Mathematics (MATH)

MATH 00020     PRE-ALGEBRA      2 Credit Hours

Course covers properties of whole numbers, fractions, decimals, percents, signed numbers and order of operations. Mental math and elementary algebraic thinking skills are emphasized. Use of calculators is not allowed. Course does not count toward graduation.

Prerequisite: 0-9 ALEKS math score.

Schedule Type: Emporium

Contact Hours: 2 other

Grade Mode: Standard Letter

MATH 00021     BASIC ALGEBRA I      2 Credit Hours

Course includes operations on integers, fractions, decimals and percents, and properties of real numbers. Introduction to variables, first degree equations and problem-solving with formulas. Equations and inequalities in one variable, linear equations, rate of change and slope, graphing in the cartesian plane. Course does not count toward graduation.

Prerequisite: Minimum 10 ALEKS math score.

Pre/corequisite: MATH 00020 with a minimum C grade.

Schedule Type: Emporium

Contact Hours: 2 other

Grade Mode: Standard Letter

MATH 00022     BASIC ALGEBRA II      2 Credit Hours

Introduction to functions, systems of linear equations, exponents, polynomial operations, scientific notation. Factoring polynomials, solving quadratics by factoring, radicals and rational exponents. Course does not count toward graduation.

Prerequisite: Minimum 25 ALEKS math score; or MATH 00021 with a minimum C grade.

Schedule Type: Emporium

Contact Hours: 2 other

Grade Mode: Standard Letter

MATH 00095     SPECIAL TOPICS IN MATHEMATICS      1-4 Credit Hours

(Repeatable for credit) Topics in mathematics not covered in regular courses. Offered when opportunities and resources permit; the topic is announced when the course is scheduled. Course does not count toward graduation.

Prerequisite: None.

Schedule Type: Emporium

Contact Hours: 1-4 other

Grade Mode: Standard Letter

MATH 10040     INTRODUCTORY STATISTICS PLUS (KMCR)      5 Credit Hours

(Equivalent to MATH 10041) An introduction to statistical thinking and statistical methods with a review of basic algebra. Emphasis is on statistical literacy, conceptual understanding and active learning in the classroom. This course also provides just-in-time remediation to help students achieve the same learning outcomes as MATH 10041. No credit earned for this course if a student already earned credit for MATH 10041.

Prerequisite: ALEKS Math score between 25 and 34; or MATH 00021 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, TAG Mathematics, Transfer Module Mathematics

MATH 10041     INTRODUCTORY STATISTICS (KMCR)      4 Credit Hours

(Equivalent to MATH 10040) An introduction to statistical thinking and statistical methods. Emphasis is on statistical literacy, conceptual understanding and active learning in the classroom. No credit earned for this course if a student already earned credit for MATH 10040.

Prerequisite: Minimum 22 ACT math score; or minimum 530 SAT math score; or minimum 35 ALEKS Math score; or MATH 00022 with a minimum C grade; or any higher level MATH course.

Schedule Type: Emporium

Contact Hours: 4 other

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 10050     QUANTITATIVE REASONING PLUS (KMCR)      5 Credit Hours

(Equivalent to MATH 10051) In the broadest sense mathematics should provide students the needed quantitative tools, logical reasoning and problem-solving skills, and a sense that quantitative modeling can be used to describe and understand developments in many areas of daily living. Since critical thinking is the primary objective and outcome for our course, in each area of concentration (numeracy, mathematical modeling, and probability and statistics) students will need to read and glean information from the problem situation, convert the information into a usable form, perform any needed routine calculations, make or draw a conclusion, and then communicate the result via explanation using quantitative reasoning by writing coherent statements and paragraphs. This course also provides just-in-time remediation to help students achieve the same learning outcomes as MATH 10051.

Prerequisite: ALEKS Math score between 25 and 34; or MATH 00021 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, TAG Mathematics, Transfer Module Mathematics

MATH 10051     QUANTITATIVE REASONING (KMCR)      4 Credit Hours

(Equivalent to MATH 10050) In the broadest sense, mathematics should provide students the needed quantitative tools, logical reasoning and problem solving skills, and a sense that quantitative modeling can be used to describe and understand developments in many areas of daily living. Since critical thinking is the primary objective and outcome for this course, in each area of concentration (numeracy, mathematical modeling and probability and statistics), students will read and glean information from the problem situation, convert the information into a usable form, perform any needed routine calculations, make or draw a conclusion, and then communicate the result via explanation using quantitative reasoning by writing coherent statements and paragraphs.

Prerequisite: Minimum 22 ACT math score; or minimum 530 SAT math score; or minimum 35 ALEKS Math score; or MATH 00022 with a minimum C grade; or any higher level MATH course.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 10675     ALGEBRA FOR CALCULUS BOOST (KMCR)      5 Credit Hours

(Equivalent to MATH 10775 and MATH 11010) Course includes an extensive and rich immersion into the structure of functions. Routine analysis includes discussion of domain, range, zeros, general function behavior (increasing, decreasing, extrema, etc.). Operations with functions, including addition, subtraction, multiplication, division, composition and inversion. Functions are studied as a tool to analyze rates of change in real-world scenarios. The emphasis is on linear, polynomial, exponential and rational functions, with an extensive problem-solving component. A two-week review of intermediate algebra skills is included in the course, as is extra time studying quadratic functions, absolute value functions, systems of equations and extended time on logarithms.

Prerequisite: Minimum 22 ACT math score; or minimum 530 SAT math score; or ALEKS math score between 35-44; or MATH 00022 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 10771     BASIC MATHEMATICAL CONCEPTS I PLUS (KMCR)      5 Credit Hours

(Equivalent to MATH 14001) Course covers the development of the real-number system and its sub-systems, open sentences, numeration systems, modular arithmetic and some number theory concepts. Additional concepts covered include place value, logic, sets, algebra concepts and problem solving.

Prerequisite: Minimum 35 ALEKS math score; or minimum 22 ACT math score; or minimum 530 SAT math score; or MATH 00022 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 10772     MODELING ALGEBRA PLUS (KMCR)      5 Credit Hours

(Equivalent to MATH 11009) Study of algebra arising in the context of real-world applications, including linear, polynomial, exponential and logarithmic models. Includes a review of factoring and functions. Course is intended for students not planning to take calculus. No credit earned toward a degree for this course if student already earned credit for MATH 11010.

Prerequisite: Minimum 35 ALEKS math score; or minimum 22 ACT math score; or minimum 530 SAT math score; or MATH 00022 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 10775     ALGEBRA FOR CALCULUS PLUS (KMCR)      4 Credit Hours

(Equivalent to MATH 10675 or MATH 10775 or MATH 11010) Course includes an extensive and rich immersion into the structure of functions. Routine analysis includes discussion of domain, range, zeros, general function behavior (increasing, decreasing, extrema, etc.). Operations with functions, including addition, subtraction, multiplication, division, composition and inversion. Functions are studied as a tool to analyze rates of change in real-world scenarios. The emphasis is on linear, polynomial, exponential and rational functions, with an extensive problem-solving component. Skill review is included in the course, as is time studying quadratic functions, absolute value functions, systems of equations and extended time on logarithms.

Prerequisite: ALEKS math score between 45 and 54; or MATH 10772 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 11008     EXPLORATIONS IN MODERN MATHEMATICS (KMCR)      3 Credit Hours

Topics from various branches of mathematics will be chosen to introduce the student to the wide varieties of ways in which mathematics affects everyday life.

Prerequisite: Minimum 35 ALEKS math score; or minimum 22 ACT math score; or MATH 00022 or any higher MATH course with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 11009     MODELING ALGEBRA (KMCR)      4 Credit Hours

(Equivalent to MATH 10772) Study of algebra arising in the context of real-world applications, including linear, polynomial, exponential and logarithmic models. Intended for students not planning to take calculus. No credit earned toward a degree for this course if the student already earned credit for MATH 11010.

Prerequisite: Minimum 45 ALEKS math score.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 11010     ALGEBRA FOR CALCULUS (KMCR)      3 Credit Hours

(Equivalent to MATH 10675 and MATH 10775) Course includes an extensive and rich immersion into the structure of functions. Routine analysis includes discussion of domain, range, zeros, general function behavior (increasing, decreasing, extrema, etc.). Operations with functions, including addition, subtraction, multiplication, division, composition and inversion. Functions are studied as a tool to analyze rates of change in real-world scenarios. Emphasis is on linear, polynomial, exponential and rational functions, with an extensive problem-solving component.

