# LSU Mathematics Courses

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.

College Algebra (3) Ge, F, S, Su
Prerequisites: Placement by department. Credit will not be given for both this course and MATH 1015 or 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.

Plane Trigonometry (3) Ge, F, S, Su
Prerequisites: MATH 1021 or placement by department. Credit will not be given for both this course and MATH 1015 or 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.

College Algebra and Trigonometry (5) Ge, F, S
Prerequisites: Placement by department. Credit will not be given for both this course and MATH 1015, 1021, or 1022. This course fulfills 5 hrs. of the 6-hr. Gen. Ed. 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.

Introduction to Contemporary Mathematics (3) Ge, F, S, Su
Prerequisites: Primarily for students in liberal arts and social sciences.
Here is the description of this course in the 2020-2021 and subsequent catalogs:
"Mathematical approaches to practical life problems. Topics include counting techniques and probability, statistics, graph theory, and linear programming."

Here is the description of this course in the 2019-2020 and previous catalogs:
"Mathematical approaches to contemporary problems, handling of data and optimization using basic concepts from algebra, geometry and discrete mathematics."
• Textbook: Thinking Mathematically, 7E Blitzer by Blitzer (required)
• Notes: Text: Blitzer, Thinking mathematically, 7e, 2019. Access to the textbook can be obtained in one (1) of 4 ways. Students needs to puchase one (1) of the following 4 items. 18 wk-title-specific access code card : 978-0135903575 24-month title-specific access code card: 978-01345705095 Looseleaf +24 month title-specific access code and card bundle: 978-0135167458 Bound book + 24 month title-specific access code and card bundle : 978-0134708300 Dr. Julia Ledet is teaching for Fall 2020. Also Michael Muffuletto. Fall 2020

The Nature of Mathematics (3) Ge, F, S, Su
Prerequisites: Not for science, engineering, or mathematics majors. For students who desire an exposure to mathematics as part of a liberal education.
Here is the description of this course in the 2020-2021 and subsequent catalogs:
Using mathematics to solve problems and reason quantitatively. Topics include set theory, logic, personal finance, and elementary number theory.

Here is the description of this course in the 2019-2020 and previous catalogs:
Logic; the algebra of logic, computers, and number systems; networks and combinatorics; probability and statistics.
• Textbook: Thinking Mathematically, 7E Blitzer by Blitzer (optional)
• Notes: Math 1029-1100, Blitzer, Thinking mathematically, 7e, 2019. Access to the textbook can be obtained in several ways. Students need to purchase one (1) of the following 4 items. 18-wk title specific access code card:978-0135903575 24-month title specific access code card: 978-0134-705095 Looseleaf +24 month title-specific access code card bundle : 978-0135167458 Bound book +224 month title specific access code card bundle: 978-0134708300 Elizabeth Dougherty is teaching for Fall 2020.

Number Sense and Open-Ended Problem Solving (3) F, S
Prerequisites: MATH 1021 or 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.

Geometry, Reasoning and Measurement (3) F, S, Su
Prerequisites: 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.

Calculus with Business and Economic Applications (3) Ge, F, S, Su
Prerequisites: MATH 1021 or 1023. Credit will be given for only one of the following: MATH 1431 or 1550 or 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.

Differential Calculus (3) F, S, Su
Prerequisites: An appropriate ALEKS placement score: see https://www.math.lsu.edu/ugrad/ALEKS for details.
Math 1530 and Math 1540, together, cover the material of Math 1550.
Credit will not be given for this course and MATH 1431, 1550, or 1551.
Limits and derivatives of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
• Textbook: Calculus, early transcendentals, 8th edition by James Stewart. (required)
• Detailed course information
• Notes: This course first appeared in the 2020-2021 catalog. The Math Department expects this course to be approved as an Integrative Learning Core course by July 2020. Prof. Ameziane Harhad will be teaching for fall 2020. This course will use the same texts as Math 1550.

