Department of Mathematics

Introduction

Mathematics has always been a fundamental component of human thought and culture, and the growth of technology in recent times has further increased its importance. UNC–Chapel Hill offers several degrees in mathematics and the mathematical sciences, providing students a choice of careers in this field. Among the jobs in industry, government, and the academic world that involve mathematics are actuary, analyst, modeler, optimizer, statistician, and computer analyst.

Students intending to teach mathematics in elementary and middle school and students enrolled in the School of Education who intend to major in mathematics should consult the School of Education section of the Catalog or the director of mathematical education in the Department of Mathematics. A section in the mathematics program of the Catalog suggests course selections for future high school teachers.

Advising

All majors and minors have a primary academic advisor assigned in ConnectCarolina. Students should regularly meet with their advisors and review their Tar Heel Trackers to be sure that they are satisfying distribution and degree requirements. In addition, drop in advising is available each semester in the math department. Students who have declared a math major and have completed MATH 233 are required to attend a math department advising session to discuss course selections and any other questions before a hold on registration is lifted. The department’s director of undergraduate studies, assistant director of undergraduate studies, and manager of student services (see contact tab above) are also available by appointment. Further information on courses, undergraduate research opportunities, the honors program, careers, and graduate schools may be obtained from the department’s website.

Placement into Mathematics Courses

Standardized test scores such as the Advanced Placement (AP) or the American College Test (ACT) can be used for placement into mathematics courses. Students who do not have placement scores via the AP or ACT may take the department's ALEKS Placement Test. Please visit the placement page of the department’s website for specific information regarding placement and departmental placement tests.

Graduate School and Career Opportunities

The B.S. degree program, especially if it includes the sequences MATH 521MATH 522 and MATH 577MATH 578, is excellent preparation for graduate study in the mathematical sciences. The B.A. degree can be excellent preparation for graduate study in many fields, including admission into professional schools of law, business, and medicine. Both degrees are viewed by many employers as attractive, especially when accompanied by electives in areas such as statistics, computer science, economics, and operations research. Undergraduate mathematics majors with critical thinking skills and good analytical abilities are in demand in many business, industry, and government fields.

Professors

David Adalsteinsson, Idris Assani, Prakash Belkale, Roberto Camassa, Ivan V. Cherednik, Hans Christianson, M. Gregory Forest, Boyce Griffith, Jingfang Huang, Shrawan Kumar, Jeremy Marzuola, Richard McLaughlin, Jason Metcalfe, Sorin Mitran, Richárd Rimányi, Lev Rozansky, Justin Sawon, Michael E. Taylor, Alexander N. Varchenko, Mark Williams.

Associate Professors

Yaiza Canzani, Karin Leiderman Gregg, Jiuzu Hong, Katherine Newhall, David Rose.

Assistant Professors

Arunima Bhattacharya, Olivia Dumitrescu, Shahar Kovalsky, Caroline Moosmueller, Casey Rodriguez, Pedro Sáenz, Andrey Smirnov.

Teaching Faculty

Emily Burkhead, Linda Green, Mark McCombs, Elizabeth McLaughlin, Miranda Thomas.

Professors Emeriti

Joseph A. Cima, James N. Damon, Patrick B. Eberlein, Ladnor D. Geissinger, Sue E. Goodman, Jane M. Hawkins, Robert G. Heyneman, Christopher Jones, Ancel Mewborn, Karl E. Peterson, Joseph F. Plante, Robert Proctor, Michael Schlessinger, William W. Smith, James D. Stasheff, Jonathan M. Wahl, Warren R. Wogen.

MATH–Mathematics

Undergraduate-level Courses

MATH 10.  Review of Basic Algebra.  3 Credits.  

Correctional Education Course. This course covers basic algebra topics and prepares students for an introductory college-level algebra course, such as MATH 110.

Rules & Requirements  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 51.  First-Year Seminar: 'Fish Gotta Swim, Birds Gotta Fly': The Mathematics and the Mechanics of Moving.  3 Credits.  