Prerequisite: Minimum 55 ALEKS math score; or MATH 10772 or MATH 11009 with a minimum B grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 11012     INTUITIVE CALCULUS (KMCR)      3 Credit Hours

Course is designed to give an overview of differential and integral calculus to business and life-science majors. Course does not include trigonometric functions. No credit earned toward a degree for this course if the student already earned credit for MATH 12002.

Prerequisite: Minimum 67 ALEKS math score; or minimum C grade in MATH 10675 or MATH 10775 or MATH 11010.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 11022     TRIGONOMETRY (KMCR)      3 Credit Hours

Solution of triangles, trigonometric equations and identities.

Prerequisite: Minimum 67 ALEKS math score; or minimum C grade in MATH 10675 or MATH 10775 or MATH 11010.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 12002     ANALYTIC GEOMETRY AND CALCULUS I (KMCR)      5 Credit Hours

Concepts of limit, continuity and derivative, and the indefinite and definite integral for functions of one real variable. Maximization, related rates, fundamental theorem of calculus. No credit earned toward a degree for this course if the student already earned credit for MATH 12011 and MATH 12012.

Prerequisite: Minimum 78 ALEKS math score; or MATH 11022 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 12003     ANALYTIC GEOMETRY AND CALCULUS II      5 Credit Hours

Continued study of techniques and applications of integration; trigonometric, logarithmic and exponential functions; polar coordinates; vectors; parametric equations; sequences and series.

Prerequisite: MATH 12002 or MATH 12012 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 5 lecture

Grade Mode: Standard Letter

Attributes: Transfer Module Mathematics

MATH 12011     CALCULUS WITH PRECALCULUS I (KMCR)      3 Credit Hours

Introduction to differential calculus with a review of algebra and trigonometry. Includes exponents, factoring, functions, graphs, tangent lines, limits, continuity, derivatives and related rates. No credit earned toward a degree for this course if the student already earned credit for MATH 12002.

Prerequisite: Minimum 67 ALEKS math score.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 12012     CALCULUS WITH PRECALCULUS II (KMCR)      3 Credit Hours

Development of integral calculus and continued study of differential calculus. Includes curve sketching optimization fundamental theorem of calculus areas between curves, exponential and logarithmic functions. No credit earned toward a degree for this course if student already earned credit for MATH 12002.

Prerequisite: MATH 12011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning, Transfer Module Mathematics

MATH 12013     BRIEF CALCULUS II      3 Credit Hours

This is a condensed version of MATH 12003 to meet the needs of majors that do not require the full force of Math 12003. The course starts with integration by parts, approximating integrals, and applications of integrals. It follows with a brief introduction to series, parametric equations and polar coordinates, and finishes with vectors and geometry of space. No credit earned toward a degree for this course if student already earned credit for MATH 12003.

Prerequisite: Minimum C grade in MATH 12002 or MATH 12012 or MATH 12021.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 12021     CALCULUS FOR LIFE SCIENCES      4 Credit Hours

Differential and integral calculus using examples and problems in life sciences.

Prerequisite: Minimum 78 ALEKS math score; or MATH 11022 or MATH 12011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 12022     PROBABILITY AND STATISTICS FOR LIFE SCIENCES      3 Credit Hours

Probability and statistics with applications in medical and biological sciences.

Prerequisite: Minimum C grade in MATH 12002 or MATH 12012 or MATH 12021.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 14001     BASIC MATHEMATICAL CONCEPTS I (KMCR)      4 Credit Hours

(Equivalent to MATH 10771) Development of the real number system and its sub-systems, open sentences, numeration systems, modular arithmetic and some number theory concepts.

Prerequisite: Minimum 45 ALEKS math score; or any higher level MATH course (except MATH 10041, MATH 10051 or MATH 11008).

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 14002     BASIC MATHEMATICAL CONCEPTS II (KMCR)      4 Credit Hours

Basic concepts of probability, statistics and geometry.

Prerequisite: MATH 10771 or MATH 14001 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

Attributes: Kent Core Mathematics and Critical Reasoning

MATH 19002     TECHNICAL MATHEMATICS II      4 Credit Hours

Emphasizes advanced topics in algebra and trigonometry, analytic geometry, derivatives and integrals.

Prerequisite: None.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 19099     FIELD EXPERIENCE IN MATHEMATICS INSTRUCTION (ELR)      1 Credit Hour

(Repeatable for credit) Learning through tutoring. A supervised lab experience in providing explanations of mathematical concepts.

Prerequisite: Special approval.

Schedule Type: Lecture

Contact Hours: 1 lecture

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement

MATH 20011     DECISION-MAKING UNDER UNCERTAINTY      3 Credit Hours

An introductory course on applied statistics. The course provides a hands-on approach to understanding, quantification and decision-making under various forms of uncertainty. The main topics include visualization of uncertainty, probabilistic quantification of uncertainty, Bayesian and non-Bayesian ways of decision-making under uncertainty. Class activities incorporate active learning elements, including in-classroom computation with professional-grade software for statistical analysis and simulation.

Prerequisite: MATH 12002 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 20095     SPECIAL TOPICS IN MATHEMATICS      1-5 Credit Hours

(Repeatable for credit) Various special courses will be announced in the schedule of classes under this course number with different section numbers.

Prerequisite: Special approval.

Schedule Type: Lecture

Contact Hours: 1-5 lecture

Grade Mode: Standard Letter

MATH 21001     LINEAR ALGEBRA      3 Credit Hours

Systems of linear equations and the associated matrix operations, linear transformations, vector spaces, bases, eigenvectors.

Prerequisite: Minimum C grade in MATH 11012 or MATH 12002 or MATH 12012 or MATH 12021.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: TAG Mathematics

MATH 21002     APPLIED LINEAR ALGEBRA      3 Credit Hours

This is an introductory course in linear algebra. The goal of the course is to teach the math fundamentals of linear algebra in a way that focuses more on applications. The topics include systems of linear equations, matrix operations, vector spaces, eigenvalues and eigenvectors, singular value decompositions, and their applications.

Prerequisite: Minimum C grades in MATH 12002 or MATH 11012 or MATH 12012 or MATH 12021.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 21092     COMPUTER PRACTICUM (ELR)      2 Credit Hours

(Repeatable for credit) Supervised work experience in a computer installation.

Prerequisite: None.

Schedule Type: Practical Experience

Contact Hours: 2 other

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement

MATH 22005     ANALYTIC GEOMETRY AND CALCULUS III      4 Credit Hours

Study of functions of several variables, including partial derivatives and multiple integrals.

Prerequisite: MATH 12003 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 23022     DISCRETE STRUCTURES FOR COMPUTER SCIENCE      3 Credit Hours

(Cross-listed with CS 23022) Discrete structures for computer scientists with a focus on: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, applications and modeling. Specific topics include logic, sets, functions, relations, algorithms, proof techniques, counting, graphs, trees, Boolean algebra, grammars and languages.

Prerequisite: Minimum 55 Compass Algebra score and either minimum 540 SAT math score or minimum 23 ACT math score; or CS 10051 and minimum C grade in MATH 11010.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 30011     BASIC PROBABILITY AND STATISTICS      3 Credit Hours

Analysis and representation of data. Controlled experiments and observations. Measurement errors. Correlation and regression. Sampling. Probability models and tests of models. Inference. This course cannot be used to meet the mathematics requirements for a BA in Mathematics or a BS in Applied Mathematics or Mathematics.

Prerequisite: Minimum 67 ALEKS math score; or minimum C grade in MATH 10675 or MATH 10775 or MATH 11010; or any course MATH 11012 to MATH 12022; or any course MATH 20000 to MATH 49999.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 30055     MATHEMATICAL THEORY OF INTEREST      3 Credit Hours

A calculus-based introduction to the mathematics of finance. Limited to deterministic analysis of interest rates annuities bonds and immunization. Emphasizes the mathematical theory of the subject matter.

Prerequisite: MATH 12003 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 31011     PROOFS IN DISCRETE MATHEMATICS      3 Credit Hours

The study of discrete mathematical structures including sets, functions, and relations. The course includes an introduction to logical thinking with an emphasis on proof techniques. The course also emphasizes combinatorics topics such as recursion and counting.

Prerequisite: MATH 12002 with a minimum C grade.

