UTexas

Mathematics (M)

M 301  College Algebra  3 Hours  

(TCCN: MATH 1314, MATH 1414)  
3 Lecture Hours  0 Lab Hours  
Subjects include a brief review of elementary algebra; linear, quadratic, exponential, and logarithmic functions; polynomials; systems of linear equations; applications. May not be counted toward a degree in mathematics. Credit for Mathematics 301 may not be earned after a student has received credit for any calculus course with a grade of C- or better. Three lecture hours a week for one semester.
Pre/Corequisites: A passing score on the mathematics section of the Texas Higher Education Assessment (THEA) test (or an appropriate assessment test).  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 302  Introduction to Mathematics  3 Hours  

(TCCN: MATH 1332)  
3 Lecture Hours  0 Lab Hours  
Intended primarily for general liberal arts students seeking knowledge of the nature of mathematics as well as training in mathematical thinking and problem solving. Topics include number theory and probability; additional topics are chosen by the instructor. Mathematics 302 and 303F may not both be counted. A student may not earn credit for Mathematics 302 after having received credit for any calculus course. May not be counted toward a degree in the College of Natural Sciences. Three lecture hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: Texas Success Initiative (TSI) exemption or a TSI Mathematics Assessment score of 350 or higher.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 303D  Applicable Mathematics  3 Hours  

(TCCN: MATH 1324)  
3 Lecture Hours  0 Lab Hours  
An entry-level course for the nontechnical student, dealing with some of the techniques that allow mathematics to be applied to a variety of problems. Topics include linear and quadratic equations, systems of linear equations, matrices, probability, statistics, exponential and logarithmic functions, and mathematics of finance. Mathematics 303D and 303F may not both be counted. A student may not earn credit for Mathematics 303D after having received credit for Mathematics 305G or any calculus course. May not be counted toward a degree in the College of Natural Sciences. Three lecture hours a week for one semester.
Pre/Corequisites: An appropriate score on the mathematics placement exam.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 303F  Mathematics of Investment  3 Hours  

3 Lecture Hours  0 Lab Hours  
Simple and compound interest, equivalent rates, equivalent values, annuities, amortization, sinking funds, bonds, depreciation. Mathematics 302 and 303F may not both be counted; Mathematics 303D and 303F may not both be counted. May not be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in mathematics or toward the Bachelor of Science in Mathematics degree. Three lecture hours a week for one semester.
Pre/Corequisites: Three units of high school mathematics at the level of Algebra I or higher.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 403K  Calculus I for Business and Economics  4 Hours  

(TCCN: MATH 1325)  
3 Lecture Hours  2 Lab Hours  
Differential and integral calculus of algebraic, logarithmic, and exponential functions with applications. Only one of the following may be counted: Mathematics 403K, 408C, 408K, 408N, 408Q, 408R. May not be counted toward a degree in the College of Natural Sciences. Three lecture hours and two discussion sessions a week for one semester.
Pre/Corequisites: An appropriate score on the mathematics placement exam.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 403L  Calculus II for Business and Economics  4 Hours  

3 Lecture Hours  2 Lab Hours  
Differential and integral calculus of functions of several variables with applications, infinite series, improper integrals; introductions to probability, differential equations, matrices, systems of linear equations, and linear programming. Mathematics 403L and 408L (or 308L) may not both be counted. May not be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in mathematics or toward the Bachelor of Science in Mathematics degree. Three lecture hours and two discussion sessions a week for one semester.
Pre/Corequisites: Mathematics 403K, 408C, 308L, or 408N with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 305E  Analytic Geometry  3 Hours  

3 Lecture Hours  0 Lab Hours  
Combines development of methods (including adequate treatment of theory) and acquisition of skills with applications. Mathematics 305E and 305K may not both be counted. Mathematics 305E and 305G may not both be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in Mathematics or towards the Bachelor of Science in Mathematics degree. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 301.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 305G  Preparation for Calculus  3 Hours  

(TCCN: MATH 2312, MATH 2412)  
3 Lecture Hours  0 Lab Hours  
Study of advanced functions and their graphs and applications, including exponential, logarithmic, and trigonometric functions. Introduction to rates, slopes, and derivatives. Mathematics 305G and any college-level trigonometry course may not both be counted. A student may not earn credit for Mathematics 305G after having received credit for any calculus course with a grade of at least C-. Mathematic 301, 305G, and equivalent courses may not be counted toward a degree in mathematics. Three lecture hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: An appropriate score on the mathematics placement exam.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408C  Differential and Integral Calculus  4 Hours  

5 Lecture Hours  0 Lab Hours  
Introduction to the theory and applications of differential and integral calculus of functions of one variable; topics include limits, continuity, differentiation, the mean value theorem and its applications, integration, the fundamental theorem of calculus, and transcendental functions. Only one of the following may be counted: Mathematics 403K, 408C, 408K, 408N, 408Q, 408R. Three lecture hours and two discussion hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: An appropriate score on the mathematics placement exam or Mathematics 305G with a grade of at least B-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408D  Sequences, Series, and Multivariable Calculus  4 Hours  

5 Lecture Hours  0 Lab Hours  
This is the second semester of the accelerated calculus sequence. The theory and applications of sequences and infinite series, including those involving functions of one variable, and an introduction to the theory and applications of differential and integral calculus of functions of several variables; subjects include methods of integration, parametric equations, sequences, infinite series, power series, functions of several variables, partial derivatives, and multiple integrals. Only one of the following may be counted: Mathematics 403L, 408D, 408M (or 308M). Three lecture hours and two discussion hours a week for one semester.
Pre/Corequisites: Mathematics 408C, 408L, or 408S with a grade of at least C-.  
Restrictions: Certain sections of this course are designated as advanced placement or honors sections; they are restricted to students who have scored well on the Advanced Placement Calculus BC exam or have the consent of the mathematics adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408K  Differential Calculus  4 Hours  

(TCCN: MATH 2313, MATH 2413)  
5 Lecture Hours  0 Lab Hours  
Introduction to the theory and applications of differential calculus of functions of one variable; topics include limits, continuity, differentiation, and the mean value theorem and its applications. Only one of the following may be counted: Mathematics 403K, 408C, 408K, 408N, 408Q, 408R. Three lecture hours and two discussion hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: An appropriate score on the mathematics placement exam or Mathematics 305G with a grade of at least B-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 308L, 408L  Integral Calculus  3-4 Hours  

