# Fall 2004

 Math 1A - Section 1 - Calculus Instructor: Richard Borcherds Lectures: TuTh 2:00-3:30pm, Room 2050 Valley Life Science Course Control Number: 54303 Office: 927 Evans, e-mail: reb [at] math [dot] berkeley [dot] edu Office Hours: TuTh 3:30-5:00pm Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: Stewart, Calculus: Early Transcendentals, 5th edition, Brooks/Cole. Syllabus: An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. Course Webpage: math.berkeley.edu/~reb/1A Grading: 20% quizzes and homework, 20% each midterm, 40% final. Homework: Homework for each week is given in the course handout (available at math.berkeley.edu/~reb/1A) and is due in the discussion section on Monday the next week. Comments: See the course page math.berkeley.edu/~reb/1A for the course handout. Math 1A - Section 2 - Calculus Instructor: Mark Haiman Lectures: MWF 11:00am-12:00pm, Room 155 Dwinelle Course Control Number: 54348 Office: 771 Evans, e-mail: Office Hours: TBA Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: James Stewart, Calculus: Early Transcendentals, 5th edition (Brooks/Cole, 2003). We will cover chapters 1-6. Syllabus: An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. Intended for majors in engineering and the physical sciences. Course Webpage: math.berkeley.edu/~mhaiman/math1A Math 1A - Section 3 - Calculus Instructor: Daniel Tataru Lectures: TuTh 3:30-5:00pm, Room 155 Dwinelle Course Control Number: 54393 Office: 841 Evans, e-mail: tataru [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: Stewart, Calculus: Early Transcendentals, 5th edition, Brooks/Cole. Recommended Reading:Syllabus: This course provides an introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. It is intended for majors in engineering and the physical sciences. Course Webpage: http://math.berkeley.edu/~tataru/1A/ (to come) Grading: 20% quizzes and homework, 20% each midterm, 40% final Homework: Homework will be assigned on the web every class, and due once a week. Math 1B - Section 1 - Calculus Instructor: Ole Hald Lectures: MWF 10:00-11:00am, Room 1 Pimentel Course Control Number: 54432 Office: 875 Evans, e-mail: hald [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Calculus Instructor: Zvezdelina Stankova Lectures: TuTh 12:30-2:00pm, Room 2050 Valley Life Science Course Control Number: 54477 Office: 719 Evans, e-mail: stankova [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Vaughan Jones Lectures: TuTh 3:30-5:00pm, Room 1 Pimentel Course Control Number: 54516 Office: 929 Evans, e-mail: vfr [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and Calculus Instructor: Tsit-Yuen Lam Lectures: MWF 12:00-1:00pm, Room 155 Dwinelle Course Control Number: 54555 Office: 871 Evans, e-mail: lam [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Donald Sarason Lectures: MWF 8:00-9:00am, Room 10 Evans Course Control Number: 54594 Office: 779 Evans, e-mail: sarason [at] math [dot] berkeley [dot] edu Office Hours: MW 9:30-11:30am Prerequisites: Math 16A Required Text: Goldstein, Lay and Schneider, Calculus and its Applications, 10th edition, Prentice-Hall Syllabus: Functions of several variables, trigonometric functions, techniques of integration, differential equations, Taylor polynomials and infinite series, probability and calculus (Chapters 7-12 of the textbook) Course Webpage: http://math.berkeley.edu/~sarason/Class_Webpages/Fall_2004/Math16B_S1.html Grading: The course grade will be based on two midterm exams, the final exam, and section performance. Details will be provided at the first lecture. Homework: There will be weekly homework assignments. Comments: At the first lecture, a lecture schedule, exam dates, and a schedule of homework assignments will be provided. My lectures tend to be slow moving. They cannot possible cover all of the course material; that would be true even if I spoke much more quickly than I do. So expect to pick up a lot by reading the textbook. Needless to say, if you attend lecture, it would be best to look beforehand at the relevant parts of the textbook to get at least a rough idea of the topics that will be discussed. Before enrolling in the course, check the final exam date to make sure you do not have a conflict. There will be no make-up exams, neither final nor midterms. Math 24 - Section 1 - Freshman Seminars Instructor: Jenny Harrison Lectures: F 3:00-4:00pm, Room 891 Evans Course Control Number: 54633 Office: 851 Evans, e-mail: harrison [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: The Staff Lectures: MWF 8:00-9:00am, Room 4 LeConte Course Control Number: 54636 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Rob Kirby Lectures: MWF 9:00-10:00am, Room 2050 Valley Life Science Course Control Number: 54684 Office: 919 Evans, e-mail: kirby [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53M - Section 1 - Multivariable Calculus With Computers Instructor: Alexander Givental Lectures: MWF 2:00-3:00pm, Room 100 Lewis Course Control Number: 54735 Office: 701 Evans, e-mail: givental [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Marc Rieffel Lectures: MWF 12:00-1:00pm, Room 1 Pimentel Course Control Number: 54756 Office: 811 Evans, e-mail: rieffel [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 1B or equivalent Required Text: Richard Hill, Elementary Linear Algebra with Applications W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems Recommended Reading: Syllabus: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product on spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. Course Webpage: http://math.berkeley.edu/~rieffel/54web.html Grading: Homework: Comments: Math H54 - Section 1 - Honors Linear Algebra and Differential Equations Instructor: Robert Coleman Lectures: MWF 1:00-2:00pm, Room 9 Evans Course Control Number: 54806 Office: 901 Evans, e-mail: coleman [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: First year calculus and motivation. Required Text: Richard Hill, Elementary Linear Algebra with Applications W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems Recommended Reading: Syllabus: Linear Algebra, the theory of linear equations, is the simplest of higher mathematics. The theory of Differential Equations involves some of the deepest ideas in mathematics. In this course, I will teach enough linear algebra so that some important properties of differential equation can be revealed. Course Webpage: Grading: Homework: Comments: Math 54M - Section 1 - Linear Algebra and Differential Equations Instructor: Fraydoun Rezakhanlou Lectures: MWF 