This seminar allows students to have hands-on exposure to a class of physical and computer experiments designed to challenge intuition on how motion is achieved in nature. Honors version available.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 62.  First-Year Seminar: Combinatorics.  3 Credits.  

Students will discuss combinatorics' deep roots in history, its connections with the theory of numbers, and its fundamental role for natural science, as well as various applications, including cryptography and the stock market. Honors version available.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 65.  First-Year Seminar: Colliding Balls and Springs: The Microstructure of How Materials Behave.  3 Credits.  

Students will follow the intellectual journey of the atomic hypothesis from Leucippus and Democritus to the modern era, combining the history, the applications to science, and the mathematics developed to study particles and their interactions.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 68.  First-Year Seminar: The Mathematics of Voting.  3 Credits.  

What properties should a fair election have and are these properties achievable in theory and in practice? How can mathematics and statistics be used to expose election fraud and gerrymandering? Students will address these questions as they compare different election systems, evaluate their strengths, weaknesses, and abuses, and design improvements to current structures. Topics will include gerrymandering, ranked voting, approval voting, and Arrow's Impossibility Theorem.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 69.  First-Year Seminar: Unfolding Infinity: Mathematical Origami and Fractal Symmetry.  3 Credits.  

This seminar engages students in an exploration of the interplay between mathematics, origami, and fractal symmetry. Learning objectives will include mastering basic origami folding techniques, identifying and applying fundamental symmetry operations, recognizing and analyzing fractal symmetry, and creating geometric tessellations. Students will use image editing software (Illustrator and Photoshop), mathematical imaging software (Ultra Fractal), and the laser cutter in UNC's BeAM space, to design and create modular origami and fractal tessellation artwork.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 70.  First-Year Seminar: Topology and Symmetry.  3 Credits.  

In this seminar, students will explore ideas from topology and geometry and their application to symmetry patterns. Students will learn to identify and classify two-dimensional symmetry patterns and create their own designs. Students will relate symmetry patterns to their folded-up counterparts, called orbifolds, and use tools from topology and geometry to determine which patterns are possible and which patterns can never be achieved.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 89.  First-Year Seminar: Special Topics.  3 Credits.  

Special topics course. Content will vary each semester. Honors version available.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-SEMINAR.
Grading Status: Letter grade.  
MATH 110.  Algebra.  3 Credits.  

Provides a one-semester review of the basics of algebra. Basic algebraic expressions, functions, exponents, and logarithms are included, with an emphasis on problem solving. This course does not satisfy any general education requirements. It is intended for students who need it as a prerequisite for other classes. A student cannot receive credit for this course after receiving credit for MATH 231 or higher.

Rules & Requirements  
Grading Status: Letter grade.  
MATH 110L.  Algebra Corequisite.  1 Credits.  

This course provides just-in-time instruction and practice on basic algebra to support students in Algebra. It also provides additional practice on some of the more difficult topics from MATH 110. This course is intended for students currently enrolled in MATH 110 who need additional review of algebra.

Rules & Requirements  
Requisites: Corequisite, MATH 110.  
Grading Status: Pass/Fail.  
IDEAs in Action General Education logoMATH 115.  Reasoning with Data: Navigating a Quantitative World.  3 Credits.  

Students will use mathematical and statistical methods to address societal problems, make personal decisions, and reason critically about the world. Authentic contexts may include voting, health and risk, digital humanities, finance, and human behavior. This course does not count as credit towards the psychology or neuroscience majors.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Making Connections Gen Ed: QR.  
Grading Status: Letter grade.  
Same as: BIOL 115, PSYC 115, STOR 115.  
IDEAs in Action General Education logoMATH 116.  Intuitive Calculus.  3 Credits.  

Provides an introduction in as nontechnical a setting as possible to the basic concepts of calculus. The course is intended for the nonscience major. A student may not receive credit for this course after receiving credit for MATH 152 or 231.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Making Connections Gen Ed: QR.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 117.  Aspects of Finite Mathematics.  3 Credits.  