Pre/corequisite: MATH 21001 or MATH 32051 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 32044     ORDINARY DIFFERENTIAL EQUATIONS      3 Credit Hours

An introduction to ordinary differential equations and applications. Topics include solution methods, series solutions and singular points. Laplace transforms and linear systems. Applications include population dynamics, forced oscillations and resonance.

Prerequisite: MATH 21001 and MATH 22005 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: TAG Mathematics

MATH 32051     MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES I      4 Credit Hours

Mathematics background beyond calculus I and II for upper-division courses in the physical sciences. Topics include complex numbers and arithmetic, linear algebra, partial differentiation and multiple integrals.

Prerequisite: MATH 12003 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 32052     MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES II      4 Credit Hours

Additional mathematics background for upper-division courses in the physical sciences. Topics include vector analysis, Fourier series and transforms ordinary differential equations and partial differential equations.

Prerequisite: MATH 32051 with a minimum C grade; or MATH 21001 and MATH 22005 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 34001     FUNDAMENTAL CONCEPTS OF ALGEBRA      3 Credit Hours

Professionalized course in algebra for prospective secondary teachers. Postulational development of number system of algebra; other systems, related topics, applications. This course cannot be used to meet the mathematical requirements for a BA in Mathematics or a BS in either Applied Mathematics or Mathematics. No credit earned toward a degree for this course if a student already earned credit for MATH 41001.

Prerequisite: MATH 12002 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 34002     FUNDAMENTAL CONCEPTS OF GEOMETRY      3 Credit Hours

Professionalized course in geometry for secondary school teachers. Origin and development of the geometry of Euclid with modern refinements, topics, approaches. Other geometries, applications. This cannot be used to meet the mathematics requirement for a BA in Mathematics or a BS in either Applied Mathematics or Mathematics.

Prerequisite: MATH 12002 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 38001     HANDS-ON MATHEMATICS      3 Credit Hours

Students take turns learning a topic and then teach that topic to the class. No text is required; the students use web resources and materials supplied by the instructor. Many of the topics have a hands-on component. Some examples are two- and three-dimensional tiling problems, the Towers of Hanoi and other problems with an inductive solution, and ‘magic tricks’ with a basis in algebra, parity or modular arithmetic.

Prerequisite: MATH 12003 with a minimum C grade.

Schedule Type: Seminar

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40011     PROBABILITY THEORY AND APPLICATIONS      3 Credit Hours

(Slashed with MATH 50011) Permutations and combinations, discrete and continuous distributions, random variables, conditional probabilities, Baye's formula, mathematical expectation, law of large numbers, normal approximations, basic limit theorems.

Prerequisite: MATH 22005 or MATH 32051 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40012     THEORY OF STATISTICS      3 Credit Hours

(Slashed with MATH 50012) Sample spaces, continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, types of error, level and power of tests, sequential and nonparametric methods.

Prerequisite: MATH 40011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40015     APPLIED STATISTICS      3 Credit Hours

(Slashed with MATH 50015) Course is based on classical linear regression techniques with an emphasis on real data using the principles of sound data analysis. Close attention is given to issues of interpretation, diagnostics, outliers and influential points, goodness of fit and model selection. Topics include simple and multiple linear regression, transformation and modifications of covariates and responses, design matrices, variable selection and logistic regression. Students with statistics courses from other disciplines should consult with the Department of Mathematical Sciences for possible prerequisite overrides.

Prerequisite: (MATH 21001 with a minimum C grade OR MATH 21002 with a minimum C grade) AND (MATH 12022 with a minimum B grade OR MATH 20011 with a minimum C grade OR MATH 30011 with a minimum B grade OR MATH 40012 with a minimum C grade).

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40024     COMPUTATIONAL STATISTICS      3 Credit Hours

(Slashed with MATH 50024) This course is about the use of computational tools to manage, explore, summarize, and visualize data, as well as the computational underpinnings of fitting statistical models. It uses mostly the statistical computation language R, but also other languages like Python and Matlab. It also covers: simulation and random number generation, computationally intensive methods like the bootstrap and permutation tests, Expectation-Maximization and related algorithms, and dimensionality reduction via matrix decomposition. Students with statistics courses from other disciplines should consult with the Department of Mathematical Sciences for possible prerequisite overrides.

Prerequisite: (MATH 21001 with a minimum C grade OR MATH 21002 with a minimum C grade) AND (MATH 12022 with a minimum B grade OR MATH 20011 with a minimum C grade OR MATH 30011 with a minimum B grade OR MATH 40012 with a minimum C grade).

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40028     STATISTICAL LEARNING      3 Credit Hours

(Slashed with MATH 50028) This course is about the statistical foundations of modern machine learning techniques. The main focus is classification and prediction, using regression-based, tree-based, and kernel-based methods. Specific methods include logistic regression, classification and regression trees, random forests, and support vector machines. The course also includes an introduction to unsupervised and semi-supervised learning.

Prerequisite: MATH 40015 and MATH 40024 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40051     TOPICS IN PROBABILITY THEORY AND STOCHASTIC PROCESSES      3 Credit Hours

(Slashed with MATH 50051) Topics from conditional expectations, Markov chains, Markov processes, Brownian motion and Martingales and their applications to stochastic calculus.

Prerequisite: MATH 40011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40055     ACTUARIAL MATHEMATICS I (ELR) (WIC)      4 Credit Hours

(Slashed with MATH 50055) Topics from survival models, stochastic analysis of annuities and life insurance and casualty models. .

Prerequisite: MATH 30055 and MATH 40011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement, Writing Intensive Course

MATH 40056     ACTUARIAL MATHEMATICS II      4 Credit Hours

(Slashed with MATH 50056) Benefit premiums, benefit reserves and their analysis, decrement models, joint survivorship, risk models.

Prerequisite: MATH 40055 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 40059     STOCHASTIC ACTUARIAL MODELS      3 Credit Hours

(Slashed with MATH 50059) Topics from investment risk, mean variance analysis, CAPM, financial derivatives, binomial pricing model, stochastic calculus, Black-Scholes pricing model, and Greeks.

Prerequisite: Minimum C grade in MATH 30055 and MATH 40011.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 40093     VARIABLE TITLE WORKSHOP IN MATHEMATICS      1-6 Credit Hours

(Repeatable for credit) Studies special topics in mathematics. Not acceptable for credit toward a major or minor in math without approval of student's adviser.

Prerequisite: Special approval.

Schedule Type: Workshop

Contact Hours: 1-6 other

Grade Mode: Satisfactory/Unsatisfactory

MATH 41001     MODERN ALGEBRA I (ELR) (WIC)      3 Credit Hours

(Slashed with MATH 51001) Basic properties of groups, subgroups, factor groups. Basic properties of rings, integral domains and homomorphisms.

Prerequisite: MATH 22005 or MATH 32051 with a minimum C grade; and MATH 31011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement, Writing Intensive Course

MATH 41002     MODERN ALGEBRA II (ELR) (WIC)      3 Credit Hours

(Slashed with MATH 51002) A continuation of MATH 41001, emphasizing properties of rings, their ideals, polynomial ring extensions, fields, finite degree extensions, roots of polynomials, constructability.

Prerequisite: Minimum C grade in MATH 41001.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement, Writing Intensive Course

MATH 41021     THEORY OF MATRICES      3 Credit Hours

(Slashed with MATH 51021) A rigorous study of the topics introduced in matrix algebra. Topics included are vector space preliminaries, canonical forms of matrices, diagonalizability criteria.

Prerequisite: MATH 21001 and MATH 22005 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 41038     INTERMEDIATE LOGIC      3 Credit Hours

(Slashed with MATH 51038; Cross-listed with CS 41038 and PHIL 41038 and PHIL 51038) A detailed, systematic study of symbolic logic for philosophy majors, mathematics majors, computer science majors, and anyone else interested in advanced study in logic. The aim of the course is twofold: first, to develop a facility in understanding and using symbolic logic for various purposes, and second, to understand and appreciate symbolic logic as an area of study in itself. Topics include the distinction between syntactic, object-level proofs and semantic, meta-level proofs, the distinction between axiomatic systems and natural deduction systems of object-level proofs, various systems of modal logic, and some non-classical logics.

