# 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.

Prerequisites: Placement by department. Not for degree credit. Concurrent enrollment in Math 1021.

Academic support course providing corequisite materials designed to promote mastery of the specific skills and knowledge required for success in Math 1021 College Algebra. Math topics include factoring polynomials, using exponents, simplifying expressions, graphing basic functions, and solving elementary equations. Learning support topics include reframing the student’s academic mindset, improving time management, and developing non-cognitive skills that improve student learning.

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**Notes:**Began in 2023-2024 catalog.

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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- Textbook: MyMathLab Trigsted access code for Trigsted's Algebra and Trigonometry. 3e, 2019 by (required)
- Detailed course information
**Notes:**Last offered in 2020.

Prerequisites: Placement by department. Not for degree credit. Concurrent enrollment in Math 1029.

Academic support course providing prerequisite materials designed to promote mastery of the specific skills and knowledge required for success in Math 1029 Topics in Contemporary Mathematics. Content includes supplemental material aligned with the content in Math 1029. Learning support topics include reframing the student’s academic mindset, improving time management, and developing non-cognitive skills that improve student learning.

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**Notes:**Began in 2023-2024 catalog.

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

In the 2022-2023 and earlier catalogs, Math 1029 had no prereq.

In the 2023-2024 and subsequent catalogs, the Math 1029 prereq is "Placement by department."

In the 2022-2023 and earlier catalogs, Math 1029 had no prereq.

In the 2023-2024 and subsequent catalogs, the Math 1029 prereq is "Placement by department."

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."

"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."

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- Textbook: Thinking Mathematically, 7E Blitzer by (required)
**Notes:**Text: Blitzer, Thinking mathematically, 7e, 2019. Access to the textbook can be obtained in one (1) of 4 ways. Students needs 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: 978-01345705095 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

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.

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.

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- Textbook: Thinking Mathematically, 7E Blitzer by (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.

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.

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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)
**Notes:**Elizabeth Dougherty is teaching for Spring, 2023.

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 Singapore Math.com Dr. Scott Baldridge teaching fall, 2022

Prerequisites: MATH 1021 or 1023. Credit will not be given for this course MATH 1510, 1530, 1540, 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. Dottie Vaughn will be teaching Spring, 2023.

Prerequisites: An appropriate ALEKS placement score. Credit will not be given for this course and MATH 1431 , 1530, 1540, 1550, or 1551.

Introduction to differential and integral calculus of functions of one variable, and matrix algebra and systems of linear equations.

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**Notes:**Began in 2023-2024 catalog. General Education Integrative Learning Core status not yet obtained, but expected in spring 2023.

Elementary combinatorics and discrete and continuous probability theory. Representation of data, statistical models, and testing.

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**Notes:**Began in 2023-2024 catalog. General Education Integrative Learning Core status not yet obtained, but expected in spring 2023.

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, 1510, 1550, or 1551.

Math 1530 and Math 1540, together, cover the material of Math 1550.

Credit will not be given for this course and MATH 1431, 1510, 1550, or 1551.

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

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

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, 1510, 1550, or 1551.

Math 1530 and Math 1540, together, cover the material of Math 1550.

Credit will not be given for this course and Math 1431, 1510, 1550, or 1551.

Integrals of algebraic, exponential, logarithmic, and trigonometric functions, with applications.

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

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, 1510, 1530, 1540, or 1551.

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, 1510, 1530, 1540, 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 WebAssign printed access card.
- Textbook: Briggs/Cochran Calculus: Early Transcendentals, 3E by (optional)
- Detailed course information
**Notes:**In the 2019-2020 and previous catalogs, this course was entitled "Analytic Geometry and Calculus I."

On WebAssign website. This text ISBN number has enhanced WebAssign printed access card. Student solutions manual for Stewart's single variable Calculus: early transcendentals, 8th edition. ISBN 978-130-527-2422.

Prerequisites: An appropriate ALEKS placement score.

