# Mathematics

Mathematics is a discipline central to the liberal arts curriculum and to scholarly endeavors in all domains to prepare students for careers requiring strong analytical skills. The department at Emory offers educational programs and conducts research in mathematics, as well as several interdisciplinary areas.

## Concentrations

## Faculty

- Chair
- James Nagy
- Director of Undergraduate Studies
- Neha GuptaBree Ettinger
- Core
- David BorthwickMichael CarrJulianne ChungMatthias ChungBree EttingerManuela GirottiMichelangelo GrigniNeha GuptaKenneth MandelbergManuela ManettaTalea MayoJames NagyElizabeth NewmanLevon NurbekyanCosmin PohoataAlexander PolyanskiiVictoria PowersParimala RamanVojtech RodlRobert Roth Jr.Lars RuthottoMaja TaskovicMarco TezzeleSuresh VenapallyAlessandro VenezianiJuan Villeta-GarciaYiran WangYuanzhe XiShanshuang YangLiana Yepremyan

## Courses

### MATH 100-Level Courses

Convex sets, linear inequalities, linear programming, two-person games, finite graphs. Applications in management, economics, and behavioral sciences.

- Credit Hours
- 3
- GER
- QR
- Requisites
- None
- Cross-Listed
- None

Pre-calculus topics practiced in the context of elementary calculus concepts (limits, derivatives, and antiderivatives). For students who need a review of transcendental functions while learning calculus. Provides a solid foundation for subsequent calculus courses.

- Credit Hours
- 3
- GER
- QR
- Requisites
- None
- Cross-Listed
- None

Limits, continuity, derivatives, antiderivatives, the definite integral.

- Credit Hours
- 3
- GER
- QR
- Requisites
- Students completing MATH 119 or equivalent cannot enroll for MATH 111. For concerns, please contact the Mathematics department.
- Cross-Listed
- None

Techniques of integration, exponential and logarithm functions, sequences and series, polar coordinates.

- Credit Hours
- 3
- GER
- QR
- Requisites
- This course requires MATH 111 OR MATH_OX111 OR MATH 115 OR MATH 119 OR MATH_OX119 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

This class is for freshmen who have earned a 4 or 5 on the AP AB exam, or a 5 on the IB HL exam. Topics include: techniques of integration, exponential and logarithm functions, sequences and series, and polar coordinates.

- Credit Hours
- 3
- GER
- QR
- Requisites
- This class is for freshmen who have earned a 4 or 5 on the AP AB exam, or a 5 on the IB HL exam. Topics include: techniques of integration, exponential and logarithm functions, sequences and series, and polar coordinates.
- Cross-Listed
- None

Integration, differential equations, multivariable calculus, and discrete probability and statistics, with an emphasis on applications to biology.

- Credit Hours
- 4
- GER
- QR
- Requisites
- MATH 111 or MATH 111L or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Rotating topics in math. May be repeated for credit when the topic varies. Prerequisites and co requisites depend on the topic offered.

- Credit Hours
- 1 - 4
- GER
- None
- Requisites
- None
- Cross-Listed
- None

Topics will be announced each semester when class is scheduled.

- Credit Hours
- 3
- GER
- FS
- Requisites
- None
- Cross-Listed
- None

### MATH 200-Level Courses

Development and use of mathematical models from probability and statistics with applications.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- This course requires MATH 112 OR MATH_OX112 OR MATH 112Z OR MATH_OX112Z OR MATH 119 OR MATH_OX119 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

This course is a short treatment of MATH 112 and 211 with a lab component. It is not appropriate for students who have taken MATH 211. Topics include: advanced integration, Taylor series; and multivariable differentiation, optimization and integration; and applications to statistics and science.

- Credit Hours
- 4
- GER
- QR
- Requisites
- MATH 111 or MATH 111L or MATH_OX 111 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Vectors; multivariable functions; partial derivatives; multiple integrals; vector and scalar fields; Green's and Stokes' theorems; divergence theorem.

- Credit Hours
- 3
- GER
- QR
- Requisites
- MATH 112 or MATH 112Z or MATH_OX 112 or MATH_OX 112Z or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

This is a standard first semester Differential Equations course which covers first and second-order differential equations and systems of differential equations, with an emphasis placed on developing techniques for solving differential equations.

- Credit Hours
- 3
- GER
- QR
- Requisites
- MATH 112 or MATH 112S or MATH 112Z or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Systems of linear equations, matrices, determinants, linear transformations, eigenvalues and eigenvectors, least-squares.

- Credit Hours
- 4
- GER
- QR
- Requisites
- MATH 111 or MATH_OX 111 or MATH 112 or MATH_OX 112 or MATH 112Z or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

An introduction to theoretical mathematics. Logic and proofs, operations on sets, induction, relations, functions.

