Example:

15  MATH  252 H

Honors Calculus II

Elementary Probability and Statistics

15 MATH 147, 148, 149

Topics in Mathematics

15 MATH 155, 156, 157

Applied Calculus

15 MATH 224, 226, 227

Finite Math & Applied Calculus

15 MATH 225, 226, 227

Calculus I, II

15 MATH 251, 252

STATISTICS FOR THE HEALTH SCIENCES

15 STAT 146

3 UG CR

Prerequisite:

Two years of high school algebra. MPT score of 420 or above recommended.

Text:

Knapp, R.G., Basic Statistics for Nurses, 2e

Statistical models and inference applied to problems in the health sciences, with emphasis on the role that statistics plays in medical research. Primarily for students in the College of Nursing and Health.

ELEMENTARY PROBABILITY AND STATISTICS I, II, III

15 STAT 147, 148, 149

3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics requirement.)

Prerequisite:

Knowledge of high school algebra. Score of 420 or above on the Math Placement Test recommended.

Text:

Moore, McCabe, and Craig, Introduction to the Practice of Statistics, 6e

15 STAT 147

DATA: Distributions and graphs, summarizing data, normal distribution, scatterplots, categorical data, designing samples and experiments.  

15 STAT 148

PROBABILITY AND INFERENCE: Sampling distributions, probability, sample proportions and means, binomial distribution, confidence intervals, inference introduction.

15 STAT 149

TOPICS IN INFERENCE:  Inference for means and proportions, inference for two-way tables, one-way analysis of variance (ANOVA), inference for regression.

MATH FOR EARLY CHILDHOOD EDUCATION I, II, III, IV

15 MATH 151, 152, 153, 154

3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics requirement.)

Prerequisite:

Text:

Long & DeTemple, Mathematical Reasoning for Elementary Teachers, 5e

15 MATH 151

Problem-solving principles and strategies, number systems, operations estimations, fractions, decimals, and percents.

15 MATH 152

Algebraic expressions, graphing points and lines, geometry of shape (congruence, similarity), and measurement.

15 MATH 153

Topics from statistics to probability.

15 MATH 154

Geometric transformations in the plane, including rigid motions and dilations/contractions, reflection and rotational symmetries, tilings, tessellations, grid design, and distortions.

TOPICS IN MATHEMATICS I, II, III

15 MATH 155, 156, 157

3 UG CR ea. qtr. (May be used for the 9-credit A&S mathematics requirement.)

Prerequisite:

Two years of high school algebra and plane geometry or the equivalent. Score of 420 or above on Math Placement Test recommended. Courses may be taken in any order.

Text:

Tannenbaum, Excursions in Modern Mathematics (custom), 7e

15 MATH 155

Management Science:  Euler circuits, Hamiltonian circuits, traveling salesman problems, minimum-cost spanning trees, critical path analysis, scheduling tasks, bin packing, mixture problems, linear programming.

15 MATH 156

Collecting and describing data; probability; statistical inference.

15 MATH 157

Voting systems, fair division, and apportionment.

COLLEGE ALGEBRA I, II

15 MATH 173,174

3 UG CR ea. qtr. (Cannot be used for the 9-credit A&S mathematics requirement. This sequence is intended for students who need preparation for a college-level calculus course.)

Prerequisite:

42-Math-101 (Elementary Algebra III) or score of 430 or higher on the Math Placement Test.

Text:

Swokowski, College Algebra I & II (custom),  12e

15 MATH 173

Review of basic algebra. Graphing, quadratic equations, linear and nonlinear inequalities, modeling, functions.  Pre-req: Score of 430 or above on Math Placement Test. 

15 MATH 174

Inverse functions; polynomial, rational, exponential, and logarithmic functions, systems of linear equations, systems of inequalities. Pre-req: 15 Math 173 or a score of 500 or above on the Math Placement Test.

TRIGONOMETRY

15 MATH 181

3 UG CR (Cannot be used for the 9-credit A&S mathematics requirement. This course is intended for students who preparing for the 5-credit hour calculus sequence.)

Prerequisite:

15 MATH 174 or score of 530 or above on Math Placement Test.

Text:

Swokowski, Trigonometry (custom),  12e

Right triangle trigonometry, laws of sines and cosines, trigonometric functions and graphs, trigonometric identities, vectors, conic sections, polar coordinates.

COOPERATIVE LEARNING IN CALCULUS  0, I, II, III, IV

15 MATH 200, 201, 202, 203, 204

1 UG CR ea. qtr

Co-requisite:

Registration in corresponding Calculus class

Text:

BOOK NOT REQUIRED (Text based on book from Calculus 0, I, II, III, and IV.)

15 MATH 200

Guided group work to complement the Calculus 0 (15 Math 250) curriculum.

15 MATH 201

Guided group work to complement the Calculus I (15 Math 251) curriculum.

15 MATH 202

Guided group work to complement the Calculus II (15 Math 252) curriculum.

15 MATH 203

Guided group work to complement the Calculus III (15 Math 253) curriculum.

15 MATH 204

Guided group work to complement the Calculus IV (15 Math 264) curriculum.

FOUNDATIONS OF APPLIED CALCULUS, FINITE MATH, APPLIED CALCULUS I, II

15 MATH 224, 225, 226, 227

3 UG CR ea. qtr. Either 224, 226, 227 or  225, 226, 227 can be used for the 9-credit A&S mathematics requirement.

15 MATH 224

Foundations of Applied Calculus. Review of algebraic skills needed for calculus, including exponents, radicals, linear equations and inequalities, linear systems and exponential and logarithm functions.

Prerequisite:

A score of 470 or better on the Math Placement Test.

Text:

Connally, Hughes-Hallet, Gleason, et al.  Functions Modeling Change, 3e (custom edition for the University of Cincinnati)

15 MATH 225

Finite Mathematics. Linear models, systems of linear equations and matrices, matrix algebra and applications, linear programming, non-linear models.

Prerequisite:

15 Math 174. Score of 530 or better on the Math Placement Test.

Text:

 Sullivan & Mizrahi, Finite Mathematics: An Applied Approach, 10e

15 MATH 226

Applied Calculus I. Functions, graphs, limits, continuity, differentiation, curve sketching, optimization. Properties of exponential and logarithmic functions.

Prerequisite:

15 Math 224, 15 Math 174, or score of 575 or better on the Math Placement Test.

15 MATH 227

Applied Calculus II. Antidifferentiation, the definite integral, area, probability, functions of two variables, partial derivatives, maxima and minima, Lagrange multipliers.

Prerequisite:

15 Math 226.

Text:

Hughes-Hallet/Gleason/Lock/Flath/et al. Applied Calculus, 3e

HONORS FINITE MATHEMATICS & CALCULUS I, II, III

15 MATH 225H, 226H, 227H

3 UG CR ea. qtr. May be used for the 9-credit A&S mathematics requirement.

Prerequisite:

University Honors scholars and students in Honors Plus Program.

15 MATH 225H

Topics from Finite Math, such as solving systems of linear equations, matrices, linear programming.

