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2021-2022 General Catalog 
    
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2021-2022 General Catalog [ARCHIVED CATALOG]

**COURSE SEARCH**

The following is a listing of all courses of instruction offered by departments at LSU. This listing was up-to-date and as correct as possible at the time of publication of this catalog.

Since this catalog was prepared well in advance of its effective date, some courses may have been added, others may have been dropped, and/or changes in content may have been made.
 

Mathematics

No student may receive more than nine semester hours of credit in mathematics courses numbered below 1530, with the exception of students who are pursuing the elementary education degree and following the 12 hour sequence specified in that curriculum. No student who has already received credit for a mathematics course numbered 1530 or above may be registered in a mathematics course numbered below 1530, unless given special permission by the Department of Mathematics.
  

  • MATH 1009 Mathematics for Prospective Elementary School Teachers I (3)

    Offered by Independent and Distance Learning only. Logic; counting numbers, integers, rational numbers, real numbers; emphasis on field properties; set nomenclature and some number theory; units of measurement.
  

  • MATH 1010 Mathematics for Prospective Elementary School Teachers II (3)

    Prereq.: MATH 1009 . Offered by Independent and Distance Learning only. Continuation of MATH 1009 . Measurement, informal geometry, systems of equations, introduction to probability and statistics.
  

  • MATH 1015 Basic Mathematics and Applications (3)

    This course does not serve as a prerequisite for calculus. Credit will not be given for both this course and MATH 1021 , MATH 1022 , or MATH 1023 . Offered by Independent and Distance Learning only. Basic mathematical skills of graphing, formulas for geometric measurement, systems of linear equations and inequalities, review of quadratic equations, logarithms and application to exponential growth and decay, triangle trigonometry and its application to geometry and measurements.
  

  • MATH 1021 College Algebra (3)

    [LCCN: CMAT 1213, College Algebra] This is a General Education course. Prereq.: placement by department. Credit will not be given for both this course and MATH 1015  or MATH 1023 . Solving equations and inequalities; function properties and graphs with transformations; inverse functions; linear, quadratic, polynomial, rational, exponential and logarithmic functions with applications; systems of equations.
  

  • MATH 1022 Plane Trigonometry (3)

    [LCCN: CMAT 1223, Trigonometry] This is a General Education course. Prereq.: MATH 1021  or placement by department. Credit will not be given for both this course and MATH 1015  or MATH 1023 . Trigonometric functions with applications; graphs with transformations; inverse functions; fundamental identities and angle formulas; solving equations; solving triangles with applications; polar coordinate system; vectors.
  

  • MATH 1023 College Algebra and Trigonometry (5)

    [LCCN: CMAT 1235 Algebra and Trigonometry] This is a General Education course. Prereq.: placement by department. Credit will not be given for both this course and MATH 1015 , MATH 1021 , or MATH 1022 . This course fulfills 5 hrs. of the 6 hour General Education Analytical Reasoning requirement; a second Analytical Reasoning course will be required.
     Function properties and graphs; inverse functions; linear, quadratic, polynomial, rational, exponential and logarithmic functions; with applications systems of equations; partial fraction decomposition; conics; trigonometric functions and graphs; inverse trigonometric functions; fundamental identities and angle formulas; solving equations and triangles with applications; polar coordinate system; vectors.
  

  • MATH 1025 Mathematics of Commerce (3)

    Prereq.: MATH 1015 , MATH 1021 , or MATH 1023 .  Offered by Independent and Distance Learning only. Interest, discount, annuities, depreciation and insurance.
  

  • MATH 1029 Introduction to Contemporary Mathematics (3)

    [LCCN: CMAT 1103, Contemporary Math] This is a General Education course. Primarily for students in liberal arts and social sciences. Mathematical approaches to practical life problems. Topics include counting techniques and probability, statistics, graph theory, and linear programming.
  

  • MATH 1100 The Nature of Mathematics (3)

    [LCCN: CMAT 1103, 1313, Contemporary Math, Finite Math] This is a General Education course. Not for science, engineering or mathematics majors. For students who desire an exposure to mathematics as part of a liberal education. Using mathematics to solve problems and reason quantitatively. Topics include set theory, logic, personal finance, and elementary number theory.
  

