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Timetable Information for Spring 2005

Graph Theory Classes
Course Section Course Reference Number Title, Instructor and Description
Math 412 G13
G14		 37940
37941		 Graph Theory (Hartke, S.)
Math 412 X13
X14		 37937
37939		 Graph Theory (West, D.)

The above sections will have common tests on the following dates:

Rooms will be announced at a later date.

Honors Calculus Sequence
Course Section Course Reference Number Title, Instructor and Description
Math 230 D1H 37566 Calculus II
Concurrent registration in Math 249 Q1H
Math 249 Q1H 37808

Honors Course in Mathematics
Concurrent registration in Math 230 D1H
Math 242 C1H 37848 Calculus of Several Variables
Concurrent registration in Math 249 S1H
Math 249 S1H 37809

Honors Course in Mathematics
Concurrent registration in Math 242 C1H

Honors courses in the calculus sequence require concurrent registration in associated sections of MATH 249. These section are listed above. Each honors calculus course is therefore worth 4 hours credit.

Merit Worshop Classes

Course Section Course Reference Number Title, Instructor and Description
Math 220 AD8 37535 Calculus I
Math 220 AD9 37536

Calculus I
Math 230 W1 37787

Calculus II
Math 230 W2 37788 Calculus II
Math 230 W3 37789 Calculus II
Math 242 AD2 37849

Calculus of Several Variables
Math 242 AD7 39442

Calculus of Several Variables

The Merit Workshop is an interactive group learning environment for selected students. For a detailed description of the format of a Merit worshop class, consult the Merit Class description. For general information regarding the Merit Workshop Program, consult the Merit Program Website

Registration in Merit Workshop sections requires approval from the Merit Workshop Director (see contact information below). Concurrent enrollment for 2 hours of credit in the Merit Section of Math 199 is required for Math 220. Concurrent enrollment for 1 hour of credit in the Merit Section of Math 199 is required for Math 230 and Math 242.

Merit Workshop Director: Jennifer McNeilly
178 Altgeld Hall
217-244-1659
jrmcneil@math.uiuc.edu

Active Learning Calculus Classes

Course Section Course Reference Number Title, Instructor and Description
Math 220 AE1 37542 Calculus I (Ahlgren, S.)
This is a Discovery Program course
Math 220 AB1 37543

Calculus I (Ahlgren, S.)
Small group learning lab concurrent with Math 220 AE1
Math 220 BE1 37545 Calculus I
Uses small group learning methods
Math 220 BB1 37540

Calculus I
Small group learning lab concurrent with Math 220 BE1
Math 230 AE1 37777 Calculus II
Uses small group learning methods
Math 230 AB1 37776

Calculus II
Small group learning lab concurrent with Math 230 AE1

Math 230 BE1 37780 Calculus II (Tyson, J.)
Uses small group learning methods
Math 230 BB1 37779

Calculus II (Tyson, J.)
Small group learning lab concurrent with Math 230 BE1

The Active Learning Calculus sequence is an environment open to all students. It uses guided reading assignments, group problem solving, and graphing calculators. Each active learning class has an associated 2 hour lab. For a detailed description of the format of an active learning class, consult the Active Learning Class description.

Calculus and Mathematica Classes

Course Section Course Reference Number Title, Instructor and Description
Math 220 D8 37547 Calculus I
For a description of this course, see C&M Math 220
Math 220 X8 37548

Calculus I
For a description of this course, see C&M Math 220
Math 225 Q8 37545

Introductory Matrix Theory
This is a second eight week course, meeting 14-MAR-05 - 4-MAY-05
For a description of this course, see C&M Math 225
Math 225 S8 37844

Introductory Matrix Theory
For a description of this course, see C&M Math 225
Math 230 B8 37781

Calculus II
For a description of this course, see C&M Math 230
Math 230 C8 37782

Calculus II
For a description of this course, see C&M Math 230
Math 230 D8 37783

Calculus II
For a description of this course, see C&M Math 230
Math 242 G8 37890

Calculus of Several Variables
For a description of this course, see C&M Math 242
Math 242 X8 37889

Calculus of Several Variables
For a description of this course, see C&M Math 242
Math 380 Z8 37910

Advanced Calculus
This is an asynchronous course. It does not have a regular meeting place or meeting time and is intended for students who wish to take the course in an independent study mode. Consult Debra Woods for further information.
Math 385 F8 37921

Intro Differential Equations
For a description of this course, see C&M Math 385
Math 385 G8 37922

