grade point average in mathematics and consent of chair.
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405-3 Intermediate Differential Equations
This course features the study of several sets of differential equations with the aid of computers. The equations are actual applications taken from the areas of biology, chemistry, economics, engineering, finance, medicine and physics. Where possible, problems will be chosen to match student’s interests. Students from these areas are particularly welcome. Basic theory of differential equations is cited, particularly as it is needed or encountered in the problems. Prerequisite: 305, but highly motivated students with a good calculus background and an interest in learning to use mathematical software may enroll with permission of the instructor.
406-3 Linear Analysis
An elementary introduction to function spaces and operators as used in quantum mechanics, partial differential equations, etc. Topics include: discrete and continuous models for the vibrating string; separation of variables and eigenfunction analysis; inner product spaces; operators on inner product spaces; the spectral theorem for Hermitian operators on finite dimensional spaces with selected applications; the Courant-Fisher maxmin characterization of eigenvalues; the spectral theorem for compact Hermitian operators with selected applications to Sturm-Liouville boundary value problems and Fredholm integral equations. Prerequisite: 221 and 305.
407-3 Introduction to Partial Differential Equations
The purpose of this course is to teach the student how to solve linear partial differential equations that arise in engineering and the sciences. Topics studied will include: the heat equation, the wave equation, Laplace’s equation, separation of variables, boundary and initial value problems, uniqueness via the energy methods, the maximum principle and characteristics. Solutions to the vibrating string and dissipation of heat in a bar will be discussed. Prerequisite: 251 and 305.
409-3 Fourier Analysis
A practical modern introduction to the theory, techniques and applications of elementary Fourier analysis. Topics include: the Fourier synthesis and analysis equations for periodic and aperiodic functions on the reals and the integers; convolution; the calculus for finding Fourier transforms, Fourier series and DFT’s; operators and their Fourier transforms; the FFT and related algorithms; generalized functions, such as Dirac’s delta, the comb, and “1/x”, and selected applications of Fourier analysis to sampling theory, partial differential equations, probability, the synthesis of musical tones, diffraction and wavelets. Prerequisite: 221 and 305.
411-1 to 6 (1 to 3, 1 to 3) Mathematical Topics for Teachers
Mathematical Topics for Teachers. Variety of short courses in mathematical ideas useful in curriculum enrichment in elementary and secondary mathematics. May be repeated as topics vary. Does not count toward a mathematics major.
412-3 Problem Solving Approaches to Basic Mathematical Skills
Content of basic skills at all levels of education and the development of these skills from elementary school through college; emphasis on problem solving and problem solving techniques; determination of student skills and proficiency level. Credit may not be applied toward degree requirements in mathematics. Prerequisite: Math/CI 322 or equivalent.
417-3 Applied Matrix Theory
Selected applications of matrices to physics, chemistry and economics. This material is also useful for engineering and computer science. Topics will include matrix representation of symmetry groups, non-negative matrices and the subsidy problem, location of eigenvalues. Prerequisite: 221.
418-3 Computer Algebra Systems
This course presents modern computer algebra systems (CAS) as a research tool in mathematics. The use of a CAS in the preparation of reports, theses and dissertations will also be covered. Topics will include: solv-ing differential equations with a CAS; plotting techniques with a CAS; symbolic packages for such areas as abstract algebra, number theory; and combinatorics; programming with a CAS; exporting results to TeX or word processing software; The AMS-LaTeX package. Prerequisite: graduate standing and consent of instructor.
419-3 Introduction to Abstract Algebra II
A detailed study of polynomial equations in one variable. Solvable groups and the Galois theory of field extensions are developed and applied to extensions of the quadratic formula, proving the impossibility of trisecting an angle with only a straight-edge and a compass, and to the basic facts about finite fields as needed in coding theory and computer science. Prerequisite: 319 or consent.
421-3 Linear Algebra
The extension of basic linear algebra to arbitrary scalars. The theory and computation of Jordan forms of matrices (as needed e.g., for certain diffusion equations). Inner products, quadratic forms and Sylvester’s Law of Inertia. Prerequisite: 221.
425-3 Introduction to Number Theory
Properties of integers, primes, divisibility, congruences, quadratic forms, diophantine equations, and other topics in number theory. Prerequisite: 319 or consent of department.