  • MATH 1201 Number Sense and Open-Ended Problem Solving (3)

    Prereq.: MATH 1021  or MATH 1023 .  Primarily for students in the early childhood education PK-3 teacher certification curriculum or the elementary grades education curriculum. Cardinality and integers; decimal representation and the number line; number sense; open ended problem solving strategies; expressions and equation solving; primes, factors, and proofs; ratio and proportion; written communication of mathematics.
  

  • MATH 1202 Geometry, Reasoning and Measurement (3)

    Prereq.: MATH 1201 . Primarily for students in the early childhood education PK-3 teacher certification curriculum or the elementary grades education curriculum. Geometry and measurement in two and three dimensions; similarity; congruence; Pythagorean Theorem; written communication of mathematics.
  

  • MATH 1431 Calculus with Business and Economic Applications (3)

    [LCCN: CMAT 2103, Applied Calculus] This is a General Education course. Prereq.: MATH 1021  or MATH 1023 . Credit will not be given for this course and MATH 1530 , MATH 1540 , MATH 1550 , or MATH 1551 . 3 hrs. lecture; 1 hr. lab. Differential and integral calculus of algebraic, logarithmic and exponential functions; applications to business and economics such as maximum-minimum problems, marginal analysis and exponential growth models.
  

  • MATH 1435 Mathematics for Business Analysis (3)

    Prereq.: MATH 1431 . Offered by Independent and Distance Learning only. Sets and counting; probability, including conditional probability, discrete and continuous random variables, variance and normal distributions; matrices and echelon method for solving systems of equations; functions of several variables and partial derivatives.

     
  

  • MATH 1530 Differential Calculus (3)

    This is a General Education course. An honors course, MATH 1551 , is also available. Prereq.: An appropriate ALEKS placement score. Credit will not be given for this course and MATH 1431 , MATH 1550 , or MATH 1551 . Limits and derivatives of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
  

  • MATH 1540 Integral Calculus (3)

    This is a General Education course. An honors course, MATH 1551 , is also available. Prereq.: MATH 1530 . Credit will not be given for this course MATH 1431 , MATH 1550 , OR MATH 1551 . Integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
  

  • MATH 1550 Differential and Integral Calculus (5)

    [LCCN: CMAT 2115, Calculus I] This is a General Education course. An honors course, MATH 1551 , is also available. Prereq.: An appropriate ALEKS placement score. MATH 1530  and MATH 1540 , together, cover the material of MATH 1550. Credit will not be given for this course and MATH 1431 , MATH 1530 , MATH 1540 , or MATH 1551 . Limits, derivatives, and integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications. 
  

  • MATH 1551 HONORS: Differential and Integral Calculus (5)

    This is a General Education course. Same as MATH 1550 , with special honors emphasis for qualified students. Prereq.: An appropriate ALEKS honors placement score. Credit will not be given for this course and MATH 1431 , MATH 1530 , MATH 1540 , or MATH 1550 .
  

  • MATH 1552 Analytic Geometry and Calculus II (4)

    [LCCN: CMAT 2124, Calculus II] This is a General Education course. An honors course, MATH 1553 , is also available. Prereq.: MATH 1550  or MATH 1551 . Credit will not be given for both this course and MATH 1553  or MATH 1554 . Techniques of integration, parametric equations, analytical geometry, polar coordinates, infinite series, vectors in low dimensions; introduction to differential equations and partial derivatives.
  

  • MATH 1553 HONORS: Analytic Geometry and Calculus II (4)

    This is a General Education course. Same as MATH 1552  with special honors emphasis for qualified students. Credit will not be given for both this course and MATH 1552  or MATH 1554 .
  

  • MATH 1554 Calculus II for Life Sciences (4)

    [LCCN: CMAT 2124, Calculus II] This is a General Education course. Prereq.: MATH 1550  or MATH 1551 .  Credit will not be given for this course and either MATH 1552  or MATH 1553 . Does not serve as a prerequisite requirement for higher level Math courses. Designed for biological science majors. Techniques of integration, introduction to differential equations, stability of equilibrium points, elementary linear algebra, elements of multivariable calculus, systems of differential equations.
  