Intro Differential Equations
For a description of this course, see C&M Math 385
Math 385 Z8 37923

Intro Differential Equations
This is an asynchronous course. It does not have a regular meeting place or meeting time and is intended for students who wish to take the course in an independent study mode. Consult Debra Woods for further information.
For a description of this course, see C&M Math 385
Math 415 E83 37984

Linear Algebra
For a description of this course, see C&M Math 415
Math 415 E84 37986

Linear Algebra
For a description of this course, see C&M Math 415
Math 415 Z83 37991

Linear Algebra
This is an asynchronous course. It does not have a regular meeting place or meeting time and is intended for students who wish to take the course in an independent study mode. Consult Debra Woods for further information.
For a description of this course, see C&M Math 415
Math 415 Z84 37988

Linear Algebra
This is an asynchronous course. It does not have a regular meeting place or meeting time and is intended for students who wish to take the course in an independent study mode. Consult Debra Woods for further information.
For a description of this course, see C&M Math 415
Math 461 G83 38063

Probability Theory I
For a description of this course, see C&M Math 461
Math 461 G84 38064

Probability Theory I
For a description of this course, see C&M Math 461

Calculus & Mathematica courses involve learning a subject through extensive computer interaction using Mathematica software. For a detailed description of the format of a Mathematica class, consult the Mathematica Class description. For general information regarding the Calculus & Mathematica Program, consult the Calculus & Mathematica Program Website

Students registering in a Calculus & Mathematica class are permitted to register in an associated section of Math 290 on a one-time basis for an additional hour of credit. See Math 290, Symbolic Computation Lab.

Graduate Topics Courses

Course Section Course Reference Number Title and Description
Math 595 AG 39565 Algebraic Groups (Haboush, B.)
This course will cover the first chapters of T.A. Springer's book, "Linear Algebraic, Groups." We will begin with a definition of linear algebraic groups, Lie algebras and algebras of invariant differential operators. We will study generalized semi-simple and unipotent parts, diagonable unipotent and solvable groups, Grassman varieties, flag varieties and certain homogeneous spaces. We will conclude with a discussion of root systems classification theory and some Schubert calculus.
Math 595 AGV 39566 Real Algebraic Geometry and Computer Vision (Fossum, R.)
Real Algebraic Geometry, most simply stated, is the study of the sets of real solutions of systems of real polynomial equations. More specifically a semi-algebraic set in Rn is a set of solutions to a boolean combination of inequalities involving polynomials with coefficients in R. This course will introduce real algebraic geometry in a comprehensible manner with an eye toward applications to robotics, complexity, computer vision and related topics. Graduate students in ECE, CS, as well as Mathematics may benefit from this course. Many unsolved theoretical and applicable problems will be raised. There are many problems suitable for a Ph.D. thesis. An outline of topics to be discussed: (1) Elementary Properties of single-variable polynomials; (2) Semi-algebraic sets; (3) Real Algebraic sets; (4) Complexity; ( 5) Real Spectrum; (6) Nash Functions; ( 7) Topology of Real Algebraic Varieties.
Math 595 AMA 39567 Asymptotic Methods in Analysis (Hildebrand, A.J. )
This course is an introduction to classical asymptotic methods such as the Laplace method, the saddle point method, and Abelian and Tauberian theorems. These methods have a wide variety of applications in both Pure and Applied Mathematics, but are usually not covered in the standard undergraduate or graduate curriculum. The course will focus on applications in number theory (e.g., the Hardy-Ramanujan asymptotic formula for the partition function), combinatorics (e.g., asymptotic formulas for Stirling and Bell numbers), and analysis (e.g., the asymptotic behavior of Bessel functions).
Math 595 BS 38186

Banach Spaces (Junge, M.)
description to be posted
Math 595 CAG 39568 Complex Algebraic Geometry (Bradlow, S.)
This course focuses on the study of compact complex manifolds, in the process laying the foundation for further study in algebraic geometry. Topics covered include complex manifolds, holomorphic vector bundles and sheaves, Hermitian differential geometry, Hodge theory for Kahler manifolds, Dolbeault cohomology, Chern classes, vanishing theorems, algebraic varieties, Hermitian-Einstein equations, and the Kodaira embedding theorem. Prerequisites: 520 or consent of instructor.
Math 595 CG 39569 Combinatorics and Geometry (Furedi, Z. )
This is a course on Extremal Combinatorics and Geometric Codes. The aim of this course is twofold. First, it gives a solid introduction to the theory of extremal graphs and hypergraphs by reviewing the most important notions, results and problems and by pointing out connections to coding theory and discrete and computational geometry. Second, it supplies a series of research problems to interested students on or close to thesis level. Prerequisites: Familiarity with basic terms of Graph Theory (MATH 412) and Combinatorics (MATH 413) or MATH 473 or MATH 482 or consent of instructor.
Math 595 CGG 41484