Introduction to basic concepts of finite mathematics, including topics such as counting methods, finite probability problems, and networks. The course is intended for the nonscience major. A student cannot receive credit for this course after receiving credit for MATH 231 or higher.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Making Connections Gen Ed: QR.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 118.  Aspects of Modern Mathematics.  3 Credits.  

Introduction to mathematical topics of current interest in society and science, such as the mathematics of choice, growth, finance, and shape. The course is intended for the non-science major. A student cannot receive credit for this course after receiving credit for MATH 231 or higher.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Making Connections Gen Ed: QR.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 119.  Introduction to Mathematical Modeling.  3 Credits.  

Provides an introduction to the use of mathematics for modeling real-world phenomena in a nontechnical setting. Models use algebraic, graphical, and numerical properties of elementary functions to interpret data. This course is intended for the nonscience major.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Making Connections Gen Ed: QR.  
Grading Status: Letter grade.  
MATH 129P.  Precalculus Mathematics.  0 Credits.  

Awarded as placement credit based on test scores. Does not fulfill a graduation requirement.

Rules & Requirements  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 130.  Precalculus Mathematics.  3 Credits.  

Covers the basic mathematical skills needed for learning calculus. Topics are calculating and working with functions and data, introduction to trigonometry, parametric equations, and the conic sections. A student may not receive credit for this course after receiving credit for MATH 231.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-LAUNCH (only designated sections), FC-QUANT.
Making Connections Gen Ed: QR.  
Requisites: Prerequisite, MATH 110; a grade of C- or better is required.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 152.  Calculus for Business and Social Sciences.  3 Credits.  

An introductory survey of differential and integral calculus with emphasis on techniques and applications of interest for business and the social sciences. This is a terminal course and not adequate preparation for MATH 232. A student cannot receive credit for this course after receiving credit for MATH 231 or 241.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-LAUNCH (only designated sections), FC-QUANT.
Making Connections Gen Ed: QR.  
Requisites: Prerequisite, MATH 110.  
Grading Status: Letter grade.  
MATH 190.  Special Topics in Mathematics.  3 Credits.  

An undergraduate seminar course that is designed to be a participatory intellectual adventure on an advanced, emergent, and stimulating topic within a selected discipline in mathematics. This course does not count as credit towards the mathematics major.

Rules & Requirements  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 210.  Mathematical Tools for Data Science.  3 Credits.  

This course introduces students to the tools of linear algebra and optimization, including solving linear systems, matrices as linear transformations, eigenvalues and eigenvectors, singular value decomposition, derivatives, and the method of gradient descent. Applications to data science are included such as image compression, principal component analysis, and neural networks. Computational tools (e.g. Python) will be used to implement algorithms. No programming experience needed. A student cannot receive credit after receiving credit for MATH 347.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Making Connections Gen Ed: QR.  
Requisites: Prerequisite, MATH 110 or 110P.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 231.  Calculus of Functions of One Variable I.  4 Credits.  

Limits, derivatives, and integrals of functions of one variable. Students may not receive credit for both MATH 231 and MATH 241. Honors version available.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-LAUNCH (only designated sections), FC-QUANT.
Making Connections Gen Ed: QR.  
Requisites: Prerequisites, MATH 110 and 130; Requires a grade of C- or better in MATH 130 or placement by the department.  
Grading Status: Letter grade.  
MATH 231L.  Calculus I Corequisite.  1 Credits.  

This course provides just-in-time instruction and review on algebra and trigonometry to support students in MATH 231. It also provides additional practice on some of the more difficult topics from Calculus 1. This course is intended to be taken by students currently enrolled in MATH 231 who need review of algebra and trigonometry.

Rules & Requirements  
Requisites: Prerequisites, MATH 110 and 130; requires a grade of C- or better in MATH 130 or placement by the department; Corequisite, MATH 231.  
Grading Status: Pass/Fail.  
IDEAs in Action General Education logoMATH 232.  Calculus of Functions of One Variable II.  4 Credits.  

Calculus of the elementary transcendental functions, techniques of integration, indeterminate forms, Taylor's formula, infinite series. Honors version available.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-LAUNCH (only designated sections), FC-QUANT.
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, A grade of C- or better in MATH 231 or placement by the department.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 233.  Calculus of Functions of Several Variables.  4 Credits.  

