LSU

Mathematics

Mathematics

No student may receive more than nine semester hours of credit in mathematics courses numbered below 1550, 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 1550 or above may be registered in a mathematics course numbered below 1550, unless given special permission by the Department of Mathematics.

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.

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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.

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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.

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Prerequisites: Primarily for students in liberal arts and social sciences.

Mathematical approaches to contemporary problems, handling of data and optimization using basic concepts from algebra, geometry and discrete mathematics.

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- Textbook: thinking mathematically plus new MYMATHLAB, nwith pearson e-text, 6th Edition by (required)
**Notes:**Students: You can either buy the text shrink wrapped with a MyMathLab access code or you can buy just the stand-alone MyMathLab Access code, ISBN 10-013147894-X.

Prerequisites: Not for science, engineering, or mathematics majors. For students who desire an exposure to mathematics as part of a liberal education.

Logic; the algebra of logic, computers, and number systems; networks and combinatorics; probability and statistics.

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- Textbook: Topics In COntemporary mathematics, 10th E. by (optional)
**Notes:**Sam Wilson will be teaching for fall, 2018. The isbn listed is the bundle package for the text and the stu. sol. manual.

Prerequisites: MATH 1021 and 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.

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- Textbook: Elementary Mathematics for Teachers by (required)
- Textbook: Primary Mathematics 4A (2003) by (required)
- Textbook: Primary Mathematics 5A (2003) by (required)
- Textbook: Primary Mathematics 5A (2003) by (required)
- Textbook: Primary Mathematics 6A (2003) by (required)

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.

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- Textbook: Elementary Geometry for Teachers by (required)
- Textbook: Primary Mathematics 4A (2003) by (required)
- Textbook: Primary Mathematics 5A (2003) by (required)
- Textbook: Primary Mathematics 3B (2003) by (required)
- Textbook: Primary Mathematics 5B (2003) by (required)
**Notes:**book 6: Primary Mathematics, 6B, ISBN 978-981-01-85152 book 7: new elementary mathematics textbook, 1, ISBN 978-981-271-411-4 These textbooks are all ordered from SingaporeMath.com

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.

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- Textbook: Calculus for BUsiness, economics, Life Sciences, and Social Sciences, BRIEF VERSION, 2019 by (recommended)
- Detailed course information
**Notes:**Dr.Vaughn is teaching this class for spring, 2019.

Prerequisites: An appropriate ALEKS placement score: see https://www.math.lsu.edu/ugrad/ALEKS for details. An honors course, MATH 1551, is also available. Credit will be given for only one of the following: MATH 1431, 1550, or 1551.

Limits, derivatives, and integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications.

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- Textbook: Calculus, early transcendentals, 8th edition by (required) New adoption for math 1550 for fall, 2016. Enhanced web assign Printed Access card.
- Detailed course information
**Notes:**On Web Assign website> This text ISBN Number has enhanced web assign printed access card. Student solutions manual for stewart's single variable Calculus: early transcendentals, 8th edition. ISBN 978-130-527-2422. MATH 1550 sec. 15 ONLY will be using the mymathlab access card by Briggs and Cochran.

Prerequisites: An appropriate ALEKS placement score. Credit will not be given for this course and Math 1431 or 1550.

Same as Math 1550, but with special honors emphasis for qualified students.

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- Textbook: Calculus, early transcendentals, 8th edition by (required) The learning program: WebAssign has e-book access included.
**Notes:**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.

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.

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- Textbook: Calculus, early transcendentals, 8th edition by (required) This text used also in Math 1550, 2057, & in all sections of Math 1552 except as noted below. The learning program WebAssign has e-book access included.
- Textbook: Calculus: Early Transcendentals, 2nd edition, 2015 by (required) This text is equivalent to Stewart, & in spring 2015 is used only for section 17. Only the MyMathLab access code is required, & it contains the e-text.
- Detailed course information

Same as MATH 1552, with special honors emphasis for qualified students.

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- Textbook: Calculus, early transcendentals, 8th edition by (required)

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.

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- Textbook: Calculus for Biology and Medicine, 3E by (required)
**Notes:**Prof. C. Li will be teaching for spring 2016.

Topics selected from formal logic, set theory, counting, discrete probability, graph theory, and number theory.
Emphasis on reading and writing rigorous mathematics.

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- Textbook: Discrete Mathematics and its applications, 7th edition by (required)

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.

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**Notes:**Prior to 2019, course title was: "Integral Transforms and Their Applications."

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.

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.

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- Textbook: Calculus, early transcendentals, 8th edition by (required)

(effective fall 2012). - Detailed course information

Prerequisites: Credit will not be given for both this course and MATH 2057.

Same as MATH 2057, with special honors emphasis for qualified students.

