MATHEMATICAL SCIENCES COURSES
(MATHS)

[500 level] [600 level] 

Please click here to see the Anticipated Graduate Course Offerings Schedule.

Graduate Course Offerings for the Second Summer Session 2007.

511 Abstract Algebra 1. (3) In-depth treatment of group theory. Includes a brief review of basics, followed by topics such as factor groups, isomorphism theorems, series of groups, Burnside counting and the Sylow theorems, free groups, group presentations, and other advanced topics.
Prerequisite: MATHS 311 or the equivalent.
Not open to students who have credit in MATHS 411.

512 Abstract Algebra 2. (3) In-depth treatment of ring and field theory covering ideals, quotient rings, homomorphisms, polynomial rings, unique factorization domains, field extensions and geometric constructions, finite fields and additional topics from field automorphisms, Galois theory and applications to coding theory.
Prerequisite: MATHS 411 or MATHS 511.
Not open to students who have credit in MATHS 412.

514 Algebra and Functions for Elementary and Middle School Teachers. (3) Algebra as the study of patterns, as a symbolic language, as a tool for problem solving, as the study of functions, as generalized arithmetic, and as a way of modeling physical situations.  Also, issues related to teaching.
Prerequisite: At least one year of elementary or middle school teaching experience or permission of the department chairperson.

516 Theory of Numbers. (3) Topics include the division algorithm, positional notation, divisibility, primes, congruences, divisibility criteria; the sigma, divisor and phi functions; Diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson.
Not open to students who have credit in MATHS 416.

517 Number Systems and Number Theory for Elementary and Middle School Teachers. (3) Number systems, properties and characteristics of classes of numbers, number sense, number theory, operations and their relationships, and algorithms.
Prerequisite:  At least one year of elementary or middle school teaching experience or permission of the department chairperson.

522 Theory of Sampling and Surveys. (3) Survey designs; simple random, stratified, cluster, and systematics sampling; ratio estimates; regression estimates; cost and variance functions.
Prerequisite: MATHS 321 or equivalent.

528 Regression and Time Series Models. (3) Addresses regression topics that include simple and multiple linear regression, polynomial regression, regression diagnostics, and forecasting.  Introduces time series topics that include exponential smoothing, auto-regressive, integrated, moving average (ARIMA) models, and forecasting.
Prerequisite: MATHS 321 or the equivalent.
Not open to students who have credit in MATHS 428.

529 Analysis of Variance in Experimental Design Models. (3) Multivariate normal distribution; quadratic forms; linear models; simple random, randomized block, Latin squares, factorial, split-plot, balanced incomplete block designs; analysis of covariance; confounding; and multiple comparison tests.
Prerequisite: MATHS 321 or the equivalent.
Not open to students who have credit in MATHS 429.

542 Geometry and Measurement for Elementary and Middle School Teachers. (3)
Students will develop visualization skills: identify two- and three-dimensional shapes and know their properties; connect geometry to other mathematical topics; research historical topics relevant to elementary and middle school geometry.
Prerequisite:  At least one year of elementary or middle school teaching experience or permission of the department chairperson.

551 Mathematics of Finance. (4) Mathematical theory of compound interest, force of interest, annuities, equations of value, yield rates, amortization, sinking funds, bonds, depreciation, and current topics in finance.
Prerequisite: MATHS 166. Not open to students who have credit in MATHS 351.

552 Mathematics of Life Contingencies 1. (4) Survival distributions, life tables; the mathematics of life insurance, life annuities, net premiums, and net premium reserves.
Parallel: MATHS 551. Not open to students who have credit in MATHS 452.

553 Mathematics of Life Contingencies 2. (4) The mathematics of multiple life functions, multiple decrement models, valuation theory for pension plans, insurance models including expenses, nonforfeiture benefits, and dividends.
Prerequisite: MATHS 552.
Not open to students who have credit in MATHS 453.

555 Problems in Actuarial Science. (2) Limits, continuity, differentiability, integrability, series, sequences, derivatives, integrals, partial derivatives, and multiple integrals; axioms of probability, random variables, conditional probability and Bayes' theorem, joint and conditional probabilitiy distributions and expectations; loss frequency, loss severity, retention, deductible, coinsurance, and risk premium.
Prerequisite: MATHS 267, 321, RMI 270.
Not open to students who have credit in MATHS 355.

556 Introduction to Operations Research. (3) Optimization techniques of linear programming, dynamic programming, and integer programming.  Optimal solutions of PERT-PERM networks.  Optimal decision strategies.
Prerequisite: MATHS 162 or 166, 217, or permission of the department chairperson.
Not open to students who have credit in MATHS 456.