Vector algebra, solid analytic geometry, partial derivatives, multiple integrals. Honors version available.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FY-LAUNCH (only designated sections), FC-QUANT.
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 232.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 235.  Mathematics for Data Science.  4 Credits.  

This course introduces students to some of the key mathematical tools underlying algorithmic data science. The primary focus of the course is matrix algebra and multivariable calculus. The mathematical topics covered in the course will be motivated and connected by concrete applications in data science, with an emphasis on machine learning and optimization.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: FC-QUANT.
Requisites: Prerequisites, MATH 231 and MATH 232.  
Grading Status: Letter grade.  
Same as: STOR 235.  
MATH 290.  Special Topics in Mathematics.  1-3 Credits.  

Permission of the instructor. Elective topics in mathematics. This course has variable content and may be taken multiple times for credit.

Rules & Requirements  
Repeat Rules: May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 6 total completions.  
Grading Status: Letter grade.  
MATH 294.  Undergraduate Seminar in Mathematics.  1-3 Credits.  

Permission of the instructor. A seminar on a chosen topic in mathematics in which the students participate more actively than in usual courses.

Rules & Requirements  
Repeat Rules: May be repeated for credit. 6 total credits. 2 total completions.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 296.  Directed Exploration in Mathematics.  1-3 Credits.  

By permission of the director of undergraduate studies. Experimentation or deeper investigation under the supervision of a faculty member of topics in mathematics that may be, but need not be, connected with an existing course. No one may receive more than seven semester hours of credit for this course. Formerly offered as MATH 290.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: RESEARCH.
Making Connections Gen Ed: EE- Mentored Research.  
Repeat Rules: May be repeated for credit; may be repeated in the same term for different topics; 7 total credits. 7 total completions.  
Grading Status: Letter grade.  
MATH 307.  Revisiting Real Numbers and Algebra.  3 Credits.  

Central to teaching precollege mathematics is the need for an in-depth understanding of real numbers and algebra. This course explores this content, emphasizing problem solving and mathematical reasoning.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
MATH 347.  Linear Algebra for Applications.  3 Credits.  

Algebra of matrices with applications: determinants, solution of linear systems by Gaussian elimination, Gram-Schmidt procedure, and eigenvalues. Previously offered as MATH 547.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 232.  
Grading Status: Letter grade.  
MATH 381.  Discrete Mathematics.  3 Credits.  

This course serves as a transition from computational to more theoretical mathematics. Topics are from the foundations of mathematics: logic, set theory, relations and functions, induction, permutations and combinations, recurrence. Honors version available.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 232.  
Grading Status: Letter grade.  
MATH 383.  First Course in Differential Equations.  3 Credits.  

Introductory ordinary differential equations, first- and second-order differential equations with applications, higher-order linear equations, systems of first-order linear equations (introducing linear algebra as needed). Honors version available.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 233.  
Grading Status: Letter grade.  
MATH 383L.  First Course in Differential Equations Laboratory.  1 Credits.  

Course is computational laboratory component designed to help students visualize ODE solutions in Matlab. Emphasis is on differential equations motivated by applied sciences. Some applied linear algebra will appear as needed for computation and modeling purposes.

Rules & Requirements  
Requisites: Prerequisite, MATH 233; pre- or corequisite, MATH 383.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 396.  Undergraduate Reading and Research in Mathematics.  1-3 Credits.  

Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. No one may receive more than three semester hours credit for this course.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: RESEARCH.
Making Connections Gen Ed: EE- Mentored Research.  
Repeat Rules: May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 6 total completions.  
Grading Status: Letter grade.  

Advanced Undergraduate and Graduate-level Courses

MATH 406.  Mathematical Methods in Biostatistics.  1 Credits.  

Special mathematical techniques in the theory and methods of biostatistics as related to the life sciences and public health. Includes brief review of calculus, selected topics from intermediate calculus, and introductory matrix theory for applications in biostatistics.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 232.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 410.  Teaching and Learning Mathematics.  4 Credits.  