Credit will not be given for this course and Math 1431, 1510, 1530, 1540, or 1550.

Credit will not be given for this course and Math 1431, 1510, 1530, 1540, 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:**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.

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 (optional) This text is equivalent to Stewart, & was used only in spring 2015 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. Credit will not be given for this course and MATH 1552 or 1554.

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- Textbook: Calculus, early transcendentals, 8th edition by (required)
**Notes:**Prof. B. Hoffman (1)teaching spring, 2023 Pro. T. Homan (2)teaching spring, 2023.

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.

Prerequisites: Permission of department.

Research seminar. Under the guidance of an experienced research mathematician, participants will investigate a research problem with a low barrier to entry and potential for significant findings. Each participant will communicate regularly with the mentor and will prepare oral and written expositions of their findings. The course is intended to develop students’ mathematical identities and improve their competitiveness for acceptance into more-advanced research experiences for undergraduates.

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**Notes:**Began in 2023-2024 catalog.

Prerequisites: Credit or registration in MATH 1540, 1550 or 1551.

Credit will not be given for this course and CSC 2259.

Credit will not be given for this course and CSC 2259.

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 It Applications, 8th edition by (optional)
**Notes:**Prof. V. Rios, teaching SPring, 2023

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:**Prof. Pete Wolenski teaching for Spring, 2023

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.

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**Notes:**Prof. P. Wolenski will teach for Spring, 2023

Prerequisites: Credit or registration in MATH 1552 or MATH 1553.

Mathematical tools underpinning machine learning applications: properties of Euclidean space, elementary topology, and convex sets and functions. This is a bridge course in writing rigorous proofs. It is designed for students to start thinking about mathematical concepts beyond calculus that are used in modern applications of Data Science, such as, for example, convex analysis and optimization.

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**Notes:**Began in 2023-2024 catalog.

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
**Notes:**Prof. X> Wan teaching spring, 2023 (1) Prof. A. Bulut teaching spring, 2023 (2) Prof. A. Zeitlin teaching spring, 2023 (3,4)

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, 8th edition by (required)
**Notes:**Prof. Bill Hoffman will teach Fall 2021.

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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**Notes:**Prof. Jim Madden teaching Spring, 2023.

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:**Prof. Jiuyi Zhu, teaching Spring, 2023 (1) Prof. Boris Rubin teaching Spring, 2023 (2,3)

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) This text is for Summer 2021 and Fall 2021
- Textbook: Ordinary Differential Equations by (required) This text is for Summer 2021
- Detailed course information
**Notes:**The e-text of the book is on WebAssign. Dr. Ding will have the class key that students need when they enroll in WebAssign for the course. Prof. Bhattacharya (1) Spring 2022. Prof. A. Harhad (2) Spring 2022.

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) e-text is also available at LSU Library e-texts requests for teachers/students.
**Notes:**Prof. C. Bibby teaching spring, 2023.

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
**Notes:**Prof. M. Tom (1, 2) teaching spring, 2023. Prof. A. Azhang (3) teaching spring, 2023.

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 will be teaching for Fall,2022.

Prerequisites: Permission of department.

Research seminar. Under the guidance of an experienced research mathematician, participants will investigate a research problem with a low barrier to entry and potential for publishable findings. Each participant will communicate regularly with the mentor and will prepare oral and written expositions of their findings. The course is intended to develop undergraduates’ identity as mathematicians and improve their competitiveness for acceptance into nationally recognized summer Research Experiences for Undergraduates programs.

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**Notes:**Began in 2023-2024 catalog.

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.

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**Notes:**Prof. Rebecca Nguyen will teach fall, 2021.

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:**Rebecca Nguyen will be teaching Spring, 2022.

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 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

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.

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- Textbook: Fundamentals of Probability : With Stochastic Processes, 4th edition, (2018) by (required) This text available e-text, Taylor and Francis Publisher, ISBN 9780429457951.
- Detailed course information
**Notes:**Prof. Li Chen teaching for Spring, 2023.