9:00-10:00am, Room 1 LeConte Course Control Number: 54807 Office: 815 Evans, e-mail: rezakhan [at] math [dot] berkeley [dot] edu Office Hours: MWF 10:00-11:00am Prerequisites: Required Text: Hill, Elemetary Linear Algebra Boyce-DiPrima, Elemetary DE and Boundary Value Problems, Wiley, 8th edition Recommended Reading: Syllabus: The M version of Math 54 schedules students to meet with their teaching assistants twice a week in the computer lab 38B located in the basement of Evans hall. Students will have computer-based homework exercises. No prior computer experience is required. Course Webpage: Grading: homework and quizzes, 150 points 3 midterms, the best two counting, worth 75 points each, totalling 150 points Final Exam, 200 points Total: 500 points possible. Homework: Due every Tuesday in your TA section. You must give a detailed solution for each problem - the correct answer is not sufficient. Late homework is not accepted by the TA's under any circumstances. To allow for sickness, we delete the single worst homework set from your record and add up the rest for a total possible of 120 points. There will be three quizzes (given in section) that count, for a total of 30 points. Quizzes will vary with the TA section. The first assignment is due in your TA section on Tuesday, September 7. Comments: The first midterm will be in class on Monday, October 4. The second midterm will be on Wednesday, November 3. The third midterm will be on Wednesday, December 1. The Final Exam will be on Monday, December 20. Make sure you can make the final exam - check the schedule now to see that it is acceptable to you. It is not possible to have make-up exams. Incompletes. Official University policy states that an Incomplete can be given only for valid medical excuses with a doctor's certificate, and only if at the point the grade is given the student has a passing grade (C or better). If you are behind in the course, Incomplete is not an option! Math 55 - Section 1 - Discrete Mathematics Instructor: George M. Bergman Lectures: MWF 3:00-4:00pm, Room 10 Evans Course Control Number: 54828 Office: 865 Evans, e-mail: gbergman [at] math [dot] berkeley [dot] edu Office Hours: Tu 10:30-11:30am, W 4:15-5:15pm, F 10:30-11:30am Prerequisites: Math 1A-1B, or consent of the instructor Required Text: Kenneth H. Rosen, Discrete Mathematics and its Applications, 5th edition, McGraw-Hill Syllabus: We will cover Chapters 1-5 and 7 in Rosen. We'll also use some notes prepared by a previous instructor (available online both in pdf and in postscript format) to supplement Chapter 5. Grading: Grades will be based on two Midterms (15% + 20%), a Final (35%), and weekly Quizzes in Section (30%). The Department cannot at present afford graders for homework in lower-division courses, but I will assign problems for you to do, the solutions will be discussed in section, and section Quizzes will be based largely on them. Homework: Weekly Comments: Math 1A-1B and (if you've had them) 53 and 54 have all been about smooth functions of one or more real variables. This course is about some very different topics. The main reason 1A-1B is a prerequisite is to be sure students have enough familiarity with mathematical thinking; it also means that I will be free to occasionally make connections with topics from that sequence. But if you haven't had it and want to take this course, come see me and we will discuss whether you are ready. Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: The Staff Lectures: MWF 12:00-1:00pm, Room 70 Evans Course Control Number: 54849 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: The Staff Lectures: TuTh 3:30-5:00pm, Room 241 Cory Course Control Number: 54852 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H90 - Section 1 - Honors Problem Solving Instructor: Olga Holtz Lectures: MF 4:00-6:00pm, Room 71 Evans Course Control Number: 54855 Office: 821 Evans, e-mail: holtz [at] math [dot] berkeley [dot] edu Office Hours: MF 11:00am-12:00pm Prerequisites: Very good grasp of pre-calculus math is a must; basic calculus and linear algebra background is desirable. Required Text: No required text, will use several problem books. Recommended Reading: Gleason, A. M.; Greenwood, R. E.; Kelly, L. M.; The William Lowell Putnam Mathematical Competition. Problems and solutions: 1938--1964. Mathematical Association of America, Washington, D.C., 1980. ISBN 0-88385-428-7 MR0837662 The William Lowell Putnam mathematical competition. Problems and solutions: 1965--1984. Edited by Gerald L. Alexanderson, Leonard F. Klosinski and Loren C. Larson. Mathematical Association of America, Washington, DC, 1985. ISBN 0-88385-441-4 MR1933844 (2003k:00002) Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi; The William Lowell Putnam Mathematical Competition, 1985--2000. Problems, solutions, and commentary. MAA Problem Books Series. ISBN 0-88385-807-X Contests in higher mathematics. Miklos Schweitzer Competitions 1962--1991. Edited by Gbor J. Szkely. Problem Books in Mathematics. Springer-Verlag, New York, 1996. ISBN 0-387-94588-1 Syllabus: None Course Webpage: http://math.berkeley.edu/~holtz/H90.html Grading: Based entirely on homework. Homework: 10-12 problems weekly. Comments: This course is for hard working students who enjoy solving challenging math problems, especially for those who want to participate and do well on the Putnam competition in December. Math C103 - Section 1 - Introduction to Mathematical Economics Instructor: D. Ahn Lectures: TuTh 3:30-5:00pm, Room 130 Wheeler Course Control Number: 54915 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Donald Sarason Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54918 Office: 779 Evans, e-mail: sarason [at] math [dot] berkeley [dot] edu Office Hours: MW 9:30-11:30am Prerequisites: Math 53 and 54 Required Text: Charles Pugh, Real Mathematical Analysis, Springer-Verlag, 2002 Recommended Reading:Syllabus: Review of elementary set theory, countable and uncountable sets, the system of real numbers and its basic properties, convergence, continuity, differentiation, integration, Euclidean spaces, metric spaces, compactness, connectedness. Course Webpage: http://www.math.berkeley.edu/~sarason/Class_Webpages/Fall_2004/Math104_S1.html Grading: The course grade will be based on two midterm exams, the final exam, and homework. Details will be provided at the first class meeting. All exams will be open book. Homework: Homework will be assigned weekly and will be carefully graded. Comments: The course has two basic goals. One is to present