557 Loss Distributions. (4) Loss and frequency distributions, limited expected value, effects of inflation, parametric and non-parametric models, identification procedures for insurance company data, bootstrapping, Bayesian analysis, compound frequency, methods for censored and truncated data, classical and Bayesian credibility models, experience rating.
Prerequisite: MATHS 321.
Not open to students who have credit in MATHS 457

558 Practicum in Actuarial Science. (2) Presentations by and discussions with practicing actuaries on problems drawn from their fields of expertise, including life insurance, casualty insurance, health insurance, and professional ethics.  Completion of authentic, meaningful projects identified by participating actuaries.
Prerequisite:  MATHS 351 or 551, RMI 270 or 597, or permission of the department chairperson.
Not open to students who have credit in MATHS 458.

560 History of Mathematics. (3) The development of mathematics from prehistoric times to the seventeenth century. Topics may include number concepts and numeration, algebra, geometry, trigonometry, analytic geometry, and calculus.
Prerequisite: MATHS 161 or 165.
Not open to students who have credit in MATHS 460.

562 Numerical Analysis 1. (3) Topics include error analysis, approximation and interpolation of functions, solutions of nonlinear equations, approximate differentiation and integration, and orthogonal polynomials. Includes programming of numerical algorithms.
Prerequisite:  CS 120 ; MATHS 162 or 166.
Not open to students who have credit in MATHS 362 or CS 362 or CS 562.

563 Numerical Analysis 2. (3) Topics include approximate solution of linear and nonlinear systems of equations by direct and iterative methods, spline interpolation, numerical solution of ordinary and partial differential equations. Includes programming of numerical algorithms.
Prerequisite: MATHS 217 and CS 362 or MATHS 362 or 562.
Not open to students who have credit in CS 363 or 563.

568 Unpaid Professional Experience in Mathematical Sciences. (1-8) Supervised unpaid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation.
Prerequisite: permission of the department chairperson.
A total of 8 hours of credit may be earned in MATHS 568 and 569 combined.

569 Paid Professional Experience in Mathematical Sciences. (1-8) Supervised paid work and learning experience as a practicing mathematician, statistician, or actuarial scientist. Practical problem-solving experience will be gained through an internship, practicum, or other such situation.
Prerequisite: permission of the department chairperson.
A total of 8 hours of credit may be earned in MATHS 568 and 569 combined.

571 Real Analysis 1. (3) Properties of the real numbers.  Cardinality.  Topological properties of metric spaces: compactness, completeness, connectedness.  Continuous functions.  Differential calculus of real- and vector-valued functions of one and several real variables.
Prerequisite: MATHS 217, 267.
Not open to students who have credit in MATHS 471.

572 Real Analysis 2. (3) Inverse and implicit function theorems, extremum problems.  Infinite series and products.  Functions of bounded variation.  The Riemann-Stieltjes integral and Fundamental Theorem of Calculus.  Sequences of functions.  Multiple Riemann integrals.
Prerequisite: MATHS 471 or 571.
Not open to students who have credit in MATHS 472.

573 Boundary Value Problems. (3) Fourier Series and integrals, heat and wave equations in one dimension, Laplace equation in two dimensions, problems in higher dimensions, and numerical methods of solving boundary value problems.
Prerequisite: MATHS 374.
Not open to students who have credit in MATHS 473.

575 Topics in Partial Differential Equations. (3) Classical solution techniques for linear PDEs. Topics include first- and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green’s functions, and fundamental solutions. A computer algebra system is utilized.
Prerequisite: MATHS 267, 374, or permission of the department chairperson.
Not open to students who have credit in MATHS 475.

[500 level] [600 level] 

601 Workshop in Mathematics Education. (1-12) A one- or two-week workshop addressing specific topics in mathematics education. 
A total of 12 hours of credit may be earned.

619 Special Studies in Algebra. (1-8) Individual work under the direction of a staff member of the Department of Mathematical Sciences will involve assigned reading and reports and may involve class attendance in related courses.
Prerequisite: permission of the department chairperson.
MATHS 619,649, 669,  679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

620 Mathematical Theory of Statistics 1. (4) Probability set functions, random variables, density functions, distribution functions, mathematical expectations, moment generating functions, Chebyshev's inequality, marginal and conditional distributions, distributions of functions of random variables, limiting distributions, sampling distributions, Central Limit Theorem.
Prerequisite: MATHS 166.