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 (supplemental)
**Notes:**Dr. Rui Han teaching, fall, 2022. Note: Should be a great class!

Prerequisites: MATH 2020.

The foundations of geometry, including work in Euclidean and non-Euclidean geometries.
The product code for this text on AMS is: AMStext/51

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- Textbook: Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motion by (required)
**Notes:**Prof. P. Dani teaching spring, 2023.

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 2022.

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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- Textbook: Linear Algebra and Learning from Data. by (required)
**Notes:**Dr. Frederic Marazzato teaching for fall 2022. There are also lecture videos on the text on You Tube.

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:**Prof. Dan Cohen, teaching Spring, 2023.

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: An Introduction to Mathematical Modeling, 2000 by (required)
**Notes:**Prof. Yuri Antipov, teaching spring, 2023

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. H. Zhang will teach for Spring, 2022.

Ordinary differential equations, with attention to theory.

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- Textbook: An Introduction to Ordinary Differential Equations (1989) by (required) Dover Publications
**Notes:**Prof. R. Lipton, teaching Spring, 2023.

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) 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 teaching spring, 2023. 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].

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- Textbook: Advanced Calculus: An Introduction to Linear Analysis, 1st Edition (2008) by (required)
**Notes:**Prof. L. Richardson will teach for Spring 2023.

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) 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.

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

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**Notes:**Prof. David Vela-Vick teaching spring, 2023.

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, 7E , 2022 by (required) Used beginning Fall 2013.
- Detailed course information
**Notes:**Prof. Leonard Richardson will be teaching for fall 2022

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.O. Dasbach teaching spring, 2023.

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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- Textbook: Loss Models: From Data to Decisions, 5th edition, 2019 by (required)
- Textbook: ASM Study Manual for STAM-Short-term Actuarial mathematics, 1st edition, 3rd printing, by (required)
- Textbook: ASM Flashcards for SOA STAM exam, 1st edition, 3rd printing, ASM by (optional)
**Notes:**Prof. Larry Smolinsky will teach fall, 2021.

Prerequisites: MATH 4040.

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

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**Notes:**Prof. Larry Smolinsky teaching Spring 2022 using own notes.

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:**Prof. Smolinsky will teach fall, 2021.

Prerequisites: MATH 4045.

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:**Prof. Smolinsky will teach, Spring 2023

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.**More info»

- 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 or EE 3150.

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

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- Textbook: Mathematical Statistics and Data Analysis, 3rd Edition (2007) by (recommended)
- Textbook: Introduction to Statistical Theory by (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."

Markov chains, Poisson process, and Brownian motion.

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- Textbook: A first look at Stochastic Processes by (required)
**Notes:**Prof. H. He teaching for spring, 2022.

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.

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**Notes:**Prof. Li-Yeng Sung teaching for fall, 2022.

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

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- Textbook: Numerical Analysis, 9th by (optional) this is suggested readings.
**Notes:**Prof. Shawn Walker teaching fall, 2022.Suggested readings but not required: Numerical Analysis 9th edition. Burden and Faires, ISBN 978-0-538-73351-9. Cengage.

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. X. Wan will teach, Spring 2022.

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 Done Right by (required)
**Notes:**Prof.H. He teaching spring, 2023.

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

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- Textbook: The Foundations of Mathematics by (required) 2nd edition, Oxford Univ. Press.
**Notes:**Dr. Scott Baldridge teaching for fall 2022

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.G. Ding, teaching spring, 2023.

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 (Classic Version ) 5th, by (required)
**Notes:**Prof. Dirk Vertigan will teach this class for fall 2020.

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:**Prof. Richard Ng will teach, fall 2021.

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: Introduction to Abstract Algebra, 4th edition by (required)
**Additional course materials:**e-version of text can be downloaded from the book webpage.**Notes:**Prof. Milen Yakimov will teach for fall 2020.

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: Introduction to Abstract Algebra, 4th edition by (required)
**Notes:**Prof. Dan Cohen teaching spring, 2023.