a rigorous development of the fundamental ideas underlying calculus (and much of the rest of mathematics). The other is to foster students in acquiring (or coerce them into acquiring) skill in mathematical reasoning and in constructing coherent, rigorous mathematical proofs. The lectures will discuss the basic ideas, but students can expect to have to pick up much on their own from the textbook. Many students find Math 104 difficult. Unless you aced lower-division mathematics, and perhaps even if you did, Math 104 is probably not a wise choice as a first upper-division math course. Lower-division math involves a heavy dose of symbol manipulation. Math 104 is concerned with the ideas that justify the symbolism. Math 104 - Section 2 - Introduction to Analysis Instructor: Alexander Yong Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54921 Office: 1035 Evans, e-mail: ayong [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53, Math 54. Required Text: Charles Pugh, Real Mathematical Analysis Recommended Reading: Walter Rudin, Principles of Mathematical Analysis Kenneth Ross, Elementary Analysis: the theory of calculus Syllabus: Review of elementary set theory, countable and uncountable sets, the system of real numbers and its basic properties, convergence, continuity, differentiation, integration, Euclidean spaces, metric spaces, compactness, connectedness. Course Webpage: http://math.berkeley.edu/~ayong/Fall2004_Math104.html Grading: TBA Homework: TBA Exams: TBA Comments: Send ayong [at] math [dot] berkeley [dot] edu (me) an email about you and your (mathematical) background so I can get to better know you. Math 104 - Section 3 - Introduction to Analysis Instructor: Paul Chernoff Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54924 Office: 933 Evans, e-mail: chernoff [at] math [dot] berkeley [dot] edu Office Hours: M 1:30-2:30pm; W 11:00am-12:00pm; F 1:30-2:30pm Prerequisites: Math 53 and 54 Required Text: K. Ross, Elementary Analysis: The Theory of Calculus, first edition (13th or later printing advised), published by Springer. Recommended Reading: M. Protter, Basic Elements of Real Analysis, paperback, published by Springer. Syllabus: Primarily Chapters 1-4 of Ross: The real number system; convergence of sequences and series. Convergence and uniform convergence of sequences of functions; power series. Main facts about differentiation and integration. Some discussion of metric spaces. Grading: 15% homework, 45% midterms and quizzes, 40% final. Homework: Weekly assignments. Comments: This is a very challenging course. Its content is very important. It is also important to master the art of writing mathematics clearly and concisely.   I welcome and encourage questions and comments. Math 104 - Section 4 - Introduction to Analysis Instructor: Jack Silver Lectures: TuTh 11:00am-12:30pm, Room 75 Evans Course Control Number: 54927 Office: 753 Evans, e-mail: silver [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 6 - Introduction to Analysis Instructor: Justin Holmer Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54933 Office: Office Hours: TBA Prerequisites: Check with the department to see what the formal prerequisites are. I would recommend at least a complete course in single-variable calculus, covering limits, derivatives, integrals, techniques of integration, sequences and series, and Taylor's theorem. This prerequisite course may have (usually will have) emphasized computation over formal definitions and proofs. The present course will cover essentially the same topics, but now the emphasis will shift to the rigorous definitions and proofs. Required Text: K. A. Ross, Elementary Analysis: The Theory of Calculus, Springer-Verlag ($35). Recommended Reading: W. Rudin, Principles of Mathematical Analysis, McGraw-Hill ($140), is the classic text on this material. Syllabus: (1) basic concepts of logic, set theory, real numbers; (2) sequences; (3) continuity; (4) sequences and series of functions; (5) differentiation; (6) integration; (7) metric spaces and basic topology. We will aim to cover most of the Ross text with some supplemental material on metric spaces taken from another text I have yet to select (such as M. Protter, "Basic Elements of Real Analysis.") The focus of this course, aside from the specific material covered, is learning to read and write proofs. Course Webpage: I will set up a course webpage when I arrive later this summer. It will have links to homework assignments, exams, solutions for exams, and up-to-date grades. Grading: 25% Quizzes/Homework, 20% Midterm I, 20% Midterm II, 35% Final Exam. Homework: Assigned and collected weekly. You are encouraged to form study groups to toss around ideas, but each student is required to submit a write-up of the solutions in his/her own words. Problems will be selected from the Ross text or posted on the course web site. Lowest homework score is dropped. Comments: I am a newly hired Morrey Jr. Asst. Prof., and have not yet arrived on campus. If you would like to contact me before the semester begins, email: holmer [at] math [dot] uchicago [dot] edu. Math H104 - Section 1 - Honors Introduction to Analysis Instructor: Arthur Ogus Lectures: MWF 1:00-2:00pm, Room 31 Evans Course Control Number: 54936 Office: 877 Evans, e-mail: ogus [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: F. Alberto Grünbaum Lectures: TuTh 8:00-9:30am, Room 155 Dwinelle Course Control Number: 54939 Office: 903 Evans, e-mail: grunbaum [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 54, or a course with equivalent linear algebra content. (Math 74 also recommended for students not familiar with proofs.) Required Text: S. H. Friedberg, A. J. Insel and L. E. Spence, Linear Algebra, 4th edition Syllabus: In this class we take a second look at linear algebra, something you have seen in Math 54. The basic issues are the same: solving linear equations, doing least square problems, finding eigenvalues and eigenvectors of a matrix, thinking of a matrix as a linear map between vector spaces, writing matrices in a more revealing form by choosing a basis appropriately, etc. We will revisit all these items form a more general viewpoint than that of Math 54, and proofs will play an important part in this class. There are TWO reasons for looking anew at these basic tasks: with the advent of the computer age there has been a revival in the search for ways of performing these basic tasks with faster and more accurate algorithms. Think of applications like signal processing, medical imaging, Pixar animation, etc. The