(TCCN: MATH 2314, MATH 2414)  
3,4 Lecture Hours  0 Lab Hours  
Introduction to the theory and applications of integral calculus of functions of one variable; topics include integration, the fundamental theorem of calculus, transcendental functions, sequences, and infinite series. Only one of the following may be counted: Mathematics 403L, 408L (or 308L), 408S. For Mathematics 308L, three lecture hours a week for one semester; for 408L, three lecture hours and two discussion hours a week for one semester.
Pre/Corequisites: Mathematics 408C, 408K, or 408N with a grade of at least C-, or Mathematics 408R or 408Q with a grade of at least B.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 308M, 408M  Multivariable Calculus  3-4 Hours  

(TCCN: MATH 2315, MATH 2415)  
3,5 Lecture Hours  0 Lab Hours  
Introduction to the theory and applications of differential and integral calculus of functions of several variables. Includes parametric equations, polar coordinates, vectors, vector calculus, functions of several variables, partial derivatives, gradients, and multiple integrals. Only one of the following may be counted: Mathematics 403L, 408D, 408M (or 308M). For Mathematics 308M, three lecture hours a week for one semester; for 408M, three lecture hours and two discussion hours a week for one semester.
Pre/Corequisites: Mathematics 408L or 408S with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408N  Differential Calculus for Science  4 Hours  

(TCCN: MATH 2413)  
5 Lecture Hours  0 Lab Hours  
Introduction to the theory of differential calculus of functions of one variable, and its application to the natural sciences. Subjects may include limits and differentiation, with applications to rates of change, extremes, graphing, and exponential growth and decay. Only one of the following may be counted: Mathematics 403K, 408C, 408K, 408N, 408Q, 408R. Three lecture hours and two discussion hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: An appropriate score on the mathematics placement exam or Mathematics 305G with a grade of at least B-.  
Restrictions: Restricted to students in the College of Natural Sciences.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408Q  Differential and Integral Calculus for Business  4 Hours  

5 Lecture Hours  0 Lab Hours  
Focus on the key concepts of calculus. These include: using successive approximations to solve problems that cannot be solved directly (Euler's Method), tracking the rate at which quantities are changing (derivatives) using rates of change to find optimal solutions to real-world problems (max/min), computing bulk quantities by adding up the pieces (integration), and understanding functions of several variables by studying one variable at a time. Designed for business students. Only one of the following may be counted: Mathematics 403K, 408C, 408K, 408N, 408Q, 408R. Three lecture hours and two discussion hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: An appropriate score on the mathematics placement exam or Mathematics 305G with a grade of at least B-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408R  Differential and Integral Calculus for the Sciences  4 Hours  

5 Lecture Hours  0 Lab Hours  
A calculus course for students in the life sciences. Emphasizes representations and analysis of data. Subjects include functions, rates, and derivatives and their applications to problems in biology; differential equations; Riemann integrals; the Euler method; and fundamental theorems of calculus. Only one of the following may be counted: Mathematics 403K, 408C, 408K, 408N, 408Q, 408R. Three lecture hours and two discussion hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: An appropriate score on the mathematics placement exam or Mathematics 305G with a grade of at least B-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 408S  Integral Calculus for Science  4 Hours  

(TCCN: MATH 2414)  
5 Lecture Hours  0 Lab Hours  
Introduction to the theory of integral calculus of functions of one variable, and its applications to the natural sciences. Subjects may include integration and its application to area and volume, and transcendental functions, sequences, and series and their application to numerical methods. Only one of the following may be counted: Mathematics 403L, 408L (or 308L), 408S. Three lecture hours and two discussion hours a week for one semester.
Pre/Corequisites: Mathematics 408C, 408K, or 408N with a grade of at least C-, or Mathematics 408R or 408Q with a grade of at least B.  
Restrictions: Restricted to students in the College of Natural Sciences.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 110C, 210C, 310C, 410C  Conference Course  1-4 Hours  

1,2,3,4 Lecture Hours  0 Lab Hours  
Supervised study in mathematics, with hours to be arranged.
Pre/Corequisites: Written consent of instructor; forms are available in the department office or in the Mathematics, Physics, and Astronomy Advising Center.  
Grading: Student Option  
Repeatable for credit: Yes (Unlimited)  
Academic Level: Lower Division  

M 210E  Emerging Scholars Seminar  2 Hours  

0 Lecture Hours  3 Lab Hours  
Supplemental problem-solving laboratory for precalculus, calculus, or advanced calculus courses for students in the Emerging Scholars Program. Three or four laboratory hours a week for one semester.
Restrictions: Restricted to students in the Emerging Scholars Program.  
Grading: Pass/Fail  
Repeatable for credit: Yes (Unlimited)  
Academic Level: Lower Division  

M 310P  Modern Mathematics: Plan II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Significant developments in modern mathematics. Topics may include fractals, the fourth dimension, statistics and society, and techniques for thinking about quantitative problems. May not be counted toward a degree in mathematics. Three lecture hours a week for one semester.
Core Curriculum: 020  
Restrictions: Restricted to Plan II students.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 110T, 210T, 310T, 410T  Topics in Mathematics  1-4 Hours  

1,2,3,4 Lecture Hours  0 Lab Hours  
One, two, three, or four lecture hours a week for one semester.
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: 0  

M 315C  Foundations, Functions, and Regression Models  3 Hours  

3 Lecture Hours  0 Lab Hours  
In-depth study of topics from secondary school mathematics. Emphasizes the development of the concept of function, exploring function patterns in data sets, and the connections between the main topics of mathematics associated with a secondary school curriculum. Use of appropriate technology is explored. Three lecture hours a week for one semester.
Core Curriculum: 020  
Pre/Corequisites: Credit or registration for Mathematics 408C and enrollment in a teaching preparation program, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 316K  Foundations of Arithmetic  3 Hours  

(TCCN: MATH 1350)  
3 Lecture Hours  0 Lab Hours  
An analysis, from an advanced perspective, of the concepts and algorithms of arithmetic, including sets; numbers; numeration systems; definitions, properties, and algorithms of arithmetic operations; and percents, ratios, and proportions. Problem solving is stressed. May not be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in mathematics or toward the Bachelor of Science in Mathematics degree. Credit for Mathematics 316K may not be earned after the student has received credit for any calculus course with a grade of C- or better, unless the student is registered in the College of Education. Three lecture hours a week for one semester.
Pre/Corequisites: One of the following with a grade of at least C-: Mathematics 301, 302, 303D, 305G, 316, Educational Psychology 371, Statistics and Data Sciences 302, 304, or 306.  
Restrictions: Restricted to students in a teacher preparation program.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 316L  Foundations of Geometry, Statistics, and Probability  3 Hours  

