# Courses

# Courses

This page contains the undergraduate-level MATH courses. The complete list, including the graduate courses, can be found in UNC’s course catalog.

**MATH 50 – First-Year Seminar: The Predictability of Chance and Its Applications in Applied Mathematics.
Credits: 3**

**Description:**This seminar will examine the ways in which some types of behavior of random systems cannot only be predicted, but also applied to practical problems.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 51 – First-Year Seminar: 'Fish Gotta Swim, Birds Gotta Fly': The Mathematics and the Mechanics of Moving.
Credits: 3**

**Description:**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

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 52 – First-Year Seminar: Fractals: The Geometry of Nature.
Credits: 3**

**Description:**Many natural objects have complex, infinitely detailed shapes in which smaller versions of the whole shape are seen appearing throughout. Such a shape is a fractal, the topic of study. Honors version available

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 53 – First-Year Seminar: Symmetry and Tilings.
Credits: 3**

**Description:**Through projects using software programs, Web sites, and readings, students will discover the geometric structure of tilings, learn to design their own patterns, and explore the many interdisciplinary connections.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 54 – First-Year Seminar: The Science of Conjecture: Its Math, Philosophy, and History.
Credits: 3**

**Description:**Seminar will cover the history and philosophy of probability, evidence, and conjecture, consider the development of the field of probability, and look at current and future uses of probability. Honors version available

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 55 – First-Year Seminar: Geometry and Symmetry in Nature.
Credits: 3**

**Description:**The nature of space imposes striking constraints on organic and inorganic objects. This seminar examines such constraints on both biological organisms and regular solids in geometry.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 56 – First-Year Seminar: Information and Coding.
Credits: 3**

**Description:**With the growth of available information on almost anything, can it be reliably compressed, protected, and transmitted over a noisy channel? Students will take a mathematical view of cryptography throughout history and information handling in modern life. Honors version available

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 57 – First-Year Seminar: The Fourth Dimension.
Credits: 3**

**Description:**The idea of a fourth dimension has a rich and varied history. This seminar explores the concept of fourth (and higher) dimensions both mathematically and more widely in human thought.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 58 – First-Year Seminar: Math, Art, and the Human Experience.
Credits: 3**

**Description:**Students will explore the relevance of mathematical ideas to fields typically perceived as "nonmathematical" (e.g., art, music, film, literature) and how these "nonmathematical" fields influence mathematical thought. Honors version available

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 59 – First-Year Seminar: The Mystery and Majesty of Ordinary Numbers.
Credits: 3**

**Description:**Problems arising from the arithmetic of ordinary counting numbers have for centuries fascinated both mathematicians and nonmathematicians. This seminar will consider some of these problems (both solved and unsolved).

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 60 – First-Year Seminar: Simulated Life.
Credits: 3**

**Description:**This seminar introduces students to the thought process that goes into developing computational models of biological systems. It will also expose students to techniques for simulating and analyzing these models. Honors version available

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 61 – First-Year Seminar: The Language of Mathematics: Making the Invisible Visible.
Credits: 3**

**Description:**This course will consider mathematics to be the science of patterns and will discuss some of the different kinds of patterns that give rise to different branches of mathematics.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 62 – First-Year Seminar: Combinatorics.
Credits: 3**

**Description:**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

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 63 – First-Year Seminar: From "The Sound of Music" to "The Perfect Storm."
Credits: 3**

**Description:**Students will develop the conceptual framework necessary to understand waves of any kind, starting from laboratory observations. Honors version available

**Same As:**MASC 57

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: PL, QI; IDEAs in Action: FY-SEMINAR, FC-NATSCI or FC-QUANT

**MATH 64 – First-Year Seminar: A View of the Sea: The Circulation of the Ocean and Its Impact on Coastal Water.
Credits: 3**

**Description:**Why is the Gulf Stream so strong, why does it flow clockwise, and why does it separate from the United States coast at Cape Hatteras? Students will study the circulation of the ocean and its influence on coastal environments by reading the book A View of the Sea by the eminent oceanographer Hank Stommel and by examining satellite and on-site observations.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 65 – First-Year Seminar: Colliding Balls and Springs: The Microstructure of How Materials Behave.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 66 – First-Year Seminar: Non-Euclidean Geometry in Nature and History.
Credits: 3**

**Description:**The seminar will investigate non-Euclidean geometry (hyperbolic and spherical) from historical, mathematical, and practical perspectives. The approach will be largely algebraic, in contrast to the traditional axiomatic method.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 67 – The Mathematics of Climate Change: Can We Predict the Future of Our Planet?
Credits: 3**

**Description:**Is the Earth warming? Predictions are based largely on mathematical models. We shall consider the limitations of models in relation to making predictions. Examples of chaotic behavior will be presented.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: CI, QI; IDEAs in Action: FY-SEMINAR

**MATH 68 – First-Year Seminar: The Mathematics of Voting.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 69 – First-Year Seminar: Unfolding Infinity: Mathematical Origami and Fractal Symmetry.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 70 – First-Year Seminar: Topology and Symmetry.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; IDEAs in Action: FY-SEMINAR

**MATH 89 – First-Year Seminar: Special Topics.
Credits: 3**

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

**Grading Status:**Letter Grade

**Gen Ed:**IDEAs in Action: FY-SEMINAR

**Repeat Rules:**May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 2 total completions.

**MATH 110 – Algebra
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**MATH 110L – Algebra Corequisite
Credits: 1**

**Description:**This course provides just-in-time instruction and practice on basic algebra to support students in Calculus 1. 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.