  • MATH 2020 Solving Discrete Problems (3)

    Prereq.: MATH 1550  or MATH 1551 .  Topics selected from formal logic, set theory, counting, discrete probability, graph theory, and number theory. Emphasis on reading and writing rigorous mathematics.
  

  • MATH 2025 Linear Algebra and Wavelets (3)

    Prereq.: MATH 1550  or MATH 1551 .  Topics: Haar wavelets, multiresolution analysis, and applications to imaging and signal processing. Emphasis on reading and writing rigorous mathematical proofs through linear algebra and wavelet transforms.
  

  • MATH 2030 Discrete Dynamical Systems (3)

    Prereq.: Credit or registration in MATH 1552  or MATH 1553 . The mathematical topics covered are fundamental in mathematical analysis, and are chosen from the area of discrete dynamical systems. These topics include precise definitions of limits, continuity, and stability properties of fixed points and cycles. Quadratic maps and their bifurcations are studied in detail, and metric spaces are introduced as the natural abstraction to explore deeper properties of symbolic dynamics, chaos, and fractals.
  

  • MATH 2057 Multidimensional Calculus (3)

    An honors course, MATH 2058 , is also available.  Prereq.: MATH 1552  or MATH 1553 .  Credit will not be given for both this course and MATH 2058 . Three-dimensional analytic geometry, partial derivatives, multiple integrals.
  

  • MATH 2058 HONORS: Multidimensional Calculus (3)

    Same as MATH 2057 , with special honors emphasis for qualified students. Credit will not be given for both this course and MATH 2057 .
  

  • MATH 2060 Technology Lab (1)

    Prereq.: credit or concurrent enrollment in MATH 2057  or MATH 2058 . Students are encouraged to enroll in MATH 2057  and MATH 2060 concurrently. Use of computers for investigating, solving and documenting mathematical problems; numerical, symbolic and graphical manipulation of mathematical constructs discussed in MATH 1550 , MATH 1552  and MATH 2057 .
  

  • MATH 2065 Elementary Differential Equations (3)

    Prereq.: MATH 1552  or MATH 1553 .  Credit will be given for only one of the following: MATH 2065, MATH 2070 , MATH 2090 . Ordinary differential equations; emphasis on solving linear differential equations.
  

  • MATH 2070 Mathematical Methods in Engineering (4)

    Prereq.: MATH 1552  or MATH 1553 . Credit will be given for only one of the following: MATH 2065 , MATH 2070, MATH 2090 . Ordinary differential equations, Laplace transforms, linear algebra and Fourier series; physical applications stressed.
  

  • MATH 2085 Linear Algebra (3)

    Prereq.: MATH 1552  or MATH 1553 . Credit will not be given for both this course and MATH 2090 . Systems of linear equations, vector spaces, linear transformations, matrices, determinants.
  

  • MATH 2090 Elementary Differential Equations and Linear Algebra (4)

    Prereq.: MATH 1552  or MATH 1553 . Credit will not be given for both this course and MATH 2065 , MATH 2070 ,or MATH 2085 . Introduction to first order differential equations, linear differential equations with constant coefficients, and systems of differential equations; vector spaces, linear transformations, matrices, determinants, linear dependence, bases, systems of equations, eigenvalues, eigenvectors, and Laplace transforms.
  

  • MATH 2203 Measurement: Proportional and Algebraic Reasoning (3)

    Prereq.: Professional Practice I Block, 12 sem. hrs. of mathematics including MATH 1201  and MATH 1202 , and concurrent enrollment in EDCI 3125 .
     Mathematics content course designed to be integrated in Praxis II with the principles and structures of mathematical reasoning applied to the grades 1-6 classroom. 2 hrs. lecture; 2 hrs. lab/field experience (as part of Professional Practice II Block). Development of a connected, balanced view of mathematics; interrelationship of patterns, relations, and functions; applications of algebraic reasoning in mathematical situations and structures using contextual, numeric, graphic, and symbolic representations; written communication of mathematics.
  