621 Mathematical Theory of Statistics 2. (4) Classical and Bayesian estimation, sufficiency, completeness, uniqueness, likelihood function, exponential families, Rao-Blackwell theorem, Rao-Cramer inequality, hypothesis testing, Neyman-Pearson lemma likelihood ratio tests, distribution of quadratic forms, correlation, and regression.
Prerequisite: MATHS 620.

623 Data Analysis and Probability for Teachers. (3) Students will select and use appropriate statistical methods to analyze data, develop, and evaluate inferences and predictions that are based on data, and understand and apply the basic concepts of probability.
Prerequisite: At least one year of teaching experience or permission of the department chairperson.

625 Probability Theory and Applications. (3) Basic probability theory, random variables, conditional probability and conditional expectation, Poisson process, interarrival time and waiting time distributions.
Prerequisite: MATHS 166 or equivalent.

626 Probability and Stochastic Processes. (3) Discrete and continuous time Markov chains, queuing theory, renewal theory.
Prerequisite: MATHS 625.

627 Applied Statistics. (3) Descriptive statistics, binomial and normal distributions, confidence intervals, tests of significance, regression and correlation, analysis of variance. Applications stressed. Some use of statistical packages will be made. No previous computer experience necessary.

628 Monte Carlo Methods. (4) The theory of Monte Carlo methods and their applications in scientific computing.  Study of pseudorandom number generation, statistical tests for randomness, generation of non-uniform random variables, and variance reduction techniques.  Selected applications from numerical integration, computational finance, and linear algebra.  Low-discripancy sequences and hybrid-Monte Carlo methods.
Prerequisite: MATHS 625.

631 Technology for Mathematics Teachers. (3)   Modeling, computation, and communication tools used in teaching mathematics.
Prerequisite:  At least one year of teaching experience or permission of the department chairperson.

632 Assessment in Mathematics Education. (3) Issues related to assessment in mathematics education and the relationship of assessment to curriculum and instruction.  Examination of various types of assessments administered in mathematics classrooms, as well as large-scale local, national, and international assessments.
Prerequisite: At least one year of teaching experience or permission of the department chairperson

641 Topics in Geometry. (3)  A survey of topics in contemporary geometry from various perspectives, including conjecture and exploration, formal analysis, and application beyond geometry.
Prerequisite:  MATHS 345 or the equivalent.

645 Topology 1. (3) Set theoretic preliminaries, the axiom of choice, Zorn's lemma and the well ordering principle, topological spaces, continuity, separation axioms, nets and filters, connectedness , local connectedness,  product and quotient topologies, metric spaces, meterization.
Prerequisite: MATHS 472 or 572   

646 Topology 2. (3) Uniform spaces, paracompactness, open coverings, compactness, compactification , local compactness, function spaces, Stone-Weierstrass theorem, complete spaces, Banach fixed-point theorem, introductory homotopy theory. Introduction to homology theory, Jordan curve theorem, Brouwer fixed point theorem.
Prerequisite: MATHS 645.

649 Special Studies in Geometry or Topology. (1-8) Individual work under the direction of a staff member of the Department of Mathematical Sciences will involve assigned reading and reports and may involve class attendance in related courses.
Prerequisite: permission of the department chairperson.
MATHS 619,649, 669, and 679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

655 Topics in Actuarial Science. (4) Advanced actuarial principles in the fields of investments and asset management. Topics include capital markets, investment vehicles, derivatives-applications, principles of portfolio management, asset-liability management, design and valuation for the various actuarial models.
Prerequisite:   MATHS 551.

657 Survival Models. (4) Basic functions related to survival models, common parametric models, maximum likelihood estimation for censored or truncated data, nonparametric estimation, hypothesis testing, models with covariables, exposure to risk, practical aspects of tabular survival models.
Parallel:   MATHS 552.

658 Risk Theory. (4) Individual and collective risk theory.  Probability of  ruin.  Probability distributions of random numbers of random variables.
Parallel:   MATHS 552.

659 Research in Actuarial Science. (3) Research study in actuarial subjects of current interest in life, property/casualty, and/or pension.  Literature searches on selected topics.  Articles from research journals will be read and discussed.  Will use actuarial skills from several courses.  A paper will be required.
Prerequisite:  MATHS 552.

660 Topics in the History of Mathematics. (3) In-depth study of selected topics in the history of mathematics.
Prerequisite:  MATHS 162 or 165, 460 or 560.

669 Special Studies in Applied Mathematics. (1-8) Individual work under the direction of a staff member of the Department of Mathematical Sciences will involve assigned reading and reports and may involve class attendance in related courses.
Prerequisite: permission of the department chairperson.
MATHS 619,649, 669, and 679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

670 Elements of Analysis. (3) An introduction to elementary point-set topology; development of the limit concept related to sequences and functions; introduction to the development of real numbers through Cauchy sequences; applications of the limit concept in continuity, derivatives and integrals of elementary functions.
Prerequisite:  MATHS 166.
Not open to students who have credit in MATHS 470.

