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Timetable Information for Spring 2008
| Topics Courses |
Finite Mathematics Classes
| Course | Section | Course Reference Number | Title |
| Math 124 | A1 | 37550 | Algebra |
| Math 124 | B1 | 37552 | Algebra |
| Math 124 | C1 | 41627 | Algebra |
| Math 124 | E1 | 37556 | Algebra |
| Math 124 | X1 | 37553 | Algebra |
All sections of Math 124 will have combined evening exams at 7 pm on Wednesdays: Feb 13, Mar 12, and Apr 16.
Honors Calculus Sequence
| Course | Section | Course Reference Number | Title, Instructor and Description |
| Math 231 | D1H | 46047 | Calculus
II Concurrent registration in Math 249 P1H |
| Math 249 | P1H | 37808 |
Honors Course
in Mathematics |
Each honors calculus course is worth 4 hours credit.
Merit Worshop Classes
| Course | Section | Course Reference Number | Title, Instructor and Description |
| Math 220 | AD8 | 37535 | Calculus |
| Math 220 | AD9 | 37536 |
Calculus |
| Math 231 | CD5 | 46044 |
Calculus II |
| Math 231 | CD6 | 46045 |
Calculus II |
| Math 231 | W1 | 46050 | Calculus II |
| Math 231 | W2 | 46051 | Calculus II |
| Math 231 | W3 | 46052 | Calculus II |
| Math 241 | AD7 | 46059 |
Calculus III |
| Math 241 | AD8 | 48355 |
Calculus III |
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 231 and Math 241.
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 and Description |
| Math 220 | AE1 | 37542 | Calculus
Uses small group learning methods |
| Math 220 | AB1 | 37543 |
Calculus
|
| Math 220 | BE1 | 37545 | Calculus
Uses small group learning methods |
| Math 220 | BB1 | 37540 |
Calculus
|
| Math 231 | AE1 | 46025 | Calculus
II Uses small group learning methods |
| Math 231 | AB1 | 46017 |
Calculus
II |
| Math 231 | BE1 | 46031 | Calculus
II Uses small group learning methods |
| Math 231 | BB1 | 46030 |
Calculus
II |
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 and Description |
| Math 220 | D8 | 37547 | Calculus
For a description of this course, see C&M Math 220 |
| Math 220 | X8 | 37548 |
Calculus
|
| Math 225 | T8 | 37845 |
Introductory
Matrix Theory |
| Math 225 | S8 | 37844 |
Introductory
Matrix Theory |
| Math 231 | B8 | 46028 |
Calculus
II |
| Math 231 | C8 | 46039 |
Calculus
II |
| Math 231 | D8 | 46048 |
Calculus
II |
| Math 241 | C8 | 46075 |
Calculus
III |
| Math 241 | X8 | 46076 |
Calculus
III |
| Math 285 | F8 | 48605 |
Intro
Differential Equations |
| Math 285 | G8 | 48606 |
Intro
Differential Equations |
| Math 415 | E83 | 37984 |
Linear
Algebra |
| Math 415 | E84 | 37986 |
Linear
Algebra |
| Math 415 | Z83 | 37991 |
Linear
Algebra |
| Math 415 | Z84 | 37988 |
Linear
Algebra |
| Math 461 | G83 | 38063 |
Probability
Theory I |
| Math 461 | G84 | 38064 |
Probability
Theory I |
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.
