|MATH 101: Trigonometry & Algebra||Credits: 4||− Description|
|MATH 105: Discrete Mathematics||Credits: 4||− Description|
|MATH 106: Intro Ideas & Methods Of Math||Credits: 4||− Description|
|MATH 107: Intro. Probability and Statistics||Credits: 4||− Description|
Content: Fall, spring. Sample spaces, probability, Bayes theorem, independence, random variables, binomial distributions, normal distribution, sampling distributions, confidence intervals.
|MATH 108: Intro To Linear Algebra||Credits: 4||− Description|
|MATH 109: Game Theory, Graphs and Math. Models||Credits: 4||− Description|
Content: Convex sets, linear inequalities, linear programming, two-person games, finite
graphs. Applications in management, economics, and behavioral sciences.
|MATH 111: Calculus I||Credits: 4||− Description|
Content: Fall, spring. Limits, derivatives, antiderivatives, the definite integral.
|MATH 112: Calculus II||Credits: 4||− Description|
Content: Fall, spring. Prerequisite: Math 111, 115, or placement. Techniques of integration,
exponential and logarithm functions, sequences and series, polar coordinates.
|MATH 112Z: Calculus II||Credits: 4||− Description|
Content: Fall. For first-year students who have received a score of 4 or 5 on Calculus AB
advanced placement exam.
|MATH 115: Life Science Calculus I||Credits: 4||− Description|
Content: Fall. First semester calculus with an emphasis on applications to the life sciences.
This course is recommended by the biology department and the NBB program for
|MATH 116: Life Sciences Calculus II||Credits: 4||− Description|
Content: Spring. Integration, differential equations, multivariable calculus, and discrete probability and statistics, with an emphasis on applications to biology.
Prerequisites: Math 115 or AP calculus placement. Students with the AP prerequisite are strongly
advised to meet the instructor before the beginning of the term.
|MATH 119: Calculus with Business Applications||Credits: 4||− Description|
Content: Fall, spring. Derivatives, logarithmic and exponential functions, integrals. Applications and techniques emphasized. (Note: This course is designed primarily for students who plan to enter the Goizueta Business School at Emory. It should not be taken by students who have either taken or plan to take Mathematics 111 or 112.)
|MATH 130: Basic Programming & Computer||Credits: 2||− Description|
|MATH 190: Freshman Seminar: Sports, Games and Gambling||Credits: 4||− Description|
Content: In this course we will learn some mathematics from the areas of
probability, game theory, and combinatorial design theory by
investigating topics from the world of sports, competitive games
of strategy, casino games, lotteries, and the mathematical theory
of games. Depending upon the interests of students in the class,
possible topics include backgammon, poker, othello (and other
board games), football and basketball pools, baseball statistics,
evaluation of individual player performances in team sports such
as basketball and hockey, and card games such as hearts, casino
and blackjack (although the complexity of the game and the use
of multiple deck shoes make a mathematical analysis of blackjack
beyond the scope of this seminar, we can still make intelligent
empirical observations about various playing and betting strategies;
i.e., we can still have a good time playing the game).
|MATH 190: Freshman Seminar: Theory of Knots||Credits: 4||− Description|
Content: Knots are familiar objects. We use them to tie our shoes, wrap our packages, and moor our boats. Yet they are also quite mysterious: if you have two tangled up ropes, for instance, can you tell if they are tied in the same knot?
This course will introduce some of the mathematical techniques people have developed to study knots, partially in an attempt to answer this very question. Additionally, these studies lead to deep results about topology and geometry. We will also see various applications, like how knot theory is relevant to the study of DNA.
Particulars: Text: The Knot Book, by Colin Adams
|MATH 190: Freshman Seminar: Cryptology||Credits: 4||− Description|
Content: When you buy something on the web, you broadcast your credit card number to untold numbers of other computers. How is your number kept secret? When you swipe your credit card at the grocery store checkout, sometimes the machine knows that it mis-read your card without calling Visa. How does it know? These questions and others will be answered. Also, we will discuss the role of secret codes and codebreaking in wartime, criminal activity, and the lives of law-abiding citizens.