430-3 Introduction to Topology
Study of the real line and the plane, metric spaces, topological spaces, compactness, connectedness, continuity, products, quotients and fixed point theorems. This course will be particularly useful to students who intend to study analysis or applied mathematics. Prerequisite: 302 or 352 or consent of instructor.
435-3 Elementary Differential Geometry
An introduction to modern differential geometry through the study of curves and surfaces in R^3. Local curve theory with emphasis on the Serret-Frenet formulas; global curve theory including Fenchel’s theorem; local surface theory motivated by curve theory; global surface theory including the Gauss-Bonnet theorem. Prerequisite: 221 and 251.
447-3 Introduction to Graph Theory (Same as Computer Science 447)
Graph theory is an area of mathematics which is fundamental to future problems such as computer security, parallel processing, the structure of the World Wide Web, traffic flow and scheduling problems. It is also playing an increasingly important role within computer science. Topics covered include: trees, coverings, planarity, colorability, digraphs, depth-first and breadth-first searches. Prerequisite: 349 or consent of instructor.
449-3 Introduction to Combinatorics (Same as Computer Science 449)
This course will introduce the student to various basic topics in combinatorics that are widely used throughout applicable mathematics. Possible topics include: elementary counting techniques, pigeonhole principle, multinomial principle, inclusion and exclusion, recurrence relations, generating functions, partitions, designs, graphs, finite geometry, codes and cryptography. Prerequisite: 349 or consent of instructor.
450-3 Methods of Advanced Calculus
This course presents multivariable calculus, an area that is fundamental to fields such as continuum mechanics, differential geometry, electromagnetism, relativity, and thermodynamics. Topics will include: parametric curves and surfaces, the inverse and implicit function theorems, contraction mapping and fixed point theorems, differentials, convergence of multivariate integrals, coordinate systems in space, Jacobians, surfaces, volumes and Green’s, Gauss’, and Stokes’ theorems. The emphasis in this course will be on explicit computations. Prerequisite: 251.
452-3 Introduction to Analysis
This course develops the basic mathematical tools that are necessary for the understanding of all other advanced courses in analysis. Its principal content is a rigorous development of one-variable calculus. Topics will include: sets, axioms for the real numbers, continuity and limits, differentiation, the Riemann integral, and infinite sequences and series of functions. If time allows, additional topics may be chosen from areas such as Riemann-Stieltjes integration or the analysis of functions of several variables. Prerequisite: 250.
455-3 Complex Analysis with Applications
This course introduces the mathematical techniques that are commonly used to analyze those problems in the sciences and engineering that are inherently two dimensional in nature. Its content is the analysis of differentiable functions of a single complex variable. Topics will include: the complex plane, analytic functions, the Cauchy-Riemann equations, line integrals, the Cauchy integral formula, Taylor and Laurent series, the residue theorem, and conformal mappings. Applications will be made to topics selected from fluids, electrostatics and control theory. Prerequisite: 251 or consent of instructor.
458-3 Statistical Methods in Business and Industry
The course gives an introduction to statistical techniques using a limited calculus background. Topics covered include probability; random variables; standard distributions such as the binomial, Poisson, normal and exponential; estimation including the method of moments and of maximum likelihood; tests of hypotheses; simple linear regression. Applications to business and engineering problems will be emphasized. The course does not count toward a mathematics major or a mathematics minor. Prerequisite: 140 or equivalent.
460-3 Transformation Geometry
Geometry viewed as the study of properties invariant under the action of a group. Topics include collineations, isometries, Frieze groups, Leonardo’s Theorem, the classification of isometries of Euclidean and hyperbolic geometries. Recommended elective for secondary education majors in mathematics. Prerequisite: 221 and 319.
471-3 Optimization Techniques (Same as Computer Science 471)
An elementary introduction to algorithms for finding extreme values of nonlinear functions of several variables with and without constraints. Topics include: convex sets and functions; the arithmetic-geometric mean inequality; Taylor’s theorem for functions of several variables; positive definite, negative definite, and indefinite matrices; iterative methods for unconstrained optimization such as the method of steepest descent; the Kuhn-Tucker algorithm; unconstrained and constrained geometric programming; Lagrange multipliers, and penalty function methods. Students will use a computer to study the numerical properties of these algorithms. Prerequisite: 250 and 221.