Text:

Sullivan & Mizrahi, Finite Mathematics: An Applied Approach, 10e

15 MATH 226H

Honors version of 15 MATH 226.

15 MATH 227H

Honors version of 15 MATH 227.

Text:

Hughes-Hallet/Gleason/Lock/Flath/et al. Applied Calculus, 3e

CALCULUS 0

15 MATH 250

5 UG CR

Prerequisite:

A score of 550 or better on the Math Placement Test.

Text:

Faires, Pre-Calculus, 4e

For students who need more preparation before entering 15 Math 251.

CALCULUS I, II, III

15 MATH 251, 252, 253

Math 251, 5 UG CR ea. qtr. Math 252 & 253, 4 UG CR ea. qtr.
15 MATH 251, 252 may be used to satisfy the A&S mathematics requirement.

Prerequisite:

Calculus 251. A score of 670 or better on the Math Placement Test OR a C- or better in 15 MATH 250. A passing grade in the previous-numbered Calculus course is required to take the next sequential Calculus course.

15 MATH 251

Functions, limits and continuity, derivatives, applications of the derivative, antiderivatives. Aut., Win., Spr. Qtrs.  (5 CR) 

Text:

Rogawski, Calculus: Early Transcendentals

15 MATH 252

The integral, inverse functions, techniques of integration, applications of the integral.

15 MATH 253

Sequences and series, vectors, lines and planes, vector-valued functions. 

Text:

Stewart, Calculus: Concepts and Contexts, 3e

HONORS CALCULUS I, II, III

15 MATH 251H, 252H, 253H

Math 251, 5 UG CR ea. qtr. Math 252 & 253, 4 UG CR ea. qtr.

Prerequisite:

University Honors scholars with placement score of 860 or better on the Math Placement Test or advanced placement. A passing grade in the previous-numbered Calculus course is required to take the next sequential Calculus course. 

15 MATH 251H

Honors version of 15 MATH 251.

Text:

Rogawski, Calculus: Early Transcendentals

15 MATH 252H

Honors version of 15 MATH 252.

15 MATH 253H

Honors version of 15 MATH 253.

Text:

Stewart, Calculus: Concepts and Contexts, 3e

CALCULUS II, III LABS

15 MATH 256, 257

1 UG CR ea. qtr

15 MATH 256

Calc II Lab to accompany Calculus II (Co-requisite: Calculus 252.)

Text:

Hollis, Calc Lab with Mathematica – Single Variable, 6e

15 MATH 257

Calc III Lab to accompany Calculus III (Co-requisite: Calculus 253.) 

Text:

Hollis, Calc Lab with Mathematica – Multi-Variable, 6e

CALCULUS IV

15 MATH 264

5 UG CR ea. qtr

Prerequisite:

Calculus III (15 MATH 253).

Text:

Stewart, Calculus: Concepts and Contexts, 3e

Partial derivatives, multiple integrals, calculus of vector fields.

HONORS CALCULUS IV

15 MATH 264H

5 UG CR ea. qtr

Prerequisite:

Calculus III (15 MATH 253) and Honors Scholars status.

Honors version of 15 Math 264.  

DIFFERENTIAL EQUATIONS

15 MATH 273

5 UG CR

Prerequisite:

Calculus III (15 MATH 253).

Text:

Boyce & DiPrima, Elementary Differential Equations with Boundary Value Problems, 9e

First-order linear differential equations, first-order separable differential equations, first-order homogeneous differential equations, exact differential equations, linear dependence for solutions of a second-order linear homogeneous differential equation, Wronskians, second-order linear homogeneous differential equations with constant coefficients, method of undetermined coefficients, method of variation of parameters, series expansions of solutions of second-order linear differential equations at ordinary points, Euler equations, introduction to regular singular points, higher-order linear differential equations, higher-order linear homogeneous differential equations with constant coefficients, the method of undetermined coefficients, Laplace transform.

MATRIX METHODS

15 MATH 276

3 UG CR Credits may not be applied toward a degree in mathematics

Prerequisite:

Calculus III (15 MATH 253).

Text:

Bronson, Matrix Methods, 3e

Matrices, systems of linear equations, Gaussian elimination, determinants, computation of inverses, eigenvalues and eigenvectors, coordinate transformations, systems of differential equations, applications to mechanical systems and electrical circuits.

MATHEMATICS FOR MIDDLE SCHOOL TEACHERS I, II, III

15 MATH 307, 308, 309

4 UG CR

Prerequisite:

Applied Calculus II (15 MATH 227) with at least C-.

15 MATH 307

 Inquiry-based, integrated approach to middle school content areas of arithmetic (number systems, proportional reasoning, fractions, place value), geometry (shapes, measurement, transformations), algebra (with connections to arithmetic and geometry, as well as real-world problem-solving), functions and graphs, and discrete mathematics. Emphasis on developing mathematical understanding needed to teach these concepts effectively.

Text:

Lamon, Teaching Fractions and Ratios for Understanding, 2e
Bunt, Historical Roots of Elementary Mathematics (1988)

Prerequisite:

Mathematics for Middle School Teachers I (15 MATH 307) with at least C-.

Text:

Stump, Roebuck, and Bishop, Alegbra for Elementary and Middle School Teachers (custom), 2e
Driscoll, Fostering Algebraic Thinking: A Guide for Teachers, Grades 6 - 10, 1e (1999)

15 MATH 309

 4 UG CR

Prerequisite:

Mathematics for Middle School Teachers II (15 MATH 308) with at least C-.

Text:

Beem, Geometry Connections (2005)

LINEAR ALGEBRA I, II

15 MATH 351, 352

3 UG CR ea. qtr.

Prerequisite:

Calculus III (15 MATH 253)

Text:

Wright, Introduction to Linear Algebra (custom), 1e

15 MATH 351

Linear equations, matrices, Euclidean n-space and its subspaces, bases, dimension, coordinates.  

15 MATH 352

Orthogonality, linear transformations, determinants, eigenvalues and eigenvectors, diagonalization.   

INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS

15 MATH 355

3 UG CR

Prerequisite:

Calculus IV (15 MATH 264) and Linear Algebra II (15 MATH 352).

Text:

Braun, Differential Equations and Their Applications, 4e

First order differential equations. Linear differential equations of higher order. Differential operators and systems of linear differential equations.  

INTRODUCTION TO ABSTRACT MATHEMATICS

15 MATH 357

3 UG CR

Prerequisite:

Linear Algebra II (15 MATH 352).

Text:

Smith, et al, A Transition to Advanced Mathematics, 6e

Logic, proofs, set theory, relations, functions, and cardinality.

PROBABILITY AND STATISTICS I, II, III

15 STAT 361, 362, 363

3 UG CR ea. qtr.

Prerequisite:

Calculus III (15 MATH 253)

Text:

Walpole & Myers, Probability and Statistics for Engineers and Scientists, 8e

15 STAT 361

Sample statistics. Probability, sample spaces, counting rules conditional probability. Discrete and continuous random variables, their distributions and expected values, Binomial, Poisson, hypergeometric, normal and gamma distributions. Covariance, correlation. Sampling distributions of means and sums.