- Credit Hours
- 3
- GER
- QR
- Requisites
- This course requires MATH 111 as prerequisite AND MATH 112 or MATH_OX112 or MATH 112Z or MATH_OX112Z or equivalent transfer credit.
- Cross-Listed
- None

Topics in the history of mathematics and their philosophical background. Genesis and evolution of ideas in analysis, algebra, geometry, mechanics, foundations. Historical and philosophical aspects of concepts of infinity, mathematical rigor, probability, etc.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- MATH 112 or MATH 112S or MATH 112Z or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Topics in the history of mathematics and their philosophical background. Genesis and evolution of ideas in analysis, algebra, geometry, mechanics, foundations. Historical and philosophical aspects of concepts of infinity, mathematical rigor, probability, etc.

- Credit Hours
- 4
- GER
- MQRW
- Requisites
- MATH 112 or MATH 112S or MATH 112Z or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

This course is the first half of the advanced math introductory sequence. It covers the basics of linear algebra: vector spaces, linear transformations, determinants, and eigenvalues, with an emphasis on mathematical rigor. This class is for freshmen who scored a 5 on the Calculus AP BC exam.

- Credit Hours
- 4
- GER
- None
- Requisites
- AP Calculus BC or equivalent transfer credit as prerequisite. Used for: MATH 275
- Cross-Listed
- None

This course is the second half of the advanced mathematics introductory sequence. It covers the basics of vector calculus: differentiable mappings, differential forms, and integration theory.

- Credit Hours
- 4
- GER
- QR
- Requisites
- MATH 275 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Rotating topics in mathematics. May be repeated for credit when the topic varies. Pre and co requisites depend on the topic offered.

- Credit Hours
- 1 - 4
- GER
- None
- Requisites
- None
- Cross-Listed
- None

Rotating topics in mathematics. May be repeated for credit when the topic varies. Pre and co requisites depend on the topic offered.

- Credit Hours
- 1 - 5
- GER
- CW
- Requisites
- None
- Cross-Listed
- None

May be repeated for credit, total credit not to exceed six hours. Cannot be used to meet course requirements for a Math major or minor. Topics vary by instructor.

- Credit Hours
- 1 - 4
- GER
- None
- Requisites
- None
- Cross-Listed
- None

### MATH 300-Level Courses

Solution of linear and nonlinear systems of equations, interpolation, least-squares approximation, numerical integration, and differentiation.

- Credit Hours
- 4
- GER
- MQR
- Requisites
- (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) and (CS 170 or CS_OX 170) or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Analytic functions, elementary functions, integrals, power series, residues, and conformal mapping.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- [(MATH 211 or MATH_OX211) and (MATH 250 or MATH_OX 250)] or MATH 276 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Axiomatic treatment of vector spaces, inner product spaces, minimal polynomials, Cayley Hamilton theorem, Jordan form, and bilinear forms.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- MATH 250 or MATH_OX 250 or MATH_OX 250Q or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

This course introduces the basic concepts of algebraic and analytic number theory. Topics include: congruence relations, the distribution of prime numbers, quadratic reciprocity, Diophantine equations, continued fractions, and generating functions.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- MATH 250 or MATH_OX 250 or MATH_OX 250Q or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Combinations and permutations, counting techniques, recurrence relations, and generating functions. Block designs, finite planes, and coding theory. Introduction to graph theory.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) and (MATH 250 or MATH_OX 250 or MATH 276) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Curves and surfaces in 3-space. The geometry of the Gauss map. Special surfaces. The intrinsic geometry of surfaces. Surfaces and computer graphics.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 211 or PHYS 211 or MATH_OX 211 or MATH 276) and (MATH 221 or MATH_OX 221 or MATH 321) and (MATH 250 or MATH_OX 250 or MATH 276) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Principles of mathematical modeling; case studies using nonlinear ordinary differential equations, difference equations, and partial differential equations.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- This course requires MATH 221 OR MATH_OX221 OR MATH 321 AND MATH 224 OR MATH 250 OR MATH_OX250 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Theory of linear programming, duality, optimal flows in networks, and mathematical programming.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) and (CS 170 or CS_OX 170) or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Nonlinear optimization problems arise in a wide range of applications, for example, in economics, physics, engineering, imaging. This introductory course covers a wide range of examples and both theory and practice of unconstrained and constrained optimization.

- Credit Hours
- 3
- GER
- None
- Requisites
- (MATH 211 or PHYS 211 or MATH_OX 211 or MATH 276) and (MATH 221 or MATH_OX 221 or MATH 321) and (MATH 250 or MATH_OX 250 or MATH 276) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

PDEs and their origin, classification of PDEs, analytical methods for the solution of PDEs, qualitative properties of the solutions, eigenvalue problems and introduction to numerical methods.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 211 or MATH_OX 211 or MATH 276) and (MATH 212 or MATH_OX 212) and (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Partial Differential Equations (PDE's) are a formidable tool for describing real-life problems. In this course we use PDE's for cardiovascular problems and other real-life situations. Students will visit radiology labs and learn about image processing and numerical simulations in medicine.