**Prerequisite:**Corequisite, MATH 110

**Grading Status:**Pass/Fail

**MATH 115 – Reasoning with Data: Navigating a Quantitative World
Credits: 3**

**Description:**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.

**Same As:**BIOL 115, PSYC 115, STOR 115.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FC-QUANT.

**MATH 116 – Intuitive Calculus.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FC-QUANT.

**MATH 117 – Aspects of Finite Mathematics.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FC-QUANT.

**MATH 118 – Aspects of Modern Mathematics.
Credits: 3**

**Description:**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 nonscience major. A student cannot receive credit for this course after receiving credit for MATH 231 or higher.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FC-QUANT.

**MATH 119 – Introduction to Mathematical Modeling.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FC-QUANT.

**MATH 129P – Precalculus Mathematics.
Credits: 0**

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

**Grading Status:**Letter Grade

**MATH 130 – Precalculus Mathematics.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 110; a grade of C- or better is required.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FY-LAUNCH (only designated sections), FC-QUANT.

**MATH 152 – Calculus for Business and Social Sciences.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 110

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FY-LAUNCH (only designated sections), FC-QUANT.

**MATH 190 – Special Topics in Mathematics.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**MATH 210 – Mathematical Tools for Data Science.
Credits: 3**

**Description:**This course introduces students to the tools of linear algebra and optimization, including solving linear systems, matrices as linear transformations, eigenvalues and eigenvectors, approximations, root finding, derivatives, and optimization in multiple dimensions. This course emphasizes multidimensional thinking and applications to data science. A student cannot receive credit for this course after receiving credit for MATH 347.

**Prerequisite:**MATH 110 or MATH 110P

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FC-QUANT.

**MATH 231 – Calculus of Functions of One Variable I.
Credits: 4**

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

**Prerequisite:**MATH 110 and MATH 130; Requires a grade of C- or better in MATH 130 or placement by the department.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QR; Ideas in Action: FY-LAUNCH (only designated sections), FC-QUANT.

**MATH 231L – Calculus I Corequisite.
Credits: 1**

**Description:**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.

**Prerequisite:**MATH 110 and MATH 130; requires a grade of C- or better in MATH 130 or placement by the department; Corequisite, MATH 231.

**Grading Status:**Pass/Fail

**MATH 232 – Calculus of Functions of One Variable II.
Credits: 4**

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

**Prerequisite:**A grade of C- or better in MATH 231 or placement by the department.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; Ideas in Action: FY-LAUNCH (only designated sections), FC-QUANT.

**MATH 233 – Calculus of Functions of Several Variables.
Credits: 4**

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

**Prerequisite:**MATH 232.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI; Ideas in Action: FY-LAUNCH (only designated sections), FC-QUANT.

**MATH 290 – Special Topics in Mathematics.
Credits: 1-3**

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

**Grading Status:**Letter Grade

**Repeat Rules:**May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 6 total completions.

**MATH 294 – Undergraduate Seminor in Mathematics.
Credits: 1-3**

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

**Grading Status:**Letter Grade

**Repeat Rules:**May be repeated for credit. 6 total credits. 2 total completions.

**MATH 296 – Directed Exploration in Mathematics.
Credits: 1-3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: EE- Mentored Research; IDEAs in Action: RESEARCH.

**Repeat Rules:**May be repeated for credit; may be repeated in the same term for different topics; 7 total credits. 7 total completions.

**MATH 307 – Revisiting Real Numbers and Algebra.
Credits: 3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 347 – Linear Algebra for Applications.
Credits: 3**

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

**Prerequisite:**MATH 232.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 381 – Discrete Mathematics.
Credits: 3**

**Description:**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

**Prerequisite:**MATH 232.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 383 – First Course in Differential Equations.
Credits: 3**

**Description:**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

**Prerequisite:**MATH 233.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 383L – First Course in Differential Equations Laboratory.
Credits: 1**

**Description:**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.

**Prerequisite:**MATH 233; pre- or corequisite, MATH 383.

**Grading Status:**Letter Grade

**MATH 396 – Undergraduate Reading and Research in Mathematics.
Credits: 1-3**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: EE- Mentored Research; IDEAs in Action: RESEARCH.