15 STAT 362

Point estimation, confidence intervals for means, proportions, variances and differences of means and proportions. Hypothesis testing. Chi-square tests. Simple linear regression. Model building. SAS software  package may be used.    

15 STAT 363

More linear regression, multiple linear regression, analysis of variance, experimental design, reliability, and quality control. SAS software package may be used.   

ENGINEERING STATISTICS

15 STAT 366

3 UG CR Credits may not be applied toward a degree in mathematics.

Prerequisite:

Calculus III (15 MATH 253)

Text:

Montgomery, Runger, & Hubele, Engineering Statistics, 4e

Descriptive statistics, probability, binomial, Poisson, and normal distributions. Confidence intervals, and hypothesis testing, regression analysis.

APPLIED BOUNDARY VALUE PROBLEMS

15 MATH 377

3 UG CR Credits may not be applied toward a degree in mathematics.

Prerequisite:

Calculus IV (15 MATH 264) and Differential Equations (15 MATH 273).

Text:

Haberman, Elementary Applied Partial Differential Equations, 4e

Fourier series, partial differential equations, boundary value problems, and engineering applications.

INTRODUCTION TO ALGEBRA

15 MATH 401, 402

3 UG CR ea. qtr.

Prerequisite:

Introduction to Abstract Mathematics (15 MATH 357).

Text:

Hungerford, Abstract Algebra: An Introduction, 2e

15 MATH 401

Prime numbers, integer factorization, modular arithmetic, rings, homomorphisms, factorization of polynomials.

15 MATH 402

Introduction to the theory of groups.

HISTORY OF MATHEMATICS

15 MATH 404

3 UG CR

Prerequisite:

Introduction to Geometry I (15 MATH 406).

Text:

Dunham, Journey Through Genius, (1991)

A survey of the history of mathematics from ancient times through the invention of the calculus. Egyptian and Babylonian computational systems, Pythagoreanism, Euclid, the work of Archimedes, Hindu-Arabic numeration and algebra, the algebra of the Renaissance, Galileo’s mathematization of nature, the geometry of Descartes and Fernat, the calculus of Newton and Leibniz.   

INTRODUCTION TO GEOMETRIES I, II

15 MATH 406, 407

15 MATH 406

Text:

No Book Needed at this time

15 MATH 406

An axiomatic treatment of synthetic geometry is given, beginning with a development of neutral geometry. Neutral geometry is geometry without the Parallel Postulate, so the theorems of neutral geometry are valid in both hyperbolic and Euclidean geometry. The formal development of Euclidean geometry begins with the addition of the Parallel Postulate. The main tools in Euclidean geometry are congruence and similarity of figures; triangles, quadrilaterals, and circles are studied in detail.

15 MATH 407

Prerequisite:

Intro to Geometry I (15 MATH 406)

Text:

No Book Needed at this time

15 MATH 407

Vector methods provide and alternate context for developing geometry. The vector algebraic approach brings together linear algebra, geometry, and trigonometry. Affine geometry is studied in the context of vector spaces, the inner product is added to the vector space axioms for the study of Euclidean geometry. Transformations give a third method to treat geometry and illustrate connections between geometry, linear algebra, and abstract algebra. Affine transformations are used to investigate affine geometry. Isometries and similarities are used for the study of Euclidean geometry. Symmetry is considered in terms of the group of rigid motions that leave invariant a geometric figure. Transformation groups and symmetry groups provide connections with abstract algebra.

INTRODUCTION TO ANALYSIS I, II

15 MATH 408, 409

15 MATH 408

3 UG CR

Prerequisite:

Introduction to Abstract Math (15 MATH 357)

Text:

Wright, duplicated notes (see http://math.uc.edu/408)

15 MATH 408

The Real and Rational Number Systems: algebraic, order and completeness properties; Sequences: boundedness, monotonicity, convergence; Limits of Real-valued Functions; Continuous Functions: local and global properties, Intermediate Value Theorem.

15 MATH 409

3 UG CR

Prerequisite:

Introduction to Analysis I (15 MATH 408)

Text:

Wright, duplicated notes (see http://math.uc.edu/409)

15 MATH 409

The Derivative: differentiation of algebraic and basic transcendental functions, Mean Value Theorem, applications of the derivative to analyze monotonicity, convexity, and local extrema, Taylor’s Theorem; The Riemann Integral: algebraic properties, Fundamental Theorem of Calculus. Infinite Series: convergence tests, absolute and conditional convergence, power series.

DISCRETE MATH & ITS APPLICATIONS

15 MATH 410

3 UG CR Credits may not be applied toward a degree in mathematics.

Prerequisite:

Calculus III (15 MATH 253) and Probability & Stats I (15 MATH 361)

Text:

Rosen, Discrete Math & Its Applications, 6e

Logic, proofs, induction, relations, graphs, and trees.

UNDERGRADUATE INTERNSHIP IN MATHEMATICAL SCIENCES

15 MATH 498

1-6 UG CR

Prerequisite:

Completion of both Introduction to Ordinary Differential Equations (15 MATH 355) and Introduction to Abstract Mathematics (15 MATH 357) and at least a 3.0 math GPA.

Text:

NO BOOK NEEDED

Practical work-related experience in a supervised internship where job responsibilities involve statistical or mathematical reasoning or computation.For math majors or math as a second major.  Must be coordinated with a mathematical sciences faculty member and approved by the Undergraduate Program Director. Credit to be awarded varies and depends on work experience. Credit does not count toward the 61 necessary for the major/second major.

SENIOR CAPSTONE EXPERIENCE IN MATHEMATICAL SCIENCES

15 MATH 501

1 UG CR

Prerequisite:

Senior standing in mathematics.

Text:

NO BOOK NEEDED

For math majors/second majors to get credit for the completion of their (required) senior capstone project or capstone course work. The actual capstone experience is individually selected by students with approval of the Undergraduate Program Director.

ADVANCED CALCULUS I, II, III

15 MATH 504, 505, 506

3 UG or GR CR ea. qtr.

Prerequisite:

Calculus IV (15 MATH 264), Introduction to Ordinary Differential Equations (15 MATH 355), and Introduction to Abstract Mathematics (15 MATH 357).

Text:

Rosenlicht, Introduction to Analysis, (1986)

15 MATH 504

Ordered sets, the real field, the complex field, Euclidean space, finite, countable and uncountable sets, metric spaces, compact sets, convergent sequences of numbers, Cauchy sequences, upper and lower limits, Bolzano-Weierstrass theorem, series, the number e, convergence tests for series, absolute convergence, addition and multiplication of series, rearrangements.                 

15 MATH 505

Limits and continuity of functions, continuity and compactness, connectedness and continuity, discontinuities, monotone functions, derivatives, the Mean Value theorem, l'Hopital's rule, higher order derivatives, Taylor's theorem, Riemann-Stieltjes integral, integration and differentiation of vector-valued functions, rectifiable curves.

15 MATH 506

Uniform convergence for sequences and series of functions, equi-continuous families of functions, the Stone-Weierstrass theorem, functions of several variables.