Integral Calculus (3) F, S, Su
Prerequisites: Math 1530.
Math 1530 and Math 1540, together, cover the material of Math 1550.
Credit will not be given for this course and Math 1431, 1550, or 1551.
Integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
• Textbook: Calculus, early transcendentals, 8th edition by James Stewart. (required)
• Detailed course information
• Notes: This course first appeared in the 2020-2021 catalog. The Math Department expects this course to be approved as an Integrative Learning Core course by May 2020. Prof. Harhad will teach for Spring 2021. This course uses the same text as math 1550, 1552 and 2057.

Differential and Integral Calculus (5) Ge, F, S, Su
Prerequisites: An appropriate ALEKS placement score: see https://www.math.lsu.edu/ugrad/ALEKS for details.
Math 1530 and Math 1540, together, cover the material of Math 1550.
An honors course, MATH 1551, is also available.
Credit will not be given for this course and Math 1431, 1530, 1540, or 1551.
Limits, derivatives, and integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications.

HONORS: Differential and Integral Calculus (5) Ge, F
Prerequisites: An appropriate ALEKS placement score.
Credit will not be given for this course and Math 1431, 1530, 1540, or 1550.
Same as Math 1550, but with special honors emphasis for qualified students.
• Textbook: Calculus, early transcendentals, 8th edition by James Stewart. (required) The learning program: WebAssign has e-book access included.
• Notes: In the 2019-2020 and previous catalogs, this course was entitled "HONORS: Analytic Geometry and Calculus I."
Note: Ebook: students can go to WebAssign website. There is a free trial for 14 days that every student receives once they enter the course key their professor gives them. Once they enter the key it gives the student the option to use it for 14 days or buy the ebook and homework option.

Analytic Geometry and Calculus II (4) Ge, F, S, Su
Prerequisites: MATH 1550 or MATH 1551. This is a General Education Course. An honors course, MATH 1553 is also available. Credit will not be given for this course and MATH 1553 or 1554.
Techniques of integration, parametric equations, analytic geometry, polar coordinates, infinite series, vectors in low dimensions; introduction to differential equations and partial derivatives.

HONORS: Analytic Geometry and Calculus II (4) Ge, F, S
Same as MATH 1552, with special honors emphasis for qualified students. Credit will not be given for this course and MATH 1552 or 1554.

Calculus II for Life Science Majors (4) Ge, V
Prerequisites: MATH 1550 or 1551. Credit will not be given for this course and either MATH 1552 or 1553. Does not meet the prerequisites 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.

Solving Discrete Problems (3) F, S
Prerequisites: MATH 1550 or 1551.
Topics selected from formal logic, set theory, counting, discrete probability, graph theory, and number theory. Emphasis on reading and writing rigorous mathematics.

Linear Algebra and Wavelets (3) F
Prerequisites: MATH 1550 or 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.

Discrete Dynamical Systems (3) S
Prerequisites: Credit or registration in MATH 1552 or 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.
• Notes: Prof. P. Wolenski will teach for Spring, 2022

Multidimensional Calculus (3) F, S, Su
Prerequisites: MATH 1552 or 1553. An honors course, MATH 2058, is also available. Credit will not be given for this course and MATH 2058.
Three-dimensional analytic geometry, partial derivatives, multiple integrals.

HONORS: Multidimensional Calculus (3) F
Prerequisites: Credit will not be given for both this course and MATH 2057.
Same as MATH 2057, with special honors emphasis for qualified students. Prof. Bill Hoffman will teach fall, 2021.

Technology Lab (1) F, S
Prerequisites: Credit or concurrent enrollment in MATH 2057 or 2058. Students are encouraged to enroll in MATH 2057 (or 2058) and 2060 concurrently.
Use of computers for investigating, solving, and documenting mathematical problems; numerical, symbolic, and graphical manipulation of mathematical constructs discussed in MATH 1550, 1552, and 2057.
• Notes: Prof. Jim Madden will be teaching for Spring, 2022.

Elementary Differential Equations (3) F, S, Su
Prerequisites: MATH 1552 or 1553. Credit will be given for only one of the following: MATH 2065, 2070, or 2090.
Ordinary differential equations; emphasis on solving linear differential equations.