second reason is equaly important: the ability to do abstract reasoning gives a beautiful and powerful tool not only to organize the material you already know but also to make new discoveries. If you are going to be more than just a user of "black boxes" of software (which I also love to use) you have to develop your own mental tools to judge the merit and quality of these packages. Practical advice: start doing the homework as soon as possible. Learn to walk around with these problems in your head, sometimes you will wake up with some new idea on how to solve them. Try to put together a group of two or three of you that meets regularly to discuss the material in the class; try to explain the material to each other: there is a chance that you will discover that you do not really understand it yourself. This is the first step in learning and you should repeat this till you all understand what is going on. Ask questions, propose counterexamples, challenge each other.... Grading: The grade will be based on your homework (25%), two midterms (20% and 20%) and a final (35%). Homework: There will be a weekly homework assignment, with problems from the book. Homework Assignment: First week (due Monday, September 7) sect 1.1, 3b,d,7 sect 1.2, 1(all),18,21 sect 1.3, 9,11 sect 1.4, 10,11 sect 1.5, 1,3,7,10 Exams: First midterm, October 5, in class; second midterm, November 9, in class; final exam, Friday, December 17, 12:30-3:30pm Math H110 - Section 1 - Honors Linear Algebra Instructor: Jack Wagoner Lectures: MWF 11:00am-12:00pm, Room 85 Evans Course Control Number: 54966 Office: 899 Evans, e-mail: wagoner [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Arthur Ogus Lectures: MWF 2:00-3:00pm, Room 71 Evans Course Control Number: 54864 Office: 877 Evans, e-mail: ogus [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Vera Serganova Lectures: TuTh 12:30-2:00pm, Room 2 Evans Course Control Number: 54972 Office: 709 Evans, e-mail: serganova [at] math [dot] berkeley [dot] edu Office Hours: TuTh 10:30am-12:00pm Prerequisites: Math 53, 54 Required Text: Hungerford, Abstract Algebra: An Introduction Syllabus: We start with elementary number theory, then study elements of groups and rings theory. After this we proceed to more advanced topics such as Sylow theorems and fields extensions. We will discuss applications to geometric constructions and codes. We will have a 15-minute quiz every second Thursday and one midterm. Course Webpage: http://math.berkeley.edu/~serganov/ Grading: 15% quizzes, 15% homework, 20% midterm 50% final Homework: Homework will be assigned on the web and due once a week. Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Alexander Givental Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54975 Office: 701 Evans, e-mail: givental [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Dan Voiculescu Lectures: TuTh 9:30-11:00am, Room 61 Evans Course Control Number: 54978 Office: 783 Evans, e-mail: dvv [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 115 - Section 1 - Introduction to Number Theory Instructor: Paul Vojta Lectures: MWF 3:00-4:00pm, Room 70 Evans Course Control Number: 54981 Office: 883 Evans, e-mail: vojta [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: Niven, Zuckerman, Montgomery, An introduction to the theory of numbers, Wiley Syllabus: To be determined. Here is the catalog description: Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems. Course Webpage: http://math.berkeley.edu/~vojta/115.html Grading: Homeworks, 30%; midterms, 15% and 20%; final exam, 35%. Homework: Assigned weekly. Comments: Watch the course web page for further developments. Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Olga Holtz Lectures: MWF 3:00-4:00pm, Room 241 Cory Course Control Number: 54984 Office: 821 Evans, e-mail: holtz [at] math [dot] berkeley [dot] edu Office Hours: MF 11:00am-12:00pm Prerequisites: 53 and 54. Required Text: Mathematics for physicists by Susan M. Lea, Publisher: Thomson Brooks/Cole, 2004. ISBN 0-534-37997-4 Recommended Reading: Mathematical Methods in the physical sciences by Mary L. Boas, Publisher: Wiley Text Books; 2 edition, 1983. ISBN: 0-471-04409-1; Mathematical physics by Eugene Butkov, Publisher: Benjamin Cummings, 1968. ISBN: 0-201-00727-4 Syllabus: Review of series, in particular power series. Review of partial differentiation, including implicit differentiation. Functions of one complex variable. Fourier transform and Fourier series. Laplace transform. Calculus of variations. Course Webpage: http://math.berkeley.edu/~holtz/121A/ Grading: 30% homework, 20% 1st midterm, 20% 2nd midterm, 30% final. Homework: 10-12 problems weekly. Comments: The goal of this course is to learn basic complex analysis, integral transforms, and variational calculus to be able to apply them with ease and solid understanding to problems from physics. Math 121A - Section 2 - Mathematical Tools for the Physical Sciences Instructor: F. Alberto Grünbaum Lectures: TuTh 9:30-11:00am, Room 81 Evans Course Control Number: 54987 Office: 903 Evans, e-mail: grunbaum [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and 54. Required Text: Mary Boas, Mathematical methods in the physical sciences, Wiley, 2nd edition. Syllabus: This class is designed for students in the physical sciences and engineering who need to go from a lower division mathematical foundation into a more advanced level and cannot take a series of classes where this material is introduced at a slower and more detailed pace. The book does a very good job at covering a large amount of basic material that will be useful in a variety of science and engineering classes. There are a handful of more "modern topics" that will be covered mainly in the second semester by means of notes handed out in class. Grading: Midterm (30%) Homework (30%) Final (40%) Homework: There will be a weekly assignment of problems from the book. Math 125A - Section 1 - Mathematical Logic Instructor: G. Mints Lectures: TuTh 11:00am-12:30pm, Room 85 Evans Course Control Number: 54993 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 127 - Section 1 - Mathematical and Computational Methods in Molecular Biology Instructor: Lior Pachter Lectures: TuTh 8:00-9:30am, Room 70 Evans Course Control Number: 54996 Office: 1081 Evans, e-mail: lpachter [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: John Strain Lectures: TuTh 8:00-9:30am, Room 10 Evans Course Control Number: 54999 Office: 1099 Evans, e-mail: strain [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 