ABSTRACT ALGEBRA I, II, III

15 MATH 511, 512,  513

3 UG or GR CR ea. qtr.

Prerequisite:

Linear Algebra II (15 MATH 352), Introduction to Abstract Mathematics (15 MATH 357). Sequence may be started with either 511 or 512 (i.e. 511 is not a prerequisite for 512; however, 512 is a prerequisite for 513).

Text:

Lang, Linear Algebra (Undergraduate Texts in Mathematics) , 3e (Book used in 15 MATH 511 only)

15 MATH 511

Advanced Linear Algebra:  Abstract vector spaces, determinants, eigenvalues and eigenvectors, algebra of linear transformations, canonical forms including triangular, Jordan and rational forms.
             

Text:

Artin, Algebra (1991)

15 MATH 512

Definition and basic properties of groups, subgroups, permutation groups, direct products, isomorphisms, homomorphisms, normal subgroups and factor groups.

Text:

Artin, Algebra (1991)

15 MATH 513

Selected topics in number theory. Binary relations and binary operations. Definitions and basic properties of rings and fields, integral domain, quotient fields, quotient rings and ideals, factorization of polynomials over fields, unique factorization domains, Euclidean domains, Gaussian integers, extension fields, algebraic extensions, geometric constructions, finite fields.

NUMERICAL ANALYSIS I, II, III

15 MATH 514, 515, 516

3 UG or GR CR ea. qtr.

Prerequisite:

Calculus IV (15 MATH 264); Differential Equations (15 MATH 273) or Introduction to Ordinary Differential Equations (15 MATH 355); Matrix Methods (15 MATH 276) or Linear Algebra II (15 MATH 352); a working knowledge of some programming language.

Text:

Atkinson, An Introduction to Numerical Analysis, 2e

15 MATH 514

Chapters 1, 4, 5. Introduction to a floating point arithmetic, roundoff error, error propagation.Solution of non-linear equations by bisection, secant, regula-falsi, and Newton methods with emphasis on error analysis and utility of computations. Polynomial interpolation, error bounds and the Runge phenomenon. Cubic spline interpolation and extremal properties. Orthogonal polynomials and least squares approximation.Computer applications.
          

15 MATH 515

Chapters 2, 4. Gauss elimination, pivoting strategies. Error analysis and vector norms. Iterative methods for linear systems including Jacobi and Gauss-Seidel methods. Eigenvalue-eigenvector computations by power, inverse power, and Rayleigh quotient  methods. Householder transformations, Hessenberg matrices and the Q-R method. The singular value decomposition and least squares problems. Computer applications.

15 MATH 516

Chapters 6, 7, 8. Numerical differentiation. Newton-Cotes and Gaussian quadrature, Romberg integration, FFT, Adaptive quadrature. Numerical methods for initial value ordinary differential equations including methods of Runge-Kutta type and predictor-corrector methods. Stability, consistency, and convergence are analyzed. Finite difference methods for two-point boundary value problems. Decent methods for optimization problems. Computer applications.

APPLIED MATHEMATICS PRACTICUM     

15 MATH 517, 518, 519

3 UG or GR CR ea. qtr.

Prerequisite:

Calculus IV (15 MATH 264), Differential Equations (15 MATH 273), and computer programming experience.

Text:

TBA

15 MATH 517

Techniques in applied mathematics; ordinary and partial differential equations, numerical methods, perturbation techniques, modeling. Under the guidance of the instructor, teams of students solve problems from industry, government, etc. and present reports on their findings. Offered variable quarters.    

15 MATH 518

A continuation of 15 MATH 517.  

15 MATH 519

A continuation of 15 MATH 518.

MATHEMATICAL STATISTICS I, II, III

15 STAT 521, 522, 523

3 UG or GR CR ea. qtr.

Prerequisite:

Calculus IV (15 MATH 264) and Probability and Statistics I
(15 MATH 361).

Text:

Hogg, McKean, and Craig, Introduction to Mathematical Statistics, 6e

15 STAT 521

Chapters 1, 2, 3 (through 3.4).  Random variables, probability distribution functions, mathematical expectation, inequalities, moment-generating functions, transformation of variables, marginal and conditional distributions, independence, binomial, Poisson, Gamma and normal distributions. 

15 STAT 522

Chapters 3 (starting 3.5), 4, 5.  Multivariate Normal, t- and F- distributions, sampling distributions: order statistics, distribution of sample mean and sample variance, stochastic convergence, central limit theorem, confidence intervals, hypothesis testing, chi-square tests, Monte Carlo methods, bootstrap methods . 

15 STAT 523

Chapters 6, 7,8.  , Uniformly most powerful tests, likelihood ratio tests, sufficient statistics, Rao-Blackwell theorem, exponential family , Rao-Cramer bound , sequential tests, minimax and classification procedure.

LINEAR PROGRAMMING I, II    

15 MATH 524, 525

3 UG or GR CR ea. qtr. 

Prerequisite:

Calculus IV (15 MATH 264); Linear Algebra II (15 MATH 352)

Text:

No Book Needed at this time

15 MATH 524

The simplex method (initialization, iteration, termination, sensitivity), the revised simplex method, duality, complementary slackness, the transportation problem, applications.

15 MATH 525

The transshipment problem, caterer problem, networks, max flow/min cut, matching problems, primal dual algorithm, Ford-Fulkerson algorithm, integer programming (cutting planes and branch and bound), interior point methods (ellipsoid method, Karmarkar’s method), applications.

NON-LINEAR OPTIMIZATION

15 MATH 526

3 UG or GR CR 

Prerequisite:

Calculus IV (15 MATH 264)

Text:

No Book Needed at this time

Methods of unconstrained optimization, the steepest descent method, Newton’s Method, conjugate direction methods, quasi-Newton and variable metric methods, theory and methods of constrained penalty methods.

APPLIED STATISTICAL INFERENCE

15 STAT 531

3 UG or GR CR

Prerequisite:

Calculus IV (15 MATH 264) and Linear Algebra II (15 MATH 352)

Text:

Milton and Arnold, Introduction to Probability and Statistics, 4e

Quick review of probability distributions. Inferences about population means and variance.

APPLIED REGRESSION ANALYSIS

15 STAT 532

3 UG or GR CR

Prerequisite:

Applied Statistical Inference (15 MATH 531) or Probability and Statistics I and II (15 MATH 361, 362)

Text:

Milton and Arnold, Introduction to Probability and Statistics, 4e

Correlation and multiple regression.  One-way ANOVA and multiple comparisons. Projects using SAS packages.  

ANALYSIS OF VARIANCE

15 MATH 533

3 UG or GR CR

Prerequisite:

Applied Regression Analysis (15 MATH 532)

Text:

Neter et al, Applied Linear Statistical Models, 5e

ANOVA for some standard experimental designs and unbalanced designs.  Repeated measures and the analysis of covariance.

SAS PROGRAMMING

15 STAT 534

3 UG or GR CR

Prerequisite:

Applied Regression Analysis (15 MATH 532) ~ can be taken concurrently.