Prerequisite: None.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 41045     METALOGIC      3 Credit Hours

(Slashed with MATH 51045; Cross-listed with CS 41045 and CS 51045 and PHIL 41045 and PHIL 51045) A detailed, systematic study of metalogic for philosophy majors, mathematics majors, computer science majors, and anyone else interested in advanced study in logic. Topics include the soundness and completeness of the propositional and predicate calculi, the decidablility of propositional calculus, the undecidability of predicate calculus, Gödel’s incompleteness proof for languages capable of expressing arithmetic, the co-extensionality of the set of general recursive functions, abacus computable functions, and Turing computable functions, and the philosophical motivations for the ChurchTuring Thesis that all computable functions are Turing computable.

Prerequisite: PHIL 41038.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42001     ANALYSIS I (ELR) (WIC)      3 Credit Hours

(Slashed with MATH 52001) Topics include basic structure of the real numbers, Cauchy sequences, convergence, completeness of the real numbers, continuity, differentiation and Riemann integration.

Prerequisite: MATH 22005 or MATH 32051 with a minimum C grade; and MATH 31011 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement, Writing Intensive Course

MATH 42002     ANALYSIS II (ELR) (WIC)      3 Credit Hours

(Slashed with MATH 52002) Topics include further development of integration theory, infinite series, uniform convergence, several variable calculus and metric spaces.

Prerequisite: MATH 42001 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

Attributes: Experiential Learning Requirement, Writing Intensive Course

MATH 42011     MATHEMATICAL OPTIMIZATION      3 Credit Hours

(Slashed with MATH 52011) Analytic and numerical techniques for location of extreme points of functions and calculus of variations. Both constrained and unconstrained problems are considered.

Prerequisite: Minimum C grade in MATH 21001 and MATH 22005 or MATH 32051.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42021     GRAPH THEORY AND COMBINATORICS      3 Credit Hours

(Slashed with MATH 52021) Fundamentals and applications of combinatorial mathematics. Topics include traversability, colorability, networks, inclusion and exclusion, matching and designs.

Prerequisite: MATH 12003 and MATH 21001 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42024     NUMBERS AND GAMES      3 Credit Hours

(Slashed with MATH 52024) The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory.

Prerequisite: MATH 21001 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42031     MATHEMATICAL MODELS AND DYNAMICAL SYSTEMS      3 Credit Hours

(Slashed with MATH 52031) Formulation and analysis of mathematical models for a variety of phenomena. Mathematical methods from optimization dynamical systems and probability are developed and applied. Modern software tools are utilized.

Prerequisite: MATH 32044 or MATH 32052 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42039     MODELING PROJECTS (ELR) (WIC)      3 Credit Hours

(Slashed with MATH 52039) Individual and small-group projects concerned with the formulation and analysis of mathematical models in a variety of areas. Written and oral reports are required.

Prerequisite: MATH 42031 with a minimum C grade.

Schedule Type: Seminar

Contact Hours: 3 other

Grade Mode: Standard Letter-IP

Attributes: Experiential Learning Requirement, Writing Intensive Course

MATH 42041     ADVANCED CALCULUS      3 Credit Hours

(Slashed with MATH 52041) The calculus and applications of scalar and vector functions of several variables. Vector differential and integral calculus. Applications to field theories, electricity and magnetism and fluid flow.

Prerequisite: MATH 21001 with a minimum C grade; and MATH 22005 or MATH 32051.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42045     PARTIAL DIFFERENTIAL EQUATIONS      3 Credit Hours

(Slashed with MATH 52045) An introduction to Fourier series, Fourier transforms and partial differential equations. Wave, heat and potential equations of mathematical physics. Additional topics include Green's functions and the Method of Characteristics for wave equations.

Prerequisite: MATH 32044 or MATH 32052 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42048     COMPLEX VARIABLES      3 Credit Hours

(Slashed with MATH 52048) Algebra of complex numbers, analytic functions, mappings, Cauchy integral theory, residue theory and applications.

Prerequisite: MATH 22005 or MATH 32051 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42201     NUMERICAL COMPUTING I      3 Credit Hours

(Cross-listed with CS 42201 and CS 52201; slashed with MATH 52201). An introduction to numerical methods and software for solving many common scientific computing problems. Linear systems, least-squares data fitting, nonlinear equations and systems, and optimization problems.

Prerequisite: Minimum C grade in all the following MATH 12003; and MATH 21001 or MATH 32051; and CS 13001 or (CS 13011 and CS 13012).

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 42202     NUMERICAL COMPUTING II      3 Credit Hours

(Cross-listed with CS 42202 and CS 52202) (Slashed with MATH 52202) A continuation of MATH 42201. Topics include interpolation, numerical differentiation and integration, and numerical solution of ordinary differential equations.

Prerequisite: MATH 42201 with a minimum C grade; and MATH 32044 or MATH 32052 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 45011     DIFFERENTIAL GEOMETRY      3 Credit Hours

(Slashed with MATH 55011) Analytic and metric differential geometry of curves and surfaces.

Prerequisite: MATH 22005 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 45021     EUCLIDEAN GEOMETRY      3 Credit Hours

(Slashed with MATH 55021) Geometry of Euclid extended to advanced topics of the triangle, quadrilaterals and circles: cross-ratio, groups, constructions, geometric generalizations; inversion.

Prerequisite: MATH 21001 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 45022     LINEAR GEOMETRY      3 Credit Hours

(Slashed with MATH 55022) Using transformations as a tool to study geometry and to differentiate between different kinds of geometry. Linear algebra methods applied to geometry.

Prerequisite: MATH 21001 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 46001     ELEMENTARY TOPOLOGY      3 Credit Hours

(Slashed with MATH 56001) Metric spaces, introduction to topological spaces, separation axioms.

Prerequisite: MATH 22005 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 47011     THEORY OF NUMBERS      3 Credit Hours

(Slashed with MATH 57011) Divisibility properties of the integers, prime numbers, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, rational approximations.

Prerequisite: MATH 12003 with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 47021     HISTORY OF MATHEMATICS      3 Credit Hours

(Slashed with MATH 57021) Survey from Babylonian and Egyptian mathematics to 20th century mathematics with emphasis on the development of algebra, geometry, calculus, number theory.

Prerequisite: MATH 23022 or higher with a minimum C grade.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 49995     SELECTED TOPICS IN MATHEMATICS AND ITS APPLICATIONS      1-4 Credit Hours

(Repeatable for credit) Various special courses will be announced in the schedule of classes under this course number with different section numbers.

Prerequisite: Special approval.

Schedule Type: Lecture

Contact Hours: 1-4 lecture

Grade Mode: Standard Letter

MATH 49996     INDIVIDUAL STUDY      1-4 Credit Hours

(Repeatable for credit) Individual investigation in mathematics.

Prerequisite: Special approval.

Schedule Type: Individual Investigation

Contact Hours: 1-4 other

Grade Mode: Standard Letter

MATH 49998     RESEARCH (ELR)      1-15 Credit Hours

(Repeatable for credit) Research in mathematics.

Prerequisite: Special approval.

Schedule Type: Research

Contact Hours: 1-15 other

Grade Mode: Satisfactory/Unsatisfactory-IP

Attributes: Experiential Learning Requirement

MATH 50011     PROBABILITY THEORY AND APPLICATIONS      3 Credit Hours

(Slashed with MATH 40011) Permutations and combinations, discrete and continuous distributions, random variables, conditional probabilities, Baye's formula, mathematical expectation, law of large numbers, normal approximations, basic limit theorems.

Prerequisite: Graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 50012     THEORY OF STATISTICS      3 Credit Hours

(Slashed with MATH 40012) Sample spaces, continuous distributions, sampling distributions, point and interval estimation, hypothesis testing, types of error, level and power of tests, sequential and nonparametric methods.

Prerequisite: MATH 40011 or MATH 50011; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 50015     APPLIED STATISTICS      3 Credit Hours

(Slashed with MATH 40015) Course is based on classical linear regression techniques with an emphasis on real data using the principles of sound data analysis. Close attention is given to issues of interpretation, diagnostics, outliers and influential points, goodness of fit and model selection. Topics include simple and multiple linear regression, transformation and modifications of covariates and responses, design matrices, variable selection and logistic regression.

Prerequisite: Applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 50024     COMPUTATIONAL STATISTICS      3 Credit Hours

(Slashed with MATH 40024) This course is about the use of computational tools to manage, explore, summarize, and visualize data, as well as the computational underpinnings of fitting statistical models. It uses mostly the statistical computation language R, but also other languages like Python and Matlab. It also covers: simulation and random number generation, computationally intensive methods like the bootstrap and permutation tests, Expectation-Maximization and related algorithms, and dimensionality reduction via matrix decomposition.