Study of how people learn and understand mathematics, based on research in mathematics, mathematics education, psychology, and cognitive science. This course is designed to prepare undergraduate mathematics majors to become excellent high school mathematics teachers. It involves field work in both the high school and college environments.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: COMMBEYOND.
Making Connections Gen Ed: EE- Field Work.  
Grading Status: Letter grade.  
MATH 411.  Developing Mathematical Concepts.  3 Credits.  

Permission of the instructor. An investigation of various ways elementary concepts in mathematics can be developed. Applications of the mathematics developed will be considered.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Grading Status: Letter grade.  
MATH 418.  Basic Concepts of Analysis for High School Teachers.  3 Credits.  

An examination of high school mathematics from an advanced perspective, including number systems and the behavior of functions and equations. Designed primarily for prospective or practicing high school teachers.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH 233 and 381.  
Grading Status: Letter grade.  
MATH 521.  Advanced Calculus I.  3 Credits.  

The real numbers, continuity and differentiability of functions of one variable, infinite series, integration. Honors version available.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH 233 and 381; A grade of A- or better in STOR 215 may substitute for MATH 381.  
Grading Status: Letter grade.  
MATH 522.  Advanced Calculus II.  3 Credits.  

Functions of several variables, the derivative as a linear transformation, inverse and implicit function theorems, multiple integration. Honors version available.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH 383 and 521.  
Grading Status: Letter grade.  
MATH 523.  Functions of a Complex Variable with Applications.  3 Credits.  

The algebra of complex numbers, elementary functions and their mapping properties, complex limits, power series, analytic functions, contour integrals, Cauchy's theorem and formulae, Laurent series and residue calculus, elementary conformal mapping and boundary value problems, Poisson integral formula for the disk and the half plane.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 383.  
Grading Status: Letter grade.  
MATH 524.  Elementary Differential Equations.  3 Credits.  

Linear differential equations, power series solutions, Laplace transforms, numerical methods.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 383.  
Grading Status: Letter grade.  
MATH 528.  Mathematical Methods for the Physical Sciences I.  3 Credits.  

Theory and applications of Laplace transform, Fourier series and transform, Sturm-Liouville problems. Students will be expected to do some numerical calculations on either a programmable calculator or a computer. This course has an optional computer laboratory component: MATH 528L.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 383.  
Grading Status: Letter grade.  
MATH 528L.  Laboratory for Mathematical Methods for the Physical Sciences I.  1 Credits.  

Training in the use of symbolic and numerical computing packages and their application to the MATH 528 lecture topics. Students will need a CCI-compatible computing device.

Rules & Requirements  
Requisites: Prerequisite, MATH 383; pre- or corequisite, MATH 528.  
Grading Status: Letter grade.  
MATH 529.  Mathematical Methods for the Physical Sciences II.  3 Credits.  

Introduction to boundary value problems for the diffusion, Laplace and wave partial differential equations. Bessel functions and Legendre functions. Introduction to complex variables including the calculus of residues. This course has an optional computer laboratory component: MATH 529L.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 521, 524, or 528.  
Grading Status: Letter grade.  
MATH 529L.  Laboratory for Mathematical Methods for the Physical Sciences II.  1 Credits.  

Training in the use of symbolic and numerical computing packages and their application to the MATH 529 lecture topics. Students will need a CCI-compatible computing device.

Rules & Requirements  
Requisites: Prerequisite, MATH 383; pre- or corequisite, MATH 529.  
Grading Status: Letter grade.  
MATH 533.  Elementary Theory of Numbers.  3 Credits.  

Divisibility, Euclidean algorithm, congruences, residue classes, Euler's function, primitive roots, Chinese remainder theorem, quadratic residues, number-theoretic functions, Farey and continued fractions, Gaussian integers.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 381; A grade of A- or better in STOR 215 may substitute for MATH 381.  
Grading Status: Letter grade.  
MATH 534.  Elements of Modern Algebra.  3 Credits.  