(TCCN: MATH 1351)  
3 Lecture Hours  0 Lab Hours  
An analysis, from an advanced perspective, of the basic concepts and methods of geometry, statistics, and probability, including representation and analysis of data; discrete probability, random events, and conditional probability; measurement; and geometry as approached through similarity and congruence, through coordinates, and through transformations. Problem solving is stressed. May not be counted toward the major requirement for the Bachelor of Arts, Plan I, degree with a major in mathematics or toward the Bachelor of Science in Mathematics degree. Credit for Mathematics 316L may not be earned after the student has received credit for any calculus course with a grade of C- or better, unless the student is registered in the College of Education. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 316K with a grade of at least C.  
Restrictions: Restricted to students in a teacher preparation program.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Lower Division  

M 119S, 219S, 319S, 419S, 519S, 619S, 719S, 819S, 919S  Topics in Mathematics  1-9 Hours  

0 Lecture Hours  0 Lab Hours  
This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  

M 321M  History of Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Survey major mathematical developments beginning with the ancient Greeks and tracing those developments through Hindu-Indian mathematics, Arabic mathematics, and European mathematics up to the nineteenth century. Only one of the following may be counted: Core Texts and Ideas 371M, 375 (Topic: History of Mathematics), Mathematics 321M, 375T (Topic: History of Mathematics). Three lecture hours a week for one semester.
Same as: CTI 371M  
Core Curriculum: 010  
Pre/Corequisites: Upper-division standing.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 325K  Discrete Mathematics  3 Hours  

(TCCN: MATH 2305)  
3 Lecture Hours  0 Lab Hours  
Provides a transition from the problem-solving approach of Mathematics 408C and 408D to the rigorous approach of advanced courses. Subjects include logic, set theory, relations and functions, combinatorics, and graph theory and graph algorithms. Three lecture hours a week for one semester.
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 326K  Foundations of Number Systems  3 Hours  

3 Lecture Hours  0 Lab Hours  
Study of number-related topics in middle-grade and secondary school mathematics. Topics include place value; meanings of arithmetic operations; analysis of computation methods; historical development of number concepts and notation; and rational, irrational, algebraic, transcendental, and complex numbers. Emphasis is on communicating mathematics, developing pedagogical understanding of concepts and notation, and using both informal reasoning and proof. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-.  
Restrictions: Restricted to students in a teacher preparation program or who have consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 427J  Differential Equations with Linear Algebra  4 Hours  

5 Lecture Hours  0 Lab Hours  
Ordinary differential equations, introduction to vector spaces, linear operators and eigenvalues, systems of linear differential equations, introduction to partial differential equations and Fourier series. Mathematics 427J and 427K may not both be counted. Five lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 427K  Advanced Calculus for Applications I  4 Hours  

(TCCN: MATH 2320, MATH 2420)  
5 Lecture Hours  0 Lab Hours  
Ordinary and partial differential equations and Fourier series. Mathematics 427J and 427K may not both be counted. Five lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 427L  Advanced Calculus for Applications II  4 Hours  

5 Lecture Hours  0 Lab Hours  
Matrices, elements of vector analysis and calculus of functions of several variables, including gradient, divergence, and curl of a vector field, multiple integrals and chain rules, length and area, line and surface integrals, Green's theorems in the plane and space, and, if time permits, complex analysis. Five class hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 328K  Introduction to Number Theory  3 Hours  

3 Lecture Hours  0 Lab Hours  
Provides a transition from the problem-solving approach of Mathematics 408C and 408D to the rigorous approach of advanced courses. Properties of the integers, divisibility, linear and quadratic forms, prime numbers, congruences and residues, quadratic reciprocity, number theoretic functions. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 325K, 333L, or 341 with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 329F  Theory of Interest  3 Hours  

3 Lecture Hours  0 Lab Hours  
Measurement of interest, present and accumulated value, amortization, sinking funds, bonds, duration, and immunization. Covers the interest-theory portion of an exam of the Society of Actuaries and the Casualty Actuarial Society. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 308L, 408L, 408M, or 408S with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 129S, 229S, 329S, 429S, 529S, 629S, 729S, 829S, 929S  Topics in Mathematics  1-9 Hours  

0 Lecture Hours  0 Lab Hours  
This course is used to record credit the student earns while enrolled at another institution in a program administered by the University's Study Abroad Office. Credit is recorded as assigned by the study abroad adviser in the Department of Mathematics. University credit is awarded for work in an exchange program; it may be counted as coursework taken in residence. Transfer credit is awarded for work in an affiliated studies program.
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  

M 329W  Cooperative Mathematics  3 Hours  

0 Lecture Hours  40 Lab Hours  
This course covers the work period of mathematics students in the Cooperative Education program, which provides supervised work experience by arrangement with the employer and the supervising instructor. The student must repeat the course each work period and must take it twice to receive credit toward the degree; at least one of these registrations must be during a fall or spring semester. No more than three semester hours may be counted toward the major requirement; no more than six semester hours may be counted toward the degree. The student's first registration must be on the pass/fail basis. Forty laboratory hours a week for one semester.
Pre/Corequisites: Application through the College of Natural Sciences Career Design Center; Mathematics 408D, 408L, or 408S with a grade of at least C-; a grade of at least C- in two of the following courses: Mathematics 325K, 427J or 427K, 341, 362K, or 378K; and consent of the undergraduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 333L  Structure of Modern Geometry  3 Hours  

3 Lecture Hours  0 Lab Hours  
Axiom systems, transformational geometry, introduction to non-Euclidean geometries, and other topics in geometry; use of these ideas in teaching geometry. Three lecture hours a week for one semester.
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 339C  Actuarial Case Studies  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduces aspects of basic ratemaking, reserving, catastrophe modeling, and rate classification in a property & casualty actuarial context. Explores loss & premium trending, loss triangles, loss development, loss ratios, on-level premium, and accident year vs. calendar year vs. policy year data. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 329F with a grade of at least C-; and Mathematics 339J or 339U with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 339D  Introduction to Financial Mathematics for Actuaries  3 Hours  