Text:

Delwiche & Slaughter, The Little SAS Book: A Primer, 3e

This course will study various aspects of the SAS statistical package from a programming language perspective. It will emphasize the SAS data steps including the infile, input, merge, set, do-loop, if-then commands, etc. SAS mathematical, statistical, and data functions are discussed, as well as learning to write MACROs and how to do extensive matrix computations using PROC IML, also PROC INSIGHT, and the high resolution graphics procedures. The concentration is on programming issues rather than on statistical procedures; however, several statistical procedures are discussed and illustrated.    Win., Sum. Qtrs.

APPLIED STATISTICS USING S-PLUS

15 STAT 535

3 UG or GR CR

Prerequisite:

Probability and Statistics (15 MATH 361, 362, 363) or Applied Statistical Inference (15 MATH 531) or Applied Regression Analysis (15 MATH 532) or Analysis of Variance (15 MATH 533).

Text:

TBA

To obtain and enhance statistical analysis and programming skills using S-Plus. Various modern techniques in linear statistical modeling, write statistical functions, create graphs.   

PROBABILISTIC ASPECTS OF FINANCIAL MODELING 

15 MATH 540

3 UG or GR CR

Prerequisite:

Probability & Statistics (15 MATH 361) or Mathematical Statistics I (15 MATH 521). Applied Probability and Stochastic Processes (15 MATH 577) recommended. 

Text:

Bingham & Kiesel, Risk-Neutral Valuation (2004)

An introduction to the mathematical theory behind discrete and continuous time financial models. Covers martingales, martingales measures, change of measure, martingale representation, and Black Scholes formula.

COMPUTATIONAL FINANCIAL MATHEMATICS I, II, III

15 MATH 541, 542, 543

3 UG or GR CR ea qtr.

Prerequisite:

Calculus IV (15 MATH 264), Differential Equations (15 MATH 273), Matrix Methods (15 MATH 276), Probability & Statistics (15 MATH 361) or equivalent courses. 15 MATH 541 is a prerequisite for 15 MATH 542; 15 MATH 542 is a prerequisite for 15 MATH 543.

Text:

Stojanovic, Computational Financial Mathematics Using Mathematica, (2003)

15 MATH 541

Symbolic and numerical solutions of ODEs, Brownian motion, stochastic calculus, Black Scholes formula, computer lab using Mathematica.  

15 MATH 542

Stock market statistics, Bayesian and non-Bayesian estimates, implied volatility, numerical PDEs, optimal control of PDEs. Computer lab using Mathematica.   

15 MATH 543

American options, optimal stopping, Dupire PDE, portfolio rules, portfolio optimization, computer lab using Mathematica.    

NUMBER THEORY

15 MATH 551

3 UG or GR CR ea. qtr. 

Prerequisite:

Intro. To Algebra I, II (15 MATH 401, 402)

Text:

Silverman, A Friendly Introduction to Number Theory, 3e

Number-theoretic functions, congruences, diphantine equations, primitive roots and indices, quadratic residues, quadratic reciprocity.

PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER ANALYSIS I, II

15 MATH 553, 554

3 UG or GR CR ea. qtr. 

Prerequisite:

Calculus IV (15 MATH 264); Differential Equations (15 MATH 273) or Introduction to Ordinary Differential Equations (15 MATH 355)

Text:

Haberman, Elementary Applied Partial Differential Equations, 4e

15 MATH 553

Heat equation, separation of variables, LaPlace equation, Fourier series, vibrating strings, and membranes. 

15 MATH 554

Sturm-Liouville problems. PDE with at least three independent variables, Green’s functions, non-homogenous problem, Fourier transform, characterization.

APPLIED LINEAR ALGEBRA I, II

15 MATH 555, 556

3 UG or GR CR ea. qtr. 

Prerequisite:

Linear Algebra I (15 MATH 351) or Matrix Methods (15 MATH 276)

Text:

Lancaster & Tismenetsky, The Theory of Matrices (with Applications), 2e

15 MATH 555

Gaussian elimination, triangular factorization, band matrices, linear independence, computation of column space and nullspace of a matrix, orthogonality and geometry of Rn projections onto subspaces, least squares approximation, the pseudo-inverse. 

15 MATH 556

Stability of linear differential and difference equations, the Spectral Theorem for symmetric matrices, positive definite matrices, the generalized eigenvalue problem, the Rayleigh quotient and minimax principles.  

SCIENTIFIC PROGRAMMING WITH MATLAB

15 MATH 560

3 UG or GR CR

Prerequisite:

Calculus IV (15 MATH 264), Linear Algebra (15 MATH 351, 352) or Differential Equations (15 MATH 273)

Text:

TBA

Applications of scientific programming with MATLAB to calculus, linear algebra, or differential equations.

NUMERICAL METHODS IN APPLIED MATHEMATICS

15 MATH 561

3 UG or GR CR

Prerequisite:

Calculus IV (15 MATH 264), Differential Equations (15 MATH 273), and Matrix Methods (15 MATH 276)

Text:

No Book Needed at this time

Methodology and ideas behind numerical schemes, focusing on finite difference and finite element methods applied to problems in elasticity, fluid dynamics, heat conduction, groundwater flow, and wave propagation. 

APPLIED COMPLEX ANALYSIS

15 MATH 568

3 UG or GR CR

Prerequisite:

Calculus IV (15 MATH 264) and either Differential Equations (15 MATH 273) or Introduction to Ordinary Differential Equations (15 MATH 355)

Text:

Saff and Snider, Fundamentals of Complex Analysis for Mathematics, Science, and Engineering, 2e OR
Needham, Visual Complex Analysis (1999)

Introduction to the geometric aspects of elementary complex analysis. Topics covered include: complex numbers; mapping properties of elementary functions; conformal mapping and Mobius transformations; and applications to fluid flow.

TIME SERIES

15 STAT 571

3 UG or GR CR

Prerequisite:

Probability and Statistics II (15 MATH 362) or Mathematical Statistics (15 MATH 522) or any course on regression.

Text:

Brockwell and Davis, Introduction to Time Series and Forecasting
(with CD), 2e

Estimation and use of the autocorrelation function (ACF) and partial autocorrelation function (PACF); linear stationary models, including autoregressive (AR), moving average (MA), and ARIMA models; model identification, estimation, and forecasting; spectrum and periodgram of stationary processes. Techniques will be illustrated using computer software on real time series data.

RELIABILITY - SURVIVAL ANALYSIS

15 STAT 572

3 UG or GR CR

Prerequisite:

Mathematical Statistics (15 MATH 522) or a course on statistical inference.

Text:

Lee & Wang, Statistical Methods for Survival Data Analysis, 3e
Allison, Survival Analysis Using the SAS System, (1995)

Topics in applied life data analysis including reliability analysis (as in engineering fields) and survival analysis (as in medical and actuarial fields.)  Survival and hazard functions, life table and product limits estimates, exponential, Weibull, and other parametric models. Censored data, co-variate models (parametric, non-parametric, semi-parametric), maximum likelihood methods. Examples given and analyzed using PROC LIFETEST, LIFEREG, PHGLM, etc. in SAS.   

APPLIED BAYESIAN ANALYSIS

15 STAT 573

3 UG or GR CR

Prerequisite:

Mathematical Statistics III (15 MATH 523) or equivalent course on statistical inference.