Binary operations, groups, subgroups, cosets, quotient groups, rings, polynomials.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 381; A grade of A- or better in STOR 215 may substitute for MATH 381.  
Grading Status: Letter grade.  
MATH 535.  Introduction to Probability.  3 Credits.  

Introduction to mathematical theory of probability covering random variables; moments; binomial, Poisson, normal and related distributions; generating functions; sums and sequences of random variables; and statistical applications. Students may not receive credit for both STOR 435 and STOR 535.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH/STOR 235 or MATH 233; and STOR 215 or MATH 381 or COMP 283.  
Grading Status: Letter grade.  
Same as: STOR 435.  
MATH 548.  Combinatorial Mathematics.  3 Credits.  

Counting selections, binomial identities, inclusion-exclusion, recurrences, Catalan numbers. Selected topics from algorithmic and structural combinatorics, or from applications to physics and cryptography.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 381.  
Grading Status: Letter grade.  
MATH 550.  Topology.  3 Credits.  

Introduction to topics in topology, particularly surface topology, including classification of compact surfaces, Euler characteristic, orientability, vector fields on surfaces, tessellations, and fundamental group.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH 233 and 381.  
Grading Status: Letter grade.  
MATH 551.  Euclidean and Non-Euclidean Geometries.  3 Credits.  

Critical study of basic notions and models of Euclidean and non-Euclidean geometries: order, congruence, and distance.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 381; A grade of A- or better in STOR 215 may substitute for MATH 381.  
Grading Status: Letter grade.  
MATH 553.  Mathematical and Computational Models in Biology.  3 Credits.  

This course introduces analytical, computational, and statistical techniques, such as discrete models, numerical integration of ordinary differential equations, and likelihood functions, to explore various fields of biology.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, (BIOL 201 and BIOL 202) or (BIOL 103 and BIOL 104); and MATH 231; and (MATH 232 or STOR 120 or STOR 155); or permission of the instructor for students lacking the prerequisites; Corequisite, BIOL 553L/MATH 553L.  
Grading Status: Letter grade.  
Same as: BIOL 553.  
MATH 553L.  Mathematical and Computational Models in Biology Laboratory.  1 Credits.  

This lab introduces analytical, computational, and statistical techniques, such as discrete models, numerical integration of ordinary differential equations, and likelihood functions, to explore various fields of biology.

Rules & Requirements  
Requisites: Prerequisites, (BIOL 201 and 202) or BIOL 103 and BIOL 104); and MATH 231; and (MATH 232 or STOR 120 or STOR 155); or permission of the instructor for students lacking the prerequisites; Corequisite, BIOL 553/MATH 553.  
Grading Status: Letter grade.  
Same as: BIOL 553L.  
MATH 555.  Introduction to Dynamics.  3 Credits.  

Topics will vary and may include iteration of maps, orbits, periodic points, attractors, symbolic dynamics, bifurcations, fractal sets, chaotic systems, systems arising from differential equations, iterated function systems, and applications.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 383.  
Grading Status: Letter grade.  
MATH 560.  Optimization with Applications in Machine Learning.  3 Credits.  

This course will provide an introduction to convex optimization, including convex sets and functions, modeling, conic problems, optimality conditions and algorithms. The second part of the course will address non-convex problems, focusing on contemporary optimization challenges in large-scale optimization and practical approaches for machine learning and deep learning.

Rules & Requirements  
Requisites: Prerequisites, MATH 233, MATH 347, and COMP 110 or COMP 116.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 563.  Introduction to Fluid Mechanics.  3 Credits.  

Mathematical methods applied to problems in fluid dynamics. Particular attention will be given to the power of dimensional analysis and scaling arguments. Topics will include: particle motion (e.g. the dynamics of sports balls), animal locomotion (e.g. swimming and flying), viscous flows (e.g. geological fluid dynamics), rotating and stratified flows (geophysical fluid dynamics), gravity currents and plumes (environmental fluid mechanics), drops, bubbles, and films.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: RESEARCH.
Requisites: Prerequisite, MATH 528.  
Grading Status: Letter grade.  
MATH 564.  Mathematical Modeling in the Life Sciences.  3 Credits.  