**Repeat Rules:**May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. 6 total completions.

**MATH 406 – Mathematical Methods in Biostatistics.
Credits: 1**

**Description:**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.

**Prerequisite:**MATH 232.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 410 – Teaching and Learning Mathematics.
Credits: 4**

**Description:**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.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: EE- Field Work; IDEAs in Action: COMMBEYOND.

**MATH 411 – Developing Mathematical Concepts.
Credits: 3**

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

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 418 – Basic Concepts of Analysis for High School Teachers.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 233, MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 515 – History of Mathematics.
Credits: 3**

**Description:**A general survey of the history of mathematics with emphasis on elementary mathematics. Some special problems will be treated in depth.

**Prerequisite:**MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 521 – Advanced Calculus I.
Credits: 3**

**Description:**A grade of A- or better in STOR 215 may substitute for MATH 381. The real numbers, continuity and differentiability of functions of one variable, infinite series, integration. Honors version available

**Prerequisite:**MATH 233, MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 522 – Advanced Calculus II.
Credits: 3**

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

**Prerequisite:**MATH 383, MATH 521.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 523 – Functions of a Complex Variable with Applications.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 383.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 524 – Elementary Differential Equations.
Credits: 3**

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

**Prerequisite:**MATH 383.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 528 – Mathematical Methods for the Physical Sciences I.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 383.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 528L – Laboratory for Mathematical Methods for the Physical Sciences I.
Credits: 1**

**Description:**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.

**Prerequisite:**MATH 383; pre- or corequisite, MATH 528.

**Grading Status:**Letter Grade

**MATH 529 – Mathematical Methods for the Physical Sciences II.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 521, MATH 524, or MATH 528.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 529L – Laboratory for Mathematical Methods for the Physical Sciences II.
Credits: 1**

**Description:**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.

**Prerequisite:**MATH 383; pre- or corequisite, MATH 529.

**Grading Status:**Letter Grade

**Gen Ed:**QI

**MATH 533 – Elementary Theory of Numbers.
Credits: 3**

**Description:**A grade of A- or better in STOR 215 may substitute for MATH 381. 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.

**Prerequisite:**MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 534 – Elements of Modern Algebra.
Credits: 3**

**Description:**A grade of A- or better in STOR 215 may substitute for MATH 381. Binary operations, groups, subgroups, cosets, quotient groups, rings, polynomials.

**Prerequisite:**MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 535 – Introduction to Probability.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 233.

**Same As:**STOR 435

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 548 – Combinatorial Mathematics.
Credits: 3**

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

**Prerequisite:**MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 550 – Topology.
Credits: 3**

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

**Prerequisite:**MATH 233, MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 551 – Euclidean and Non-Euclidean Geometries.
Credits: 3**

**Description:**A grade of A- or better in STOR 215 may substitute for MATH 381. Critical study of basic notions and models of Euclidean and non-Euclidean geometries: order, congruence, and distance.

**Prerequisite:**MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 553 – Mathematical and Computational Models in Biology.
Credits: 3**

**Description:**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.

**Prerequisite:**BIOL 201 and 202, MATH 231, and either MATH 232 or STOR 155; Co-requisite, BIOL 553L/MATH 553L; permission of the instructor for students lacking the requisites.

**Same As:**BIOL 553

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 553L – Mathematical and Computational Models in Biology Laboratory.
Credits: 1**

**Description:**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.

**Prerequisite:**BIOL 201 and 202, MATH 231, and either MATH 232 or STOR 155; Co-requisite, BIOL 553/MATH 553; Permission of the instructor for students lacking the prerequisites.

**Same As:**BIOL 553L

**Grading Status:**Letter Grade

**MATH 555 – Introduction to Dynamics.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 383.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 560 – Optimization with Applications in Machine Learning.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 233, MATH 347, and COMP 110 or COMP 116.

**Grading Status:**Letter grade

**MATH 564 – Mathematical Modeling in the Life Sciences.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 383, MATH 347.

**Same As:**BIOL 534.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 566 – Introduction to Numerical Analysis.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 383 or MATH 347.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 577 – Linear Algebra.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 381 and MATH 383; A grade of A- or better in STOR 215 may substitute for MATH 381.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 578 – Algebraic Structures.
Credits: 3**

**Description:**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.

**Prerequisite:**MATH 347 or MATH 577.

**Grading Status:**Letter Grade

**Gen Ed:**Making Connections: QI.

**MATH 590 – Topics in Mathematics.
Credits: 3**

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

**Grading Status:**Letter Grade

**Repeat Rules:**May be repeated for credit; may be repeated in the same term for different topics; 12 total credits. 4 total completions.

**MATH 594 – Nonlinear Dynamics.
Credits: 3**

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

**Prerequisite:**MATH 383; permission of the instructor for students lacking the prerequisite.

**Same As:**PHYS 594

**Grading Status:**Letter Grade

### For Additional Information Contact

Erin Willis

**Undergraduate Student Services Manager**

336 Phillips Hall

919-962-0198

ewillis3@email.unc.edu