  • MATH 3002 Mathematics Classroom Presentations (2)

    Prereq.: SCI 2010  and SCI 2012 . Current standards for middle and high school mathematics and the mathematics certification exam. Students will prepare and present middle and/or high school mathematics lessons that incorporate this content and appropriate use of technology.
  

  • MATH 3003 Functions & Modeling (3)

    Prereq.: SCI 2011  or SCI 2012 . Using problem-based learning, technology and exploring in depth relationships between various areas of mathematics, students strengthen mathematical understandings of core concepts taught at the secondary level. Connections between secondary and college mathematics are investigated. Various topics from current standards for functions and statistics are included.
  

  • MATH 3050 Interest Theory (5)

    Prereq.: MATH 1552  or MATH 1553 .  Measurement of interest (including accumulated and present value factors), annuities certain, yield rates, amortization schedules and sinking funds, bonds and related securities, derivative instruments, and hedging and investment strategies. 
  

  • MATH 3355 Probability (3)

    Prereq.: Credit or registration in MATH 2057  or MATH 2058 .  Credit will not be given for this course and EE 3150 .  Introduction to probability, emphasizing concrete problems and applications; random variables, expectation, conditional probability, law of large numbers, central limit theorem and stochastic processes.
  

  • MATH 3903 Methods of Problem Solving (2)

    Prereq.: MATH 1552  or MATH 1553 , and MATH 2070 , MATH 2085  or MATH 2090  or consent of the department. Pass-fail grading. May be taken for a max. of 6 hrs. of credit when topics vary. Instruction and practice in solving a wide variety of mathematical and logical problems as seen in the Putnam competition.
  

  • MATH 4005 Geometry (3)

    Prereq.: MATH 2020 . Foundations of geometry, including work in Euclidean and non-Euclidean geometries.
  

  • MATH 4019 Calculus Internship Capstone (2)

    Prereq.: MATH 3003 . Students will be mentored by a calculus instructor and will participate in the planning and instruction of a recitation section for a calculus course. Skills and topics for teaching Calculus and Calculus AP will be included. 
  

  • MATH 4020 Capstone Course (3)

    Prereq.: Students should be within two semesters of completing the requirements for a mathematics major and must have completed a 4000-level mathematics course with a grade of “C” or better, or obtain permission of the department. Provides opportunities for students to consolidate their mathematical knowledge and to obtain a perspective on the meaning and significance of that knowledge. Course work will emphasize communication skills, including reading, writing and speaking mathematics.
  

  • MATH 4023 Applied Algebra (3)

    Prereq.: MATH 2085  or MATH 2090 . Credit will not be given for both this course and MATH 4200 . Finite algebraic structures relevant to computers: groups, graphs, groups and computer design, group codes, semigroups, finite-state machines.
  

  • MATH 4024 Mathematical Models (3)

    Prereq.: MATH 1552  or MATH 1553  and credit or registration in MATH 2085  or MATH 2090 . Construction, development and study of mathematical models for real situations; basic examples, model construction, Markov chain models, models for linear optimization, selected case studies.
  

  • MATH 4025 Optimization Theory and Applications (3)

    Prereq.: MATH 2057  or MATH 2058  and credit or registration in MATH 2085  or MATH 2090 .. Basic methods and techniques for solving optimization problems; n-dimensional geometry and convex sets; classical and search optimization of functions of one and several variables; linear, nonlinear and integer programming.
  
  

  • MATH 4031 Advanced Calculus I (3)

    Prereq.: MATH 2057  or MATH 2058  and either MATH 2085  or MATH 2090 . Completeness of the real line, Bolzano-Weierstrass theorem and Heine-Borel theorem; continuous functions including uniform convergence and completeness of C [a,b]; Riemann integration and the Darboux Criterion.
  