671 Continuous and Discrete Mathematics for Elementary and Middle School Teachers. (3) Fundamental concepts and applications of calculus and discrete mathematics.
Prerequisite:  MATHS 512, 542, or permission of the department chairperson.

675 Theory of Functions of Real Variables 1. (3) The concept of measurability, simple functions, properties of measures, integration of positive as well as complex functions, sets of measure zero, Riesz representation theorem, Borel and Lesbesgue measures, LP-spaces, Elementary Hilbert space theory.
Prerequisite:  MATHS 472 or 572.

676 Theory of Real Variables 2. (3) Banach spaces, Baire's theorem. Hahn-Banach theorem, complex measures, total variation, absolute continuity, Radon-Nikodym theorem, bounded linear functionals on LP, the Riesz representation theorem, product measures, the Fubini theorem, completion of product measures.
Prerequisite: MATHS 675.

677 Complex Variables 1. (3) Complex numbers systems, differentiation and integration, functions (analytic, entire, meromorphic) of one complex variable, singularities, complex integration, Cauchy's theorem, Cauchy's integral formula, power series, Laurent series, calculus of residues.
Prerequisites: MATHS 472 or 572.

678 Complex Variables 2. (3) Analytic continuation, Riemann surfaces, theorems of Weierstrass and Mittag-Leffer, solution of two-dimensional potential problem, conformal mapping, Schwartz-Christiffol transformations and their applications.
Prerequisite: MATHS 677.

679 Special Studies in Analysis. (1-8) Individual work under the direction of a staff member of the Department of Mathematical Sciences will involve assigned reading and reports and may involve class attendance in related courses.
Prerequisite: permission of the department chairperson.
MATHS 619,649, 669, and 679, singly or in combination, may be taken for a total of no more than 8 hours of credit.

680 Special Studies in the Teaching of Mathematics. (1-6) The student will work under the direction of a staff member in the Department of Mathematical Sciences. Assigned reading and reports; possible class attendance in related courses.
prerequisites: Permission of the department chair person.
A total of 6 hours of credit may be earned.

689 Research Methods in Mathematics and Statistics. (3) The scientific method in mathematical research. Location of relevant journal articles, reference books, and reviews. Development of research and problem-solving techniques. Each student will write a mathematical paper. The instructor will assist students whose work is of exceptional quality in submitting their results for publication.

690 Curriculum and Instruction in Mathematics Education (3). This course will focus on the mathematics curriculum, with emphasis on current issues and trends and on teaching strategies, with emphasis on standards-based teaching.  Looking at mathematics curriculum from a K-12 perspective, we will work on understanding these recommendations in light of previous mathematics curriculum experiences.
Prerequisite: at least one year of teaching experience or permission of the department chairperson.

691 Developmental and Remedial Instruction in Elementary and Middle School Mathematics (3). Materials and methods used in developing conceptual understanding of mathematics for all students in elementary and middle school. Includes assessment and remediation techniques.

693 Problem Solving and Communication Strategies in Mathematics (3). Development of problem-solving strategies and skills for teachers and their students. Oral and written communication strategies to promote problem solving and mathematical reasoning in student-centered mathematics classrooms.
Prerequisite: at least one year of teaching experience or permission of the department chairperson.

694 Research Methods in Mathematics Education. (3) Research analysis and methodology in mathematics education.
Prerequisite: At least one year of teaching experience and 9 hours of graduate credit in mathematics or mathematics education.

695 Learning Theories in Mathematics Education (3). In-depth study of learning theories; discussing the psychology of mathematics learning (i.e., what we know about the ways in which students learn mathematics).  These issues will be discussed from a “teacher’s perspective,” looking for classroom implications of our knowledge about children’s mathematical thinking.
Prerequisite: at least one year of teaching experience or permission of the department chairperson.

696 Action research in Mathematics education. (3) Teachers design and conduct action research projefcts in their own mathematics classrooms and present their findings in oral and written reports.

697 Teacher Leadership in Mathematics Education (3). Development of strategies and skills for teacher leadership in mathematics education, with a focus on models for professional development of mathematics teachers.
 Prerequisite: Maths 690, 694.

699 Seminar in Mathematics. (1-6) For students who wish to pursue some particular problem or group of problems in mathematics. Assigned readings and conferences.
A total of 6 hours of credit may be earned.

[500 level] [600 level]