Topics Courses
| Course | Section | CFN | Title and Description |
| Math 198 | G1H | 37820 | Freshman
Mathematics Seminar: Hypergraphics2008. Students in this tutorial/lab course learn basic geometrical programming in the REU-Lab of the Mathematics Department. Novice programmers may use fully functional real time interactive animations (RTICA) to explore the 4th dimension, non-Euclidean geometries, fractals, cellular automata, chaotic dynamical systems etc. Expert programmers are encouraged to modify or (re)write these, and to create new ones for future Math 198 students. Previous programming experience or advanced calculus are not required. Good spatial intuition, some trigonometry, and much geometrical curiosity are prerequisites. Some elementary physics and calculus are recommended. Experienced programmers are also welcome, but they will complete an individual course of study. Detailed tutorials and supervised practice sessions will augment the course for novice programmers. See more about this course at http://new.math.uiuc.edu/math198/ |
| Math 199 | FTM | 49060 | Undergraduate Open Seminar: Preparing Future Teachers of Mathematics |
| Math 490 | B13/B14 | 44789 | Advanced Topics in Mathematics: Mathematical Issues in National Security II. See http://www.math.uiuc.edu/Courses/math490palmore_sp08.pdf for more information. |
Math 595 Graduate Topics Courses
| Course | Section | Course Reference Number | Title and Description |
| Math 595 | BSO | 48217 | Banach
Spaces and Operator Spaces (Z. Ruan) In this course, we plan to spend most of time to introduce some important results in Banach spaces. We plan to cover the following topics. 1) Recall some fundamental theorems in functional analysis; 2) Tensor products of Banach spaces; 3) Local Property of Banach spaces; 4) Grothedieck's approximation property for Banach spaces; 5) Vector measures and Radon-Nikodym property; 6) Grothendieck's inequality Then we will discuss operator spaces, which is a natural quantization of Banach spaces. Prerequisite: Math 541. Text: Introduction to Tensor Products of Banach Spaces, Raymond A. Ryan, Springer Monographs in Mathematics. |
| Math 595 | DM2 | 49463 | Differentiable
Manifolds II (C. Leininger) This is the follow up course to the Differentiable Manifolds I, Math 520 course. The topics will include: Vector bundles, principal bundles, connections and curvature from different perspectives; Laplace-Beltrami operator on Riemannian manifolds, spectral theory and harmonic forms. Prerequisites: Differentiable Manifolds I. |
| Math 595 | RT | 43500 | Ramsey
Theory: Finite or Infinite (S. Solecki) This will be a course on Ramsey theory and its connections with logic (model theory and set theory). Recent years have seen a number of applications of finite and infinite dimensional Ramsey theory to dynamics of topological groups and to the structure of Banach spaces that have been of interest to logicians. In turn, these applications have been stimulating development in Ramsey theory. Furthermore, finite Ramsey theory has found connections with finite model theory, while infinite dimensional Ramsey theory have been using methods and notions of set theory, in particular, descriptive set theory. The aim of the course will be to present elements of classical Ramsey theory, structural Ramsey theory (as developed by Nesetril, Rödl, Prömel and Voigt), and infinite dimensional Ramsey theory with an eye on applications to dynamics and to Banach spaces. |
| Math 595 | IHF | 48719 | Introduction
to Hypergeometric Functions with Applications to Number Theory and
Combinatorics (B. Berndt) This course is an introduction to hypergeometric series. No previous acquaintance with them is necessary. For the first portion of the course, I will most often follow the presentation of the subject in the book, Special Functions. In particular, we will prove classical theorems due to Euler, Gauss, Kummer, Sears, Saalschiitz, Whipple, Dougall, Bailey, and others. We also will prove several results due to Ramanujan, primarily from his notebooks. Both Ramanujan and the lecturer love infinite series and closed form evaluations of them. Thus, we shall evaluate several infinite series, mostly from Ramanujan's notebooks, in closed form. The automated WZ-method of summing series due to H.S. Wilf and D. Zeilberger will be a topic. Hypergeometric series arise in countless applications, and so applications to combinatorics and to number theory will be given. In particular, connections with elliptic functions will be made. The only prerequisite is Math 448. However, Math 453 may be helpful on very rare occasions. |
| Math 595 | LC | 39575 | Local
Cohomology (S. Dutta) 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 quasi-coherent 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 Text: Local Cohomology by Brodmann and Sharp, Cambridge University Press. |
| Math 595 | MI | 48222 | Motivic