Cohomology and geometry of groups (Mineyev, I.)
Homology (and cohomology) is a convenient and important
language used by many branches of mathematics. This course will develop the homological language in the context of groups, with applications to geometry, topology, and analysis. We will start from scratch and define homology and cohomology of groups, modules, finiteness properties of groups (such as being finite generated or finitely presented), hyperbolic groups, cohomological dimension, bounded cohomology, l^p-(co)homology. All these concepts play important role in modern mathematics. We will discuss Stallings' cohomological characterization of free groups and Gersten's characterization of hyperbolic groups. If any time is left after that, there are several possibilities: - Since groups give rise to rings and Banach algebras, we might have a "more analytic" discussion: l^2-homology and l^2-Betti numbers, cohomology of Banach algebras, amenability. - A "more geometric" discussion: rigidity for groups and relation with bounded cohomology. - A "more homological" discussion: spectral sequences.
Math 595 EFA 39570 Elliptic Functions and Number Theoretic Applications (Berndt, B.)
This course will consist of two parts. The first 8 or 9 weeks of the course will be devoted to Ramanujan's approach to number theory through the theories of q-series and theta functions. Thus, first we will develop the basic theorems in q-series and theta functions. We then will apply these theorems to the theory of partitions. The remaining portion of the course will be devoted to the classical theory of elliptic functions, including basic facts arising from their double periodicity. Properties of the famous elliptic functions of Weierstrass, Jacobi, and others will be established. We also shall examine in detail elliptic integrals, establish a inversion formula for elliptic integrals, and discuss the famous and eminently useful arithmetic-geometric mean. A more detailed course description is available in pdf format. Prerequisites: A course in complex analysis and a course in elementary number theory.
Math 595 FT 39571 Floer Theory (Kerman, E. )
Floer theory, which combines ideas from Morse theory and the study of pseudoholomorphic curves, is one of the central tools in modern symplectic topology and low dimensional topology. Some of the spectacular recent developements in this area include the Symplectic Field theory of Eliashberg, Hofer and Givental and the Heegard Floer homology of Ozsvath and Szabo. The goal of this course will be to describe the ideas and analytic techniques involved in Floer theory and to discuss several applications. We will spend at least the first third of the course on Morse homology which is a beautiful topic itself as well as an illuminating finite-dimensional prototype of Floer homology. We will then focus on the Hamilt,onian Floer homology of monotone symplectic manifolds. Finally we will survey some recent generalizations and applications of Floer theory depending on the tastes of the audience. Prerequisites: I will try to teach the class assuming only standard results from differential topology and algebraic topoogy (at the level of Guillemin and Pollack's book Differential Topology and Vassiliev's book Introduction to Topology, respectively). The material also requires a fair amount of nonlinear functional analysis, but this will be covered in class as required.
Math 595 GFT 39572 Geometric Function Theory (Wu, J.-M. )
The course explores geometric aspects of function theory in the complex plane and Rl\n. Fundamental tools of the subject, classical and modem theory, and directions of current research will be discussed. The main topics are: CONFORMAL MAPPINGS - distortion, boundary behavior and level sets; SUBHARMONIC FUNCTIONS and DIRICHLET PROBLEM; HARMONIC MEASURE - projection, dimension and applications; MODULE OF CURVE FAMILIES AND EXTREMAL DOMAINS; QUASICONFORMAL MAPPINGS - geometric and analytic definitions, Beltrami equation, Beurling-Ahlfors extensions, quasicirles. PREQUISITES. Math 542 or consent of the instructor.
Math 595 LC 39575 Local Cohomology (Dutta, S.)
This course will be a study of Local Cohomology introduced by Grothendieck and its various applications. The main topics will include: Cohen-Macaulay Rings and Modules, Injective Modules over noethierian rings, Gorenstein rings, local cohomology -- connection with dimension and depth, local duality theorem of Grothendieck, Cohomology of quasicoherent and coherent sheaves, Serre's Theorem on coherent sheaves on projective spaces, classification of Line-bundles on pn, Hartshorne - Lichtenbaum Theorem and Faltings Connectedness Theorem. Prerequisite: Math 403
Math 595 LD 38183 Large Deviations (Sowers, R. )
The study of rare events occupies an important part in many probabilistic analyses. While there are many types of rare events, the theory of exponentially small events appears frequently enough that it deserves special consideration. We will explore the circle of ideas known as large deviations, which studies the structure and transformations of such exponentially small events. We will start with a study of how quickly the law of large numbers holds, develop some general theories, such as the Gartner-Ellis theorem and the contraction principle, and then apply them in a number of ways. Along the way, we will understand connections with other areas of mathematics and engineering; for example, the connection between the exit problem and singularly perturbed PDE's, and the connection between empirical measures of Markov chains and entropy.
Math 595 MTM 39573 Model Theory of Metric Structures (Henson, C.W.  )
A complete course description and prerequisites are available (pdf format) at http://www.math.uiuc.edu/~henson/Math595/Spring2005/advt05.pdf.
Math 595 NA 39574 Nonstandard Analysis (Loeb, P. )
The notion of an infinitesimal quantity has been used in mathematics for over 2200 years. It eluded rigorous treatment until the work using model theory of Abraham Robinson in 1960 established a rigorous foundation for the use of infinitesimals in mathematics. Recent extensions and applications of his theory, called nonstandard analysis, have produced new results in many areas including operator theory, stochastic processes, mathematical economics and mathematical physics. In all of these areas, infinitely small and infinitely large quantities can play an essential role in the creative process. At the level of calculus, the integral can now be correctly defined as the nearest ordinary number to a sum of infinitesimal quantities. In Probability theory, Brownian motion can now be rigorously parameterized by a random walk with infinitesimal increments. In economics, an ideal economy can be formed from an infinite number of agents, each having an infinitesimal influence on the economy. We will give an introduction to this fruitful area of mathematics starting with a simple form of nonstandard analysis that is suitable for the results of calculus and basic real analysis. The presentation is intended to give the beginner a feeling for the fundamental arguments of nonstandard analysis with a minimal use of model theory. Students with no background in mathematical logic should easily pick up what is needed to continue with the course. The course will then take up the general theory and its applications to functional analysis, topology, measure and probability theory, and some mathematical economics. We will finish with the work of Y. Sun who showed that the measure spaces introduced by the course instructor can be used to finally make sense of the notion an infinite number of equally weighted, independent random variables in probability theory and of such agents in an economy.
Math 595/ECE 559 RB 41543