Text:

Ghosh et al, An Introduction to Bayesian Analysis: Theory and Methods, 1e

Basic principles of Bayesian inference, including the concepts of prior and posterior distributions. Choice of prior distribution. Bayesian inference in one-parameter and two-parameter distributions where closed form answers are possible. Bayesian inference using (a) direct simulation and Monte Carlo, (b) Markov Chain Monte Carlo (MCMC), and their applications. Hierarchical models and applications. Testing point null hypothesis and the related issues in model selection and comparison, as time permits.

NON-PARAMETRIC STATISTICS

15 STAT 574

3 UG or GR CR

Prerequisite:

Mathematical Statistics (15 MATH 523) or Probability and Statistics II (15 MATH 362) and consent of instructor.

Text:

Lehmann, Nonparametrics: Statistical Methods Based on Ranks, 1e

One- and two-sample location problems. Wilcoxion statistics, rank tests, one- and two-way layout tests for independence, linear rank statistics, Kolmogorov test.

ROBUST STATISTICS

15 STAT 575

3 UG or GR CR

Prerequisite:

Probability and Statistics II (15 MATH 362) or equivalent.

Text:

Hoaglin, Mosteller, Tukey, Understanding Robust and Exploratory Data Analysis, (2000)

Methods of data analysis that are used when a sample is not assumed to have come from a normal distribution. Classical methods of inference and estimation, while optimal with "normal" data are highly sensitive to arbitrarily small amounts of contamination in the sample. Theoretical, applied, and computational aspects of robustness will be covered. Topics may include Monte Carlo adaptive estimation, jackknifing, and bootstrapping.  

TOPICS IN APPLIED STATISTICS

15 STAT 576

3 UG or GR CR

Prerequisite:

Mathematical Statistics (15 MATH 523) or permission of instructor.

Text:

Congdon, Bayesian Statistical Modeling, 2e

This course covers selected topics in applied statistics, depending on the area of specialty of the instructor.     

APPLIED PROBABILITY & STOCHASTIC PROCESSES I, II

15 MATH 577, 578

3 UG or GR CR ea. qtr.

Prerequisite:

Calculus IV (15 MATH 264) and Probability & Statistics I (15 MATH 361)

Text:

Lawler, Introduction to Stochastic Processes, 2e

15 MATH 577

Basic elements of probability theory and stochastic processes, Markov chains, the Poisson process.   

15 MATH 578

Additional topics from the theory of stochastic processes, plus applications. 

MATH AND MATHEMATICA

15 MATH 580

3 UG or GR CR

Prerequisite:

Calculus IV (15 MATH 264), Linear Algebra (15 MATH 352) or Matrix Methods (15 MATH 276) and Differential Equations (15 MATH 273 or 355). No prior knowledge of programming or Mathematica  required.

Text:

NO BOOK NEEDED AT THIS TIME

Projects using Mathematica. 

INTEGRAL EQUATIONS   

15 MATH 582

3 UG or GR CR

Prerequisite:

Advanced Calculus I, II (15 MATH 504, 505) or permission from instructor.

Text:

Jerri, Introduction to Integral Equations.

Finite rank kernels, Fredholm’s alternative, operators on Banach spaces, and application to Neumann series, resolvent for small values of the parameter. Operators on Hilbert spaces and application to the Hilbert-Schmidt theory of integral equations with symmetric kernels. Spectral theorem for compact operators and eigenvalue expansions.   

CALCULUS OF VARIATIONS

15 MATH 583

3 UG or GR CR

Prerequisite:

Linear Algebra II (15 MATH 352) or Matrix Methods (15 MATH 276); Calculus IV (15 MATH 264); Differential Equations (15 MATH 273) or Introduction to Ordinary Differential Equations (15 MATH 355).

Text:

Troutman, Variational Calculus with Elementary Convexity.

Euler-Lagrange equations, transversals, application to mechanics of particles and continua, integral constraints and application to isoperimetric problem, algebraic constraints and application to geodesics on surfaces, Hamilton-Jacobi method, solutions in bounded regions, differential constraints, Jacobi's sufficient condition.  

COMBINATORICS

15 MATH 584

3 UG or GR CR

Prerequisite:

Matrix Methods (15 MATH 276) or Linear Algebra I (15 MATH 351).

Text:

Brualdi, Introductory Combinatorics, 4e

Introduction to the theory and practice of enumeration, the Pigeonhole principle, permutations and combinations, binomial coefficients, inclusion-exclusion principle, recurrence relations, generating functions.   

GRAPH THEORY

15 MATH 588

3 UG or GR CR

Prerequisite:

Linear Algebra I (15 MATH 351) or Matrix Methods (15 MATH 276).

Text:

Merris, Graph Theory, 1e

Fundamental concepts of graphs and directed graphs, trees, connectivity, factorization, covering and packing, line graphs, planarity, traversability, colorability.

INDIVIDUAL WORK

15 MATH 591, 592, 593

3 UG or GR CR

Variable graduate credits.

SPECIAL TOPICS IN MATHEMATICS I, II, III

15 MATH 597, 598, 599

3 UG or GR CR ea. qtr.

15 MATH 597

Text:

TBA

15 MATH 598

Text:

Mendelson, Introduction to Topology, 3e

15 MATH 599

Basic ideas of mathematical modeling in the biosciences, using ODE and PDE. Focus on the immersed boundary method for biofluids.

Text:

TBA

COMPLEX ANALYSIS I, II, III

15 MATH 601, 602, 603

4 UG or GR CR ea. qtr.

Prerequisite:

Advanced Calculus III (15 MATH 506).

Text:

Ahlfors, Complex Analysis, 3e

The complex number system, elementary analytic functions and power series, conformal mapping and linear fractional transformations, Cauchy's Integral Theorem, Cauchy's Integral Formula, local properties of analytic functions, Schwarz's Lemma, calculus of residues, the Schwarz reflection principle, normal families, Riemann Mapping Theorem, harmonic functions, Dirichlet problem, entire and Meromorphic functions.  

GENERAL TOPOLOGY I, II, III

15 MATH 604, 605, 606

4 UG or GR CR ea. qtr.

Prerequisite:

Advanced Calculus III (15 MATH 506).

Text:

Lee, Introduction to Smooth Manifolds, (2002)

The topics to be covered include topologies, bases, subspaces, continuity, compactness and paracompactness, connectedness, some separation axioms, product spaces, quotient spaces, the compact-open topology, homotopy, the fundamental group, the Seifert – Van Kampen theorem, covering space theory (the lifting theorem, the group of Deck transformations, classification of covering spaces), smooth manifolds, the tangent bundle, regular values, the smooth approximation theorem, surfaces, homology, the Eilenberg-Steenrod axioms, the Euler characteristic, universal coefficient and Kunneth theorems, cohomology, products, Poincare duality, as well as additional topics chosen by the instructor.  

REAL ANALYSIS I, II, III

15 MATH 607, 608, 609

4 UG or GR CR ea. qtr.

Prerequisite:

Advanced Calculus III (15 MATH 506).