  • MATH 4032 Advanced Calculus II (3)

    Prereq.: MATH 4031  or equivalent. Derivative, including uniform convergence, the mean value theorem and Taylor’s Theorem; absolute and uniform convergence of series, completeness of sequence spaces, dual spaces; real analytic functions; functions of bounded variation, the Stieltjes integral and the dual of C [a,b].
  

  • MATH 4035 Advanced Calculus of Several Variables (3)

    Prereq.: MATH 4031 . Topology in n-dimensional space, differential calculus in n-dimensional space, inverse and implicit function theorems.
  

  • MATH 4036 Complex Variables (3)

    Prereq.: MATH 2057  or MATH 2058 . Analytic functions, integration, power series, residues and conformal mapping.
  

  • MATH 4038 Mathematical Methods in Engineering (3)

    Also offered as ME 4563 . Prereq.: MATH 2065  or MATH 2070  or MATH 2090 ; and MATH 2057  or MATH 2058 . Vector analysis; solution of partial differential equations by the method of separation of variables; introduction to orthogonal functions including Bessel functions.
  

  • MATH 4039 Introduction to Topology (3)

    Prereq.: MATH 2057   or MATH 2058 .  Examples and classification of two-dimensional manifolds, covering spaces, the Brouwer theorem and other selected topics.
  

  • MATH 4040 Short-term Actuarial Mathematics I (3)

    Prereq.: MATH 3355 . Actuarial models for insurance and annuities. Severity-of-loss and frequency-of-loss models, aggregate models, risk models, empirical estimation.
  

  • MATH 4041 Short-term Actuarial Mathematics II (3)

    Prereq.: MATH 4040  and one of MATH 4056 , EXST 3201 , or EXST 4050 .  Actuarial models for insurance and annuities.Statistical estimation procedures, credibility theory, and pricing and reserving.
  

  • MATH 4045 Long-term Actuarial Mathematics I (3)

    Prereq.: MATH 2085 , MATH 3050 , and MATH 3355 .  Survival models and their estimation. Distribution of the time-to-death random variable and its significance for insurance and annuity functions, net premiums, and reserves.
  

  • MATH 4046 Long-term Actuarial Mathematics II (3)

    Prereq.: MATH 4045  and one of MATH 4056 , EXST 3201 , or EXST 4050 .  Parametric survival models with multiple-life states; life insurance and annuity premium calculations; reserving and profit measures; participating insurances, pension plans, and retirement benefits.
  

  • MATH 4056 Mathematical Statistics (4)

    Prereq.: MATH 3355 . Statistical inference including hypothesis testing, estimators, and goodness-of-fit. Analysis of time series including moving-average, regression, autoregressive, and autoregressive-moving-average models.
  

  • MATH 4058 Elementary Stochastic Processes (3)

    Prereq.: MATH 3355  and either MATH 2085  or MATH 2090 .   Markov chains, Poisson process and Brownian motion.
  

  • MATH 4064 Numerical Linear Algebra (3)

    Prereq.: MATH 1552  or MATH 1553  and one of MATH 2057  or MATH 2058  or MATH 2085  or MATH 2090 . Gaussian elimination and LU factorization, tridiagonal systems, vector and matrix norms, singular value decomposition, condition number, least squares problem, QR factorization, iterative methods, power methods for eigenvalues and eigenvectors, applications.
  

  • MATH 4065 Numerical Analysis (3)

    Prereq.: MATH 2057  or MATH 2058 . An introduction to numerical methods in basic analysis, including root-finding, polynomial interpolation, numerical integration and differentiation, splines and wavelets.
  

  • MATH 4066 Numerical Differential Equations (3)

    Prereq.: Must take MATH 2057  or MATH 2058  and one of the following: 1) MATH 2070 , 2) MATH 2090 , 3) MATH 4027 , or 4) both MATH 2085  and MATH 2065 . Numerical solutions of initial value problems and boundary value problems for ordinary and partial differential equations.
  

  • MATH 4153 Finite Dimensional Vector Spaces (3)

    Prereq.:  MATH 2085  or MATH 2090 .  Vector spaces, linear transformations, determinants, eigenvalues, vectors and topics such as inner product space and canonical forms.
  