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- Textbook: Calculus: Early Transcendentals, 7th edition, with Enhanced WebAssign (EWA) by (required)

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.

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- Textbook: CalcLabs with Mathematica for Stewart's Multivariable calculus, 5th, but for 7th edition stewart by (required)
**Notes:**Alexander Perlis will be teaching for Fall 2018.

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.

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- Textbook: Ordinary Differential Equations by (required)
- Detailed course information
**Notes:**Richard Moscatello will be teaching sections 1 and 2 for fall, 2018. Michael Malisoff will be teaching sec. 3 for fall 2018.

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.

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- Textbook: A First Course in DIfferential equations with Modeling applications, Loose-Leaf version, 11th + web assign, Printed Access card, by (required)
- Detailed course information
**Notes:**Ameziane Harhad will be teaching for spring, 2019. Both sections.

Systems of linear equations, vector spaces, linear transformations, matrices, determinants.

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- Textbook: Linear Algebra With Applications (Classic version)5th edition by (required)
**Notes:**Prof. Len Richardson will be teaching for fall, 2018.

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.

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- Textbook: Differential equations and linear algebra , 4E by (required)
- Detailed course information

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.

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- Textbook: Teaching School Mathematics: Algebra by (optional)
**Notes:**Michael Muffuletto and Dr. Julia Ledet will be teaching for fall, 2018.

Prerequisites: BASC 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.

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**Notes:**Sharon Besson teaches this in fall 2019.

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.

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**Notes:**

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.

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- Textbook: Interest Theory:Financial Mathematics and Deterministic Valuation (2nd edition), 2018 by (required)
**Notes:**First offered in fall 2019. Previously numbered Math 4050. Professor Cochran teaches this in fall 2019.

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 Dr. George Cochran will be teaching for fall 2019.

Introduction to probability, emphasizing concrete problems and applications; random variables, expectation, conditional probability, law of large numbers, central limit theorem, stochastic processes.

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- Textbook: Fundamentals of Probability : With Stochastic Processes, 4th edition, (2018) by (required)
- Detailed course information
**Notes:**

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.

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- Textbook: Putnam and Beyond, 2nd edition., 2017 by (required)
**Notes:**Dr. Mahlburg teaches this in fall 2019, using own notes.

Prerequisites: MATH 2020.

The foundations of geometry, including work in Euclidean and non-Euclidean geometries.

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- Textbook: Euclidean and Non-Euclidean Geometries, 4th edition, 2007 by (required)
**Notes:**

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.

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**Notes:**Dr. Ameziane Harhad teaches this in fall 2019.

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.

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**Notes:**Professors James Madden and Peter Wolenski co-teach this in spring 2019.

Finite algebraic structures relevant to computers: groups, graphs, groups and computer design, group codes, semigroups, finite-state machines.

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- Textbook: Modern Algebra and Discrete Structures (1991) by (required)
**Notes:**

Construction, development, and study of mathematical models for real situations; basic examples, model construction, Markov chain models, models for linear optimization, selected case studies.

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- Textbook: Mathematical Modeling, 2nd Edition (1999) by (required)

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.

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**Notes:**Prof. Li-Yeng Sung taught this in spring 2019.

Ordinary differential equations, with attention to theory.

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- Textbook: A Second Course in Elementary Differential Equations (2004) by (required)
**Notes:**

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.

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- Textbook: Advanced Calculus: An Introduction to Linear Analysis, 1st Edition (2008) by (required)
**Notes:**Prof. Michael Malisoff taught this in spring 2019.

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].

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- Textbook: Advanced Calculus: An Introduction to Linear Analysis, 1st Edition (2008) by (required)
**Notes:**Prof. Milen Yakinov taught this in spring 2019.

Prerequisites: MATH 4031.

Topology of n-dimensional space, differential calculus in n-dimensional space, inverse and implicit function theorems.

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- Textbook: Advanced Calculus: An Introduction to Linear Analysis, 1st Edition (2008) by (required)

Analytic functions, integration, power series, residues, and conformal mapping.

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- Textbook: Complex variables with Applications, 9th edition , 2014 by (optional)
**Notes:**Prof. Yuri Antipov taught this in spring 2019

Vector analysis; solution of partial differential equations by the method of separation of variables; introduction to orthogonal functions including Bessel functions.

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- Textbook: Advanced Engineering Mathematics, 6th edition by (required) Used beginning Fall 2013.
- Detailed course information
**Notes:**

Prerequisites: MATH 2057 or 2058.

(In the 2015-2016 and earlier catalogs, the prereq for this course was Math 4031.)

(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.

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- Textbook: beginning topology, by (required)
**Notes:**Prof. Rick Litherland taught this in spring 2019.

Prerequisites: MATH 3355.

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

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**Notes:**First offered fall 2019.