Integration (L. van den Dries) This course is about a new type of measures: they are finitely additive under disjoint union, multiplicative under cartesian products, but take values in a ring that is usually not the field of real numbers. Here is an elementary example indicating what kind of things can be measured in this way. With R the field of real numbers, let B(n) be the boolean algebra of sets in n-dimensional affine space R^n generated by the affine subspaces (points, lines, planes,...). Then we have the motivic measure on B(n) that takes values in the polynomial ring Z[T] and assigns "volume" T^d to each d-dimensional affine subspace of R^n. Given sets X in B(m) and Y in B(n) one can show that X and Y have the same motivic volume iff there is a piecewise affine bijection between X and Y. A related fact is that a piecewise affine map from X to itself is injective iff it is surjective. (All this is true for any infinite field instead of R.) More generally, for certain nice categories of sets and maps between them we wish to determine the most general (motivic) measure that makes isomorphic sets have equal volume. A key example is the category of algebraic varieties over the field of rational numbers, with several possible notions of "isomorphism". Motivic integration is a rapidly growing area of research, starting with a lecture by Kontsevich in 1995, and then developed by Denef and Loeser. For a brief overview and further motivation, see the article "What is motivic measure" by Thomas Hales, Bull. AMS 42 (2005). I plan to start from scratch and first work out some basic examples dealing with "nice" sets and maps in (ordered) vector spaces. Next, I will introduce a very general setting for motivic integration, following a recent fundamental paper by Hrushovski and Kazhdan: "Integration in valued fields". While this paper does not use deep results from logic, it is imbued by a model-theoretic viewpoint. My aim is to cover a substantial part of this long paper (> 140 pages) in the best way I can manage. |
| Math 595 | TV | 40654 | Toric
Varieties (H. Schenck) Course Description. Toric varieties are objects at the interface of algebra, geometry and combinatorics. They can be studied from any one of these viewpoints, but it is the interplay between viewpoints that makes them so interesting. This course will be an introduction to algebraic geometry, which uses toric varieties as the main examples. To be particularly down-to-earth, in modern algebraic geometry, a variety is constructed by gluing together affine varieties. In the toric case, an affine variety corresponds to a polyhedral cone, and gluing affine torics simply corresponds to gluing two cones together along a common facet. Another key concept in algebraic geometry is that of a divisor (a codimension one subvariety); in the toric case a divisor corresponds to an edge of the cone. In short, there is a beautiful dictionary between discrete geometric objects (cones, polytopes, etc.) and toric varieties. The prerequisite of the class is a class in commutative algebra, at the level of Atiyah-Macdonald, although motivated students who know undergraduate algebraic geometry at the level of Cox, Little, O'Shea ``Ideals,varieties, and algorithms'' may be able keep up. The main objective of the class is to bring the abstract concepts of modern algebraic geometry to life with lots of examples. Text. Toric Varieties (notes to be handed out), Cox, Little, Schenck. |
595 Mini Courses
| Course | Section | Course Reference Number | Title and Description |
| Math 595 | BSP | 48254 | Basics
of Stochastic Processes (R. Sowers) This is a short course which quickly introduces the basics of the modern theory of stochastic processes. We shall emphasize those parts of the theory which are useful in a wide variety of disciplines. Our intended audience is not only mathematicians, but students from engineering, physics, and finance. We assume that the students will either be willing to accept, ex cathedra, basic aspects of measure theory, or have the ability to understand them on their own. See http://www.math.uiuc.edu/~r-sowers/595S08/announce.html for more information about this course. Meets Jan 14 - Mar 7, 2008. |
| Math 595 | FM | 48983 | Financial
Mathematics (R. Gorvett) Description to be posted. Meets 14-Jan-08 - 07-Mar-08. |
| Math 595 | GF | 48262 | Computer
Graphics and Geometrical Visualization (G. Francis) We present the geometry of computer graphics, emphasizing real-time interactive computer animation (RTICA) for mathematical visualization, in particular for an immersive virtual environment(IVE), such as the CUBE, CAVE, and CANVAS. of the Integrated Systems Lab (ISL) at the Beckman Institute. Topics include the structure of the OpenGL graphical pipeline, the polyhedral encoding of surfaces as triangular meshes, the geometry of linear and aerial perspective (ligh and shade), the representation of the 3-D affine group in 4-D homogeneous coordinates, the algebra of 3-D rotations in terms of unit quaternions, projective spaces and their Euclidean, spherical and Minkowski (hyperbolic) metrics. We will explore non-Euclidean splines and morphing techniques, real time interactive texture mapping, and other advanced graphics techniques for innovative mathematical application. The course also includes a survey of classical topics including binocular optics