Requires some knowledge of computer programming. Model validation and numerical simulations using ordinary, partial, stochastic, and delay differential equations. Applications to the life sciences may include muscle physiology, biological fluid dynamics, neurobiology, molecular regulatory networks, and cell biology.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH 383, and 347.  
Grading Status: Letter grade.  
Same as: BIOL 534.  
MATH 566.  Introduction to Numerical Analysis.  3 Credits.  

Requires some knowledge of computer programming. Iterative methods, interpolation, polynomial and spline approximations, numerical differentiation and integration, numerical solution of ordinary and partial differential equations.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 383, or 347.  
Grading Status: Letter grade.  
MATH 577.  Linear Algebra.  3 Credits.  

Vector spaces, linear transformations, duality, diagonalization, primary and cyclic decomposition, Jordan canonical form, inner product spaces, orthogonal reduction of symmetric matrices, spectral theorem, bilinear forms, multilinear functions. A much more abstract course than MATH 347.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisites, MATH 381 and 383; A grade of A- or better in STOR 215 may substitute for MATH 381.  
Grading Status: Letter grade.  
MATH 578.  Algebraic Structures.  3 Credits.  

Permutation groups, matrix groups, groups of linear transformations, symmetry groups; finite abelian groups. Residue class rings, algebra of matrices, linear maps, and polynomials. Real and complex numbers, rational functions, quadratic fields, finite fields.

Rules & Requirements  
Making Connections Gen Ed: QI.  
Requisites: Prerequisite, MATH 347, or 577.  
Grading Status: Letter grade.  
MATH 590.  Topics in Mathematics.  3 Credits.  

Permission of the instructor. Topics may focus on matrix theory, analysis, algebra, geometry, or applied and computational mathematics.

Rules & Requirements  
Repeat Rules: May be repeated for credit; may be repeated in the same term for different topics; 12 total credits. 4 total completions.  
Grading Status: Letter grade.  
MATH 594.  Nonlinear Dynamics.  3 Credits.  

Interdisciplinary introduction to nonlinear dynamics and chaos. Fixed points, bifurcations, strange attractors, with applications to physics, biology, chemistry, finance.

Rules & Requirements  
Requisites: Prerequisite, MATH 383; permission of the instructor for students lacking the prerequisite.  
Grading Status: Letter grade.  
Same as: PHYS 594.  
MATH 635.  Probability II.  3 Credits.  

Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.

Rules & Requirements  
Requisites: Prerequisite, STOR 634; permission of the instructor for students lacking the prerequisite.  
Grading Status: Letter grade.  
Same as: STOR 635.  
MATH 641.  Enumerative Combinatorics.  3 Credits.  

Basic counting; partitions; recursions and generating functions; signed enumeration; counting with respect to symmetry, plane partitions, and tableaux.

Rules & Requirements  
Requisites: Prerequisite, MATH 578.  
Grading Status: Letter grade.  
MATH 643.  Combinatorial Structures.  3 Credits.  

Graph theory, matchings, Ramsey theory, extremal set theory, network flows, lattices, Moebius inversion, q-analogs, combinatorial and projective geometries, codes, and designs.

Rules & Requirements  
Requisites: Prerequisite, MATH 578.  
Grading Status: Letter grade.  
MATH 653.  Introductory Analysis.  3 Credits.  

Requires knowledge of advanced calculus. Elementary metric space topology, continuous functions, differentiation of vector-valued functions, implicit and inverse function theorems. Topics from Weierstrass theorem, existence and uniqueness theorems for differential equations, series of functions.

Rules & Requirements  
Grading Status: Letter grade.  
MATH 656.  Complex Analysis.  3 Credits.  

A rigorous treatment of complex integration, including the Cauchy theory. Elementary special functions, power series, local behavior of analytic functions.

Rules & Requirements  
Requisites: Prerequisite, MATH 653.  
Grading Status: Letter grade.  
MATH 657.  Qualitative Theory of Differential Equations.  3 Credits.  

Requires knowledge of linear algebra. Existence and uniqueness theorems, linear and nonlinear systems, differential equations in the plane and on surfaces, Poincare-Bendixson theory, Lyapunov stability and structural stability, critical point analysis.