Actuarial models for insurance and annuities. Statistical estimation procedures, credibility theory, and pricing and reserving.

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**Notes:**First offered spring 2020.

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.

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**Notes:**First offered fall 2020.

Parametric survival models with multiple-life states; life insurance and annuity premium calculations; reserving and profit measures; participating insurances, pension plans, and retirement benefits.

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**Notes:**First offered 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.**

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- Textbook: Financial Mathematics: A Practical Guide for Actuaries and Other Business Professionals, 2nd Edition (2005) by (required)
**Notes:**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

Prerequisites: MATH 3355.

Statistical inference including hypothesis testing, confidence intervals, estimators, and goodness-of-fit.

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- Textbook: Mathematical Statistics and Data Analysis, 3rd Edition (2007) by (required)
**Notes:**In the 2016-2017, 2017-2018, 2018-2019 and 2020-2021 catalogs, this course carried or will carry 4 hours of credit, and covered or will cover time series.

Markov chains, Poisson process, and Brownian motion.

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**Notes:**Prof. George Cochran taught this in spring 2019. He gave the students the class notes and suggested reading.

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.

An introduction to numerical methods in basic analysis, including root-finding, polynomial interpolation, numerical integration and differentiation, splines and wavelets.

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**Notes:**Prof. Li-Yeng Sung will be teaching for fall 2019.

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.

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**Notes:**Prof. S. Brenner taught this in spring 2019. She used her own notes.

Vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, and topics such as inner product space and canonical forms.

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- Textbook: Linear Algebra by (required)
**Notes:**Prof. Arnab Ganguly taught this in spring 2019.

Rigorous development of the real numbers, sets, relations, product spaces, order and cardinality.

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- Textbook: The Foundations of Mathematics by (required)
**Notes:**Fall only.

Fundamental concepts of undirected and directed graphs, trees, connectivity and traversability, planarity, colorability, network flows, matching theory and applications.

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- Textbook: Introduction to Graph THeory (Classic Version) , 2nd edition. (2018) by (required)
**Notes:**Prof. Pramod Achar will be teaching for spring, 2019.

Topics selected from permutations and combinations, generating functions, principle of inclusion and exclusion, configurations and designs, matching theory, existence problems, applications.

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- Textbook: Introductory Combinatorics, 5th Edition (2010) by (required)

Divisibility, Euclidean algorithm, prime numbers, congruences, and topics such as Chinese remainder theorem and sums of integral squares.

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- Textbook: Elements of Number Theory by (required)
**Notes:**

Elementary properties of sets, relations, mappings, integers; groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms, and permutation groups; elementary properties of rings.

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- Textbook: Abstract Algebra: Theory and Applications, 2017 Edition by (required)
**Additional course materials:**e-version of text can be downloaded from the book webpage.**Notes:**

Prerequisites: MATH 4200.

Ideals in rings, factorization in polynomial rings, unique factorization and Euclidean domains, field extensions, splitting fields, finite fields, Galois theory.

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- Textbook: Abstract Algebra: Theory and Applications, 2017 Edition by (required)

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.

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- Textbook: A First Course in Fourier Analysis, 2nd Edition (2008) by (required)
**Notes:**Spring 2020.

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.

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- Textbook: Partial Differential Equations for Scientists and Engineers (1993) by (required)
**Notes:**

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, Chebychev polynomials, and other topics.

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- Textbook: Special Functions for Scientists and engineers by (required)
**Notes:**Karl Mahlberg teaches this in fall 2019.

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.

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- Textbook: MAth Through the Ages: A Gentle History for Teachers and Others, 2nd edition, 2015 by (required)
**Notes:**Prof. Ahma Lisan teaches this in spring 2019.

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.

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- Textbook: Lectures on SL_2 Modules by (required) math 4997, sec. 1, taught by Dan Sage.
**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). Math 4997, sec. 1, taught by Dan Sage.

Prerequisites: Consent of department. May be taken for max. of 9 sem. hrs. credit.

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.

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.

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**Notes:**Jim Madden will be teaching for fall, 2018.

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.

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.

Prerequisites: consent of department.

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

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- Textbook: How to Teach Mathematics, 2nd Edition (2000) by (strongly recommended)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

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.

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**Notes:**Texts are recommended but not required. For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

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.

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- Textbook: Abstract Algebra, 3rd Edition (2003) by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

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.

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- Textbook: Abstract Algebra, 3rd Edition (2003) by (required) Year published, 2006
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. .

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.

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- Textbook: Introduction to Commutative Algebra, Student Economy Edition by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Dr. Bill Hoffman will be teaching for spring, 2018

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.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

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.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Riley Casper will be teaching for fall 2018. Dan Sage will be teaching, spring 2017

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.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Rick Estrada will be teaching for fall, 2016..