Particulars: The style of this course will be halfway between a humanities and a mathematics class.
Prerequisites: 4 or 5 on the Calculus AB exam or equivalent on the Calculus BC exam.
|MATH 190: Freshman Seminar: Mathematics and Politics||Credits: 4||− Description|
Content: Can a game explain the irrationality of the arms race of the 1980's? Is democracy, in the sense of reflecting the will of the people, impossible? In this course we will use mathematics to explore questions like these. The "politics" in the course will cover five topics such as international conflict, yes-no voting systems, political power, and social choice. The "mathematics" will be conceptual rather than computational and will include symbolic representation and manipulation, game theory, mathematical modeling, and logical deduction.
Particulars: Text: Mathematics and Politics: Strategy, Voting, Power, and Proof, by Alan. D. Taylor
Prerequisites: There are no prerequisites, however students should have an interest in mathematics and political science.
|MATH 190: Freshman Seminar: The Mathematics of Sports, Games and Gambling||Credits: 4||− Description|
Content: The course is designed to build the laws of probability and game
theory through the models of well known games and sports.
Fundamental laws of probability will be developed and applied to
games such as poker, blackjack, backgammon, lotteries
and more. Fundamental combinatorial counting techniques will
be employed to determine outcomes (permutations and combinations).
Card tricks based on mathematical principles will be demonstrated
in order to learn basic ideas of information encoding.
Deeper fundamentals will be introduced using more involved
examples. In developing these theories, laws of fair judging can
also be investigated.
Games will be employed to develop winning strategies or determine
when a win is not possible. Graph models will be developed to
study certain situations in games and to trace strategies.
Concepts will be developed through experimentation and conjectures
made by the students. Hence, class participation will be a major
component of the course. In doing this I hope to improve their basic
intuition about what should be true as well as their general
Small group learning will also be employed, both for in class
experiments and for some assignments. Students will be encouraged
to work together in class to test experiments and raise conjectures.
They will be encouraged to present their ideas to the rest of class.
We will maintain an on-going dialogue while we develop the theorems
and laws governing the models we study.
General writing techniques will also be employed. Formal
and informal writing will be assigned, both to individuals and groups.
Communication of ideas at all levels will be stressed
throughout the course.
The Mathematics of Games and Gambling by Edward Packel,
The Mathematical Association of America New Mathematical Library,
Prerequisites: High School Algebra
|MATH 190: Freshmen Seminar: The Math of Voting and Elections||Credits: 4||− Description|
|MATH 207: Probability and Statistics with Applications||Credits: 4||− Description|
Content: Prerequisite: Math 112, 112Z, or 119. Development and use of mathematical models
from probability and statistics with applications.
|MATH 211: Multivariable Calculus||Credits: 4||− Description|
Content: Fall, spring. Prerequisite: Mathematics 112. Vectors; multivariable functions; partial derivatives; multiple integrals; vector and scalar fields; Greenís and Stokesí theorems; divergence theorem.
|MATH 211: Multivariable Calculus - Physics Applications||Credits: 4||− Description|
Content: Prerequisites: Math 112, Math 112S, or Math 112Z. This section of Math 211 is designed to meet the needs of physics majors, but math majors and others with strong interest are welcome. Topics include vectors and 3-space, functions of several variables, parametrized curves, vector fields, line integrals, surfaces, gradients, partial derivatives, multiple integrals in various coordinate systems, conservative fields, circulation, flux, Stokes' Theorem. Optimization (for economics) will not be covered.
|MATH 212: Differential Equations||Credits: 4||− Description|
Content: Fall, spring. Prerequisite: Mathematics 112. Ordinary differential equations with applications.
|MATH 221: Linear Algebra||Credits: 4||− Description|
Content: Fall, spring. Prerequisite: Mathematics 112. Systems of linear equations and matrices, determinants, linear transformations, eigenvalues, and eigenvectors.