130 - Section 1 - Classical Geometry Instructor: Vera Serganova Lectures: TuTh 3:30-5:00pm, Room 9 Evans Course Control Number: 55014 Office: 709 Evans, e-mail: serganova [at] math [dot] berkeley [dot] edu Office Hours: TuTh 10:30am-12:00pm Prerequisites: Math 110, 113 Required Text: Hartshorne, Geometry: Euclid and Beyond, Springer Recommended Reading: Euclid, Elements Syllabus: We start with reading Euclid's elements and solving geometric problems. After discussing Euclid's axiomatic method we will see the need for additional axioms provided by Hilbert. The second part of this course deals with ruler and compass constructions and non-Euclidean geometry. In particular we discuss three famous construction problems and construction of a regular 17-gon. We will have a 15-minute quiz every second Thursday and one midterm. Course Webpage: http://math.berkeley.edu/~serganov/ Grading: 15% quizzes, 15% homework, 20% midterm 50% final Homework: Homework will be assigned on the web and due once a week. Math 135 - Section 1 - Introduction to Theory Sets Instructor: G. Mints Lectures: TuTh 2:00-3:30pm, Room 85 Evans Course Control Number: 55017 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 142 - Section 1 - Elementary Algebraic Topology Instructor: Ai-Ko Liu Lectures: MWF 9:00-10:00am, Room 71 Evans Course Control Number: 55020 Office: 905 Evans, e-mail: akliu [at] math [dot] berkeley [dot] edu Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 170 - Section 1 - Mathematical Methods for Optimization Instructor: L. Craig Evans Lectures: TuTh 9:30-11:00am, Room 87 Evans Course Control Number: 55023 Office: 907 Evans, e-mail: evans [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: Joel Franklin, Methods of Mathematical Economics, SIAM Recommended Reading: Pablo Pedregal, Introduction to Optimization, Springer Syllabus: COURSE OUTLINE: Introduction 1. Linear programming 2. Nonlinear programming, convex analysis 3. Game theory 4. Calculus of variations 5. Introduction to control theory Grading: 25% homework, 25% midterm, 50% final Homework: At the start of each class, I will assign a homework problem, due in one week. Math 172 - Section 1 - Combinatorics Instructor: Alexander Yong Lectures: TuTh 12:30-2:00pm, Room 103 Moffitt Course Control Number: 55026 Office: 1035 Evans, e-mail: ayong [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: No specific prerequisites, however exposure to courses such as abstract algebra (Math 113) will be helpful. This will be an advanced undergraduate course on combinatorics. Required Text: Peter J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1994 (reprinted 1996). Recommended Reading: R. P. Stanley, Enumerative Combinatorics I R. P. Stanley, Enumerative Combinatorics II D. Stanton and D. White, Constructive combinatorics R. Brualdi, Introductory Combinatorics Syllabus: This is the ultimate fun course on combinatorics. Combinatorial methods are applied widely throughout mathematics; this class will be an introduction to various aspects of combinatorial theory. Some sample topics include: generating series, graph theory, poset theory, combinatorics of trees (parking functions, Catalan numbers, matrix-tree theorem), tableaux and the symmetric group (permutation statistics, the Schensted correspondence, hook-length formula), partitions, symmetric functions. A different with the same course number was taught in Spring 2004. This course will not depend on the material covered in that course. Although there will be some material overlap, I plan to cover a wider range of topics this term. This course should be of interest to anyone who like algorithms, computation, and problem solving. Course Webpage: http://math.berkeley.edu/~ayong/Fall2004_Math172.html Grading: TBA Homework: TBA Exams: TBA Comments: Send ayong [at] math [dot] berkeley [dot] edu (me) an email about you and your (mathematical) background so I can get to better know you. Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Daniel Geba Lectures: TuTh 2:00-3:30pm, Room 71 Evans Course Control Number: 55029 Office: 837 Evans, e-mail: dangeba [at] math [dot] berkeley [dot] edu Office Hours: TuTh 3:30-5:00pm Prerequisites: Math 104 Required Text: J. W. Brown and R. V. Churchill, Complex Variables and Applications, 6th edition, 1995. Syllabus: Complex numbers. Analytic functions. Elementary functions. Integrals. Series. Residues and poles. Application of residues. Mapping by elementary functions. Grading: Homework (25%), Midterm (25%), Final (50%) Homework: Assigned on Wednesday, due next Thursday. Worst 3 homeworks not counted. No late homeworks. Comments: No make-up exams. Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Leo Harrington Lectures: MWF 12:00-1:00pm, Room 71 Evans Course Control Number: 55032 Office: 711 Evans, e-mail: leo [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Dapeng Zhan Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 55035 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 191 - Section 1 - High School Mathematics from an Advanced Perspective Instructor: Emiliano Gomez Lectures: MW 4:00-7:00pm, Room 230-D Stephens Course Control Number: 55038 Office: 985 Evans, e-mail: emgomez [at] math [dot] berkeley [dot] edu Office Hours: To be decided in class. Most likely they will be on Monday and Wednesday afternoons/evenings (to accomodate teachers), and also by appointment. Prerequisites: Interest in math education/teaching. Willingness to work in groups. At least one upper-level math class. Required Text: Usiskin, Peressini, Marchisotto and Stanley, Mathematics for High School Teachers (an Advanced Perspective), Prentice Hall, 2003. ISBN: 0-13-044941-5 Recommended Reading: Familiarity with the high school curriculum, as well as with some high school texts, is desired but not necessary. Another recommendation is to read articles from "Mathematics Teacher", a journal of the National Council of Teachers of Mathematics. Syllabus: We will cover topics such as number systems (integers, rationals, reals, complex), equations, functions, congruence and similarity, area and volume, axioms, trigonometry. Clarity and proof will be emphasized. Topics will pertain to the high school curriculum, but we will give them a depth far beyond that which high schools students see at school. Grading: Based on weekly homework and reading assignments, a midterm take-home exam, and presentation of a semester project. Homework: Reading and exercises will be assigned and collected weekly. Comments: This course is for upper-level students interested