Mathematical Methods in Engineering (4) F, S, Su
Prerequisites: MATH 1552 or 1553. Credit will be given for only one of the following: MATH 2065, 2070, 2090.
Ordinary differential equations, Laplace transforms, linear algebra, and Fourier series; physical applications stressed. Note: The e-text of the book on web assign. Dr. Ding will have the class key that students need when they enroll in Web assign for the course.

Linear Algebra (3) F, S
Prerequisites: MATH 1552 or 1553. Credit will not be given for both this course and MATH 2090.
Systems of linear equations, vector spaces, linear transformations, matrices, determinants. Prof. F. Yang will teach, Spring 2022.

Elementary Differential Equations and Linear Algebra (4) F, S, Su
Prerequisites: MATH 1552 or 1553. Credit will not be given for both this course and MATH 2065, 2070, or 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.

Measurement: Proportional and Algebraic Reasoning (3) F, S
Prerequisites: 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.

Mathematics Classroom Presentations (2) F
Prerequisites: SCI 2010 and 2011.
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.
• Notes: Prof. Rebecca Nguyen will teach fall, 2021.

Functions and Modeling (3) S
Prerequisites: BASC 2011.
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 new math standards for functions and statistics are included.
• Notes: Rebecca Nguyen will be teaching Spring, 2022.

Interest Theory (5) F
Prerequisites: Math #1552 or #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.
• Textbook: Interest Theory:Financial Mathematics and Deterministic Valuation (2nd edition), 2018 by J. Francis and C. Ruckman (required)
• Notes: First offered in fall 2019. Previously numbered Math 4050. Professor Delzell taught this in fall 2019 & 2020.
Other required course notes (from Society of Actuaries website):
FM-24-17 Using Duration and Convexity to Approximate Change in Present Value URL
FM-25-17 Interest Rate Swaps URL
FM-26-17 Determinants of Interest Rates

Probability (3) F, S
Prerequisites: Credit or registration in MATH 2057 or 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, stochastic processes. Prof. R. Lipton, spring 2022

Methods of Problem Solving (2) F
Prerequisites: MATH 1552 or 1553, and MATH 2070, 2085, or 2090 or consent of 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.

Prerequisites: MATH 2020.
The foundations of geometry, including work in Euclidean and non-Euclidean geometries. The texts for this class are the same texts that are used in math 1202.

Calculus Internship Capstone (2) F
Prerequisites: 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 AP will be included.
• Notes: Dr. Ameziane Harhad teaches this in fall 2021.

Capstone Course (3) Grad, F, S
Prerequisites: 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.
• Textbook: Linear Algebra and Learning from Data. by Gil Strang (required)
• Notes: Dr. Pete Wolenski and Prof. Jim Madden will teach fall 2021. there are also lecture videos on the text on You Tube.

Prerequisites: MATH 2085 or 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.

Prerequisites: MATH 1552 or 1553, and credit or registration in MATH 2085 or 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.

Optimization Theory and Applications (3) Grad, S
Prerequisites: MATH 2057 or 2058, and credit or registration in MATH 2085 or 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.
• Notes: Prof. H. Zhang will teach for Spring, 2022.

Prerequisites: Math 2057 or 2058, and Math 2085 or 2090.
Ordinary differential equations, with attention to theory.

Prerequisites: MATH 2057 or 2058, and 2085 or 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.
• Textbook: Advanced Calculus: An Introduction to Linear Analysis, 1st Edition (2008) by Richardson (required) Free download e-text through my.lsu.edu account from the library
• Additional course materials: There is a free online e-book though student's myLSU access library.
• Notes: Prof. L. Richardson will teach for Spring, 2022. The text for this course and 4035 , both of these courses are ZCT courses. There is a free e-book, downloadable on any my.lsu.edu account from the LSU Library.

Prerequisites: MATH 4031.
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].

Prerequisites: MATH 4031.
Topology of n-dimensional space, differential calculus in n-dimensional space, inverse and implicit function theorems.
• Textbook: Advanced Calculus: An Introduction to Linear Analysis, 1st Edition (2008) by Richardson (required) The on-line e-book is available free through students myLSU library access
• Additional course materials: The on-line e-book free is available through students' myLSU access library!
• Notes: Prof. Len Richardson will teach for fall 2021. There is also a free e-book, downloadable on my.lsu.edu account from the library. This class is ZCT course.