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.

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- Textbook: Methods of Homological Algebra, 2nd edition by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Profs. Achar and Sage will be teaching for fall, 2017.

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.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Math 7280(1) Achar will use own notes.

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.

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- Textbook: Quantum Invariants of Knots and 3-Manifolds by (required)

(only for Math 7290, section 1). **Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edud/cur.grad.cour. Prof. Richard Ng will be teaching for spring, 2017.

Prerequisites: MATH 4032.

Abstract measure and integration theory with application to Lebesgue measure on the real line and Euclidean space.

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- Textbook: Measure and Integration: An Introduction to Real Analysis, 2nd edition. by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

Existence and uniqueness theorems, approximation methods, linear equations, linear systems, stability theory; other topics such as boundary value problems.

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- Textbook: Differential equations, Dynamical Systems, and an Introduction to Chaos, 3rd edition, (2012) by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Pete Wolenski is teaching for spring, 2013.

Prerequisites: MATH 4065 or equivalent.

Finite difference methods; finite element methods; iterative methods; methods of parallel computing; applications to the sciences and engineering.

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- Textbook: The Mathematical Theory of Finite Element Methods, 3rd Edition (2008) by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Prof. Shawn Walker will be teaching for fall, 2019

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.

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- Textbook: Topological Vector Spaces, Distributions and kernels by (strongly recommended)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour

Prerequisites: MATH 7311.

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

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- Textbook: Complex Analysis in One Variable (2001) by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Rick Estrada is teaching for fall, 2016.

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.

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**Additional course materials:**No text. Lecture notes will be provided.**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Prof. Ganguly will be teaching for fall, 2017. Will use own notes.

Prerequisites: Math 7360.

Brownian motion, basic stochastic calculus, applications to finance.

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- Textbook: Introduction to Stochastic Integration, 2006 by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Dr. Kuo will be teaching for fall, 2017. Dr. Sundar will be teaching this course for fall, 2014.

Prerequisites: Math 7360.

Wiener process, stochastic integrals, stochastic differential equations.

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- Textbook: Introduction to Stochastic Integration, 2006 by (strongly recommended)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour Prof. Kuo will be teaching for spring, 2019.

Lie groups, Lie algebras, subgroups, homomorphisms, the exponential map. Also topics in finite and infinite dimensional representation theory.

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- Textbook: Nilpotent Orbits in Semisimple Lie Algebras by (recommended)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Professor He will be teaching for spring, 2017.

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.

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- Textbook: introduction to fourier analysis and wavelets by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour Professor Nguyen will be teaching for spring , 2017.

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

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- Textbook: Introduction to Radon transforms: With elements of Fractional calculus & Harmonic Analysis (encyclopedia of math and its appl. by (strongly recommended) 1
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Phuc Nguyen will be teaching the course for spring 2015.

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.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Prof. Stephen Shipman will be teaching for fall, 2018. Will use own notes.

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.

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- Textbook: Partial Differential Equations (2002)reprint by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Dr. Li-Yeng Sung will be teaching for fall, 2015.

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.

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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

Matchings and coverings, connectivity, planar graphs, colorings, flows, Hamilton graphs, Ramsey theory, topological graph theory, graph minors.

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- Textbook: Graph Theory, (2017 edition) by (strongly recommended)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Bogdan Oporowski will be teaching for spring 2018.

Prerequisites: Consent of department. May be repeated for credit with consent of department.

Advanced topics such as combinatorics, graph theory, automata theory, or optimization.

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- Textbook: Matroid Theory, 2nd edition, 2011 by (optional)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

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.)

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- Textbook: Topology, 2nd Edition (2000) by (optional)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Prof. Dasbach will be teaching for fall, 2019.

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.

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- Textbook: Algebraic Topology by (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 Dr. Gilmer will be teaching for spring, 2019.

Basic concepts of homology, cohomology, and homotopy theory.

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- Textbook: Algebraic Topology by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

Manifolds, vector fields, vector bundles, transversality, Riemannian geometry, other topics.

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- Textbook: Topology and Geometry by (required) Springer, ISBN 978-0-387-979267
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. . Shea Vela-Vick will be teaching for spring, 2017.

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.

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- Textbook: Introduction to Symplectic Topology, 3rd edition, (2017) by (supplemental)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

Gaussian elimination: LU and Cholesky factorizations; Least squares problem: QR factorization and Householder algorithm, backward stability, singular value decomposition and conditioning; Iterative methods: Jacobi, Gauss-Seidel and conjugate gradient; Eigenproblems: power methods and QR algorithm.

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- Textbook: Fundamentals of Matrix Computations, 3rd by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour.

Prerequisites: Consent of department. May be repeated for credit with consent of department.

"S"/"U" grading.

"S"/"U" grading.