Prerequisite: Applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 50028     STATISTICAL LEARNING      3 Credit Hours

(Slashed with MATH 40028)This course is about the statistical foundations of modern machine learning techniques. The main focus is classification and prediction, using regression-based, tree-based, and kernel-based methods. Specific methods include logistic regression, classification and regression trees, random forests, and support vector machines. The course also includes an introduction to unsupervised and semi-supervised learning.

Prerequisite: MATH 40015 or 50015 and MATH 40024 or 50024; and applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 50051     TOPICS IN PROBABILITY THEORY AND STOCHASTIC PROCESSES      3 Credit Hours

(Slashed with MATH 40051) Topics from conditional expectations, Markov chains, Markov processes, Brownian Motion and Martingales and their applications to stochastic calculus.

Prerequisite: MATH 50011; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 50055     ACTUARIAL MATHEMATICS I      4 Credit Hours

(Slashed with MATH 40055) Topics from survival models, stochastic analysis of annuities and life insurance and casualty models.

Prerequisite: MATH 30055 and MATH 50011; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 50056     ACTUARIAL MATHEMATICS II      4 Credit Hours

(Slashed with MATH 40056) Benefit premiums, benefit reserves and their analysis; decrement models, joint survivorship, risk models.

Prerequisite: MATH 50055; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 50059     STOCHASTIC ACTUARIAL MODELS      3 Credit Hours

(Slashed with MATH 40059) Topics from investment risk, mean variance analysis, CAPM, financial derivatives, binomial pricing model, stochastic calculus, Black-Scholes pricing model, and Greeks.

Prerequisite: MATH 40011 or 50011 and Graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 51001     MODERN ALGEBRA I      3 Credit Hours

(Slashed with MATH 41001) Basic properties of groups, subgroups, factor groups. Basic properties of rings, integral domains and homomorphisms.

Prerequisite: MATH 21001 and MATH 22005; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 51002     MODERN ALGEBRA II      3 Credit Hours

(Slashed with MATH 41002) A continuation of MATH 51001, emphasizing properties of rings, their ideals, polynomial ring extensions, fields, finite degree extensions, roots of polynomials, constructibility.

Prerequisite: MATH 41001 or MATH 51001; and applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 51021     THEORY OF MATRICES      3 Credit Hours

(Slashed with MATH 41021) A rigorous study of the topics introduced in matrix algebra. Topics included are: canonical forms of matrices, diagonalizability criteria.

Prerequisite: MATH 21001 and MATH 22005; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 51038     INTERMEDIATE LOGIC      3 Credit Hours

(Cross-listed with CS 41038 and PHIL 41038 and PHIL 51038) (Slashed with MATH 41038) A detailed, systematic study of symbolic logic for philosophy majors, mathematics majors, computer science majors, and anyone else interested in advanced study in logic. The aim of the course is twofold: first, to develop a facility in understanding and using symbolic logic for various purposes, and second, to understand and appreciate symbolic logic as an area of study in itself. Topics include the distinction between syntactic, object-level proofs and semantic, meta-level proofs, the distinction between axiomatic systems and natural deduction systems of object-level proofs, various systems of modal logic and some non-classical logics.

Prerequisite: Graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 51045     METALOGIC      3 Credit Hours

(Cross-listed with CS 41045 and CS 51045 and PHIL 41045 and PHIL 51045) (Slashed with MATH 41045) A detailed, systematic study of metalogic for philosophy majors, mathematics majors, computer science majors, and anyone else interested in advanced study in logic. Topics include the soundness and completeness of the propositional and predicate calculi, the decidablility of propositional calculus, the undecidability of predicate calculus, Gödel’s incompleteness proof for languages capable of expressing arithmetic, the co-extensionality of the set of general recursive functions, abacus computable functions, and Turing computable functions, and the philosophical motivations for the ChurchTuring Thesis that all computable functions are Turing computable

Prerequisite: Graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52001     ANALYSIS I      3 Credit Hours

(Slashed with MATH 42001) Topics include basic structure of the real numbers, Cauchy sequences, convergence, completeness of the real numbers ,continuity, differentiation and Riemann integration.

Prerequisite: Applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52002     ANALYSIS II      3 Credit Hours

(Slashed with MATH 42002) Topics include further development of integration theory infinite series, uniform convergence, several variable calculus and metric spaces.

Prerequisite: MATH 42001 or MATH 52001; and applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52011     MATHEMATICAL OPTIMIZATION      3 Credit Hours

(Slashed with MATH 42011) Analytical and numerical techniques for location of extreme points of functions and calculus of variations. Both constrained and unconstrained problems are considered.

Prerequisite: MATH 21001 and MATH 22005; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52021     GRAPH THEORY AND COMBINATORICS      3 Credit Hours

(MATH 42021) Fundamentals and applications of combinatorial mathematics. Topics include transversability, colorability, networks, inclusion and exclusion, matching and designs.

Prerequisite: MATH 12003 and MATH 21001; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52024     NUMBERS AND GAMES      3 Credit Hours

(Slashed with MATH 42024) The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52031     MATHEMATICAL MODELS AND DYNAMICAL SYSTEMS      3 Credit Hours

(Slashed with MATH 42031) Formulation and analysis of mathematical models for a variety of phenomena. Mathematical methods from optimization, dynamical systems and probability are developed and applied. Modern software tools are utilized.

Prerequisite: MATH 32044; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52039     MODELING PROJECTS      3 Credit Hours

(Slashed with MATH 42039) Individual and small-group projects concerned with the formulation and analysis of mathematical models in a variety of areas. Written and oral reports required.

Prerequisite: MATH 52031 with a minimum C grade; and graduate standing.

Schedule Type: Seminar

Contact Hours: 3 other

Grade Mode: Standard Letter

MATH 52041     ADVANCED CALCULUS      3 Credit Hours

(Slashed with MATH 42041) The calculus and applications of scalar and vector functions of several variables. Vector differential and integral calculus. Applications to field theories, electricity and magnetism and fluid flow.

Prerequisite: MATH 21001 and MATH 22005.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52045     PARTIAL DIFFERENTIAL EQUATIONS      3 Credit Hours

(Slashed with MATH 42045) Introduction to Fourier series, Fourier transforms and partial differential equations. Wave, heat and potential equations of mathematical physics. Additional topics include Green's functions and the Method of Characteristics for wave equations.

Prerequisite: Applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52048     COMPLEX VARIABLES      3 Credit Hours

(Slashed with MATH 42048) Algebra of complex numbers, analytic functions, mappings, Cauchy integral theory, residue theory and applications.

Prerequisite: Applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52201     NUMERICAL COMPUTING I      3 Credit Hours

(Cross-listed with CS 42201 and CS 52201) (Slashed with MATH 42201) An introduction to numerical methods and software for solving many common scientific computing problems. Linear systems, least-square data fitting, nonlinear equations and systems and optimization problems.

Prerequisite: Applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 52202     NUMERICAL COMPUTING II      3 Credit Hours

(Cross-listed with CS 42202 and CS 52202) (Slashed with MATH 42202) A continuation of MATH 52201. Topics include interpolation, numerical differentiation and integration, and numerical solution of ordinary differential equations.

Prerequisite: MATH 42201 or 52201; and applied mathematics or pure mathematics major; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 55011     DIFFERENTIAL GEOMETRY      3 Credit Hours

(Slashed with MATH 45011) Analytic and metric differential geometry of curves and surfaces.

Prerequisite: MATH 22005; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 55021     EUCLIDEAN GEOMETRY      3 Credit Hours

(Slashed with MATH 45021) Geometry of Euclid extended to advanced topics of the triangle, quadrilaterals and circles: crossratio, groups, constructions, geometric generalizations; inversion.

Prerequisite: MATH 21001; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 55022     LINEAR GEOMETRY      3 Credit Hours

(Slashed with MATH 45022) Use of transformations as a tool to study geometry and to differentiate between different kinds of geometry. Linear algebra methods applied to geometry.

Prerequisite: MATH 21001; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 56001     ELEMENTARY TOPOLOGY      3 Credit Hours

(Slashed with MATH 46001) Metric spaces, introduction to topological spaces, separation axioms.

Prerequisite: MATH 22005; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 57011     THEORY OF NUMBERS      3 Credit Hours

(Slashed with MATH 47011) Divisibility properties of the integers, prime numbers, congruencies, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, rational approximations.