|MATH 234: Intro To Computer Usage&Prog I||Credits: 3||− Description|
|MATH 235: Intro To Computer Usage&Prog II||Credits: 3||− Description|
|MATH 245: Intro To Automata Theory II||Credits: 3||− Description|
|MATH 250: Foundations of Mathematics||Credits: 4||− Description|
Content: Fall, spring. Prerequisites: Math 112, 112Z, 112S or permission of the instructor. An introduction to theoretical mathematics. Logic and proofs, operations on sets, induction, relations, functions.
|MATH 261: Probability & Statistics I||Credits: 4||− Description|
|MATH 262: Probability & Statistics II||Credits: 4||− Description|
|MATH 270: History and Philosophy of Mathematics||Credits: 4||− Description|
Content: (Same as Philosophy 270.) Prerequisites: Math 112, 112Z, 112S or permission of the instructor. 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. The emergence of mathematical schools.
|MATH 311: Real Analysis I||Credits: 4||− Description|
|MATH 312: Real Analysis II||Credits: 4||− Description|
|MATH 315: Numerical Analysis||Credits: 4||− Description|
Content: Fall. Prerequisites: Mathematics 221 or 321 and Computer Science 170. Solution of linear and nonlinear systems of equations, interpolation, least-squares approximation, numerical integration, and differentiation.
|MATH 318: Complex Variables||Credits: 4||− Description|
Content: Fall. Prerequisites: Mathematics 211 and 250, or consent of instructor. Analytic functions, elementary functions, integrals, power series, residues, and conformal mapping.
|MATH 321: Abstract Vector Spaces||Credits: 4||− Description|
Content: Spring. Prerequisite: Mathematics 250. Axiomatic treatment of vector spaces, inner product spaces, minimal polynomials, Cayley-Hamilton theorem, Jordan form, and bilinear forms.
|MATH 328: Number Theory||Credits: 4||− Description|
Content: Pythagorean Triples, Divisibility and Greatest Common Divisor, Linear Equations, Factorization and Fundamental Theorem of Arithmetic, Congruences, Prime Numbers, Primality Testing, Quadratic Reciprocity, Sums of Squares, Diophantine Equations, Gaussian Integers, Continued Fractions, Generating Functions
Prerequisites: Math 250.
|MATH 330S: Introduction to Combinatorics||Credits: 4||− Description|
Content: Alternate years. Prerequisites: Mathematics 221 or 321, and 224 or 250. Combinations and permutations, counting techniques, recurrence relations, and generating functions. Block designs, finite planes, and coding theory. Introduction to graph theory.
|MATH 340: The Number System||Credits: 4||− Description|
|MATH 340E: Number System: Early Childhood||Credits: 4||− Description|
|MATH 341: Informal Geometry||Credits: 4||− Description|
|MATH 344: Differential Geometry||Credits: 4||− Description|
Content: Prerequisites: Mathematics 211, 221 or 321, and 250. Curves and surfaces in 3-space. The geometry of the Gauss map. Special surfaces. The intrinsic geometry of surfaces. Surfaces and computer graphics.
|MATH 345: Mathematical Modeling||Credits: 4||− Description|
Content: Prerequisites: Mathematics 212 and Computer Science 170. Principles of mathematical modeling; case studies using nonlinear ordinary differential equations, difference equations, and partial differential equations.
|MATH 346: Intro. to Optimization Theory||Credits: 4||− Description|
Content: Spring. Prerequisites: Mathematics 221 or 321 and Computer Science 170. Theory of linear programming, duality, optimal flows in networks, and mathematical programming.
|MATH 348: Intro To Found Of Geometry||Credits: 4||− Description|
|MATH 351: Partial Differential Equations||Credits: 4||− Description|
Content: Prerequisites: Mathematics 221 or 321 and 211. 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.
|MATH 361: Probability & Statistics I||Credits: 4||− Description|
Content: Fall. Prerequisite: Mathematics 211. Discrete and continuous probability, random variables, special distributions.