and color theory, Haussdorff dimension and fractals, chaos and strange attractors, Wolfram's cellular automata, Barnsley's iterated function systems, Julia and Mandelbrot sets, discrete and continuous logistic equations, and the Lienard-VanderPol dynamical system. Prospective students should have a good spatial intuition, some artistic abilities or ambitions, and a solid grounding in linear algebra and vector calculus. Students may participate in a tutorial on useful line and surface graphics tools that do not require programming. Students with experience programming in some computer language, such as BASIC, Pascal, C/C++, Java, Python, or Mathematica, may gain 2 credits of independent study for a graphics programming project appropriate to the course and tailored to the proficiency of the student. Text: Francis, A Topological Picturebook, Springer Paper Back, 2006. Meets Jan 14 - Mar 7, 2008 |
| Math 595 | IPC | 49352 | Introduction
to Pseudoholomorphic Curves (E. Kerman) Pseudoholomorphic curves were first introduced and applied by Gromov in his remarkable paper of 1986. They have revolutionized the field of symplectic topology and have significantly impacted many other areas, including algebraic geometry and low-dimensional topology. Applications of these objects are still being actively developed in many new directions. This mini-course will be comprised of three sections. The first will be an overview of the required results on Riemann surfaces, the domains of pseudoholomorphic curves. This will culminate in a discussion of the Deligne-Mumford compactness theorem. The second section will be a rea- sonably detailed discussion of the definition and main properties of pseudo- holomorphic curves with special emphasis on their compactness properties. In the final section of the mini-course, we will survey some applications to symplectic topology. Prerequisites: Basic differential geometry and topology. References: J-holomorphic curves and symplectic topology, by D. McDuff and D. Salamon. 1. Meets Jan 14 - Mar 7, 2008 |
| Math 595 | PST | 48256 |
General Point
Set Topology (E. Lerman)
Recommended texts are: General Topology by S. Willard; Topology by Munkres (any edition); Topology and Geometry by Bredon. Meets Jan 14 - Mar 7, 2008 |
| Math 595 | RMS | 48255 | Introduction
to Random Fragmentation and Coagulation Processes (R. Song) Fragmentation and coagulation are two natural phenomenon a that can be observed in many sciences. In this half semester topics course, we will give an theoretical account of some of the mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. The fragmentation and coalescent processes we are going to consider describe the evolution of particle systems, where particles are characterized by their sizes. In a fragmentation process, each particle splits at a rate which depends on its size, and independently of the other particles. In a coalescent process, coagulations occur at rates which depend only on the particles involved in the merging, and not on the other particles in the system. We will start by developing the theory of fragmentation chains, that is processes in which each fragment remains stable for some random time and then splits; and then we go to the general situation where each fragment may split instantaneously. We can consider two different types of coalescent processes: exchangeable coalescents, where rates of coagulation do not depend on the masses in the system and coagulations may occur simultaneously and involve an arbitrary number of components, and stochastic coalescents, where only binary coagulations are permitted and the rate of such coagulation may depend on the two fragments involved. The prerequiste for this topics course is a solid background in probability theory (like Math 561). Text: Random Fragmentation and Coagulation Processes by Jean Bertoin. Meets Mar 10 - Apr 30, 2008 |
| Math 595 | ZFT | 48258 | Polytopes
and Lattice Points (Z. Furedi) The aim of this course is twofold. First, a short introduction to the basic methods of combinatorial geometry and computation by reviewing important notions, results and problems, and investigate beautiful polytopes. Second, to supply a series of research problems to interested students on or close to thesis level. Some of the topics: We select a few chapters from the above book: Helly, Charatheodory and Radon theorem and their generalizations. Shelling, Upper bound theorem. Volumes, lattice width Geometric discrepancy. Text: J. Matousek: Lectures on Discrete Mathematics, Graduate Text in Math., Springer 2002. The knowledge of the materials covered by the following courses is very helpful: Math 242 (Calculus of several variables), Math 403 (Eucledian geometry), Math 415 (Linear algebra), Math 417 (Abstract algebra), Math 447 (Real analysis). Prerequisites: Math 580 or consent of instructor. Meets Mar 10 - Apr 30, 2008 |
Course Catalog | Course Schedule
| Department
of Mathematics 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Telephone: (217) 333-3350 Fax: (217) 333-9576 Email: office@math.uiuc.edu |
College of Liberal Arts and
Sciences Last modified February 22, 2008 |