in teaching High School mathematics, for grad students in the School of Education, and for High School teachers (who can register through UC Extension). It emphazises problem solving and group work, so that class participation is important. It MUST be taken for 4 units, unless there are very good reasons why that cannot be done. Math 198 - Section 1 - Directed Group Study Instructor: L. Craig Evans Lectures: M 4:00-5:00pm, Room 2 Evans Course Control Number: 55073 Office: 907 Evans, e-mail: evans [at] stat [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 202A - Section 1 - Introduction to Topology and Analysis Instructor: Michael Klass Lectures: MWF 12:00-1:00pm, Room 332 Evans Course Control Number: 55104 Office: 319 Evans, e-mail: klass [at] stat [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 204A - Section 1 - Ordinary and Partial Differential Equations Instructor: Alexandre Chorin Lectures: MWF 10:00-11:00am, Room 85 Evans Course Control Number: 55107 Office: 911 Evans, e-mail: chorin [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: No previous acquaintance with differential equations is assumed; some analysis (e.g., Math 104) is helpful. Required Text: Coddington and Levinson, Ordinary Differential Equations Recommended Reading: Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics Grading: Grading mostly on the homework. Homework: Homework will be assigned once a week and due a week later. Comments: My lecturing style is informal and I enjoy class discussion. Math 206 - Section 1 - Banach Algebras and Spectral Theory Instructor: Dan Voiculescu Lectures: TuTh 12:30-2:00pm, Room 6 Evans Course Control Number: 55110 Office: 783 Evans, e-mail: dvv [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 214 - Section 1 - Differential Manifolds Instructor: Jenny Harrison Lectures: MWF 11:00am-12:00pm, Room 31 Evans Course Control Number: 55113 Office: 851 Evans, e-mail: harrison [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 215A - Section 1 - Algebraic Topology Instructor: Jack Wagoner Lectures: MWF 9:00-10:00am, Room 39 Evans Course Control Number: 55116 Office: 899 Evans, e-mail: wagoner [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 218A - Section 1 - Probability Theory Instructor: David Aldous Lectures: MWF 2:00-3:00pm, Room 106 Moffitt Course Control Number: 55118 Office: 371 Evans, e-mail: aldous [at] stat [dot] berkeley [dot] edu Office Hours: W 9:30-11:30pm, 351 Evans Prerequisites: Ideally Upper division probability - familiarity with calculations using random variables. Upper division analysis, e.g. uniform convergence of functions, basics of complex numbers. Basic properties of metric spaces helpful. Required Text: R. Durrett, Probability: Theory and Examples is the required text, and the single most relevant text for the whole year's course. Quite a few of the homework problems are from there. The new 3rd edition corrects typos from the 2nd edition; either will be OK to use. The style is deliberately concise. Recommended Reading: P. Billingsley, Probability and Measure (3rd Edition) Chapters 1-30 contain a more careful and detailed treatment of the topics of this semester, in particular the measure-theory background. Recommended for students who have not done measure theory. K.L. Chung, A Course in Probability Theory covers many of the topics of 205A: more leisurely than Durrett and more focused than Billingsley. There are many other books at roughly the same first year graduate" level. Here are my personal comments on some. Y.S. Chow and H. Teicher, Probability Theory. Uninspired exposition, but has useful variations on technical topics such as inequalities for sums and for martingales. R.M. Dudley, Real Analysis and Probability. Best account of the functional analysis and metric space background relevant for research in theoretical probability. B. Fristedt and L. Gray, A Modern Approach to Probability Theory. 700 pages allow coverage of broad range of topics in probability and stochastic processes. L. Breiman, Probability. Classical; concise and broad coverage. There are some lecture notes for Jim Pitman's Fall 2002 STAT 205A which covers more ground than my course will! Syllabus: This is the first half of a year course in mathematical probability at the measure-theoretic level. It is designed for students whose ultimate research will involve rigorous proofs in mathematical probability. It is aimed at Ph.D. students in the Statistics and Mathematics Depts, but is also taken by Ph.D. students in Computer Science, Electrical Engineering, Business and Economics who expect their thesis work to involve probability. Note There is a parallel first year graduate course in probability theory, STAT 204 taught by Evans, which does not have a measure theory prerequisite. In brief, the course will cover Sketch of pure measure theory (not responsible for proofs) Measure-theoretic formulation of probability theory Classical theory of sums of independent random variables: laws of large numbers Technical topics relating to proofs of above: notions of convergence, a.s. convergence techniques Conditional distributions, conditional expectation Discrete time martingales Introduction to Brownian motion This roughly coincides with Chapters 1, 4 and (first half of) 7 in Durrett's book. Course Webpage: http://www.stat.berkeley.edu/users/aldous/205A/index.html Grading: 60% homework, 40% final. Homework: See week-by-week schedule for more details and for the weekly homework assignments. Comments: There will be a take-home final exam: tentatively December 10 - December 14. Math 221 - Section 1 - Advanced Matrix Computation Instructor: James Demmel Lectures: MWF 9:00-10:00am, Room 5 Evans Course Control Number: 55119 Office: 737 Soda, e-mail: demmel [at] cs [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 222A - Section 1 - Partial Differential Equations Instructor: Fraydoun Rezakhanlou Lectures: MWF 1:00-2:00pm, Room 5 Evans Course Control Number: 55122 Office: 815 Evans, e-mail: rezakhan [at] math [dot] berkeley [dot] edu Office Hours: MWF 10:00-11:00am Prerequisites: Math 104 Required Text: L. C. Evans, Partial Differential Equations, AMS. Recommended Reading: Syllabus: In this course we discuss the issues concerning the solvability and regularity for some basic partial differential equations. The main topics are: (1) Laplace, Diffusion and Wave equations (2) Scalar consevation laws (3) Hamilton-Jacobi equations (4) Sobolev spaces Course Webpage: Grading: There will be weekly homework assignments (due Mondays) and