Text:

Royden, Real Analysis, 3e

Elementary set theory, Axiom of Choice, elementary topology. Lebesgue Measure and integration on the real line. Abstract measure and integration theory, product measures and Fubini's theorem, absolute continuity and the Radon-Nikodym theorem, signed measures and decomposition theorems, integration on locally compact spaces, Lp-spaces and the Riesz Representation Theorem. Elementary theory of topological vector spaces, normed spaces and Hilbert spaces, elementary theory of continuous linear operators.   

ALGEBRAIC STRUCTURES I, II, III

15 MATH 610, 611, 612

4 UG or GR CR ea. qtr.

Prerequisite:

Introduction to Abstract Algebra (15 MATH 513) or permission of instructor.

Text:

Dummit, Abstract Algebra: An Introduction, 3e

15 MATH 610

Group theory: Sylow's theorems, Fundamental Theorem of abelian groups, Jordan-Holder theorems, and solvable groups.  Modules:  Free modules and Zorn’s Lemma. Modules over PID. Categories:  Products, co-products, and free objects.

15 MATH 611

Fields: Algebraic and transcendental extensions, algebraic closure, Galois theory of finite extensions, and solvability by radicals.

15 MATH 612

Linear Algebra: canonical forms; rings: semi-simple rings; Jacobson Radical. 

LINEAR MODELS AND MULTIVARIATE ANALYSIS I, II, III

15 STAT 613, 614, 615

4 UG or GR CR ea. qtr.

Prerequisite:

Applied Linear Algebra (15 MATH 555, 556) or an equivalent course which covers the contents of 15 MATH 555 and positive definite matrices; Applied Statistical Inference (15 MATH 531), Applied Regression Analysis (15 MATH 532), Analysis of Variance (15 MATH 533); Mathematical Statistics (15 MATH 523), or equivalent courses.

15 MATH 613

Review of linear algebra, matrix theory, multivariate normal distribution, central and non-central chi-square, t and F-distributions, quadratic forms, best linear unbiased estimators (BLUE). Theory of linear models. The full rank and non-full rank models, multiple linear regression, one-way ANOVA.

Text: 

S.R. Searle, Linear Models, (1997)
Littell, Freund, and Spector, SAS for Linear Models, 4 sub ed (2002)

15 MATH 614

Applications of the theory developed in Linear Models I. Selected topics from experimental design. Two way ANOVA, fixed, nested and random effects. Analysis of covariance. Split plot, and split-split plot designs, repeated measures, mixed models. Analysis using SAS.

Text: 

G.A. Milliken and D.E. Johnson, Analysis of Messy Data, vol. 1
Littell, SAS for Mixed Models, 2e

15 MATH 615

Continuation of topics from experimental design. Topics in Multivariate analysis. Multivariate T-tests, MANOVA, principal components, factor analysis, etc. Analysis using SAS

 Text: 

 R.A. Johnson & D.W. Wichern, Applied Multivariate Statistical Analysis, 6e

ORDINARY DIFFERENTIAL EQUATIONS I, II, III

15 MATH 616, 617, 618

4 UG or GR CR ea. qtr.

Prerequisite:

Advanced Calculus (15 MATH 506).

Text:

Hirsch and Smale, Differential Equations, Dynamical Systems, and Linear Algebra, (1974)  (special UC printing)

Existence and uniqueness for initial value problems. Linear systems.  Linearization, plane systems, stability.  

MATHEMATICAL LOGIC I, II, III

15 MATH 621, 622, 623

4 UG or GR CR ea. qtr.

Prerequisite:

Intro to Abstract Algebra II (15 MATH 512) or Automata & Formal Lang I (ECES 670) or permission of instructor.

Text:

Enderton, A Mathematical Introduction to Logic.

Formal systems (first order). Proof of theoretic and model theoretic techniques and interconnections. Compactness and completeness theorems. Non-Standard models with applications to analysis.  Peano arithmetic and set theory as illustrations of important first order systems.

DYNAMICAL SYSTEMS I, II, III

15 MATH 624, 625, 626

4 UG or GR CR ea. qtr.

Prerequisite:

Advanced Calculus (15 MATH 506).

Text:

Hirsch & Smale, Differential Equations, Dynamical Systems, and Linear Algebra, (1974)

Maps of the interval, period doubling to chaos, symbolic dynamics, Smale's horseshoe example, homoclinic orbits, bifurcation, Julia sets.

PARTIAL DIFFERENTIAL EQUATIONS I, II, III

15 MATH 627, 628, 629

4 UG or GR CR ea. qtr.

Prerequisite:

Advanced Calculus (15 MATH 506).

Text:

Evans, Partial Differential Equations, (2002)

15 MATH 627

Transport equations, initial value problem; Laplace equation, fundamental solution, mean-value formulas, Green’s function; Heat equation, fundamental solution, strong maximum principle; Wave equations, solution by spherical means, energy methods; Nonlinear first-order PDE, characteristics.  

15 MATH 628

Holder spaces; Sobolev spaces; Approximation by smooth functions; Extensions; Traces; Sovolev inequalities; Compact embedding; Other spaces of functions; Elliptical equations, existence of weak solutions; Regularity; Maximum principles; Eigenfunctions and eigenvalues.   

15 MATH 629

Existence of weak solutions for second-order parabolic equations, maximum principles; Galerkin approximations; Fixed point methods; Method of subsolutions and supersolutions; Semigroup theory.   

ADVANCED THEORY OF STATISTICS I, II, III

15 MATH 631, 632, 633

4 UG or GR CR ea. qtr. This sequence is a continuation of Mathematical Statistics (15 MATH 521, 522, 523).

Prerequisite:

Mathematical Statistics (15 MATH 523) and Advanced Calculus (15 MATH 506).

Text:

Berger, Statistical Decision Theory and Bayesian Analysis, 2e

15 MATH 631

Review of probability theory, distribution theory, sufficient statistics, efficiency of estimators, maximum likelihood estimators, large sample theory, consistency, asymptotic efficiency, confidence intervals and testing.

15 MATH 632

Elements of decision theory (unbiased estimation, admissibility, inadmissibility), Bayesian analysis, minimax estimators, invariant estimator, Bayes and minimax tests; likelihood ratio tests.   

15 MATH 633

Topics selected from: uniformly most powerful tests, general linear hypotheses, multiple decision problems, sequential analysis, density estimation, empirical processes, etc.

PROBABILITY THEORY I, II, III

15 MATH 634, 635, 636

4 UG or GR CR ea. qtr.

Prerequisite:

Mathematical Statistics (15 MATH 523) and Advanced Calculus (15 MATH 506).

Text:

Billingsley, Probability & Measure, 3e

15 MATH 634

Measure theory and Lebesgue integration theory (brief), probability measures, random variables, expectation laws of large numbers, Borel-Cantelli Lemmas, Zero-one laws, Glivenko-Cantelli Theorem, applications.

15 MATH 635

Weak convergence, characteristic functions, Central limit theorem, law of iterated logarithm, other limit theorems for independent and dependent sequences, conditional probability, conditional expectation.  