Cryptography: Theory & Practice (Blahut, R.and Duursma, I.)
The growth in electronic commerce offers the convenience of speed and accuracy, but presents serious problems in security. The possibility of eavesdropping and forgery demands clever safeguarding of information. Algebra and number theory have acquired great practical importance since 1976 as a result of the development of public-key cryptography. This course will be an introduction to cryptography, covering such topics as public-key vs. private-key cryptography, one-time pads, RSA cryptosystems, factoring of large integers, as well as the most current (hyper) elliptic curve cryptosystems used today in business. The instructors will use their respective backgrounds in engineering and mathematics to teach both the theoretical and practical aspects of the subject. The course will begin at a level understandable to students of either department. The instructors will each teach one hour per week. The third hour each week will present an opportunity for students taking the course to speak on a topic of their choice (each student doing this once as part of their grade) or for external speakers from academia or industry to address the class. More information about this course is available at www.math.uiuc.edu/~duursma/Math595.
Math 595 TV 40654

Toric Varieties (Haboush, B.)
We will cover much of the material in the book by W. Fulton. We will define affine tori and toric actions. We will briefly discuss the theorem of Sumehiro and we will classify affine toric varieties. We will stress the dictionary between the theory of toric varieties and the combinatoric geometry of polytypes. We will show how to compute cohomologic and geometric invariants of toric varieties.

Literature Course

Course Section Course Reference Number Title, Instructor and Description
Math 598 REC 41536

Research Experiences in Combinatorics (West, D.)
In this 2 hour research course, students work collaboratively on unsolved research problems in combinatorics. In addition to seeking new results, activities may include finding unsolved problems, seminar presentations of known or new results, and writing of research papers. Time: 2-4pm Thursdays, 159 Altgeld Hall

 

Course Catalog |  Course Schedule

Department of Mathematics
University of Illinois at Urbana-Champaign
273 Altgeld Hall, MC-382
1409 W. Green Street, Urbana, IL 61801 USA
Telephone: (217) 333-3350    Fax (217) 333-9576
office@math.uiuc.edu

Last modified December 1, 2004