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: Fourier Analysis and Its Applications by (strongly recommended)
**Notes:**Prof. Rui Han teaching Spring. 2023

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) Dover Publications.
- Textbook: Introduction to Partial Differential Equations - A Computational Approach by (required)
**Additional course materials:**It 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**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. Yuri Antipov, teaching fall, 2022.

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.

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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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**Notes:**Prof. Delzell will teach Spring 2021

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: Introduction to Linear Algebra, 6th edition by (required) sec. 4, Wolenski/Marazzato
**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.

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**Notes:**Prof. Smolinsky will teach Spring, 2021.

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.

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**Notes:**Prof. Frank Neubrander teaching spring, 2022.

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.

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**Notes:**Prof. Frank Neubrander teaching Spring, 2022.

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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**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: Commutative algebra: with a view towards Algebraic Geometry (grad texts in math) No. 150. 3rd 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, 2022.

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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- Textbook: A Classical Introduction to Modern Number Theory (soft cover) by (required)
**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Please refer to: www.math.lsu.edu graduate courses for information: Class Field Theory by Nancy Childress, Springer. Available for download. Prof. will use own notes, spring 2022.

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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- Textbook: Algebraic Geometry I: Schemes, 2nd edition, 2020 by (strongly recommended)
- Textbook: Introduction to Algebraic Geometry, 1st edition. 2021 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. Bill Hoffman will teach, fall, 2022.

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: Probability and Stochastics , 2011, soft cover 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. Li Chen will teach, fall 2021.

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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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edud/cur.grad.cour. https://bookstore.ams.org/surv-107-s/ Representations of Algebraic Groups: Second Edition

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: Real Analysis : Modern Techniques and Their Applications, 2nd edition. June 2013 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. G. Olafsson will teach, fall 2021.

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

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- Textbook: Ordinary Differential Equations, 3rd Edition (1998) 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 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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**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: Function Theory of One Complex Variable, 3rd Edition (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. Prof. R. Han teaching, Fall 2022.

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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- Textbook: Probability and Stochastics by (required) There is a free download of the text on the Author's website.
**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: Stochastic Differential Equations, 6th edition, 2003 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. P. Sundar will be teaching for spring, 2022.

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 , 2020

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) Dr. Olafsson will use own notes.
- Textbook: Elliptic Partial Differential Equations: 2nd edition by (required) math 7380(2) Dr. Brenner is teaching sec. 2
**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: Credit or registration in Math 7311.

Overview of modeling and analysis of equations of mathematical physics, such as electromagnetics, fluids, elasticity, acoustics, quantum mechanics, etc. There is a balance of breadth and rigor in developing mathematical analysis tools, such as measure theory, function spaces, Fourier analysis, operator theory, and variational principles, for understanding differential and integral equations of physics.

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**Notes:**Course created in 2022.

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. The text is the 2010 edition 2nd edition.

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- Textbook: Mathematical Control Theory, 1998 by (optional) https://www.math.lsu.edu/~xlwan/teaching/ma7390/ma7390.html
**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, 5th edition, 2017 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 2022.

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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**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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**Notes:**For detailed, semester-by-semester descriptions of 7000-level math courses, see https://www.math.lsu.edu/grad/cur.grad.cour. Prof. Christin Bibby teaching fall, 2022.

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 Prof. Vela-Vick teaching, Spring, 2021

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. Prof. Shea Vela-Vick will teach for fall, 2021.

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

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- Textbook: Topology and Geometry by (required) Prof. Zeitlin will use his own notes.
**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: Math 7550.

Introduction to Riemannian geometry, the study of smooth manifolds endowed with Riemannian metrics. Topics include Riemannian metrics, connections, geodesics, curvature, Jacobi fields, completeness, spaces of constant curvature, and calculus of variations, followed by theorems that relate curvature, topology, and analysis.

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**Notes:**Course created in 2022.

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: Graphs on Surfaces and Their Applications by (required)
**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.