Prerequisite: MATH 12003; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 57021     HISTORY OF MATHEMATICS      3 Credit Hours

(Slashed with MATH 47021) Survey from Babylonian and Egyptian mathematics to 20th-century mathematics with emphasis on the development of algebra, geometry, calculus, number theory.

Prerequisite: One course MATH 23022 or higher; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 57091     SELECTED TOPICS IN MATHEMATICS AND ITS APPLICATIONS      1-3 Credit Hours

(Repeatable for credit) Various special courses will be announced in the schedule of classes under this course number with different section numbers.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 59893     VARIABLE TITLE WORKSHOP IN MATHEMATICS      1-6 Credit Hours

(Repeatable for credit) Studies in special topics in pure and applied mathematics.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Workshop

Contact Hours: 1-6 other

Grade Mode: Satisfactory/Unsatisfactory

MATH 60051     PROBABILITY I      4 Credit Hours

(Slashed with MATH 70051) Distribution functions, measure theory, random variables, expectation, independence, convergence, concepts, law of large numbers.

Prerequisite: MATH 40011 or MATH 42002 or MATH 50011 or MATH 52002; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 60052     PROBABILITY II      3 Credit Hours

(Slashed with MATH 70052) Characteristic functions, the central limit problem, conditional expectations, Martingale theory, Brownian motion.

Prerequisite: MATH 60051; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 60061     MATHEMATICAL STATISTICS I      4 Credit Hours

(Slashed with MATH 70061) Statistics, distributions of statistics. Sampling distributions. Decision spaces and loss functions. Sufficiency and completeness. Estimation theory. Rao Blackwell and the Cramer Rao theorems.

Prerequisite: MATH 42002 or MATH 52002; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 60062     MATHEMATICAL STATISTICS II      3 Credit Hours

(Slashed with MATH 70062) Tests of statistical hypothesis. Neyman Pearson Lemma. Exponential families and invariance. Sequential tests. Non-parametric procedures.

Prerequisite: MATH 60061; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 60070     FINANCIAL MATHEMATICS      3 Credit Hours

(Slashed with MATH 70070) Topics from replication of trading strategies, arbitrage, completeness, Martingale representation theorem, fundamental theorem of finance, stochastic differential equations, Black and Scholes formula of option pricing.

Prerequisite: MATH 50051; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 60091     SEMINAR IN STATISTICS AND PROBABILITY      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in statistics and probability.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 60093     VARIABLE TITLE WORKSHOP IN MATHEMATICS      1-3 Credit Hours

(Repeatable for credit) Studies of special topics in mathematics. Not acceptable for credit toward a graduate degree in mathematics without approval of the student's adviser.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Workshop

Contact Hours: 1-3 other

Grade Mode: Satisfactory/Unsatisfactory

MATH 60094     COLLEGE TEACHING OF MATHEMATICS      1 Credit Hour

(Repeatable for credit) Techniques and problems in the teaching of college-level mathematics. Student presentations of mathematical papers and colloquia will be included.

Prerequisite: Graduate standing.

Schedule Type: Lecture

Contact Hours: 1 lecture

Grade Mode: Standard Letter

MATH 61051     ABSTRACT ALGEBRA I      4 Credit Hours

(Slashed with MATH 71051) Advanced topics in group theory including Sylow Theorems, finite Abelian groups, divisible groups and related concepts. Includes one hour problem session each week.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 61052     ABSTRACT ALGEBRA II      3 Credit Hours

(Slashed with MATH 71052) Advanced topics, commutative ring theory and field theory, including polynomial rings, unique factorization domains, matrix rings, Galois theory.

Prerequisite: MATH 61051; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 61091     SEMINAR IN ALGEBRA      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in algebra.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Satisfactory/Unsatisfactory

MATH 62041     METHODS OF APPLIED MATHEMATICS I      3 Credit Hours

(Slashed with MATH 72041) Analysis and applications of ordinary and partial differential equations and related topics. Dimensional analysis (Buckingham Pi Theorem). Perturbation methods (singular perturbations, matched asymptotic expansions, WKB approximation). Variational methods (Euler-Lagrange equations).

Prerequisite: MATH 51021 and MATH 52041 and MATH 52045 and MATH 52048; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62042     METHODS OF APPLIED MATHEMATICS II      3 Credit Hours

(Slashed with MATH 72042) Continuation of MATH 62041. Integral equations and Green's functions (Fredholm alternative, compact operators, distributions, weak solutions). Wave phenomena (dispersion, KdV equation). Stability and bifurcation (linearized stability analysis, turning points, Hopf bifurcation).

Prerequisite: MATH 62041; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62051     FUNCTIONS OF A REAL VARIABLE I      4 Credit Hours

(Slashed with MATH 72051) Introduction to modern concepts of real analysis, including metric spaces, measure and integration theory.

Prerequisite: MATH 42002 or MATH 52002; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 62052     FUNCTIONS OF A REAL VARIABLE II      3 Credit Hours

(Slashed with MATH 72052) A continuation of MATH 62051. Included are basic topics in functional analysis and Hilbert space theory.

Prerequisite: MATH 62051; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62151     FUNCTIONS OF A COMPLEX VARIABLE I      4 Credit Hours

(Slashed with MATH 72151) Topological properties of the complex plane; analytic, entire, meromorphic functions; analytic continuation; conformal mappings; Picard's Theorem; Riemann surfaces.

Prerequisite: MATH 52002; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 62152     FUNCTIONS OF A COMPLEX VARIABLE II      3 Credit Hours

(Slashed with MATH 72152) Topological properties of the complex plane; analytic, entire, meromorphic functions; analytic continuation; conformal mappings; Picard's Theorem; Riemann surfaces.

Prerequisite: MATH 62151; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62203     COMPUTATIONAL FINANCE      3 Credit Hours

(Slashed with MATH 72203) Basic numerical methods, (numerical linear algebra, nonlinear equations, curve fitting, ODEs, integration, Monte-Carlo methods), numerical solution of PDEs (stability, convergence, Black-Scholes, American options, SDEs) probabilistic methods.

Prerequisite: MATH 22005 and MATH 21001 and MATH 32044; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62251     NUMERICAL ANALYSIS I      4 Credit Hours

(Slashed with MATH 72251) Floating point computation, rounding error analysis, conditioning, interpolation (polynomial, trigonometric, spline). Numerical quadrature (Newton-Cotes, Gauss),extrapolation, Romberg integration.

Prerequisite: MATH 42002 or MATH 52002; and graduate standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 62252     NUMERICAL ANALYSIS II      3 Credit Hours

(Slashed with MATH 72252) Numerical solution of linear systems of equations (LU factorization, error analysis). Least squares, orthogonalization methods. Algebraic eigenvalue problems, QR algorithm, singular value decomposition.

Prerequisite: MATH 41021 or MATH 51021; and MATH 62251 or MATH 72251; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62261     NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS      3 Credit Hours

(Slashed with MATH 72261) Discretization methods for ordinary differential equations and systems. Initial value and boundary value problems. Numerical implementation software and analysis.

Prerequisite: MATH 32044; and MATH 42202 or MATH 52202; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62262     NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS      3 Credit Hours

(Slashed with MATH 72262) Derivation and analysis of discrete methods (finite differences, finite elements) for the numerical solution of elliptic, hyperbolic and parabolic partial differential equations.

Prerequisite: MATH 42045 or MATH 52045; and MATH 42202 or MATH 52202; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62263     NUMERICAL SOLUTION OF LARGE SPARSE LINEAR SYSTEMS      3 Credit Hours

(Slashed with MATH 72263) (Cross-listed with CS 62263 and CS 72263) Construction and analysis of iterative methods for large systems of linear algebraic equations. Jacobi, Gauss-Seidel, SOR. Polynomial acceleration methods, conjugate gradients. Multi-grid methods.

Prerequisite: MATH 41021 or MATH 51021; and MATH 42202 or MATH 52202; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62264     NUMERICAL SOLUTION OF NONLINEAR SYSTEMS      3 Credit Hours

(Cross-listed with CS 62264 and CS 72264) (Slashed with MATH 72264) Construction and analysis of numerical methods for systems of nonlinear algebraic equations and optimization problems. Numerical implementation and software.