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

Mathematical Methods in Engineering (3) Grad, F
Prerequisites: One of MATH 2065, 2070, or 2090; and one of MATH 2057 or 2058.
Vector analysis; solution of partial differential equations by the method of separation of variables; introduction to orthogonal functions including Bessel functions.

Introduction to Topology (3) Grad, S
Prerequisites: MATH 2057 or 2058.
(In the 2015-2016 and earlier catalogs, the prereq for this course was Math 4031.)
Examples and classification of two-dimensional manifolds, covering spaces, the Brouwer theorem, and other selected topics.
• Textbook: beginning topology, by Sue Goodman (required)
• Notes: Prof. D. Cohen will teach for Spring, 2022.

Short-term Actuarial Mathematics I (3) Grad, F, O
Prerequisites: MATH 3355.
Actuarial models for insurance and annuities. Severity-of-loss and frequency-of-loss models, aggregate models, risk models, empirical estimation.

Short-term Actuarial Mathematics II (3) Grad, S, E
Prerequisites: 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.
• Notes: First offered spring 2020.

Long-term Actuarial Mathematics I (3) Grad, F, E
Prerequisites: MATH 2085, 3050, and 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.
• Notes: Prof. Smolinsky will teach fall, 2021.

Long-term Actuarial Mathematics II (3) Grad, S, O
Prerequisites: 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.
• Notes: Prof. Smolinsky will teach, Spring 2021

Prerequisites: MATH 3355.
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.
Last offered fall 2018; replaced by Math 3050 beginning fall 2019.

Prerequisites: 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.
• Textbook: Mathematical Statistics and Data Analysis, 3rd Edition (2007) by John Rice (recommended)
• Textbook: Introduction to Statistical Theory by Hoel, Port, Stone (required)
• Notes: In the 2016-2017, 2017-2018, 2018-2019 and 2020-2021 catalogs, and subsequent catalogs, this course carried or will carry 4 hours of credit, and covered or will cover time series.
In the 2019-2020 catalog, this course carried 3 hours, and did not cover time series; then the description was:
"Statistical inference including hypothesis testing, confidence intervals, estimators, and goodness-of-fit."

Elementary Stochastic Processes (3) Grad, S
Prerequisites: Math 3355 and either Math 2085 or Math 2090 .
Markov chains, Poisson process, and Brownian motion.

Numerical Linear Algebra (3) Grad, F
Prerequisites: MATH 1552 or 1553, and one of MATH 2057, 2058, 2085, or 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.
• Notes: Prof. Hongchao Zhang will be teaching for fall, 2019. Will use own notes.

Prerequisites: MATH 2057 or 2058.
An introduction to numerical methods in basic analysis, including root-finding, polynomial interpolation, numerical integration and differentiation, splines and wavelets.
• Notes: Prof. Li-Yeng Sung will be teach fall, 2021 Suggested readings but not required: Numerical Analysis 10th edition, Burden and Faires, ISBN 978-130-5253667. Cengage.

Numerical Differential Equations (3) Grad, S
Prerequisites: MATH 2057 or 2058, and one of four options: (a) MATH 2070, (b) MATH 2090, (c) MATH 4027, (d) MATH 2085 and MATH 2065.
Numerical solutions to initial value problems and boundary value problems for ordinary and partial differential equations.
• Notes: Prof. X. Wan will teach, Spring 2022.

Finite Dimensional Vector Spaces (3) Grad, F, S
Prerequisites: MATH 2085 or 2090.
Vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, and topics such as inner product space and canonical forms.

Foundations of Mathematics (3) Grad, V
Prerequisites: MATH 2020, 2025, or 2030, or consent of instructor.
Rigorous development of the real numbers, sets, relations, product spaces, order and cardinality.
• Textbook: The Foundations of Mathematics by Ian Stewart and David Tall (required) 2nd edition, Oxford Univ. Press.
• Notes: Dr. Scott Baldridge teaching for fall 2020.