one take-home exam. Homework (70 points), take-home exam (30 points). Homework: Comments: Math 224A - Section 1 - Transport Processes, Conservation Laws and Symmetry Instructor: John Neu Lectures: MWF 3:00-4:00pm, Room 5 Evans Course Control Number: 55125 Office: 1051 Evans, e-mail: neu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Basic Prototypes Advection Diffusion-Einstein theory of Brownian motion Advection-diffusion, Smoluchowski PDE in stat mech Sources, delta functions and Green's functions Case studies Ideal fluid mechanics and vorticity Waves in elastic media Motion of melting fronts Asymptotic reductions by scaling Diffusion in thin domain Incompressible limit of compressible flow Shallow water theory Scaling symmetries in BVP Point source solution of diffusion equation Planar melting front Nonlinear diffusions with compact support Green's function of 2-D wave equation Advection-diffusion in a vortex Eigenvalue optimization problem-shape of the tallest building Course Webpage: Grading: Problems given at beginning of each class, 50% 2 in class MT (simple and basic), 30% Final (simple and basic), 20% Homework: Comments: Math 225A - Section 1 - Metamathematics Instructor: Leo Harrington Lectures: MWF 2:00-3:00pm, Room 31 Evans Course Control Number: 55128 Office: 711 Evans, e-mail: leo [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228A - Section 1 - Numerical Solution of Differential Equations Instructor: John Strain Lectures: TuTh 2:00-3:30pm, Room 75 Evans Course Control Number: 55131 Office: 1099 Evans, e-mail: strain [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: 128A or equivalent. Required Text: 1. J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995. 2. J. W. Thomas, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, Springer, 1999. Syllabus: Math 228B will survey the theory and practice of finite difference methods for parabolic, hyperbolic and elliptic partial differential equations. Topics will include: Basic linear partial differential equations and schemes. Convergence, stability and consistency. Practical stability analysis. ADI schemes. Numerical boundary conditions. GKSO theory. Dispersion and dissipation. Theory of nonlinear hyperbolic conservation laws. Entropy conditions and TVD schemes. Relaxation and multigrid for linear elliptic equations. Course Webpage: http://math.berkeley.edu/~strain/228b.S04/ Grading: Based on weekly homework and one or two projects. Homework: Will be posted on the class web site, and due once a week. Math 229 - Section 1 - Theory of Models Instructor: Thomas Scanlon Lectures: TuTh 11:00am-12:30pm, Room 5 Evans Course Control Number: 55134 Office: 723 Evans, e-mail: scanlon [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 240 - Section 1 - Riemannian Geometry Instructor: Ai-Ko Liu Lectures: MWF 11:00am-12:00pm, Room 5 Evans Course Control Number: 55137 Office: 905 Evans, e-mail: akliu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 249 - Section 1 - Combinatorial Commutative Algebra Instructor: Bernd Sturmfels Lectures: TuTh 8:00-9:30am, Room 81 Evans Course Control Number: 55140 Office: 925 Evans, e-mail: bernd [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 250B or equivalent background in commutative algebra, some exposure to combinatorics and geometry. Students who have already taken a previous version of Math 249 may register for this course as Math 274, Section 3, CCN 55160. Required Text: Ezra Miller and Bernd Sturmfels, Combinatorial Commutative Algebra, Springer Graduate Texts in Mathematics, to appear in late 2004. Recommended Reading: Syllabus: The book has the following 18 chapters. A rough plan to discuss a different chapter each week, so we may cover about two-thirds of the book. Your input on the selection and order of topics is welcome. 1. Squarefree Monomial Ideals 2. Borel-fixed Monomial Ideals 3. Three-dimensional Staircases 4. Cellular Resolutions 5. Alexander Duality 6. Generic Monomial Ideals 7. Semigroup Algebras 8. Multigraded Polynomial Rings 9. Syzygies of Lattice Ideals 10. Toric Varieties 11. Irreducible and Injective Resolutions 12. Ehrhart Polynomials 13. Local Cohomology 14. Plücker Coordinates 15. Matrix Schubert Varieties 16. Antidiagonal Initial Ideals 17. Minors in Matrix Products 18. Hilbert Schemes of Points To read this book click here. The posted version has now been submitted to Springer Verlag, but we are still able to make minor corrections until the end of June 2004. Please do take a look and e-mail me all your comments and corrections during the month of June. Course Webpge: Grading: Homework: Comments: Math 250A - Section 1 - Groups Rings and Fields Instructor: Kenneth A. Ribet Lectures: TuTh 12:30-2:00pm, Room 70 Evans Course Control Number: 55143 Office: 885 Evans, e-mail: ribet [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: A strong background in undergraduate abstract algebra. Required Text: Lang, Algebra, 3rd rev. ed. Syllabus: We will study such fundamental structures as groups, rings, modules and fields. It is likely that the course will end with a treatment of Galois theory. Course Webpage: http://math.berkeley.edu/~ribet/250/ Grading: Based on exams and homework, with the exact mix to be announced later Homework: Long problem sets will be assigned weekly. Math 254A - Section 1 - Number Theory Instructor: Martin Weissman Lectures: MWF 3:00-4:00pm, Room 9 Evans Course Control Number: 55146 Office: 1067 Evans, e-mail: marty [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: A strong background in abstract algebra, such as Math 250A-B, including groups, rings, fields, modules, and Galois theory. Required Text: Jurgen Neukirch, Algebraic number Theory Recommended Reading: TBA Syllabus: This will be a rigorous introduction to algebraic number theory. Topics include algebraic number fields, orders, etale algebras, valuations and localizations, ramification, units and class-groups, quadratic forms, function field analogues, quaternion algebras and central simple algebras. Two lectures per week will cover "standard" material, and one lecture per week will be a "fun" topic like "RSA cryptography", and "Why primes are like knots", and "The topograph of a quadratic form". Students are expected to read 10-15 pages per week of the textbook as well. Course Webpge: TBA Grading: Grades will be based on bi-weekly problem sets, and a final exam. Homework: Homework assignments will be available on the web. Math 256A - Section 1 - Algebraic Geometry Instructor: Robin Hartshorne Lectures: TuTh 