Rules & Requirements  
Requisites: Prerequisite, MATH 653.  
Grading Status: Letter grade.  
MATH 661.  Scientific Computation I.  3 Credits.  

Requires some programming experience and basic numerical analysis. Error in computation, solutions of nonlinear equations, interpolation, approximation of functions, Fourier methods, numerical integration and differentiation, introduction to numerical solution of ODEs, Gaussian elimination.

Rules & Requirements  
Grading Status: Letter grade.  
Same as: ENVR 661.  
MATH 662.  Scientific Computation II.  3 Credits.  

Theory and practical issues arising in linear algebra problems derived from physical applications, e.g., discretization of ODEs and PDEs. Linear systems, linear least squares, eigenvalue problems, singular value decomposition.

Rules & Requirements  
Requisites: Prerequisite, MATH 661.  
Grading Status: Letter grade.  
Same as: COMP 662, ENVR 662.  
MATH 668.  Methods of Applied Mathematics I.  3 Credits.  

Requires an undergraduate course in differential equations. Contour integration, asymptotic expansions, steepest descent/stationary phase methods, special functions arising in physical applications, elliptic and theta functions, elementary bifurcation theory.

Rules & Requirements  
Grading Status: Letter grade.  
Same as: ENVR 668.  
MATH 669.  Methods of Applied Mathematics II.  3 Credits.  

Perturbation methods for ODEs and PDEs, WKBJ method, averaging and modulation theory for linear and nonlinear wave equations, long-time asymptotics of Fourier integral representations of PDEs, Green's functions, dynamical systems tools.

Rules & Requirements  
Requisites: Prerequisite, MATH 668.  
Grading Status: Letter grade.  
Same as: ENVR 669.  
MATH 676.  Modules, Linear Algebra, and Groups.  3 Credits.  

Requires knowledge of linear algebra and algebraic structures. Modules over rings, canonical forms for linear operators and bilinear forms, multilinear algebra, groups and group actions.

Rules & Requirements  
Repeat Rules: May be repeated for credit. 6 total credits. 2 total completions.  
Grading Status: Letter grade.  
MATH 677.  Groups, Representations, and Fields.  3 Credits.  

Internal structure of groups, Sylow theorems, generators and relations, group representations, fields, Galois theory, category theory.

Rules & Requirements  
Requisites: Prerequisite, MATH 676.  
Grading Status: Letter grade.  
MATH 680.  Differentiable Manifolds.  3 Credits.  

Calculus on manifolds, vector bundles, vector fields and differential equations, de Rham cohomology.

Rules & Requirements  
Requisites: Prerequisite, MATH 681.  
Grading Status: Letter grade.  
MATH 681.  Introductory Topology.  3 Credits.  

Topological spaces, product spaces, connectedness, compactness. Classification of surfaces, fundamental group, covering spaces. Simplicial homology.

Rules & Requirements  
Grading Status: Letter grade.  
MATH 690.  Topics In Mathematics.  3 Credits.  

Permission of the department. Directed study of an advanced topic in mathematics. Topics will vary.

Rules & Requirements  
Repeat Rules: May be repeated for credit; may be repeated in the same term for different topics; 12 total credits. 4 total completions.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 691H.  Honors Research in Mathematics.  3 Credits.  

Permission of the director of undergraduate studies. Readings in mathematics and the beginning of directed research on an honors thesis.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: RESEARCH.
Making Connections Gen Ed: EE- Mentored Research.  
Grading Status: Letter grade.  
IDEAs in Action General Education logoMATH 692H.  Honors Thesis in Mathematics.  3 Credits.  

Permission of the director of undergraduate studies. Completion of an honors thesis under the direction of a member of the faculty. Required of all candidates for graduation with honors in mathematics.

Rules & Requirements  
IDEAs in Action General Education logo IDEAs in Action Gen Ed: RESEARCH.
Making Connections Gen Ed: EE- Mentored Research.  
Grading Status: Letter grade.  

Department of Mathematics

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