Prerequisite: MATH 42041 or MATH 52041; and MATH 42202 or MATH 52202; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 62291     SEMINAR IN NUMERICAL ANALYSIS      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in numerical analysis.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 3 other

Grade Mode: Standard Letter

MATH 62391     SEMINAR IN MEASURE THEORY      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in measure theory.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 62491     SEMINAR IN NONLINEAR ANALYSIS      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in nonlinear analysis.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 64091     SEMINAR IN MATHEMATICS EDUCATION      3 Credit Hours

(Repeatable for credit) Studies in geometry, algebra, mathematics for junior and senior high school. Mathematics content professionalized for teachers.

Prerequisite: MATH 34001; and graduate standing.

Schedule Type: Seminar

Contact Hours: 3 other

Grade Mode: Standard Letter

MATH 66051     INTRODUCTION TO TOPOLOGY I      4 Credit Hours

(Slashed with MATH 76051) Set theory, topological spaces, continuity, product spaces, quotient spaces, separation axioms, compactness and metrizability.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 66052     INTRODUCTION TO TOPOLOGY II      3 Credit Hours

(Slashed with MATH 76052) Geometric topology, including connectedness, continua, homotopy, the plane and 2 manifolds.

Prerequisite: MATH 76051; and graduate standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 67091     SEMINAR IN NUMBER THEORY      1-3 Credit Hours

(Repeatable for credit) (Slashed with MATH 77091) Seminar on current research in number theory.

Prerequisite: Graduate standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 67098     RESEARCH      1-15 Credit Hours

(Repeatable for credit) Research or individual investigation. Credits are applied toward degree requirements with approval if letter grade of "S" is given.

Prerequisite: Graduate standing.

Schedule Type: Research

Contact Hours: 1-15 other

Grade Mode: Standard Letter

MATH 67199     THESIS I      2-6 Credit Hours

Thesis student must register for a total of 6 hours, 2 to 6 hours in a single semester distributed over several semesters if desired.

Prerequisite: Graduate standing.

Schedule Type: Masters Thesis

Contact Hours: 2-6 other

Grade Mode: Satisfactory/Unsatisfactory-IP

MATH 67299     THESIS II      2 Credit Hours

Thesis students must continue registration each semester until all degree requirements are met.

Prerequisite: MATH 67199; and graduate standing.

Schedule Type: Masters Thesis

Contact Hours: 2 other

Grade Mode: Satisfactory/Unsatisfactory-IP

MATH 70051     PROBABILITY I      4 Credit Hours

(Slashed with MATH 60051) Distribution functions, measure theory, random variables, expectation, independence, convergence, concepts, law of large numbers.

Prerequisite: MATH 40011 or MATH 50011; or MATH 42002 or MATH 52002; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 70052     PROBABILITY II      3 Credit Hours

(Slashed with MATH 60052) Characteristic functions, the central limit problem, conditional expectations, Martingale theory, Brownian motion.

Prerequisite: MATH 60051 or MATH 70051; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 70061     MATHEMATICAL STATISTICS I      4 Credit Hours

(Slashed with MATH 60061) Statistics, distributions of statistics. Sampling distributions. Decision spaces and loss functions. Sufficiency and completeness. Estimation theory. Rao Blackwell and the Cramer Rao theorems.

Prerequisite: MATH 42002 or MATH 52002.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 70062     MATHEMATICAL STATISTICS II      3 Credit Hours

(Slashed with MATH 60062) Tests of statistical hypothesis. Neyman Pearson Lemma. Exponential families and invariance. Sequential tests. Non parametric procedures.

Prerequisite: MATH 60061 or MATH 70061; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 70070     FINANCIAL MATHEMATICS      3 Credit Hours

(Slashed with MATH 60070) Topics from replication of trading strategies, arbitrage completeness, Martingale presentation theorem, fundamental theorem of finance, stochastic differential equations, Black and Scholes formula of option pricing.

Prerequisite: MATH 50051; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 70091     SEMINAR IN STATISTICS AND PROBABILITY      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in statistics and probability.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Seminar

Contact Hours: 3 other

Grade Mode: Standard Letter

MATH 70094     COLLEGE TEACHING OF MATHEMATICS      1 Credit Hour

(Repeatable for credit) Techniques and problems in the teaching of college-level mathematics. Student presentations of mathematical papers and colloquia will be included.

Prerequisite: Doctoral standing.

Schedule Type: Lecture

Contact Hours: 1 lecture

Grade Mode: Standard Letter

MATH 70095     SELECTED TOPICS IN STATISTICS AND PROBABILITY      1-3 Credit Hours

(Repeatable for credit) Topics vary with each offering and complement topics covered in MATH 70051, MATH 70052, MATH 70061 and MATH 70062.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 71001     STRUCTURE OF RINGS AND ALGEBRAS I      3 Credit Hours

Advanced topics in ring theory, including Artinian rings, Noetherian rings, advanced commutative ring theory.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 71002     STRUCTURE OF RINGS AND ALGEBRAS II      3 Credit Hours

Advanced topics in ring theory including an introduction to homological algebra. Includes Dedekind domains, regular rings, torsion theory.

Prerequisite: MATH 71001; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 71011     ADVANCED GROUP THEORY      3 Credit Hours

Advanced topics in group theory. Topics include permutation arguments, coprime actions, transfer theorems, nonsimplicity criteria. Properties of families of groups: solvable, p solvable, nilpotent, p groups.

Prerequisite: MATH 61051 or MATH 71051; and MATH 61052 or MATH 71052; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 71012     CHARACTERS OF FINITE GROUPS      3 Credit Hours

Development of characters of finite groups, their properties, orthogonality relations, integrality conditions. Applications include Burnside's paqb theorem and existence of Frobenius kernels in Frobenius groups.

Prerequisite: MATH 61051 or MATH 71051; and MATH 61052 or MATH 71052; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 71051     ABSTRACT ALGEBRA I      4 Credit Hours

(Slashed with MATH 61051) Advanced topics in group theory, including Sylow theorems, finite Abelian groups, divisible groups and related concepts. Includes one-hour problem session each week.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 71052     ABSTRACT ALGEBRA II      3 Credit Hours

(Slashed with MATH 61052) Advanced topics, commutative ring theory and field theory, including polynomial rings, unique factorization, domains, matrix rings, Galois theory.

Prerequisite: MATH 61051 or MATH 71051; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 71091     SEMINAR IN ALGEBRA      1-3 Credit Hours

(Repeatable for credit) (Slashed with MATH 61091) Seminar on current research in algebra.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Satisfactory/Unsatisfactory

MATH 71095     SELECTED TOPICS IN ALGEBRA      1-3 Credit Hours

(Repeatable for credit) Topics vary with each offering and complement topics covered in MATH 71002, MATH 71051 and MATH 71052.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 72001     FUNCTIONAL ANALYSIS I      3 Credit Hours

A study of principles of linear analysis in the setting of normed linear spaces and topological vector spaces.

Prerequisite: MATH 72052; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72002     FUNCTIONAL ANALYSIS II      3 Credit Hours

A study of principles of linear analysis in the setting of normed linear spaces and topological vector spaces.

Prerequisite: MATH 72001; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72041     METHODS OF APPLIED MATHEMATICS I      3 Credit Hours

(Slashed with MATH 62041) Analysis and applications of ordinary and partial differential equations and related topics. Dimensional analysis (Buckingham Pi Theorem). Perturbation methods (singular perturbations, matched asymptotic expansions, WKB approximation). Variational methods (Euler-Lagrange equations).

Prerequisite: MATH 51021 and MATH 52041 and MATH 52045 and MATH 52048; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72042     METHODS OF APPLIED MATHEMATICS II      3 Credit Hours

(Slashed with MATH 62042) Continuation of MATH 72041. Integral equations and Green's functions (Fredholm alternative, compact operators, distributions, weak solutions). Wave phenomena (dispersion, KdV equation). Stability and bifurcation (linearized stability analysis, turning points, Hopf bifurcation).

Prerequisite: MATH 62041 or MATH 72041; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72051     FUNCTIONS OF A REAL VARIABLE I      4 Credit Hours

(Slashed with MATH 62051) Introduction to modern concepts of real analysis including metric spaces, measure and integration theory.

Prerequisite: MATH 42002 or MATH 52002; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 72052     FUNCTIONS OF A REAL VARIABLE II      3 Credit Hours

(Slashed with MATH 62052). A continuation of MATH 72051. Included are basic topics in functional analysis and Hilbert space theory.