3 Lecture Hours  0 Lab Hours  
Covers the financial derivative subjects on the Society of Actuary FM/2 exam: general derivatives, options, hedging, investment strategies, forwards, futures, and swaps. Covers option pricing techniques in the MFE/3F exam: binomial option pricing, Monte Carlo Valuation using risk neutral probabilities, and Black-Scholes. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 329F and Mathematics 362K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 339G  Predictive Analytics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Designed for students in mathematics and actuarial science. Explore an introduction to predictive modeling that starts with least squares as a foundation and takes a modern approach applicable to classification and prediction in the presence of large datasets. Mathematics 339G and 375T (Topic: Predictive Analytics) may not both be counted. Three lecture hours a week for one semester.
Pre/Corequisites: The following with a grade of at least C-: Mathematics 341 or 340L; and Mathematics 358K or 378K.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 339J  Probability Models with Actuarial Applications  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introductory actuarial models for life insurance, property insurance, and annuities. With Mathematics 349P, covers the syllabus for the professional actuarial exam on model construction. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 358K or 378K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: 0  

M 139S  Seminar on Actuarial Practice  1 Hour  

1 Lecture Hours  0 Lab Hours  
Presentations by working actuaries on current issues in actuarial practice. One lecture hour a week for one semester.
Pre/Corequisites: Mathematics 329F; Mathematics 339J or 339U with a grade of at least C-; and credit with a grade of at least C- or registration for one of the following: Mathematics 339J, 339U, 339V, 349P.  
Grading: Pass/Fail  
Repeatable for credit: No  
Academic Level: Upper Division  

M 339U  Actuarial Contingent Payments I  3 Hours  

3 Lecture Hours  0 Lab Hours  
Intermediate actuarial models for life insurance, property insurance, and annuities. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 362K with a grade of at least C-; credit with a grade of at least C- or registration for Mathematics 329F; and credit with a grade of at least C- or registration for Mathematics 340L or 341.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 339V  Actuarial Contingent Payments II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Advanced actuarial models for life insurance, property insurance, and annuities. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 329F and 339U with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 340L  Matrices and Matrix Calculations  3 Hours  

3 Lecture Hours  0 Lab Hours  
Techniques of matrix calculations and applications of linear algebra. Only one of the following may count: Mathematics 340L, 341, Statistics and Data Sciences 329C. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408C, 408K, or 408N with a grade of at least C-.  
Restrictions: Restricted to non-mathematics majors.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 341  Linear Algebra and Matrix Theory  3 Hours  

3 Lecture Hours  0 Lab Hours  
Vector spaces, linear transformations, matrices, linear equations, determinants. Some emphasis on rigor and proofs. Only one of the following may count: Mathematics 340L, 341, Statistics and Data Sciences 329C. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-.  
Restrictions: Restricted to mathematics majors.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 343K  Introduction to Algebraic Structures  3 Hours  

3 Lecture Hours  0 Lab Hours  
Elementary properties of groups and rings, including symmetric groups, properties of the integers, polynomial rings, elementary field theory. Students who have received a grade of C- or better in Mathematics 373K may not take Mathematics 343K. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 325K, 333L, or Philosophy 313K, and Mathematics 328K or 341 with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 343L  Applied Number Theory  3 Hours  

3 Lecture Hours  0 Lab Hours  
Basic properties of integers, including properties of prime numbers, congruences, and primitive roots. Introduction to finite fields and their vector spaces with applications to encryption systems and coding theory. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 328K or 343K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 343M  Error-Correcting Codes  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to applications of algebra and number theory to error-correcting codes, including finite fields, error-correcting codes, vector spaces over finite fields, Hamming norm, coding, and decoding. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 328K or 341 with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 344K  Intermediate Symbolic Logic  3 Hours  

3 Lecture Hours  0 Lab Hours  
A second-semester course in symbolic logic: formal syntax and semantics, basic metatheory (soundness, completeness, compactness, and Loewenheim-Skolem theorems), and further topics in logic. Three lecture hours a week for one semester.
Same as: PHL 344K  
Pre/Corequisites: Philosophy 313, 313K, or 313Q.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 346  Applied Linear Algebra  3 Hours  

3 Lecture Hours  0 Lab Hours  
Emphasis on diagonalization of linear operators and applications to dynamical systems and ordinary differential equations. Other subjects include inner products and orthogonality, normal mode expansions, vibrating strings and the wave equation, and Fourier series. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 341 or 340L with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 348  Scientific Computation in Numerical Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to mathematical properties of numerical methods and their applications in computational science and engineering. Introduction to object-oriented programming in an advanced language. Study and use of numerical methods for solutions of linear systems of equations; nonlinear least-squares data fitting; numerical integration; and solutions of multidimensional nonlinear equations and systems of initial value ordinary differential equations. Three lecture hours a week for one semester.
Pre/Corequisites: Computer Science 303E and Mathematics 341 or 340L with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 349P  Actuarial Statistical Estimates  3 Hours  

3 Lecture Hours  0 Lab Hours  
Statistical estimation procedures for random variables and related quantities in actuarial models. With Mathematics 339J, covers the syllabus for the professional actuarial exam on model construction. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 339J, and 341 or 340L, with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: 0  

M 349R  Applied Regression and Time Series  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to simple and multiple linear regression and to elementary time-series models, including auto-regressive and moving-average models. Emphasizes fitting models to data, evaluating models, and interpreting results. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 358K or 378K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 349S  Actuarial Modeling and Simulation  3 Hours  

3 Lecture Hours  0 Lab Hours  
Apply Bayesian modeling and Markov-chain Monte Carlo simulations to Actuarial applications. Use R to carry out computations, simulations, and statistical analysis. Mathematics 349S and 375T (Topic: Actuarial Modeling/Simulation) may not both be counted. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 362K, and Mathematics 378K or 358K  
Grading: Letter Grade  
Repeatable for credit: No  
Academic Level: Upper Division  

M 349T  Time Series and Survival-Model Estimation  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to the probabilistic and statistical properties of time series; parameter estimation and hypothesis testing for survival models. Covers 30 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 339U, 341 or 340L, and 358K or 378K.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 358K  Applied Statistics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Exploratory data analysis, correlation and regression, data collection, sampling distributions, confidence intervals, and hypothesis testing. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 362K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 360M  Mathematics as Problem Solving  3 Hours  

3 Lecture Hours  0 Lab Hours  
Discussion of heuristics, strategies, and methods of evaluating problem solving, and extensive practice in both group and individual problem solving. Communicating mathematics, reasoning, and connections among topics in mathematics are emphasized. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-; and written consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 361  Theory of Functions of a Complex Variable  3 Hours  

3 Lecture Hours  0 Lab Hours  
Elementary theory and applications of analytic functions, series, contour integration, and conformal mappings. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J, 427K, or 427L with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 361K  Introduction to Real Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
A rigorous treatment of the real number system, of real sequences, and of limits, continuity, derivatives, and integrals of real-valued functions of one real variable. Students who have received a grade of C- or better in Mathematics 365C may not take Mathematics 361K. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 325K, 333L, or Philosophy 313K, and Mathematics 328K or 341 with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 362K  Probability I  3 Hours  