  • MATH 4158 Foundations of Mathematics (3)

    Prereq.: MATH 2020 , MATH 2025 , or MATH 2030 , or consent of instructor.  Rigorous development of the real numbers, sets, relations, product spaces, order and cardinality.
  

  • MATH 4171 Theory of Graphs (3)

    Prereq.: MATH 2085  or MATH 2090 . Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, network flows, matching theory and applications.
  

  • MATH 4172 Combinatorics (3)

    Prereq.: MATH 2085  or MATH 2090 . Topics selected from permutations and combinations, generating functions, principle of inclusion and exclusion, configurations and designs, matching theory, existence problems, applications.
  

  • MATH 4181 Elementary Number Theory (3)

    Prereq.: MATH 2057  or MATH 2058  or MATH 2085  or MATH 2090 .  Divisibility, Euclidean algorithm, prime numbers, congruences and topics such as Chinese remainder theorem and sums of integral squares.
  

  • MATH 4200 Abstract Algebra I (3)

    Prereq.: MATH 2085  or MATH 2090 . Credit will not be given for both this course and MATH 4023 . Elementary properties of sets, relations, mappings, integers; groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms and permutation groups; elementary properties of rings.
  

  • MATH 4201 Abstract Algebra II (3)

    Prereq.: MATH 4200 . Ideals in rings, factorization in polynomial rings; unique factorization and Euclidean domains, field extensions, splitting fields, finite fields, Galois theory.
  

  • MATH 4325 Fourier Transforms (3)

    Prereq.: MATH 1552  or MATH 1553 , and one of MATH 2057 , MATH 2058 , MATH 2065 , MATH 2070 , MATH 2085 , MATH 2090 . For students majoring in mathematics, physics and engineering. Fourier analysis on the real line, the integers and finite cyclic groups; the fast Fourier transform; generalized functions; attention to modern applications and computational methods.
  

  • MATH 4340 Partial Differential Equations (3)

    Prereq.: either MATH 2057  or MATH 2058  and one of the following: 1) MATH 2070 , 2) MATH 2090 , or 3) both MATH 2065  and MATH 2085 . First-order partial differential equations and systems, canonical second-order linear equations, Green’s functions, method of characteristics, properties of solutions and applications.
  

  • MATH 4345 Special Functions (3)

    Prereq.: either MATH 2057  or MATH 2058 , and one of the following: 1) MATH 2070 , 2) MATH 2090 , or 3) MATH 2065  and MATH 2085 . Sturm-Liouville problems, orthogonal functions (Bessel, Laguerre, Legendre, Hermite), orthogonal expansions including Fourier series, recurrence relations and generating functions, gamma and beta functions, Chebychev polynomials and other topics.
  

  • MATH 4700 History of Mathematics (3)

    Prereq.: MATH 2057  or MATH 2058 , MATH 2020 , and MATH 2085  or MATH 2090 ; students entering the course should have a firm sense of what constitutes a proof. This course will have substantial mathematical content; topics such as early Greek mathematics, from Euclid to Archimedes; algebra and number theory from Diophantus to the present; the calculus of Newton and Leibniz; the renewed emphasis on rigor and axiomatic foundations in the 19th and 20th centuries; interactions of mathematics with technology and the natural sciences; biographies of significant mathematicians.
  

  • MATH 4997 Vertically Integrated Research (3)

    May be taken for a maximum of 24 hours with consent of instructor. This course is intended to provide opportunities for students to learn about mathematical research and to engage in mathematical research in a vertically integrated learning and research community. Undergraduate students, graduate students, postdoctoral researchers and faculty may work together as a unit to learn and create new mathematics. Possible formats include group reading and exposition, group research projects, written and oral presentations. Undergraduate students may have a research capstone experience or write an honors thesis as part of this course.
  

  • MATH 4999 Selected Readings in Mathematics (1-3)

    Prereq.: consent of department. May be taken for a max. of 9 sem. hrs. credit.
  