Introduction to Graph Theory (3) Grad, S
Prerequisites: MATH 2085 or 2090.
Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, network flows, matching theory and applications.

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

Elementary Number Theory (3) Grad, F
Prerequisites: MATH 2057, 2058, 2085, or 2090.
Divisibility, Euclidean algorithm, prime numbers, congruences, and topics such as Chinese remainder theorem and sums of integral squares.

Abstract Algebra I (3) Grad, F
Prerequisites: MATH 2085 or 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.

Abstract Algebra II (3) Grad, S, E
Prerequisites: MATH 4200.
Ideals in rings, factorization in polynomial rings, unique factorization and Euclidean domains, field extensions, splitting fields, finite fields, Galois theory.

Prerequisites: MATH 1552 or 1553, and one of the following: MATH 2057, 2058, 2065, 2070, 2085, 2090. For students majoring in mathematics, physics, or 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.

Partial Differential Equations (3) Grad, F
Prerequisites: Math 2057 or Math 2058, and one of the following: (1) Math 2070, (2) Math 2090, or (3) both Math 2065 and 2085.
First-order partial differential equations and systems, canonical second-order linear equations, Green's functions, method of characteristics, properties of solutions, and applications.
• Textbook: Introduction to Partial Differential Equations - A Computational Approach by Aslak Tveito, Ragnar Winther (required) Text is also available for teacher and students, LSU Library e-text
• Notes: This text can be downloaded for free from the LSU Library as part of the Springer Link Collection: https://doi-org.libezp.lib.lsu.edu/10.1007/978-3-319-02099-0 Prof. Shawn Walker will teach fall, 2021. Prof. Blaise Bourdin will be teaching for fall, 2019

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

History of Mathematics (3) Grad, S
Prerequisites: Math 2057 or 2058; Math 2020; and Math 2085 or 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.
• Notes: Prof. Delzell will teach Spring 2021

Vertically Integrated Research (3) Grad, F, S
Prerequisites: 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 in a vertically integrated learning and research community. Undergraduate students, graduate students, post-doctoral 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, and written and oral presentations. Undergraduate students may have a research capstone experience or write an honors thesis as part of this course.
• Textbook: Linear Algebra and Learning from Data. by Gil Strang (required)
• Notes: For textbooks and other detailed descriptions of the various sections of Math 4997 for each semester, see https://www.math.lsu.edu/grad/cur.grad.cour (where graduate-level courses in Math for each semester are described). 4997 - 1 , Sage and Achar 4997 - 2 , Vela-Vick and Wong - no text. Math 4997, sec. 1, taught by Dan Sage.

Prerequisites: Consent of department. May be taken for max. of 9 sem. hrs. credit.
• Notes: Prof. Smolinsky will teach Spring, 2021.

Implementing Curriculum Standards for Mathematics in the Elementary Grades (1–3) Grad, V
Prerequisites: 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.

Implementing Curriculum Standards for Mathematics in the Middle Grades (1–3) Grad, V
Prerequisites: 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.
• Notes: Jim Madden will be teaching for fall, 2018.

Implementing Curriculum Standards for Mathematics in High School (1–3) Grad, F, Su, V
Prerequisites: 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.
• Notes: Prof. Jim Madden will be teaching for fall 2021. Will use his own notes.

Seminar in Mathematics for Secondary Teachers (1–3) Grad, F, S, Su
Prerequisites: 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.

Communicating Math I (1) Grad, F
Prerequisites: consent of department.
Practical training in the teaching of undergraduate mathematics; how to write mathematics for publication; other issues relating to mathematical exposition.

Communicating Mathematics II (1) Grad, S
Prerequisites: 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.

Prerequisites: 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.

Prerequisites: 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.

Prerequisites: 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.

Topics in Number Theory (3) Grad, F, S
Prerequisites: Math 7211. May be repeated for credit with consent of department when topics vary for a max. of 9 credit hrs.
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 the Prime Number theorem, Diophantine equations, Circle method.

Topics in Algebraic Geometry (3) Grad, V
Prerequisites: Math 7211. May be repeated for credit with consent of department when topics vary for a max. of 9 credit hrs.
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.