|MATH 362: Probability & Statistics II||Credits: 4||− Description|
Content: Spring. Prerequisite: Mathematics 361. Estimation, hypothesis testing, goodness-of-fit tests, linear regression.
|MATH 411: Real Analysis||Credits: 4||− Description|
Content: Fall. Prerequisites: Mathematics 211, 221, or 321 and 250. Analysis of sets and functions
in n-space. Basic topological properties, continuity, and differentiation.
|MATH 412: Real Analysis II||Credits: 4||− Description|
Content: Spring. Prerequisite: Mathematics 411. Integration in n-space: theorems of Stokes and Fubini. Uniform convergence: theorems of Taylor and Stone-Weierstrass. Sardís theorem.
|MATH 421: Abstract Algebra I||Credits: 4||− Description|
Content: Fall. Prerequisites: Mathematics 221 or 321, and 250. Groups (definition and examples), cosets, Lagrangeís theorem, symmetric and alternating groups, Cayleyís theorem, isomorphisms, Cauchyís theorem, quotient groups and homomorphisms, and the action of a group on a set. Additional topics may include the Sylow theorems, and the theory of rotation groups.
|MATH 422: Abstract Algebra II||Credits: 4||− Description|
Content: Spring. Prerequisite: Mathematics 323. Rings (definition and examples), quotient rings and homomorphisms, Euclidean rings, polynomial rings, fields (definition), roots of polynomials, and elements of Galois theory. Additional topics may include construction by straightedge and compass, and solvability of a polynomial by radicals.
|MATH 425: Mathematical Economics (Seminar)||Credits: 4||− Description|
Content: Spring. (Same as Economics 425.) Prerequisites: Economics 201, 212 and Mathematics 211, or permission of the instructors. Introduction to the use of calculus in economic analysis; comparative static problem and optimization theory; consideration of the mathematical techniques used in game theory.
|MATH 430: Coding Theory||Credits: 4||− Description|
|MATH 445: Mathematical Economics||Credits: 4||− Description|
|MATH 486S: Topics in Toplogy: Geometric Group Theory||Credits: 4||− Description|
Content: Prerequisite: Mathematics 250. May be repeated for credit when topic varies.
|MATH 486S: Topics in Topology: Point Set Topology||Credits: 4||− Description|
Content: We will begin with a study of the topology of the real
numbers. This will be in part a review for those who had my math 250.
We will study properites of limit points and convergent sequences and
other properties that can be defined using the concept of a limit point.
These include connected, closed, compact, and separable sets. We will
study continuous functions and homeomorphisms. Most of our time will be
spend studying sets on the number line or in a Euclidean plane but we
will disuss more abstract concepts from topology.
Particulars: There will be no text. I will provide handouts with
definitions, problems and questions. I will expect you to work on these
problems at home and come to class prepared to discuss what you have
tried to do. If you can solve a problem you can present your solution.
If no one has a solution we can discuss the problem as a group.
Grades will be based primarily on class participation and homework. We
can discuss how many, if any, exams we will have and if they will be
take home or in class exams.
|MATH 487: Graph Theory||Credits: 4||− Description|
|MATH 487S: Topics in Combinatorics||Credits: 4||− Description|
Content: Prerequisites: Mathematics 221 or 321 and 250. May be repeated for credit when topic varies.
|MATH 488S: Topics in Algebra: Number Theory||Credits: 4||− Description|
Content: Prerequisites: Mathematics 221 or 321, and 250. May be repeated for credit when topic varies.
|MATH 489R: Topics in Analysis - Set Theory||Credits: 4||− Description|
|MATH 489R: Topics in Analysis - Computational Methods in Imaging||Credits: 4||− Description|
|MATH 495R: Honors||Credits: 4||− Description|
Content: By permission, normally taken in the semester of the honors thesis defense.
Fulfills Continuing Writing Requirement.
|MATH 497R: Directed Study||Credits: 1 - 4||− Description|
Content: Credit, one to four hours, as arranged with the department.