9:30-11:00am, Room 5 Evans Course Control Number: 55149 Office: 881 Evans, e-mail: robin [at] math [dot] berkeley [dot] edu Office Hours: TuTh 1:30-3:00 Prerequisites: Required Text: Robin Hartshorne, Algebraic Geometry, Springer Recommended Reading: Syllabus: This is a first course in algebraic geometry. I do not presuppose any geometry, but I will make use of results from commutative algebra as needed. The most important topics you need to know are Hilbert's Nullstellensatz, dimension theory for local rings, integral closure, and exact sequences of modules. For a more detailed list see "Results from Algebra" on pp. 470-471 of the text. References for commutative algebra are Atiyah and Macdonald; Eisenbud; or Matsumura's "Commutative ring theory". I expect to cover most of Chapters I and II of the text in the Fall semester. This course will be followed in Spring '05 by a Math 274 "topics" course on deformation theory in algebraic geometry. Course Webpage: Grading: Homework: Comments: Math 265 - Section 1 - Differential Topology Instructor: Peter Teichner Lectures: TuTh 11:00am-12:30pm, Room 31 Evans Course Control Number: 55154 Office: Office Hours: TBA Prerequisites: Required Text: None. Recommended Reading: Syllabus: In this course, we'll first introduce vector bundles and their characterstic classes, and use them to get cobordism invariants of manifolds. We'll apply the Thom-Pontrjagin construction to translate the question of computing the cobordism ring into a problem in stable homotopy. We'll solve this problem in the nonoriented case and show how to get various (generalized) homology theories out of cobordism groups. The relation to ordinary homology and K-theory will be explained via the signature and other genera. This course will be continued as a topics course in the Spring 2005, where we'll study one particularly important cohomology theory in full detail: elliptic cohomology. Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra Instructor: Edward Frenkel Lectures: MWF 2:00-3:00pm, Room 51 Evans Course Control Number: 55155 Office: 819 Evans, e-mail: frenkel [at] math [dot] berkeley [dot] edu Office Hours: MW 3:00-4:00pm and by appointment Prerequisites: Basic knowledge of Lie groups, Lie algebras and algebraic geometry. Required Text: E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, Second Edition, AMS 2004. Recommended Reading: Syllabus: We will discuss the geometric Langlands correspondence over the field of complex numbers. The local correspondence amounts to a "spectral decomposition" of the categories of smooth representations of an affine Kac-Moody algebra with respect to the local systems of the Langlands dual group over the punctured disc. In order to construct it, we will introduce a certain class of representations caled Wakimoto modules and describe the center of the completed enveloping algebra of an affine Kac-Moody algebra at the critical level. Representations of affine Kac-Moody algebras may then be used to construct the global Langlands correspondence, which associates to local systems defined over a smooth projective curve X the so-called Hecke eigensheaves on the moduli space of G-bundles on X. We will consider explicit examples of this correspondence, such as the Gaudin integrable system, which arises in the Langlands correspondence in genus zero. The lectures will be augmented by a seminar that will meet on Fridays after the lectures, in which we will discuss the classical Langlands correspondence (so as to give some motivation to the topics discussed in the course) and other related material. Course Webpage: http://math.berkeley.edu/~frenkel/Math274 Grading: Homework: Comments: Math 274 - Section 2 - Topics in Algebra Instructor: Mark Haiman Lectures: MWF 3:00-4:00pm, Room 7 Evans Course Control Number: 55158 Office: 771 Evans, e-mail: Office Hours: TBA Prerequisites: Good general algebra background. Required Text: Probably none. Recommended Reading: See course web page. Syllabus: Quantized Kac-Moody algebras and their representations; crystal and canonical bases; affine algebras; connections with combinatorics; conjectures and open problems. See course web page for more details. Course Webpage: math.berkeley.edu/~mhaiman/math274 Math 275 - Section 1 - Topics in Applied Mathematics Instructor: Lior Pachter Lectures: TuTh 2:00-3:30pm, Room 7 Evans Course Control Number: 55161 Office: 1081 Evans, e-mail: lpachter [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: The class is suitable for graduate students who have a background in discrete applied mathematics, preferrably with experience in algebra and/or combinatorics. Familiarity with basic biology will be helpful, but is neither necessary nor sufficient for taking the course. Required Text: Recommended Reading: Syllabus: A graphical model is a family of joint probability distributions for a collection of random variables that factors according to a graph. Graphical models have proved to be extremely useful for problems in computational biology, because they provide useful and versatile probabilistic frameworks for a wide range of problems, and at the same time are suitably structured for efficient inference. For example, in biological sequence analysis, specialized directed graphical models with discrete random variables are used for applications ranging from annotation and alignment to phylogeny reconstruction. Discrete graphical models are instances of statistical models that can be characterized by polynomials in the joint probabilities. The emerging and active field of algebraic statistics offers algorithms for this polynomial representation, and is a fertile area for the application of ideas from commutative algebra and algebraic geometry. We will focus on the rich interaction between the theory of algebraic statistics, and the motivating application of computational biology. Several recent papers have demonstrated that algebraic statistics can be applied to developing practical algorithms for biological applications, and conversely that computational biology questions motivate interesting research directions in the theory of algebraic statistics. After a brief primer in algebra and biology, we will survey some of this current literature. Students will be encouraged to select topics for study and to participate in class discussions. Course Webpage: http://math.berkeley.edu/~lpachter/275/ Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor: A. Diesl Lectures: Course Control Number: 55812 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: