Mathematics: M

Lower-Division Courses

M X01. College Algebra.

Subjects include a brief review of elementary algebra; linear, quadratic, exponential, and logarithmic functions; polynomials; systems of linear equations; applications.

M X02. Introduction to Mathematics.

Intended primarily for general liberal arts students seeking knowledge of the nature of mathematics as well as training in mathematical thinking and problem solving. Topics include number theory and probability; additional topics are chosen by the instructor.

M X03D. Applicable Mathematics.

An entry-level course for the nontechnical student, dealing with some of the techniques that allow mathematics to be applied to a variety of problems. Topics include linear and quadratic equations, systems of linear equations, matrices, probability, statistics, exponential and logarithmic functions, and mathematics of finance.

M X03F. Mathematics of Investment.

Simple and compound interest, equivalent rates, equivalent values, annuities, amortization, sinking funds, bonds, depreciation.

M X03K. Calculus I for Business and Economics.

Differential and integral calculus of algebraic, logarithmic, and exponential functions with applications.

M X03L. Calculus II for Business and Economics.

Differential and integral calculus of functions of several variables with applications, infinite series, improper integrals; introductions to probability, differential equations, matrices, systems of linear equations, and linear programming.

M X05E. Analytic Geometry.

Combines development of methods (including adequate treatment of theory) and acquisition of skills with applications.

M X05G. Preparation for Calculus.

Study of advanced functions and their graphs and applications, including exponential, logarithmic, and trigonometric functions. Introduction to rates, slopes, and derivatives.

M X08C. Differential and Integral Calculus.

Introduction to the theory and applications of differential and integral calculus of functions of one variable; topics include limits, continuity, differentiation, the mean value theorem and its applications, integration, the fundamental theorem of calculus, and transcendental functions.

M X08D. Sequences, Series, and Multivariable Calculus.

This is the second semester of the accelerated calculus sequence. The theory and applications of sequences and infinite series, including those involving functions of one variable, and an introduction to the theory and applications of differential and integral calculus of functions of several variables; subjects include methods of integration, parametric equations, sequences, infinite series, power series, functions of several variables, partial derivatives, and multiple integrals.

M X08K. Differential Calculus.

Introduction to the theory and applications of differential calculus of functions of one variable; topics include limits, continuity, differentiation, and the mean value theorem and its applications.

M X08L. Integral Calculus.

Introduction to the theory and applications of integral calculus of functions of one variable; topics include integration, the fundamental theorem of calculus, transcendental functions, sequences, and infinite series.

M X08M. Multivariable Calculus.

Introduction to the theory and applications of differential and integral calculus of functions of several variables. Includes parametric equations, polar coordinates, vectors, vector calculus, functions of several variables, partial derivatives, gradients, and multiple integrals.

M X08N. Differential Calculus for Science.

Introduction to the theory of differential calculus of functions of one variable, and its application to the natural sciences. Subjects may include limits and differentiation, with applications to rates of change, extremes, graphing, and exponential growth and decay.

M X08Q. Differential and Integral Calculus for Business.

Focus on the key concepts of calculus. These include: using successive approximations to solve problems that cannot be solved directly (Euler's Method), tracking the rate at which quantities are changing (derivatives) using rates of change to find optimal solutions to real-world problems (max/min), computing bulk quantities by adding up the pieces (integration), and understanding functions of several variables by studying one variable at a time. Designed for business students.

M X08R. Differential and Integral Calculus for the Sciences.

A calculus course for students in the life sciences. Emphasizes representations and analysis of data. Subjects include functions, rates, and derivatives and their applications to problems in biology; differential equations; Riemann integrals; the Euler method; and fundamental theorems of calculus.

M X08S. Integral Calculus for Science.

Introduction to the theory of integral calculus of functions of one variable, and its applications to the natural sciences. Subjects may include integration and its application to area and volume, and transcendental functions, sequences, and series and their application to numerical methods.

M X10C. Conference Course.

M X10E. Emerging Scholars Seminar.

Supplemental problem-solving laboratory for precalculus, calculus, or advanced calculus courses for students in the Emerging Scholars Program.

M X10P. Modern Mathematics: Plan II.

Significant developments in modern mathematics. Topics may include fractals, the fourth dimension, statistics and society, and techniques for thinking about quantitative problems.

M X15C. Foundations, Functions, and Regression Models.

In-depth study of topics from secondary school mathematics. Emphasizes the development of the concept of function, exploring function patterns in data sets, and the connections between the main topics of mathematics associated with a secondary school curriculum. Use of appropriate technology is explored.

M X16K. Foundations of Arithmetic.

An analysis, from an advanced perspective, of the concepts and algorithms of arithmetic, including sets; numbers; numeration systems; definitions, properties, and algorithms of arithmetic operations; and percents, ratios, and proportions. Problem solving is stressed.

M X16L. Foundations of Geometry, Statistics, and Probability.

An analysis, from an advanced perspective, of the basic concepts and methods of geometry, statistics, and probability, including representation and analysis of data; discrete probability, random events, and conditional probability; measurement; and geometry as approached through similarity and congruence, through coordinates, and through transformations. Problem solving is stressed.

M X19S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X29S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X75. Conference Course.

Supervised study in mathematics, with hours to be arranged.

M X80D. Algebra.

Continuation of Mathematics 380C.

M X82C. Algebraic Topology.

Surfaces, covering spaces, fundamental group, and homology.

M X82D. Differential Topology.

Continuation of Mathematics 382C. Manifolds and maps, differential forms, transversality, and intersection theory.

Upper-Division Courses

M X19S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X21M. History of Mathematics.

Survey major mathematical developments beginning with the ancient Greeks and tracing those developments through Hindu-Indian mathematics, Arabic mathematics, and European mathematics up to the nineteenth century.

M X25K. Discrete Mathematics.

Provides a transition from the problem-solving approach of Mathematics 408C and 408D to the rigorous approach of advanced courses. Subjects include logic, set theory, relations and functions, combinatorics, and graph theory and graph algorithms.

M X26K. Foundations of Number Systems.

Study of number-related topics in middle-grade and secondary school mathematics. Topics include place value; meanings of arithmetic operations; analysis of computation methods; historical development of number concepts and notation; and rational, irrational, algebraic, transcendental, and complex numbers. Emphasis is on communicating mathematics, developing pedagogical understanding of concepts and notation, and using both informal reasoning and proof.

M X27J. Differential Equations with Linear Algebra.

Ordinary differential equations, introduction to vector spaces, linear operators and eigenvalues, systems of linear differential equations, introduction to partial differential equations and Fourier series.

M X27K. Advanced Calculus for Applications I.

Ordinary and partial differential equations and Fourier series.

M X27L. Advanced Calculus for Applications II.

Matrices, elements of vector analysis and calculus of functions of several variables, including gradient, divergence, and curl of a vector field, multiple integrals and chain rules, length and area, line and surface integrals, Green's theorems in the plane and space, and, if time permits, complex analysis.

M X28K. Introduction to Number Theory.

Provides a transition from the problem-solving approach of Mathematics 408C and 408D to the rigorous approach of advanced courses. Properties of the integers, divisibility, linear and quadratic forms, prime numbers, congruences and residues, quadratic reciprocity, number theoretic functions.

M X29F. Theory of Interest.

Measurement of interest, present and accumulated value, amortization, sinking funds, bonds, duration, and immunization. Covers the interest-theory portion of an exam of the Society of Actuaries and the Casualty Actuarial Society.

M X29S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X29W. Cooperative Mathematics.

This course covers the work period of mathematics students in the Cooperative Education program, which provides supervised work experience by arrangement with the employer and the supervising instructor.

M X33L. Structure of Modern Geometry.

Axiom systems, transformational geometry, introduction to non-Euclidean geometries, and other topics in geometry; use of these ideas in teaching geometry.

M X39C. Actuarial Case Studies.

Introduces aspects of basic ratemaking, reserving, catastrophe modeling, and rate classification in a property & casualty actuarial context. Explores loss & premium trending, loss triangles, loss development, loss ratios, on-level premium, and accident year vs. calendar year vs. policy year data.

M X39D. Introduction to Financial Mathematics for Actuaries.

Covers the financial derivative subjects on the Society of Actuary FM/2 exam: general derivatives, options, hedging, investment strategies, forwards, futures, and swaps. Covers option pricing techniques in the MFE/3F exam: binomial option pricing, Monte Carlo Valuation using risk neutral probabilities, and Black-Scholes.

M X39G. Predictive Analytics.

Designed for students in mathematics and actuarial science. Explore an introduction to predictive modeling that starts with least squares as a foundation and takes a modern approach applicable to classification and prediction in the presence of large datasets.

M X39S. Seminar on Actuarial Practice.

Presentations by working actuaries on current issues in actuarial practice.

M X39U. Actuarial Contingent Payments I.

Intermediate actuarial models for life insurance, property insurance, and annuities.

M X39V. Actuarial Contingent Payments II.

Advanced actuarial models for life insurance, property insurance, and annuities.

M X40L. Matrices and Matrix Calculations.

Techniques of matrix calculations and applications of linear algebra.

M X41. Linear Algebra and Matrix Theory.

Vector spaces, linear transformations, matrices, linear equations, determinants. Some emphasis on rigor and proofs.

M X43K. Introduction to Algebraic Structures.

Elementary properties of groups and rings, including symmetric groups, properties of the integers, polynomial rings, elementary field theory.

M X43L. Applied Number Theory.

Basic properties of integers, including properties of prime numbers, congruences, and primitive roots. Introduction to finite fields and their vector spaces with applications to encryption systems and coding theory.

M X43M. Error-Correcting Codes.

Introduction to applications of algebra and number theory to error-correcting codes, including finite fields, error-correcting codes, vector spaces over finite fields, Hamming norm, coding, and decoding.

M X44K. Intermediate Symbolic Logic.

A second-semester course in symbolic logic: formal syntax and semantics, basic metatheory (soundness, completeness, compactness, and Loewenheim-Skolem theorems), and further topics in logic.

M X46. Applied Linear Algebra.

Emphasis on diagonalization of linear operators and applications to dynamical systems and ordinary differential equations. Other subjects include inner products and orthogonality, normal mode expansions, vibrating strings and the wave equation, and Fourier series.

M X48. Scientific Computation in Numerical Analysis.

Introduction to mathematical properties of numerical methods and their applications in computational science and engineering. Introduction to object-oriented programming in an advanced language. Study and use of numerical methods for solutions of linear systems of equations; nonlinear least-squares data fitting; numerical integration; and solutions of multidimensional nonlinear equations and systems of initial value ordinary differential equations.

M X49R. Applied Regression and Time Series.

Introduction to simple and multiple linear regression and to elementary time-series models, including auto-regressive and moving-average models. Emphasizes fitting models to data, evaluating models, and interpreting results.

M X49S. Actuarial Modeling and Simulation.

Apply Bayesian modeling and Markov-chain Monte Carlo simulations to Actuarial applications. Use R to carry out computations, simulations, and statistical analysis.

M X49T. Time Series and Survival-Model Estimation.

Introduction to the probabilistic and statistical properties of time series; parameter estimation and hypothesis testing for survival models. Covers 30 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society.

M X58K. Applied Statistics.

Exploratory data analysis, correlation and regression, data collection, sampling distributions, confidence intervals, and hypothesis testing.

M X60M. Mathematics as Problem Solving.

Discussion of heuristics, strategies, and methods of evaluating problem solving, and extensive practice in both group and individual problem solving. Communicating mathematics, reasoning, and connections among topics in mathematics are emphasized.

M X61. Theory of Functions of a Complex Variable.

Elementary theory and applications of analytic functions, series, contour integration, and conformal mappings.

M X61K. Introduction to Real Analysis.

A rigorous treatment of the real number system, of real sequences, and of limits, continuity, derivatives, and integrals of real-valued functions of one real variable.

M X62K. Probability I.

An introduction to the mathematical theory of probability, fundamental to further work in probability and statistics, includes basic probability properties, conditional probability and independence, various discrete and continuous random variables, expectation and variance, central limit theorem, and joint probability distributions.

M X62M. Introduction to Stochastic Processes.

Introduction to Markov chains, birth and death processes, and other topics.

M X64K. Vector and Tensor Analysis I.

Invariance, vector algebra and calculus, integral theorems, general coordinates, introductory differential geometry and tensor analysis, applications.

M X64L. Vector and Tensor Analysis II.

Continuation of Mathematics 364K, with emphasis on tensor and extensor analysis. Riemannian geometry and invariance.

M X65C. Real Analysis I.

A rigorous treatment of the real number system, Euclidean spaces, metric spaces, continuity of functions in metric spaces, differentiation and Riemann integration of real-valued functions of one real variable, and uniform convergence of sequences and series of functions.

M X65D. Real Analysis II.

A rigorous treatment of selected topics in real analysis, such as Lebesgue integration, or multivariate integration and differential forms.

M X65G. Curves and Surfaces.

Calculus applied to curves and surfaces in three dimensions: curvature and torsion of space curves, Gauss map and curvature of surfaces, Gauss theorem, geodesics, and the Gauss-Bonnet theorem.

M X67K. Topology I.

An introduction to topology, including sets, functions, cardinal numbers, and the topology of metric spaces.

M X67L. Topology II.

Various topics in topology, primarily of a geometric nature.

M X68K. Numerical Methods for Applications.

Continuation of Mathematics 348. Topics include splines, orthogonal polynomials and smoothing of data, iterative solution of systems of linear equations, approximation of eigenvalues, two-point-boundary value problems, numerical approximation of partial differential equations, signal processing, optimization, and Monte Carlo methods.

M X71E. Learning Assistant Experience in Mathematics.

Students assist instructors and TAs in mathematics courses. This is a hands-on experience in what it is like to teach and support students in the learning of mathematics in undergraduate courses. Students must attend classroom training and discussions and work in Calculus discussion sections or undergraduate classrooms where mathematics is being taught.

M X72. Fourier Series and Boundary Value Problems.

Discussion of differential equations of mathematical physics and representation of solutions by Green's functions and eigenfunction expansions.

M X72K. Partial Differential Equations and Applications.

Partial differential equations as basic models of flows, diffusion, dispersion, and vibrations. Topics include first- and second-order partial differential equations and classification (particularly the wave, diffusion, and potential equations), and their origins in applications and properties of solutions. Includes the study of characteristics, maximum principles, Green's functions, eigenvalue problems, and Fourier expansion methods.

M X73K. Algebraic Structures I.

A study of groups, rings, and fields, including structure theory of finite groups, isomorphism theorems, polynomial rings, and principal ideal domains.

M X73L. Algebraic Structures II.

Topics from vector spaces and modules, including direct sum decompositions, dual spaces, canonical forms, and multilinear algebra.

M X74. Fourier and Laplace Transforms.

Operational properties and application of Laplace transforms; some properties of Fourier transforms.

M X74G. Linear Regression Analysis.

Fitting of linear models to data by the method of least squares, choosing best subsets of predictors, and related materials.

M X74K. Fourier and Laplace Transforms.

Continuation of Mathematics 374. Introduction to other integral transforms, such as Hankel, Laguerre, Mellin, Z.

M X74M. Mathematical Modeling in Science and Engineering.

Tools for studying differential equations and optimization problems that arise in the engineering and physical sciences. Includes dimensional analysis and scaling, regular and singular perturbation methods, optimization and calculus of variations, and stability.

M X75. Conference Course.

Supervised study in mathematics, with hours to be arranged.

M X75C. Topics in Conference Course: Computer-Assisted.

Supervised study in mathematics on material requiring use of computing resources, with hours to be arranged.

M X75D. Discovery: An Introduction to Advanced Study in Mathematics.

Capstone course designed primarily for UTeach pre-service mathematics majors considering discovery teaching methodology and/or graduate work in mathematics or mathematics education. Ties together foundational topics in the primary strands of mathematics present in a typical graduate mathematics program; included are selected topics from analysis, algebra, number theory, and topology.

M X75S. Seminar in Instruction of Mathematics.

An exploration of subjects in mathematics instruction as taught at the secondary educational level. Practice learning and teaching through use of proofs, explorations, and connections. Subjects include foundational mathematics concepts, numbers, constructibility, and development of key mathematics topics.

M X75T. Topics in Mathematics.

M X76C. Topics in Methods of Applied Mathematics.

Variational methods and related concepts from classical and modern applied mathematics. Models of conduction and vibration that lead to systems of linear equations and ordinary differential equations, eigenvalue problems, initial and boundary value problems for partial differential equations. Topics may include a selection from diagonalization of matrices, eigenfunctions and minimization, asymptotics of eigenvalues, separation of variables, generalized solutions, and approximation methods.

M X78K. Introduction to Mathematical Statistics.

Sampling distributions of statistics, estimation of parameters (confidence intervals, method of moments, maximum likelihood, comparison of estimators using mean square error and efficiency, sufficient statistics), hypothesis tests (p-values, power, likelihood ratio tests), and other topics.

M X78N. Generalized Linear Models.

Extensions to ordinary least-squares regression, including Poisson regression, the lasso, mixed models, and ridge regression.

M X78P. Decision Analytics.

Examine decision theory with utility functions, including the use of probability, optimization, constrained optimization, and linear algebra.

M X79H. Honors Tutorial Course.

Directed reading, research, and/or projects, under the supervision of a faculty member, leading to an honors thesis.

M X80D. Algebra.

Continuation of Mathematics 380C.

M X82C. Algebraic Topology.

Surfaces, covering spaces, fundamental group, and homology.

M X82D. Differential Topology.

Continuation of Mathematics 382C. Manifolds and maps, differential forms, transversality, and intersection theory.

Graduate Courses

M X19S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X29S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X75. Conference Course.

Supervised study in mathematics, with hours to be arranged.

M X80C. Algebra.

A survey of algebraic structures, including groups, fields, rings, and modules.

M X80D. Algebra.

Continuation of Mathematics 380C.

M X81C. Real Analysis.

Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line.

M X81D. Complex Analysis.

Introduction to complex analysis.

M X81E. Functional Analysis.

Introduction to functional analysis.

M X82C. Algebraic Topology.

Surfaces, covering spaces, fundamental group, and homology.

M X82D. Differential Topology.

Continuation of Mathematics 382C. Manifolds and maps, differential forms, transversality, and intersection theory.

M X82E. Advanced Algebraic Topology.

Continuation of Mathematics 382C.

M X82F. Algebraic Topology.

Continuation of Mathematics 382E.

M X82G. Differential Geometry.

Continuation of Mathematics 382D.

M X83C. Methods of Applied Mathematics.

Topics include basic normed linear space theory; fixed-point theorems and applications to differential and integral equations; Hilbert spaces and the spectral theorem; applications to Sturm-Liouville problems; approximation and computational methods such as the Galerkin, Rayleigh-Ritz, and Newton procedures.

M X83D. Methods of Applied Mathematics.

Topics include distributions, fundamental solutions of partial differential equations, the Schwartz space and tempered distributions, Fourier transform, Plancherel theorem, Green's functions, Sobolev spaces, weak solutions, differential calculus in normed spaces, implicit function theorems, applications to nonlinear equations, smooth variational problems, applications to classical mechanics, constrained variational problems.

M X83E. Numerical Analysis: Linear Algebra.

Survey of numerical methods in linear algebra: floating-point computation, solution of linear equations, least squares problems, algebraic eigenvalue problems.

M X83F. Numerical Analysis: Interpolation, Approximation, Quadrature, and Differential Equations.

Survey of numerical methods for interpolation, functional approximation, integration, and solution of differential equations.

M X84C. Mathematical Statistics I.

The general theory of mathematical statistics. Includes distributions of functions of random variables, properties of a random sample, principles of data reduction, an overview of hierarchical models, decision theory, Bayesian statistics, and theoretical results relevant to point estimation, interval estimation, and hypothesis testing.

M X84D. Mathematical Statistics II.

Continuation of Computational Science, Engineering, and Mathematics 384R and Mathematics 384C.

M X84E. Design and Analysis of Experiments.

Design and analysis of experiments, including one-way and two-way layouts; components of variance; factorial experiments; balanced incomplete block designs; crossed and nested classifications; fixed, random, and mixed models; and split plot designs.

M X84F. Design of Experiments.

Design of experiments, including 2n and 3n factorial experiments, confounding, fractional factorials, sequential experimentation, orthogonal arrays, D-optimal experiments, and response surface methodology.

M X84G. Regression Analysis.

Simple and multiple linear regression, inference in regression, prediction of new observations, diagnosis and remedial measures, transformations, and model building. Emphasis on both understanding the theory and applying theory to analyze data.

M X84H. Multivariate Statistical Analysis.

Introduction to the general multivariate linear model; a selection of techniques, such as principle component, factor, and discriminant analysis.

M X85C. Theory of Probability.

M X85D. Theory of Probability.

Continuation of Computational Science, Engineering, and Mathematics 384K and Mathematics 385C.

M X87C. Numerical Analysis: Algebra and Approximation.

Advanced introduction to scientific computing, theory and application of numerical linear algebra, solution of nonlinear equations, and numerical approximation of functions.

M X87D. Numerical Analysis: Differential Equations.

Advanced introduction to the theory and practice of commonly used numerical algorithms for the solution of ordinary differential equations, and elliptic, parabolic, and hyperbolic partial differential equations.

M X89C. Actuarial Case Studies.

Explores aspects of basic ratemaking, reserving, catastrophe modeling, and rate classification in a property & casualty actuarial context. Covers loss & premium trending, loss triangles, loss development, loss ratios, on-level premium, accident year vs. calendar year vs. policy year data.

M X89D. Introduction to Financial Mathematics for Actuaries.

Covers the financial derivative topics on the Society of Actuary FM/2 exam: general derivatives, options, hedging, investment strategies, forwards, futures, and swaps. Covers option pricing techniques in the MFE/3F exam: binomial option pricing, Monte Carlo Valuation using risk neutral probabilities, and Black-Scholes.

M X89F. Theory of Interest.

Measurement of interest, present and accumulated value, amortization, sinking funds, bonds, duration, and immunization. Covers the interest theory portion of an exam of the Society of Actuaries and the Casualty Actuarial Society.

M X89G. Predictive Analytics.

Designed for students in mathematics and actuarial science. Explore an introduction to predictive modeling that starts with least squares as a foundation and takes a modern approach applicable to classification and prediction in the presence of large datasets.

M X89J. Probability Models with Actuarial Applications.

Introductory actuarial models for life insurance, property insurance, and annuities. With Mathematics 389P, covers the syllabus for the professional actuarial exam on model construction.

M X89P. Actuarial Statistical Estimates.

Statistical estimation procedures for random variables and related quantities in actuarial models. With Mathematics 389J, covers the syllabus for the professional actuarial exam on model construction.

M X89S. Seminar on Actuarial Practice.

Presentations by working actuaries on current issues in actuarial practice.

M X89T. Time Series and Survival-Model Estimation.

Introduction to the probabilistic and statistical properties of time series; parameter estimation and hypothesis testing for survival models. Covers 30 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society.

M X89U. Actuarial Contingent Payments I.

Intermediate actuarial models for life insurance, property insurance, and annuities.

M X89V. Actuarial Contingent Payments II.

Advanced actuarial models for life insurance, property insurance, and annuities.

M X89W. Financial Mathematics for Actuarial Applications.

Subjects include pricing, stock price, and interest rate models for actuarial applications. Tools include lognormal distribution, Brownian motion, Black-Scholes, and delta hedging.

M X90C. Topics in Algebra.

Recent topics have included algebraic geometry, number theory, algebraic curves, algebraic number theory, algebraic functions, rational curves on varieties, homological algebra.

M X91C. Topics in Analysis.

Recent topics have included measure and integration, real variables, complex analysis, functional analysis, ordinary differential equations, partial differential equations, integral transforms, operator theory, approximation theory, abstract harmonic analysis.

M X92C. Topics in Topology.

Recent topics have included algebraic topology, differential topology, geometric topology, Lie groups.

M X93C. Topics in Applied Mathematics.

Recent topics have included quantum mechanics, statistical physics, ergodic theory, group representations, statistical mechanics, quantum field theory, introductory partial differential equations, monotone operators and partial differential equations, Hilbert space methods for partial differential equations, Hamiltonian dynamics, nonlinear functional analysis, Euler and Navier-Stokes equations, microlocal calculus and spectral asymptotics, calculus of variations.

M X93C.1. Neural Dynamics, Information Theory, and Machine Learning.

M X93N. Numerical Solution of Elliptic Partial Differential Equations.

The numerical solution of large systems of linear algebraic equations arising in the solution of elliptic partial differential equations by discretization methods.

M X94C. Topics in Probability and Statistics.

Recent topics have included nonparametric statistics, advanced probability.

M X95C. Topics in Logic and Foundations.

Recent topics have included set theory, model theory, proof theory, axiomatic theorem proving, automatic theorem proving, foundations of mathematics, recursion theory.

M X96C. Topics in Mathematics.

Recent topics have included set theory, history of mathematics.

M X96D. Conference Course.

Supervised study in mathematics.

M X97C. Topics in Numerical Analysis.

Recent developments and advanced topics in the field of numerical analysis.

M X97S. Topics in Mathematics: Seminar.

M X98. Thesis.

M X98R. Master's Report.

Preparation of a report to fulfill the requirement for the master's degree under the report option.

M X98T. Supervised Teaching in Mathematics.

M X99W. Dissertation.

Professional Courses

M X19S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X29S. Topics in Mathematics.

This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.

M X75. Conference Course.

Supervised study in mathematics, with hours to be arranged.

M X80D. Algebra.

Continuation of Mathematics 380C.

M X82C. Algebraic Topology.

Surfaces, covering spaces, fundamental group, and homology.

M X82D. Differential Topology.

Continuation of Mathematics 382C. Manifolds and maps, differential forms, transversality, and intersection theory.