Prerequisite: MATH 62051 or MATH 72051; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72095     SELECTED TOPICS IN REAL ANALYSIS      1-3 Credit Hours

(Repeatable for credit) Topics vary with each offering and complement topics covered in MATH 72002, MATH 72051 and MATH 72052.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 72151     FUNCTIONS OF A COMPLEX VARIABLE I      4 Credit Hours

(Slashed with MATH 62151) Topological properties of the complex plane; analytic, entire, meromorphic functions; analytic continuation; conformal mappings; Picard's Theorem; Riemann surfaces.

Prerequisite: MATH 52002; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 72152     FUNCTIONS OF A COMPLEX VARIABLE II      3 Credit Hours

(Slashed with MATH 62152) Topological properties of the complex plane; analytic, entire, meromorphic functions; analytic continuation; conformal mappings; Picard's theorem; Riemann surfaces.

Prerequisite: MATH 72151; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72195     SELECTED TOPICS IN COMPLEX ANALYSIS      1-3 Credit Hours

(Repeatable for credit) Topics vary with each offering and complement topics covered in MATH 72151 and MATH 72152.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 72203     COMPUTATIONAL FINANCE      3 Credit Hours

(Slashed with MATH 62203) Basic numerical methods, (numerical linear algebra, nonlinear equations, curve fitting, ODEs, integration, Monte-Carlo methods) numerical solution of PDEs (stability, convergence, Black-Scholes, American options, SDEs) probabilistic methods.

Prerequisite: MATH 22005 and MATH 21001 and MATH 32044; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72251     NUMERICAL ANALYSIS I      4 Credit Hours

(Slashed with MATH 62251) Floating point computation, rounding error analysis, conditioning, interpolation (polynomial, trigonometric spline). Numerical quadrature (Newton-Cotes, Gauss), extrapolation, Romberg integration.

Prerequisite: MATH 42002 or MATH 52002; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 72252     NUMERICAL ANALYSIS II      3 Credit Hours

(Slashed with MATH 62252) Numerical solution of linear systems of equations (LU factorization, error analysis). Least squares, orthogonalization methods. Algebraic eigenvalue problems, QR algorithm, singular value decomposition.

Prerequisite: MATH 41021 or MATH 51021; and MATH 62251 or MATH 72251; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72261     NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS      3 Credit Hours

(Slashed with MATH 62261) Discretization methods for ordinary differential equations and systems. Initial value and boundary value problems. Numerical implementation software and analysis.

Prerequisite: MATH 32044; and MATH 42202 or MATH 52202; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72262     NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS      3 Credit Hours

(Slashed with MATH 62262) Derivation and analysis of discrete methods (finite differences, finite elements) for the numerical solution of elliptic, hyperbolic and parabolic partial differential equations.

Prerequisite: MATH 42045 or MATH 52045; and MATH 42202 or MATH 52202; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72263     NUMERICAL SOLUTION OF LARGE SPARSE LINEAR SYSTEMS      3 Credit Hours

(Slashed with MATH 62263) (Cross-listed with CS 62263 and CS 72263) Construction and analysis of iterative methods for large systems of linear algebraic equations. Jacobi, Gauss-Seidel, SOR. Polynomial acceleration methods, conjugate gradients. Multi-grid methods.

Prerequisite: MATH 41021 or MATH 51021; and MATH 42202 or MATH 52202; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72264     NUMERICAL SOLUTION OF NONLINEAR SYSTEMS      3 Credit Hours

(Slashed with MATH 62264) (Cross-listed with CS 62264 and CS 72264) Construction and analysis of numerical methods for systems of nonlinear algebraic equations and optimization problems. Numerical implementation and software.

Prerequisite: MATH 42041 or MATH 52041; and MATH 42202 or MATH 52202; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 72291     SEMINAR IN NUMERICAL ANALYSIS      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in numerical analysis.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 72295     SELECTED TOPICS IN NUMERICAL ANALYSIS      1-3 Credit Hours

(Repeatable for credit) Topics vary with each offering and complement topics covered in MATH 72251 and MATH 72252.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 72391     SEMINAR IN MEASURE THEORY      1-3 Credit Hours

(Repeatable for credit) Seminar on current research in measure theory.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 72491     SEMINAR IN NONLINEAR ANALYSIS      1-3 Credit Hours

(Repeatable for credit)Seminar on current research in nonlinear analysis.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 76051     INTRODUCTION TO TOPOLOGY I      4 Credit Hours

(Slashed with MATH 66051) Set theory, topological spaces, continuity, product spaces, quotient spaces separation axioms, compactness and metrizability.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 4 lecture

Grade Mode: Standard Letter

MATH 76052     INTRODUCTION TO TOPOLOGY II      3 Credit Hours

Geometric topology, including connectedness, continua, homotopy, the plane and 2 manifolds.

Prerequisite: MATH 66051 or MATH 76051; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 76095     SELECTED TOPICS IN TOPOLOGY      1-3 Credit Hours

(Repeatable for credit) Topics vary with each offering and complement topics covered in MATH 76051 and MATH 76052.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 77011     ALGEBRAIC NUMBER THEORY      3 Credit Hours

Number fields and Dedekind domains; conjugates, norm and trace, discriminant, integral bases; arithmetic or quadraic and cyclotomic number fields; theory of ideals and class group; Dirichlet's thoerem on units.

Prerequisite: MATH 57011; and MATH 61052 or MATH 71052; and doctoral standing.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 77012     ANALYTIC NUMBER THEORY      3 Credit Hours

Multiplicative functions and summatory functions, Riemann's Zeta function and the prime number theorem, L-functions and Dirichlet's theorem on primes in artithmetic progressions, asymptotic formula for partitions.

Prerequisite: MATH 57011 and MATH 62151 or MATH 72151.

Schedule Type: Lecture

Contact Hours: 3 lecture

Grade Mode: Standard Letter

MATH 77091     SEMINAR IN NUMBER THEORY      1-3 Credit Hours

(Repeatable for credit) (Slashed with MATH 67091) Seminar on current research in number theory.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Seminar

Contact Hours: 1-3 other

Grade Mode: Standard Letter

MATH 77095     SELECTED TOPICS IN MATHEMATICS      1-3 Credit Hours

(Repeatable for credit) Course topic varies with each offering.

Prerequisite: Special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 77098     RESEARCH I      1-15 Credit Hours

(Repeatable for credit) Research or individual investigation. Credits are applied toward degree requirements with approval if letter grade of "S" is given.

Prerequisite: Doctoral standing.

Schedule Type: Research

Contact Hours: 1-15 other

Grade Mode: Standard Letter

MATH 77195     SELECTED TOPICS IN NUMBER THEORY      1-3 Credit Hours

(Repeatable for credit) Content varies with each offering and complements topics covered in MATH 77011 and MATH 77012.

Prerequisite: Doctoral standing; and special approval.

Schedule Type: Lecture

Contact Hours: 1-3 lecture

Grade Mode: Standard Letter

MATH 77198     RESEARCH II      1-15 Credit Hours

(Repeatable for credit) Research or individual investigation. Credits are applied toward degree requirements with approval if letter grade of "S" is given.

Prerequisite: Doctoral standing.

Schedule Type: Research

Contact Hours: 1-15 other

Grade Mode: Satisfactory/Unsatisfactory

MATH 87098     RESEARCH      1-15 Credit Hours

(Repeatable for credit) Research or individual investigation for doctoral students who have not yet passed their candidacy examinations. Credits earned may be applied toward degree if department approves.

Prerequisite: Doctoral standing.

Schedule Type: Research

Contact Hours: 1-15 other

Grade Mode: Standard Letter

MATH 87199     DISSERTATION I      15 Credit Hours

(Repeatable for credit) Doctoral dissertation, for which registration in at least two semesters is required first of which will be semester in which dissertation work is begun and continuing until the completion of 30 hours.

Prerequisite: Admission to doctoral candidacy; and doctoral standing.

Schedule Type: Dissertation

Contact Hours: 15 other

Grade Mode: Satisfactory/Unsatisfactory-IP

MATH 87299     DISSERTATION II      15 Credit Hours

(Repeatable for credit) Continuing registration required of doctoral students who have completed the initial 30 hours of dissertation and continuing until all degree requirements are met.

Prerequisite: MATH 87199; and doctoral standing.

Schedule Type: Dissertation

Contact Hours: 15 other

Grade Mode: Satisfactory/Unsatisfactory-IP