  • MATH 6301 Implementing Curriculum Standards for Mathematics in the Elementary Grades (1-3)

    May be repeated for up to 9 sem. hrs. of credit if department certifies that topics do not overlap. This course is intended primarily for participants in teacher-training programs. Mathematics selected from nationally recognized curriculum standards for the elementary grades, treated with attention to depth and the specific needs of teachers.
  

  • MATH 6302 Implementing Curriculum Standards for Mathematics in the Middle Grades (1-3)

    May be repeated for up to 9 sem. hrs. of credit if department certifies that topics do not overlap. This course is intended primarily for participants in teacher-training programs. Mathematics selected from nationally recognized curriculum standards for the middle grades, treated with attention to depth and the specific needs of teachers.
  

  • MATH 6303 Implementing Curriculum Standards for Mathematics in High School (1-3)

    May be repeated for up to 9 sem. hrs. of credit if department certifies that topics do not overlap. This course is intended primarily for participants in teacher-training programs. Mathematics selected from nationally recognized curriculum standards for high school, treated with attention to depth and the specific needs of teachers.
  

  • MATH 6893 Seminar in Mathematics for Secondary Teachers (1-3)

    Prereq.: consent of department. May be repeated for a max. of 6 sem. hrs. when topics vary. Topics of interest to teachers of secondary school mathematics.
  

  • MATH 7001 Communicating Mathematics I (1)

    Prereq.: consent of department. Practical training in the teaching of undergraduate mathematics; how to write mathematics for publication; other issues relating to mathematical exposition.
  

  • MATH 7002 Communicating Mathematics II (1)

    Prereq.: consent of department. Practical training in the written and oral presentation of mathematical papers; the teaching of mathematics and the uses of technology in the mathematics classroom.
  

  • MATH 7210 Algebra I (3)

    Prereq.: MATH 4200  or equivalent. Groups: Group actions and Sylow Theorems, finitely generated abelian groups; rings and modules: PIDs, UFDs, finitely generated modules over a PID, applications to Jordan canonical form, exact sequences.
  

  • MATH 7211 Algebra II (3)

    Prereq.: MATH 7210  or equivalent. Fields: algebraic, transcendental, normal, separable field extensions; Galois theory, simple and semisimple algebras, Wedderburn theorem, group representations, Maschke’s theorem, multilinear algebra.
  

  • MATH 7220 Commutative Algebra (3)

    Prereq.: MATH 7211 . Commutative rings and modules, prime ideals, localization, noetherian rings, primary decomposition, integral extensions and Noether normalization, the Nullstellensatz, dimension, flatness, graded rings, Hilbert polynomial, valuations, regular rings, homological dimension, depth, completion, Cohen-Macaulay modules.
  

  • MATH 7230 Topics in Number Theory (3)

    Prereq.: MATH 7211 . May be repeated for credit with consent of department for a maximum of 9 credit hours. Topics in number theory such as algebraic integers, ideal class group, Galois theory of prime ideals, cyclotomic fields, class field theory, Gauss sums, quadratic fields, local fields, elliptic curves, L-functions and Dirichlet series, modular forms, Dirichlet’s theorem and Prime Number theorem, Diophantine equations, Circle method.
  

  • MATH 7240 Topics in Algebraic Geometry (3)

    Prereq.: MATH 7211 . May be repeated for credit with consent of department for a maximum of 9 credit hours. Topics in algebraic geometry such as affine and projective varieties, morphisms and rational mappings, nonsingular varieties, sheaves and schemes, sheaf cohomology, algebraic curves and surfaces, elliptic curves, toric varieties, real algebraic geometry.
  

  • MATH 7250 Representation Theory (3)

    Prereq.: MATH 7211 . Representations of finite groups, group algebras, character theory, induced representations, Frobenius reciprocity, Lie algebras and their structure theory, classification of semi-simple Lie algebras, universal enveloping algebras and the PBW theorem, highest weight representations, Verma modules, and finite-dimensional representations.
  

  • MATH 7260 Homological Algebra (3)

    Prereq.: MATH 7211 . Modules over a ring, projective and injective modules and resolutions, abelian categories, functors and derived functors, Tor and Ext, homological dimension of rings and modules, spectral sequences, and derived categories.
  