472-3 Linear Programming (Same as Computer Science 472)
An introduction to the theory for finding extreme values of linear functionals subject to linear constraints. Topics include: recognition, formulation, and solution of real problems via the simplex algorithm; development of the simplex algorithm; artificial variables; the dual problem and the duality theorem; complementary slackness; sensitivity analysis; and selected applications of linear programming to integer programming, cutting plane algorithm, the distribution problem, the transportation problem, and the assignment problem. Students will use a computer to study the numerical performance of these algorithms. Prerequisite: 221.
473A, B-6 (3, 3) STatistical Topics in Actuarial Science
Parts a and b may be taken only once each. (a) Reliability and Survival Models: An introduction to the statistical analysis of data on lifetimes. Topics include hazard functions and failure distribu-tions; estimation and hypothesis testing in life testing experi-ments with complete as well as censored data. Prerequisite: MATH 480 or 483 or consent of the instructor. (b) Time Series: An introduction to time series. Topics include AR, MA and ARIMA models; estimation, data analysis and forecasting with time series models. Prerequisite: MATH 480 or483 or consent of the instructor.
475-6 (3, 3) Numerical Analysis (Same as Computer Science 475)
A practical introduction to the theory and techniques for computation with digital computers. Topics include: the solution of nonlinear equations; interpolation and approximation; solution of systems of linear equations; numerical integration, solution of ordinary differential equations; computation of eigenvalues and eigen-vectors; and solution of partial differential equations. Students will use MATLAB to study the numerical performance of the algorithms introduced in the course. Prerequisite: (a) 221 and 250 (b) 305 and 475a.
480-3 Probability, Stochastic Processes, and Applications I
An introduction to the central topics of modern probability including some elementary stochastic processes. A student taking this course will learn about random variables and their properties, including sum of independent random variables and the Central Limit Theorem. In addition, random walks and discrete-time finite state Markov chains will be introduced. Applications to random number generators and image and signal processing will be discussed. Principal topics studied, in addition to those already listed, include generating functions, conditional probability and independence, expectation and moments, covariance and correlation, and characteristic functions. Prerequisite: 251.
481-3 Probability, Stochastic Processes, and Applications II
A continuation of Part I with additional emphasis on stochastic processes and applications. Students will see a thorough introduction to Markov processes and Martingales. Principal topics include the laws of large numbers, classification of states, recurrence, and convergence to the stationary distribution in Markov chains, birth processes and Poisson processes, stopping times, and the Martingale convergence theorem. Additional topics may include the renewal equation, stationary processes and the ergodic theorem and their applications, diffusion, and Kalman filtering with applications to signal processing and estimation. Prerequisite: 480.
483-4 Mathematical Statistics in Engineering and the Sciences
The course develops the basic statistical techniques used in applied fields like engineering, and the physical and natural sciences. Principal topics include probability; random variables; expectations; moment generating functions; transformations of random variables; point and interval estimation; tests of hypotheses. Applications include one-way classification data and chi-square tests for cross classified data. Prerequisite: 250.
484-3 Applied Regression Analysis and Experimental Design
The course provides an introduction to linear models and design of experiments used extensively in applied statistical work. Principal topics include linear models; analysis of variance; analysis of residuals; regression diagnostics; randomized blocks; Latin squares; factorial designs. Applications include response surface methodology and model building. Computations are an integral part of the course and will require the use of a statistical package such as SAS. Prerequisite: 483 and 221 or consent of instructor.
485-3 Applied Statistical Methods
The course gives an introduction to sampling methods and categorical data analysis which are widely used in applied areas such as a social and biomedical sciences and business. In sampling methods, topics covered include: simple random and stratified sampling; ratio and regression estimators. In categorical data analysis, topics covered include: contingency tables; loglinear models; logistic regression; model selection; use of a computer package. Prerequisite: 483 or consent of instructor.
490-3 Topics in Mathematics.
Selected topics in mathematics chosen from such areas as: a) Financial Mathematics, Math-ematical Biology or Actuarial Mathematics; b) Probability, Statistics, or Stochastic Processes; c) Mathematical topics not including Statistics, such as Operations Research, Cryptogra-phy and High Dimensional Computing in Numerical Analysis, etc. May be repeated up to 3 times as topics vary. Prerequisite: Consent of instructor.
495-1 to 6 Special Topics in Mathematics
Individual study or small group discussions in special areas of interest under the direction of a member of the faculty. Prerequisite: consent of chair and instructor.