15 MATH 636

Topics selected from martingales, Brownian motion process, invariance principle, and other material from stochastic processes.  

ANALYTICAL METHODS I, II, III

15 MATH 701, 702, 703

3 GR CR ea. qtr. Credits may not be applied toward a degree in Mathematics.

Prerequisite:

Calculus IV (15 MATH 264) and Differential Equations (15 MATH 273).

Text:

O'Neil, Advanced Engineering Mathematics, 6e

15 MATH 701

First order differential equations. Linear differential equations of second and higher order.  Equations with constant coefficients, Euler method of undetermined coefficients, variation of parameters.  Fuchs-Frobenious method for linear second-order equations, application to Bessel functions. Laplace transforms (Ch. 1, 2, 4, 5.)   

15 MATH 702

Linear algebra, Gaussian elimination, inverse matrices, determinants, diagonalization. Application to quadratic forms and to systems of linear differential equations (Ch. 6, 7.) Vector differential calculus, double and triple integrals, line integrals, potential, surface integrals, Green theorem, Stokes theorem, Gauss theorem (Ch. 8, 9.)  

15 MATH 703

Fourier analysis: Fourier series, Fourier transforms. Sturm-Liouville problems. Partial Differential Equations: Separation of variables. Heat equation, wave equation, Laplace equation. Double Fourier series, Fourier-Bessel series. Application of Laplace transforms (Ch. 10, 11, parts of 5.)   

MEASURE THEORETIC CALCULUS I, II, III

15 MATH 704, 705, 706

4 GR CR ea. qtr.

Prerequisite:

Real Analysis (15 MATH 607, 608).

Text:

Gariepy and Evans, Measure Theory and Fine Properties of Functions.

15 MATH 704

Covering theorems, differentiation of Radon measures, Riesz representation theorem, Hausdorff measure, Isodiametric Inequality, densities, Rademacher’s Theorem.  

15 MATH 705

Jacobians, the area formula, Coarea Formula, Sobolev functions, Sobolev inequalities,capacity, quasi-continuity, BV functions.   

15 MATH 706

Coarea Formula for BV functions, Isoperimetric Inequality, the reduced boundary, Gauss-Green Theorem, Lp differentiability, Whitney’s Extension Theorem, approximation by C1 functions.  

ADVANCED NUMERICAL ANALYSIS I, II, III

15 MATH 710, 711, 712

4 UG or GR CR ea. qtr.

Prerequisite:

Numerical Analysis (15 MATH 516) or equivalent experience.

Text:

TBA

Topics to be chosen from:  numerical solution of ordinary differential equations, numerical solution of partial differential equations; variational methods, finite elements; computational algebra, fast Fourier Transform. These and other topics to be included are dependent on the instructor's choice.  

STATISTICAL CONSULTING

15 MATH 720, 721, 722, 723

3 GR CR ea. qtr.

Prerequisite:

Mathematical Statistics I, II, III (15 MATH 521, 522, 523) AND Applied Statistical Inference (15 MATH 531), Applied Regression Analysis (15 MATH 532), Analysis of Variance (15 MATH 533).

Text:

No Book Needed

Students enrolled in this course will participate in the statistical consulting mission of the Statistical Consulting Laboratory of the Department of Mathematical Sciences. Under the guidance of the director(s) of the Lab, students will typically work in teams of two on projects brought to the lab by other researchers from on- and off-campus. Students will be expected to interact with these researchers. A significant amount of class time will be devoted to learning new statistical techniques necessary for particular projects, as well as developing consulting and presentation skills.

The following courses are offered for the M.A.T. Program and are offered only during the summer term.

TECHNOLOGY FOR CALCULUS

15 MATH 750

2 GR CR

Introduction to the use of technology for teaching analysis (pre-calculus and calculus). Graphing
calculators, symbolic algebra programs. Design and delivery of lessons that use technology.
Project-oriented with cooperative learning component.   

ANALYSIS I & II

15 MATH 751, 752

4 GR CR ea. qtr.

Theory of calculus of one variable. Analysis I: Continuity and differentiability. Analysis II: Riemann integral and infinite series.

GEOMETRY I & II

15 MATH 755, 756

4 GR CR ea. qtr.

First term: Axiomatic geometry, both neutral and Euclidean. Second term: Transformational geometry. use of Geometer's Sketchpad will be an integral part of the courses.

NUMBER THEORY I

15 MATH 761

4 GR CR

Congruences, divisibility, primes, number-theoretic functions, number bases and applications.

ALGEBRA AND NUMBER THEORY II

15 MATH 762

4 GR CR

The theory of rings and fields with emphasis on the algebra of polynomials. 

PROBABILITY AND STATISTICAL INFERENCE

15 MATH 763

4 GR CR

Probability axioms and finite probability spaces. Combinatorics. Binomial and Normal distributions.
Design of statistical studies and methods of statistical inference.

TECHNOLOGY FOR STATISTICS

15 MATH 764

4 GR CR

Spreadsheets and statistical packages for handling and exploring data, doing simulations, and
demonstrating concepts of statistics. Project-oriented with cooperative learning component.

M.A.T. PROJECT I

15 MATH 798

2 GR CR

Preparation and presentation of the MAT project. Summer quarter only.

M.A.T. PROJECT II

15 MATH 799

2 GR CR

Preparation and presentation of the MAT project. Summer quarter only.

MATHEMATICAL MODELS

15 MATH 802

4 GR CR

Development and analysis of mathematical models of discrete and continuous phenomena.

GRADUATE COLLOQUIUM  

15 MATH 804, 805, 806

3 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

PROSEMINAR IN THE TEACHING OF COLLEGE MATHEMATICS

15 MATH 810

3 GR CR Aut. Qtr.

PRACTICUM IN APPLIED STATISTICS I, II, III, IV

15 MATH 831, 832, 833, 834

Variable credits. Aut., Win., Spr., Sum. Qtrs.

READINGS

15 MATH 899

Variable graduate credits. Aut., Win., Spr., Sum. Qtrs.

SEMINAR IN ANALYSIS

15 MATH 901, 902, 903

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN TOPOLOGY

15 MATH 904, 905, 906

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN ALGEBRA

15 MATH 907, 908, 909

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN APPLIED MATH

15 MATH 911, 912, 913

4 GR CR ea. qtr.  Aut., Win., Spr. Qtrs.

SEMINAR IN PARTIAL DIFFERENTIAL EQUATIONS

15 MATH 914, 915, 916

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN DIFFERENTIAL EQUATIONS

15 MATH 917, 918, 919

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN STATISTICS

15 MATH 921, 922, 923

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN PROBABILITY

15 MATH 924, 925, 926

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

SEMINAR IN COMPLEX ANALYSIS

15 MATH 927, 928, 929

4 GR CR ea. qtr. Aut., Win., Spr. Qtrs.

THESIS RESEARCH

15 MATH 971

Variable graduate credits. Aut., Win., Spr., Sum. Qtrs.

PhD DISSERTATION RESEARCH

15 MATH 972

Variable graduate credits. Spr., Sum. Qtrs.

RESEARCH

15 MATH 973

Variable graduate credits. Win., Spr. Qtrs.