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

Prerequisites: 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.

Seminar in Commutative Algebra (1–3) Grad, V
Prerequisites: 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.

Seminar in Algebra and Number Theory (1–3) Grad, V
Prerequisites: Consent of department. May be repeated for credit with consent of department.
Advanced topics such as algebraic number theory, algebraic semigroups, quadratic forms, or algebraic K-theory.

Real Analysis I (3) Grad, F
Prerequisites: MATH 4032.
Abstract measure and integration theory with application to Lebesgue measure on the real line and Euclidean space.

Ordinary Differential Equations (3) Grad, S
Prerequisites: MATH 2085 and 4031; or equivalent.
Existence and uniqueness theorems, approximation methods, linear equations, linear systems, stability theory; other topics such as boundary value problems.

Numerical Analysis and Applications (3) Grad, V
Prerequisites: MATH 4065 or equivalent.
Finite difference methods; finite element methods; iterative methods; methods of parallel computing; applications to the sciences and engineering.

Prerequisites: MATH 7311 or equivalent.
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.

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

Prerequisites: 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.

Applied Stochastic Analysis (3) Grad, V
Prerequisites: Math 7360.
Brownian motion, basic stochastic calculus, applications to finance.

Prerequisites: Math 7360.
Wiener process, stochastic integrals, stochastic differential equations.

Lie Groups and Representation Theory (3) Grad, V
Prerequisites: MATH 7311, 7210, and 7510 or equivalent.
Lie groups, Lie algebras, subgroups, homomorphisms, the exponential map. Also topics in finite and infinite dimensional representation theory.

Prerequisites: 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.

Seminar in Functional Analysis (1–3) Grad, V
Prerequisites: 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

Topics in the Mathematics of Materials Science (3) Grad, F, S
Prerequisites: 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.

Theory of Partial Differential Equations (3) Grad, F
Prerequisites: 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.

Seminar in Analysis (1–3) Grad, V

Problems of existence and enumeration in the study of arrangements of elements into sets; combinations and permutations; other topics such as generating functions, recurrence relations, inclusion-exclusion, Polya’s theorem, graphs and digraphs, combinatorial designs, incidence matrices, partially ordered sets, matroids, finite geometries, Latin squares, difference sets, matching theory.

Prerequisites: MATH 2085 and MATH 4039; or equivalent.
Matchings and coverings, connectivity, planar graphs, colorings, flows, Hamilton graphs, Ramsey theory, topological graph theory, graph minors.

Seminar in Combinatorics, Graph Theory, and Discrete Structures (1–3) Grad, V
Prerequisites: Consent of department. May be repeated for credit with consent of department.
Advanced topics such as combinatorics, graph theory, automata theory, or optimization.

Prerequisites: MATH 2057 or equivalent.
Basic notions of general topology, with emphasis on Euclidean and metric spaces, continuous and differentiable functions, inverse function theorem and its consequences. (This is the catalog description only: Be sure to compare with the current syllabus which includes the fundamental group.)

Prerequisites: MATH 7510.
Theory of the fundamental group and covering spaces including the Seifert-Van Kampen theorem; universal covering space; classification of covering spaces; selected areas from algebraic or general topology.
• Textbook: Algebraic Topology by Allan Hatcher (required)
• Notes: For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Here is a link to the website for a copy of the Text. http://www.math.cornell.edu/~hatcher/AT/ATpage.html Prof. Vela-Vick teaching, Spring, 2021

Prerequisites: MATH 7210 and 7510; or equivalent.
Basic concepts of homology, cohomology, and homotopy theory.

Differential Geometry and Topology (3) Grad, S
Prerequisites: MATH 7210 and 7510; or equivalent.
Manifolds, vector fields, vector bundles, transversality, Riemannian geometry, other topics.

Seminar in Geometry and Algebraic Topology (1–3) Grad, F, S
Prerequisites: Consent of department. May be repeated for credit with consent of department.
Advanced topics such as advanced algebraic topology, transformation groups, surgery theory, sheaf theory, or fiber bundles.