3 Lecture Hours  0 Lab Hours  
An introduction to the mathematical theory of probability, fundamental to further work in probability and statistics, includes basic probability properties, conditional probability and independence, various discrete and continuous random variables, expectation and variance, central limit theorem, and joint probability distributions. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 408D, 408L, or 408S with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 362M  Introduction to Stochastic Processes  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to Markov chains, birth and death processes, and other topics. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 362K with a grade of at least B and Mathematics 340L or 341 with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 364K  Vector and Tensor Analysis I  3 Hours  

3 Lecture Hours  0 Lab Hours  
Invariance, vector algebra and calculus, integral theorems, general coordinates, introductory differential geometry and tensor analysis, applications. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J, 427K, or 427L with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 364L  Vector and Tensor Analysis II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 364K, with emphasis on tensor and extensor analysis. Riemannian geometry and invariance. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 364K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 365C  Real Analysis I  3 Hours  

3 Lecture Hours  0 Lab Hours  
A rigorous treatment of the real number system, Euclidean spaces, metric spaces, continuity of functions in metric spaces, differentiation and Riemann integration of real-valued functions of one real variable, and uniform convergence of sequences and series of functions. Students who have received a grade of C- or better in Mathematics 365C may not take Mathematics 361K. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 325K, 333L, or Philosophy 313K, and Mathematics 328K or 341 with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 365D  Real Analysis II  3 Hours  

3 Lecture Hours  0 Lab Hours  
A rigorous treatment of selected topics in real analysis, such as Lebesgue integration, or multivariate integration and differential forms. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 365C with a grade of at least C-.  
Restrictions: Recommended for students planning to undertake graduate work in mathematics.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 365G  Curves and Surfaces  3 Hours  

3 Lecture Hours  0 Lab Hours  
Calculus applied to curves and surfaces in three dimensions: curvature and torsion of space curves, Gauss map and curvature of surfaces, Gauss theorem, geodesics, and the Gauss-Bonnet theorem. Three lecture hours a week for one semester.
Pre/Corequisites: Credit with a grade of at least C- or registration for Mathematics 365C.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 367K  Topology I  3 Hours  

3 Lecture Hours  0 Lab Hours  
An introduction to topology, including sets, functions, cardinal numbers, and the topology of metric spaces. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 361K or 365C.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 367L  Topology II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Various topics in topology, primarily of a geometric nature. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 367K with a grade of at least C- or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 368K  Numerical Methods for Applications  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 348. Topics include splines, orthogonal polynomials and smoothing of data, iterative solution of systems of linear equations, approximation of eigenvalues, two-point-boundary value problems, numerical approximation of partial differential equations, signal processing, optimization, and Monte Carlo methods. Only one of the following may be counted: Computer Science 367, Mathematics 368K, Physics 329. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 348 with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 371E  Learning Assistant Experience in Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Students assist instructors and TAs in mathematics courses. This is a hands-on experience in what it is like to teach and support students in the learning of mathematics in undergraduate courses. Students must attend classroom training and discussions and work in Calculus discussion sections or undergraduate classrooms where mathematics is being taught. One class hour and three hours of fieldwork in an undergraduate mathematics course a week for one semester.
Pre/Corequisites: Mathematics 408C, 408K, 408N, 408R, or equivalent, and consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 372  Fourier Series and Boundary Value Problems  3 Hours  

3 Lecture Hours  0 Lab Hours  
Discussion of differential equations of mathematical physics and representation of solutions by Green's functions and eigenfunction expansions. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J or 427K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 372K  Partial Differential Equations and Applications  3 Hours  

3 Lecture Hours  0 Lab Hours  
Partial differential equations as basic models of flows, diffusion, dispersion, and vibrations. Topics include first- and second-order partial differential equations and classification (particularly the wave, diffusion, and potential equations), and their origins in applications and properties of solutions. Includes the study of characteristics, maximum principles, Green's functions, eigenvalue problems, and Fourier expansion methods. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J or 427K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 373K  Algebraic Structures I  3 Hours  

3 Lecture Hours  0 Lab Hours  
A study of groups, rings, and fields, including structure theory of finite groups, isomorphism theorems, polynomial rings, and principal ideal domains. Students who have received a grade of C- or better in Mathematics 373K may not take Mathematics 343K. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 325K, 333L, or Philosophy 313K, and Mathematics 328K or 341 with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 373L  Algebraic Structures II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Topics from vector spaces and modules, including direct sum decompositions, dual spaces, canonical forms, and multilinear algebra. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 373K with a grade of at least C-.  
Restrictions: Recommended for students planning to undertake graduate work in mathematics.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 374  Fourier and Laplace Transforms  3 Hours  

3 Lecture Hours  0 Lab Hours  
Operational properties and application of Laplace transforms; some properties of Fourier transforms. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J or 427K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 374G  Linear Regression Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Fitting of linear models to data by the method of least squares, choosing best subsets of predictors, and related materials. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 358K or 378K with grade of at least C-, Mathematics 341 or 340L, and consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 374K  Fourier and Laplace Transforms  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 374. Introduction to other integral transforms, such as Hankel, Laguerre, Mellin, Z. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 374 with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 374M  Mathematical Modeling in Science and Engineering  3 Hours  

3 Lecture Hours  0 Lab Hours  
Tools for studying differential equations and optimization problems that arise in the engineering and physical sciences. Includes dimensional analysis and scaling, regular and singular perturbation methods, optimization and calculus of variations, and stability. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J or 427K, and Mathematics 340L, 341, or 311 with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 175, 275, 375, 475  Conference Course  1-4 Hours  

0 Lecture Hours  0 Lab Hours  
Supervised study in mathematics, with hours to be arranged.
Pre/Corequisites: Upper-division standing.  
Grading: Student Option  
Repeatable for credit: Yes (Unlimited)  

M 375C  Topics in Conference Course: Computer-Assisted  3 Hours  

0 Lecture Hours  0 Lab Hours  
Supervised study in mathematics on material requiring use of computing resources, with hours to be arranged. Conference course.
Pre/Corequisites: Varies with the topic.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Upper Division  

M 375D  Discovery: An Introduction to Advanced Study in Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Capstone course designed primarily for UTeach pre-service mathematics majors considering discovery teaching methodology and/or graduate work in mathematics or mathematics education. Ties together foundational topics in the primary strands of mathematics present in a typical graduate mathematics program; included are selected topics from analysis, algebra, number theory, and topology. Mathematics 375D and 375T (Topic: Discovery: An Introduction to Advanced Study in Mathematics) may not both be counted. Three lecture hours a week for one semester.
Pre/Corequisites: Two proof-based mathematics courses with a grade of at least C-, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 175S  Seminar in Instruction of Mathematics  1 Hour  

1 Lecture Hours  0 Lab Hours  
An exploration of subjects in mathematics instruction as taught at the secondary educational level. Practice learning and teaching through use of proofs, explorations, and connections. Subjects include foundational mathematics concepts, numbers, constructibility, and development of key mathematics topics. Mathematics 175S and 175T may not both be counted. One lecture hour a week for one semester.
Pre/Corequisites: Upper-division standing and consent of instructor.  
Grading: Letter Grade  
Repeatable for credit: No  
Academic Level: Upper Division  

M 175T, 275T, 375T, 475T  Topics in Mathematics  1-4 Hours  

1,2,3,4 Lecture Hours  0 Lab Hours  
For each semester hour of credit earned, the equivalent of one lecture hour a week for one semester.
Pre/Corequisites: Upper-division standing; additional prerequisites vary with the topic.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Upper Division  

M 376C  Topics in Methods of Applied Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Variational methods and related concepts from classical and modern applied mathematics. Models of conduction and vibration that lead to systems of linear equations and ordinary differential equations, eigenvalue problems, initial and boundary value problems for partial differential equations. Topics may include a selection from diagonalization of matrices, eigenfunctions and minimization, asymptotics of eigenvalues, separation of variables, generalized solutions, and approximation methods. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 427J or 427K, and 340L or 341, with a grade of at least C- in each.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Upper Division  

M 378K  Introduction to Mathematical Statistics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Sampling distributions of statistics, estimation of parameters (confidence intervals, method of moments, maximum likelihood, comparison of estimators using mean square error and efficiency, sufficient statistics), hypothesis tests (p-values, power, likelihood ratio tests), and other topics. Mathematics 378K and Statistics and Data Sciences 378 may not both be counted. Three lecture hours a week for one semester.
Same as: SDS 378  
Pre/Corequisites: Mathematics 362K with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 378N  Generalized Linear Models  3 Hours  

3 Lecture Hours  0 Lab Hours  
Extensions to ordinary least-squares regression, including Poisson regression, the lasso, mixed models, and ridge regression. Mathematics 375T (Topic: Generalized Linear Models) and 378N may not both be counted. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 378K with a grade of at least C- or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 378P  Decision Analytics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Examine decision theory with utility functions, including the use of probability, optimization, constrained optimization, and linear algebra. Only one of the following may be counted: Mathematics 375T (Topic: Decision Analytics), 378P, Statistics and Data Sciences 378P. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 362K and Mathematics 378K with a grade of at least C-, or consent of the instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 379H  Honors Tutorial Course  3 Hours  

0 Lecture Hours  0 Lab Hours  
Directed reading, research, and/or projects, under the supervision of a faculty member, leading to an honors thesis. Conference course.
Core Curriculum: 010  
Pre/Corequisites: Admission to the Mathematics Honors Program; Mathematics 365C, 367K, 373K, or 374G with a grade of at least A-, and another of these courses with a grade of at least B-; and consent of the honors adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Upper Division  

M 380C  Algebra  3 Hours  

3 Lecture Hours  0 Lab Hours  
A survey of algebraic structures, including groups, fields, rings, and modules. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 380D  Algebra  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 380C. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, consent of instructor or the graduate adviser, and Mathematics 380C.  
Grading: Student Option  
Repeatable for credit: No  

M 381C  Real Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line. Computational Science, Engineering, and Mathematics 385R and Mathematics 381C may not both be counted. Three lecture hours a week for one semester.
Same as: CSE 385R  
Pre/Corequisites: Graduate standing and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 381D  Complex Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to complex analysis. Computational Science, Engineering, and Mathematics 385S and Mathematics 381D may not both be counted. Three lecture hours a week for one semester.
Same as: CSE 385S  
Pre/Corequisites: Graduate standing and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 381E  Functional Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to functional analysis. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing; Computational Science, Engineering, and Mathematics 385R or Mathematics 381C; and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 382C  Algebraic Topology  3 Hours  

3 Lecture Hours  0 Lab Hours  
Surfaces, covering spaces, fundamental group, and homology. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, an undergraduate course in topology, and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  

M 382D  Differential Topology  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 382C. Manifolds and maps, differential forms, transversality, and intersection theory. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, consent of instructor or the graduate adviser, and Mathematics 382C.  
Grading: Student Option  
Repeatable for credit: No  

M 382E  Advanced Algebraic Topology  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 382C. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 382F  Algebraic Topology  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 382E. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, consent of instructor or the graduate adviser, and Mathematics 382E.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 382G  Differential Geometry  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Mathematics 382D. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 383C  Methods of Applied Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Topics include basic normed linear space theory; fixed-point theorems and applications to differential and integral equations; Hilbert spaces and the spectral theorem; applications to Sturm-Liouville problems; approximation and computational methods such as the Galerkin, Rayleigh-Ritz, and Newton procedures. Computational Science, Engineering, and Mathematics 386C and Mathematics 383C may not both be counted. Three lecture hours a week for one semester.
Same as: CSE 386C  
Pre/Corequisites: Graduate standing.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 383D  Methods of Applied Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Topics include distributions, fundamental solutions of partial differential equations, the Schwartz space and tempered distributions, Fourier transform, Plancherel theorem, Green's functions, Sobolev spaces, weak solutions, differential calculus in normed spaces, implicit function theorems, applications to nonlinear equations, smooth variational problems, applications to classical mechanics, constrained variational problems. Computational Science, Engineering, and Mathematics 386D and Mathematics 383D may not both be counted. Three lecture hours a week for one semester.
Same as: CSE 386D  
Pre/Corequisites: Graduate standing; and Computational Science, Engineering, and Mathematics 386C or Mathematics 383C.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 383E  Numerical Analysis: Linear Algebra  3 Hours  

3 Lecture Hours  0 Lab Hours  
Survey of numerical methods in linear algebra: floating-point computation, solution of linear equations, least squares problems, algebraic eigenvalue problems. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 383C, Computer Science 383C, Mathematics 383E, Statistics and Data Sciences 393C. Three lecture hours a week for one semester.
Same as: C S 383C, CSE 383C, SDS 393C  
Pre/Corequisites: Graduate standing; Computer Science 367 or Mathematics 368K; and Mathematics 340L, 341, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 383F  Numerical Analysis: Interpolation, Approximation, Quadrature, and Differential Equations  3 Hours  

3 Lecture Hours  0 Lab Hours  
Survey of numerical methods for interpolation, functional approximation, integration, and solution of differential equations. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 383D, Computer Science 383D, Mathematics 383F, Statistics and Data Sciences 393D. Three lecture hours a week for one semester.
Same as: C S 383D, CSE 383D, SDS 393D  
Pre/Corequisites: Graduate standing; Computational Science, Engineering, and Mathematics 383C, Computer Science 383C, Mathematics 383E, or Statistics and Data Sciences 393C; and Mathematics 427K and 365C, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 384C  Mathematical Statistics I  3 Hours  

3 Lecture Hours  0 Lab Hours  
The general theory of mathematical statistics. Includes distributions of functions of random variables, properties of a random sample, principles of data reduction, an overview of hierarchical models, decision theory, Bayesian statistics, and theoretical results relevant to point estimation, interval estimation, and hypothesis testing. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384R, Mathematics 384C, Statistics and Data Sciences 384 (Topic 2). Three lecture hours a week for one semester.
Same as: CSE 384R, SDS 384.2  
Pre/Corequisites: Graduate standing; and Mathematics 362K and 378K, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 384D  Mathematical Statistics II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Computational Science, Engineering, and Mathematics 384R and Mathematics 384C. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384S, Mathematics 384D, Statistics and Data Sciences 384 (Topic 3). Three lecture hours a week for one semester.
Same as: CSE 384S, SDS 384.3  
Pre/Corequisites: Graduate standing; Computational Science, Engineering, and Mathematics 384R, or Mathematics 384C; and Mathematics 362K and 378K, Statistics and Data Sciences 382, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 384E  Design and Analysis of Experiments  3 Hours  

3 Lecture Hours  0 Lab Hours  
Design and analysis of experiments, including one-way and two-way layouts; components of variance; factorial experiments; balanced incomplete block designs; crossed and nested classifications; fixed, random, and mixed models; and split plot designs. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384U, Mathematics 384E, Statistics and Data Sciences 384 (Topic 6). Three lecture hours a week for one semester.
Same as: CSE 384U, SDS 384.6  
Pre/Corequisites: Graduate standing; and Mathematics 362K and 378K, Statistics and Data Sciences 382, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 384F  Design of Experiments  3 Hours  

3 Lecture Hours  0 Lab Hours  
Design of experiments, including 2n and 3n factorial experiments, confounding, fractional factorials, sequential experimentation, orthogonal arrays, D-optimal experiments, and response surface methodology. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, and Mathematics 378K or the equivalent or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 384G  Regression Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Simple and multiple linear regression, inference in regression, prediction of new observations, diagnosis and remedial measures, transformations, and model building. Emphasis on both understanding the theory and applying theory to analyze data. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384T, Mathematics 384G, Statistics and Data Sciences 384 (Topic 4). Three lecture hours a week for one semester.
Same as: CSE 384T, SDS 384.4  
Pre/Corequisites: Graduate standing; and Mathematics 362K and 378K, Statistics and Data Sciences 382, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 384H  Multivariate Statistical Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to the general multivariate linear model; a selection of techniques, such as principle component, factor, and discriminant analysis. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 385C  Theory of Probability  3 Hours  

3 Lecture Hours  0 Lab Hours  
Computational Science, Engineering, and Mathematics 384K and Mathematics 385C may not both be counted. Three lecture hours a week for one semester.
Same as: CSE 384K  
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 385D  Theory of Probability  3 Hours  

3 Lecture Hours  0 Lab Hours  
Continuation of Computational Science, Engineering, and Mathematics 384K and Mathematics 385C. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384L, Mathematics 384L, 385D. Three lecture hours a week for one semester.
Same as: CSE 384L  
Pre/Corequisites: Graduate standing; Computational Science, Engineering, and Mathematics 384K or Mathematics 385C; and consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 387C  Numerical Analysis: Algebra and Approximation  3 Hours  

3 Lecture Hours  0 Lab Hours  
Advanced introduction to scientific computing, theory and application of numerical linear algebra, solution of nonlinear equations, and numerical approximation of functions. Computational Science, Engineering, and Mathematics 383K and Mathematics 387C may not both be counted. Three lecture hours a week for one semester.
Same as: CSE 383K  
Pre/Corequisites: Graduate standing, and consent of instructor or the graduate adviser.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 387D  Numerical Analysis: Differential Equations  3 Hours  

3 Lecture Hours  0 Lab Hours  
Advanced introduction to the theory and practice of commonly used numerical algorithms for the solution of ordinary differential equations, and elliptic, parabolic, and hyperbolic partial differential equations. Three lecture hours a week for one semester.
Same as: CSE 383L  
Pre/Corequisites: Graduate standing; and Computer Science 383C, Mathematics 387C, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389C  Actuarial Case Studies  3 Hours  

3 Lecture Hours  0 Lab Hours  
Explores aspects of basic ratemaking, reserving, catastrophe modeling, and rate classification in a property & casualty actuarial context. Covers loss & premium trending, loss triangles, loss development, loss ratios, on-level premium, accident year vs. calendar year vs. policy year data. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and either 389J or 389U with a grade of at least C.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389D  Introduction to Financial Mathematics for Actuaries  3 Hours  

3 Lecture Hours  0 Lab Hours  
Covers the financial derivative topics on the Society of Actuary FM/2 exam: general derivatives, options, hedging, investment strategies, forwards, futures, and swaps. Covers option pricing techniques in the MFE/3F exam: binomial option pricing, Monte Carlo Valuation using risk neutral probabilities, and Black-Scholes. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 389F.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389F  Theory of Interest  3 Hours  

3 Lecture Hours  0 Lab Hours  
Measurement of interest, present and accumulated value, amortization, sinking funds, bonds, duration, and immunization. Covers the interest theory portion of an exam of the Society of Actuaries and the Casualty Actuarial Society. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and Mathematics 408D or 408L.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389G  Predictive Analytics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Designed for students in mathematics and actuarial science. Explore an introduction to predictive modeling that starts with least squares as a foundation and takes a modern approach applicable to classification and prediction in the presence of large datasets. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing; an understanding of linear algebra and mathematical statistics.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389J  Probability Models with Actuarial Applications  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introductory actuarial models for life insurance, property insurance, and annuities. With Mathematics 389P, covers the syllabus for the professional actuarial exam on model construction. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, and Mathematics 358K or 378K with a grade of at least C.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389P  Actuarial Statistical Estimates  3 Hours  

3 Lecture Hours  0 Lab Hours  
Statistical estimation procedures for random variables and related quantities in actuarial models. With Mathematics 389J, covers the syllabus for the professional actuarial exam on model construction. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing; and Mathematics 341 or 340L, and 389J with a grade of at least C in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 189S  Seminar on Actuarial Practice  1 Hour  

1 Lecture Hours  0 Lab Hours  
Presentations by working actuaries on current issues in actuarial practice. One lecture hour a week for one semester.
Pre/Corequisites: Graduate standing; and Mathematics 329F or 389F, and 389J or 389U with a grade of at least C in each.  
Grading: Credit No Credit  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389T  Time Series and Survival-Model Estimation  3 Hours  

3 Lecture Hours  0 Lab Hours  
Introduction to the probabilistic and statistical properties of time series; parameter estimation and hypothesis testing for survival models. Covers 30 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, Mathematics 341 or 340L, 358K or 378K, and 389U.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389U  Actuarial Contingent Payments I  3 Hours  

3 Lecture Hours  0 Lab Hours  
Intermediate actuarial models for life insurance, property insurance, and annuities. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing; Mathematics 362K with a grade of at least C; credit with a grade of at least C or registration for Mathematics 340L (or 341); and credit with a grade of at least C or registration for Mathematics 329F or 389F.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389V  Actuarial Contingent Payments II  3 Hours  

3 Lecture Hours  0 Lab Hours  
Advanced actuarial models for life insurance, property insurance, and annuities. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing, and Mathematics 389F and 389U with a grade of at least C in each.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 389W  Financial Mathematics for Actuarial Applications  3 Hours  

3 Lecture Hours  0 Lab Hours  
Subjects include pricing, stock price, and interest rate models for actuarial applications. Tools include lognormal distribution, Brownian motion, Black-Scholes, and delta hedging. Three lecture hours a week for one semester.
Pre/Corequisites: Mathematics 389D with a grade of at least C-.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 390C  Topics in Algebra  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent topics have included algebraic geometry, number theory, algebraic curves, algebraic number theory, algebraic functions, rational curves on varieties, homological algebra. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 391C  Topics in Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent topics have included measure and integration, real variables, complex analysis, functional analysis, ordinary differential equations, partial differential equations, integral transforms, operator theory, approximation theory, abstract harmonic analysis. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 392C  Topics in Topology  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent topics have included algebraic topology, differential topology, geometric topology, Lie groups. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 393C  Topics in Applied Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent topics have included quantum mechanics, statistical physics, ergodic theory, group representations, statistical mechanics, quantum field theory, introductory partial differential equations, monotone operators and partial differential equations, Hilbert space methods for partial differential equations, Hamiltonian dynamics, nonlinear functional analysis, Euler and Navier-Stokes equations, microlocal calculus and spectral asymptotics, calculus of variations. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  
Topic 1: Neural Dynamics, Information Theory, and Machine Learning.
  

M 393C.1  Neural Dynamics, Information Theory, and Machine Learning  3 Hours  

3 Lecture Hours  0 Lab Hours  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 393N  Numerical Solution of Elliptic Partial Differential Equations  3 Hours  

3 Lecture Hours  0 Lab Hours  
The numerical solution of large systems of linear algebraic equations arising in the solution of elliptic partial differential equations by discretization methods. Computational Science, Engineering and Mathematics 393N and Mathematics 393N may not both be counted. Three lecture hours a week for one semester.
Same as: C S 393N  
Pre/Corequisites: Graduate standing; and Computational Science, Engineering, and Mathematics 383K , Computer Science 386K, Mathematics 387C, or consent of instructor.  
Grading: Student Option  
Repeatable for credit: No  
Academic Level: Doctoral  

M 394C  Topics in Probability and Statistics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent topics have included nonparametric statistics, advanced probability. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 395C  Topics in Logic and Foundations  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent topics have included set theory, model theory, proof theory, axiomatic theorem proving, automatic theorem proving, foundations of mathematics, recursion theory. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 196C, 296C, 396C, 696C, 996C  Topics in Mathematics  1,2,3,6,9 Hours  

1,2,3,6,9 Lecture Hours  0 Lab Hours  
Recent topics have included set theory, history of mathematics. For each semester hour of credit earned, the equivalent of one lecture hour a week for one semester
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 396D, 696D, 996D  Conference Course  3,6,9 Hours  

3,6,9 Lecture Hours  0 Lab Hours  
Supervised study in mathematics. Conference course. For each semester hour of credit earned, one lecture hour a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Credit No Credit  
Repeatable for credit: Yes (Unlimited)  
Academic Level: Doctoral  

M 397C  Topics in Numerical Analysis  3 Hours  

3 Lecture Hours  0 Lab Hours  
Recent developments and advanced topics in the field of numerical analysis. Mathematics 393D and 397C may not both be counted unless the topics vary. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing.  
Grading: Student Option  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 197S, 397S  Topics in Mathematics: Seminar  1,3 Hours  

1,3 Lecture Hours  0 Lab Hours  
One or three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and consent of instructor.  
Grading: Credit No Credit  
Repeatable for credit: May be repeated for credit when the topics vary.  
Academic Level: Doctoral  

M 698  Thesis  6 Hours  

3 Lecture Hours  0 Lab Hours  
The equivalent of three lecture hours a week for two semesters.
Pre/Corequisites: For 698A, graduate standing in mathematics and consent of the graduate adviser; for 698B, Mathematics 698A.  
Grading: Credit No Credit  
Repeatable for credit: No  
Academic Level: Master's  

M 398R  Master's Report  3 Hours  

0 Lecture Hours  0 Lab Hours  
Preparation of a report to fulfill the requirement for the master's degree under the report option. The equivalent of three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing in mathematics and consent of the supervising professor and the graduate adviser.  
Grading: Credit No Credit  
Repeatable for credit: No  
Academic Level: Master's  

M 398T  Supervised Teaching in Mathematics  3 Hours  

3 Lecture Hours  0 Lab Hours  
Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing and appointment as a teaching assistant.  
Grading: Letter Grade  
Repeatable for credit: No  
Academic Level: Doctoral  

M 399W, 699W, 999W  Dissertation  3,6,9 Hours  

0 Lecture Hours  0 Lab Hours  
Pre/Corequisites: Admission to candidacy for the doctoral degree.  
Grading: Credit No Credit  
Repeatable for credit: Yes (Unlimited)  
Academic Level: Doctoral