  • MATH 7280 Seminar in Commutative Algebra (1-3)

    Prereq.: consent of department. May be repeated for credit with consent of department. Advanced topics such as commutative rings, homological algebra, algebraic curves or algebraic geometry.
  

  • MATH 7290 Seminar in Algebra and Number Theory (1-3)

    Prereq.: consent of department. May be repeated for credit with the consent of the department. Advanced topics such as algebraic number theory, algebraic semigroups, quadratic forms or algebraic K-theory.
  

  • MATH 7311 Real Analysis I (3)

    Prereq.: MATH 4032  or equivalent. Abstract measure and integration theory with application to Lebesgue measure on the real line and Euclidean space.
  

  • MATH 7320 Ordinary Differential Equations (3)

    Prereq.: MATH 2085  and MATH 4031  or equivalent. Existence and uniqueness theorems, approximation methods, linear equations, linear systems, stability theory; other topics such as boundary value problems.
  

  • MATH 7325 Numerical Analysis and Applications (3)

    Prereq.: MATH 4065  or equivalent. Finite difference methods; finite element methods; iterative methods; methods of parallel computing; applications to the sciences and engineering.
  

  • MATH 7330 Functional Analysis (3)

    Banach spaces and their generalizations; Baire category, Banach-Steinhaus, open mapping, closed graph, and Hahn-Banach theorems; duality in Banach spaces, weak topologies; other topics such as commutative Banach algebras, spectral theory, distributions, and Fourier transforms.
  

  • MATH 7350 Complex Analysis (3)

    Prereq.: MATH 7311  or equivalent. Theory of holomorphic functions of one complex variable; path integrals, power series, singularities, mapping properties, normal families, other topics.
  

  • MATH 7360 Probability Theory (3)

    Prereq.: MATH 7311  or equivalent. Probability spaces, random variables and expectations, independence, convergence concepts, laws of large numbers, convergence of series, law of iterated logarithm, characteristic functions, central limit theorem, limiting distributions, martingales.
  

  • MATH 7365 Applied Stochastic Analysis (3)

    Prereq.: MATH 7360 . Brownian motion, basic stochastic calculus, applications to finance.
  

  • MATH 7366 Stochastic Analysis (3)

    Prereq.: MATH 7360 . Wiener process, stochastic integrals, stochastic differential equations.
  

  • MATH 7370 Lie Groups and Representation Theory (3)

    Prereq.: MATH 7311 , MATH 7210 , and MATH 7510  or equivalent. Lie groups, Lie algebras, subgroups, homomorphisms, the exponential map. Also topics in finite and infinite dimensional representation theory.
  

  • MATH 7375 Wavelets (3)

    Prereq.: MATH 7311  or equivalent. Fourier series; Fourier transform; windowed Fourier transform or short-time Fourier transform; the continuous wavelet transform; discrete wavelet transform; multiresolution analysis; construction of wavelets.
  

  • MATH 7380 Seminar in Functional Analysis (1-3)

    Prereq.: consent of department. May be repeated for credit with consent of department. Advanced topics such as topological vector spaces, Banach algebras, operator theory or nonlinear functional analysis.
  

  • MATH 7384 Topics in the Mathematics of Material Science (3)

    Prereq.: consent of department. May be repeated for credit with consent of department for a max. of 9 credit hrs. Advanced topics in the mathematics of material science, including mathematical techniques for the design of optimal structural materials, solution of problems in fracture mechanics, design of photonic band gap materials and solution of basic problems in the theory of superconductivity.
  

  • MATH 7386 Theory of Partial Differential Equations (3)

    Prereq.: MATH 7330 . Sobolev spaces. Theory of second order scalar elliptic equations: existence, uniqueness and regularity. Additional topics such as: direct methods of the calculus of variations, parabolic equations, eigenvalue problems.
  

  • MATH 7390 Seminar in Analysis (1-3)

    Prereq.: consent of department. May be repeated for credit with consent of department. Advanced topics such as harmonic analysis, partial differential equations, Lie group representation theory, several complex variables or probability theory.
 

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