# Undergraduate catalog 2007 - 2008, Mathematics

Note: The class catalog is published every two years. Courses listed in the catalog may not be offered in a given term. For class offerings for each semester please click on the "Offerings" links.
Note: All courses taken towards the major or minor must be taken on a letter grade basis, not pass/fail.
 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 111S: Calculus I Credits: 4 − Description
 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 112S: Freshman Seminar: Calculus II Credits: 4 − Description
Content: Fall. Prerequisites: A score of 4 or 5 on the AB Advanced Placement Calculus exam. This section of Math 112Z is designated a freshman seminar. It is an introduction to mathematical proofs in which students learn to speak and write with the accuracy required to communicate mathematical work effectively. Course content is largely that of a calculus 2 course: Introduction of the natural logarithm via the definite integral, exponential functions, sequences and series, power series, Taylor series.
 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 its majors.
 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: 4 − 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: Sports & Games of Strat. Chanc Credits: 4 − Description
 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 communication skills. 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.
Particulars: Texts: The Mathematics of Games and Gambling by Edward Packel, The Mathematical Association of America New Mathematical Library, 1981.
Prerequisites: High School Algebra
 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:
 MATH 211P: Multivariable Calculus 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 250S: Foundations of Mathematics Credits: 4 − Description
Content: Prerequisites: Math 112, 112Z, 112S or permission of the instructor. This course provides the bridge from calculus to more abstract mathematics courses. It is a small seminar intended to develop the student's ability to work with fundamental logical and mathematical concepts. Emphasis will be placed on the careful and precise expression of ideas. The students and the instructor will construct proofs of theorems and present them in class.
 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 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 323: Abstract Algebra I Credits: 4 − Description
 MATH 324: Abstract Algebra II Credits: 4 − Description
 MATH 330: 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 341E: Informal Geometry:Early Childh 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 344S: Differential Geometry Credits: 4 − Description
 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:
 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 425S: Mathematical Economics 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 Theroy 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 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 Credits: 4 − Description
Content: Prerequisite: Mathematics 250. May be repeated for credit when topic varies.
 MATH 495RWR: Honors Credits: 1 - 4 − Description
Content: Credit, one to four hours. May be repeated, provided total credit does not exceed four hours.
 MATH 497R: Directed Study Credits: 1 - 4 − Description
Content: Credit, one to four hours, as arranged with the department.
 MATH 547: Differential Topology Credits: 4 − Description
Content: Smooth manifolds, tangent spaces and derivatives, Sard's theorem, inverse function theorem, transversality, intersection theory, fixed-point theory, vector fields, Euler characteristic, the Poincare-Hopf theorem, exterior algebras, differential forms, integration, Stokes' theorem, de Rham cohomology.