- Credit Hours
- 3
- GER
- None
- Requisites
- (MATH 211 or MATH_OX 211 or MATH 276) and (MATH 212 or MATH_OX 212) and (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Finite and continuous probability theory, distribution models (binomial, geometric, uniform, normal, Poisson, and exponential), the Chebyshev inequality, expectation and variance, moment generating functions, the central limit theorem, and applications.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- MATH 210 or MATH_OX 210 or MATH 211 or PHYS 211 or MATH_OX 211 or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Fundamentals of statistical inference: estimation, properties of estimators, methods for comparing estimators, confidence intervals, hypothesis testing, regression, and analysis of variance.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- This course requires MATH 361 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Fundamentals of statistical inference: estimation, properties of estimators, methods for comparing estimators, confidence intervals, hypothesis testing, regression, and analysis of variance.This course is an extension of MATH 362 which includes a writing lab. Students take a writing lab and learn how to articulate why the statistical methods they use are applicable, discuss what their results show and make recommendations for future studies.

- Credit Hours
- 4
- GER
- MQRW
- Requisites
- This course requires MATH 361 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Rotating topics in mathematics. May be repeated for credit when the topic varies. Pre and co requisites depend on the topic offered.

- Credit Hours
- 1 - 4
- GER
- None
- Requisites
- None
- Cross-Listed
- None

- Credit Hours
- 1 - 5
- GER
- CW
- Requisites
- None
- Cross-Listed
- None

### MATH 400-Level Courses

Analysis of sets and functions in n-space which focuses on basic topological properties of sets as well as continuity and differentiation of functions. Topics: exterme value theorem, chain rule, and inverse function theorem.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 211 or PHYS 211 or MATH_OX 211 or MATH 276) and (MATH 221 or MATH_OX 221 or MATH 321) and (MATH 250 or MATH_OX 250 or MATH 276) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

This course is a continuation of Math 411 which focuses on integration and uniform convergence in n-space. Topics include: Stoke's theorem, Fubini's theorem, Taylor's theorem, the Stone-Weierstrass theorem, and Sard's theorem.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- This course requires MATH 211 AND MATH_OX211 or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Groups (definition and examples), cosets, Lagrange's Theorem, symmetric and alternating groups, Cayley's Theorem, isomorphisms, Cauchy's Theorem, quotient groups and homomorphisms, and the action of a group on a set. Additional topics may include the Sylow Theorems.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) and (MATH 250 or MATH_OX 250 or MATH 276) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Ring Theory and Field Theory: polynomial rings, unique factorization, Euclidean domains, splitting fields of polynomials, elements of Galois theory, finite fields.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- This course requires MATH 421or equivalent transfer credit as a prerequisite.
- Cross-Listed
- None

Introduction to the use of calculus in economic analysis; comparative static problem and optimization theory; consideration of the mathematical techniques used in game theory.

- Credit Hours
- 4
- GER
- MQR
- Requisites
- (MATH 211 or MATH_OX 211 or MATH 276) and (ECON 201 or ECON_OX 201) or equivalent transfer credit as prerequisite.
- Cross-Listed
- ECON 425

- Credit Hours
- 1 - 4
- GER
- None
- Requisites
- None
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 1 - 4
- GER
- MQR
- Requisites
- MATH 250 or MATH_OX 250 or MATH_OX 250Q or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 1 - 5
- GER
- MQRW
- Requisites
- MATH 250 or MATH_OX 250 or MATH_OX 250Q or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 3
- GER
- MQR
- Requisites
- (MATH 221 or MATH_OX 221 or MATH 275 or MATH 321) and (MATH 250 or MATH_OX 250 or MATH 276) or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 1 - 4
- GER
- MQR
- Requisites
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 1 - 5
- GER
- MQRW
- Requisites
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 1 - 4
- GER
- MQR
- Requisites
- MATH 250 or MATH_OX 250 or MATH_OX 250Q or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

May be repeated for credit when topic varies.

- Credit Hours
- 1 - 5
- GER
- MQRW
- Requisites
- MATH 250 or MATH_OX 250 or MATH_OX 250Q or MATH 276 or equivalent transfer credit as prerequisite.
- Cross-Listed
- None

Normally taken in student's last semester, up to a maximum of 4 credit hours.

- Credit Hours
- 1 - 4
- GER
- XA
- Requisites
- None
- Cross-Listed
- None

Normally taken in student's last semester, up to a maximum of 4 credit hours.

- Credit Hours
- 1 - 8
- GER
- CW
- Requisites
- None
- Cross-Listed
- None

Students conduct directed or supervised research in support of a faculty member's research project or agenda. Permission of the department and a supervising faculty member is required.

- Credit Hours
- 1 - 4
- GER
- XA
- Requisites
- None
- Cross-Listed
- None

Students study, read, and write on a topic under the direction or supervision of a faculty member. Permission of the department and a supervising faculty member is required.

- Credit Hours
- 1 - 4
- GER
- None
- Requisites
- None
- Cross-Listed
- None

Students conduct independent research in support of their own research agenda or question with guidance from a faculty member. Permission of the department and a supervising faculty member is required.

- Credit Hours
- 1 - 4
- GER
- XA
- Requisites
- None
- Cross-Listed
- None