Fall 2005
Math 1A - Section 1 - Calculus Instructor: Richard Borcherds Lectures: TuTh 11:00am-12:30pm, Room 2050 Valley Life Science Course Control Number: 54303 Office: 927 Evans Office Hours: TuTh 2:00-3:30pm 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. Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~reb/courses/1A/ Grading: 40% homework and quizzes, 15% each midterm, 30% final Homework: Homework is assigned on the course web page and is due once a week. Comments: Math 1A - Section 2 - Calculus Instructor: Ai-Ko Liu Lectures: MWF 10:00-11:00am, Room 2050 Valley Life Science Course Control Number: 54351 Office: 905 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1A - Section 3 - Calculus Instructor: Vaughan Jones Lectures: MWF 3:00-4:00pm, Room 10 Evans Course Control Number: 54396 Office: 929 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Nicolai Reshetikhin Lectures: MWF 11:00am-12:00pm, Room 2050 Valley Life Science Course Control Number: 54429 Office: 915 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Calculus Instructor: Nicolai Reshetikhin Lectures: MWF 2:00-3:00pm, Room 2050 Valley Life Science Course Control Number: 54477 Office: 915 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Bernd Sturmfels Lectures: TuTh 8:00-9:30am, Room 10 Evans Course Control Number: 54525 Office: 925 Evans Office Hours: WTh 10:00-11:00am Prerequisites: Three years of high school mathematics (see the General Catalog for details). Required Text: Goldstein, Lay and Scheider, Calculus and its Applications Course Webpage: http://math.berkeley.edu/~bernd/math16a.html Grading: 5% quizzes, 10 % homework, 25% each midterm, 35% final Homework: Homework will be assigned on the web page and is due once a week. Comments: Math 16A - Section 2 - Analytical Geometry and Calculus Instructor: Thomas Scanlon Lectures: MWF 3:00-4:00pm, Room 155 Dwinelle Course Control Number: 54558 Office: 723 Evans 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: 54597 Office: 779 Evans Office Hours: TBA Prerequisites: Math 16A or the equivalent Required Text: Goldstein, Lay & Schneider, Calculus and its Applications, 10th edition, Prentice-Hall (You can save $$ by purchasing the volume containing only Chapters 7-12.) Recommended Reading: 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_2005/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: 54630 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: Alex Diesl Lectures: MWF 8:00-9:00am, Room 4 LeConte Course Control Number: 54633 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Edward Frenkel Lectures: MWF 10:00-11:00am, Room 155 Dwinelle Course Control Number: 54681 Office: 819 Evans Office Hours: MWF 11:00am-12:00pm Prerequisites: Math 1B or equivalent Required Text: Stewart, Calculus: Early Transcendentals, 5th Edition, Brooks/Cole, or Custom Version for Math 53 Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~frenkel/Math53 Grading: 25% quizzes, 20% each midterm, 35% final Homework: Homework will be assigned at every class, and due once a week. Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: Alan Weinstein Lectures: TuTh 8:10-9:30am, Room 145 Dwinelle Course Control Number: 54684 Office: 825 Evans Office Hours: Tu 12:40-2:00pm, Th 9:40-11:00am Prerequisites: Mathematics 1B or equivalent Required Text: Stewart, Analytic Geometry and Calculus (Early Transcendentals), 5th Edition or Custom Version for Math 53 Recommended Reading: Syllabus: Course Webpage: Grading: The course grade will based on weekly homework and quizzes in section meetings, two midterm exams, and a final exam. The worse of the two midterm exam grades will be dropped if the final exam grade is higher; on the other hand, there will be no makeup exams. Homework: Comments: The lectures are meant as a guide and supplement to reading the text; thus, I won't lecture on every topic in detail. Students are expected to prepare by attempting the reading assignment in advance. I encourage class participation during lecture. Section meetings will be conducted for the most part in "workshop style," with students working on problems in small groups with close supervision by the graduate student instructor. A course website (see http://www.math.berkeley.edu/~alanw/) will contain homework assignments, solutions to homework problems, and a "bulletin board" for online discussion of questions relating to the course. Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Kenneth Ribet Lectures: MWF 2:00-3:00pm, Room 155 Dwinelle Course Control Number: 54768 Office: 885 Evans Office Hours: TBA Prerequisites: Math 1B Required Text: Hill, Elementary Linear Algebra; Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems Recommended Reading: Syllabus: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as 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/~ribet/54/; this page does not yet exist but will be built well in time for the beginning of the semester. Grading: Based on two midterms, the final, homework, and quizzes. The exact weights will be similar to the weights used in other lower-division math courses. Homework: Homework will be due in discussion section twice each week. Comments: The google discussion group Math54 is ready for business. Please join it so that you can post questions, answers and comments. See you in August. Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: John Neu Lectures: TuTh 12:30-2:00pm, Room 2050 Valley Life Science Course Control Number: 54813 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H54 - Section 1 - Honors Linear Algebra and Differential Equations Instructor: Robert Coleman Lectures: MWF 2:00-3:00pm, Room 4 Evans Course Control Number: 54852 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: George Bergman Lectures: MWF 1:00-2:00pm, Room 100 Lewis Course Control Number: 54858 Office: 865 Evans Office Hours: Tu 10:30-11:30am, W 4:00-5:00pm, 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: (Section references are to the textbook.)
½ hour: Appendix A-2. Pseudocode 2 hours: §1.6-§1.8. Sets and functions 2 hours: §2.1-§2.3. Algorithms, growth of functions, complexity 4 hours: §2.4-§2.6. Number theory 4 hours: §3.3-§3.4. Proofs. Summations, induction 2 hours: §3.4-§3.5. Recursion 5 hours: §4.1-§4.6. Counting 2 hours: §6.4. Generating functions 7 hours: §5.1-§5.3. Discrete Probability 6 hours: Other material. There is a bit of freedom in the course curriculum. The last time I taught Math 55 I used this to cover most of Chapter 7 (relations). This time I expect to cover instead parts of Chapter 6 (advanced counting techniques) and 8 (graphs). Homework: Weekly Comments: Math 1A-1B and (if you've had them) 53 and 54 are about smooth functions of one or more real variables; this course is about some very different topics. The main reason 1A-1B are prerequisites 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. §6.4 is related to a topic in Math 1B (power series), so students who have had 1B may find that section easier than those who have not. Nevertheless, the author's aim was to write the book so as not to assume calculus. If you haven't had calculus 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: Tom Dorsey Lectures: MWF 3:00-4:00pm, Room 289 Cory Course Control Number: 54879 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: Walter Kim Lectures: TuTh 3:30-5:00pm, Room 70 Evans Course Control Number: 54882 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 84 - Section 1 - Sophomore Seminar Instructor: Nicolai Reshetikhin Lectures: Tu 1:00-3:00pm, Room 939 Evans Course Control Number: 54884 Office: 915 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H90 - Section 1 - Honors Problem Solving Instructor: William Kahan Lectures: M 4:00-6:00pm, Room 71 Evans Course Control Number: 54885 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C103 - Section 1 Instructor: D. S. Ahn Lectures: TuTh 3:30-5:00pm, Room 3111 Etcheverry Course Control Number: 54945 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Olga Holtz Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54948 Office: 821 Evans Office Hours: WF 2-3pm and by appointment Prerequisites: Math 53 and 54 Required Text: Walter Rudin, Principles of Mathematical Analysis, Third Edition, McGraw-Hill Recommended Reading: Charles Pugh, Real Mathematical Analysis, Springer (2002) Syllabus: The real and complex number systems. Countable and uncountable sets. Metric spaces. Compactness. Connectedness. Numerical sequences and series. Continuity. Differentiation. The Riemann-Stieltjes integral. Sequences and series of functions. Course Webpage: http://www.cs.berkeley.edu/~oholtz/104/index.html Grading: 30% homework, 30% midterm, 40% final Homework: Assigned weekly. Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Beth Samuels Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54951 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Arthur Ogus Lectures: MWF 10:00-11:00am, Room 71 Evans Course Control Number: 54954 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Dapeng Zhan Lectures: TuTh 12:30-2:00pm, Room 71 Evans Course Control Number: 54957 Office: 873 Evans Office Hours: TBA Prerequisites: Math 53 and Math 54 Required Text: Kenneth A. Ross, Elementary Analysis: the Theory of Calculus Recommended Reading: Syllabus: In this course we will study basic notations of real analysis, limits and convergence, series, continuous functions, power series, differentiation and integration, and metric spaces. Course Webpage: TBA Grading: 20% homework, 20% each midterm (2), 40% final Homework: Homework will be assigned in every class, and due once a week. Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Giulio Caviglia Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54960 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H104 - Section 1 - Honors Introduction to Analysis Instructor: Yuval Peres Lectures: TuTh 9:30-11:00am, Room 334 Evans Course Control Number: 5963 Office: 341 Evans Office Hours: TBA Prerequisites: Undergraduate courses in Calculus and Linear algebra (Math 53 and 54) and enjoyment of solving challenging problems. Required Text: Charles Pugh, Real Mathematical Analysis, Springer (2002). Recommended Reading: Walter Rudin, Principles of Mathematical Analysis, Third Edition, Mcgraw-Hill. Syllabus: The real number system. Uncountable sets. Sequences and limits. Continuous functions of one and several real variables. Metric spaces: Complete, compact and connected. Uniform convergence, Infinite series. Cantor sets. Taylor polynomials and Taylor series. The Riemann integral. Course Webpage: http://www.stat.berkeley.edu/~peres/courses/H104.html Grading: Weekly homework problems (15%); Midterm (35%); Final Exam (50%). In addition, up to 10 bonus points can be obtained for making a 15 minute presentation of an advanced topic. Homework: Homework will be assigned once a week. Comments: Math 110 - Section 1 - Linear Algebra Instructor: James Demmel Lectures: MWF 1:00-2:00pm, Room 2050 Valley Life Science Course Control Number: 54966 Office: 737 Soda Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H110 - Section 1 - Honors Linear Algebra Instructor: Jenny Harrison Lectures: MWF 10:00-11:00am, Room 85 Evans Course Control Number: 54993 Office: 851 Evans Office Hours: MW 11:00am-12:00pm Prerequisites: 3.5 GPA (math) or permission of instructor Required Text: Sheldon Axler, Linear Algebra Done Right, Springer Recommended Reading: Syllabus: We will follow the text quite closely, except that I tend to add geometrical interpretations that you don't often see. Axler's approach differs from others. He has reorganized linear algebra so that it fits together in a nice theoretical package, without all the computational messiness you see when the determinant is introduced too quickly. I have used this text once before and all of us enjoyed it. But it is hard work, so be prepared! Course Webpage: Under preparation. Grading: 25% homework, 25% midterm, 50% final Homework: Homework will be assigned on the web and due once a week. Comments: This course is highly recommended as preparation for the experimental course, "Chainlet Geometry" that I will be teaching in the spring. I hope to teach the same group of students for both semesters. Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Arthur Ogus Lectures: MWF 1:00-2:00pm, Room 75 Evans Course Control Number: 54996 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Beth Samuels Lectures: TuTh 12:30-2:00pm, Room 4 Evans Course Control Number: 54999 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Alexander Givental Lectures: TuTh 3:30-5:00pm, Room 4 Evans Course Control Number: 55002 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Marc Rieffel Lectures: MWF 8:00-9:00am, Room 71 Evans Course Control Number: 55005 Office: 811 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 115 - Section 1 - Introduction to Number Theory Instructor: Martin Weissman Lectures: TuTh 2:00-3:30pm, Room 70 Evans Course Control Number: 55008 Office: 1067 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 118 - Section 1 - Wavelets and Signal Processing Instructor: Olga Holtz Lectures: MWF 11:00am-12:00pm, Room 9 Evans Course Control Number: 55011 Office: 821 Evans Office Hours: WF 2:00-3:00pm and by appointment Prerequisites: Math 53 and 54 Required Text: None Recommended Reading: Strang and Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1997 Hernandez and Weiss, A First Course on Wavelets, CRC Press, 1996 Syllabus: data representation, Fourier series and orthogonal systems, Fourier transform, multiresolution analysis (MRA), construction of wavelets via MRA, properties of wavelets and scaling functions, splines, good representation systems, signal analysis, filter banks, applications to denoising, feature detection, and image compression Course Webpage: http://www.cs.berkeley.edu/~oholtz/118/index.html Grading: 30% homework, 30% first midterm, 40% final Homework: Assigned weekly, includes programming in MATLAB Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Vera Serganova Lectures: MWF 2:00-3:00pm, Room 3111 Etcheverry Course Control Number: 55014 Office: 709 Evans Office Hours: WF 10:00-11:30am Prerequisites: Math 53,54 Required Text: M.L. Boas, Mathematical Methods for Physical Sciences, Second Edition Recommended Reading: Syllabus: We will cover chapters 1,2,4,14,7 and 15 of the book and do a lot of examples in class. Course Webpage: http://math.berkeley.edu/~serganov Grading: 20% homework, 15% for each of 2 midterms, 50% final Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 123 - Section 1 - Ordinary Differential Equations Instructor: Robert Coleman Lectures: MWF 11:00am-12:00pm, Room 4 Evans Course Control Number: 55017 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Thomas Scanlon Lectures: MWF 11:00am-12:00pm, Room 70 Evans Course Control Number: 55020 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Ming Gu Lectures: TuTh 12:30-2:00pm, Room 100 Lewis Course Control Number: 55023 Office: 861 Evans Office Hours: TBA Prerequisites: Math 53 and 54 or equivalent Required Text: R. L. Burden and J. D. Faires, Numerical Analysis, 8th ed., published by Brooks-Cole, 2005 Recommended Reading: Syllabus: In this course, we will learn some of the most basic concepts and methods in scientific computing. We will cover the first 6 chapters as well as Chapter 8 of the book. Course Webpage: Grading: The final letter grade will be determined according to class performance curve, which is based on the number of points earned in the course. In general about 1/3 of the class will get A grades, 1/3 B grades, and 1/3 C grades or worse. Homework: Homeworks will involve written assignments to be done individually as well as matlab programming assignments. Those who want to learn more about matlab should also take the one-credit course, Math 98, for basic matlab programming skills. On-line information about Math 98 is located at http://math.berkeley.edu/~yfarjoun/math98/Math_98.html. Comments: Math 130 - Section 1 - Classical Geometries Instructor: Hung-Hsi Wu Lectures: MWF 9:00-10:00am, Room 70 Evans Course Control Number: 55041 Office: 733 Evans Office Hours: TBA Prerequisites: 110 or equivalent, and 113 Required Text: Marvin J. Greenberg, Euclidean and non-Euclidean Geometries, 3rd edition, Freeman. Recommended Reading: Hartshorne, Geometry: Euclid and Beyond, Springer, 2000. Syllabus: This course will begin with an introduction to Euclidean geometry assuming a rudimentary knowledge of linear algebra, e.g., the solvability of a system of 2 by 2 equations in terms of the determinant of the matrix of the system. The purpose is to get students to rethink, from the perspective of linear algebra, what they already know about high school geometry. In effect, we will be doing axiomatic geometry using a different set of axioms, one that is less subtle (and less cumbersome) than the usual "synthetic" approach. This would provide a good preparation for the elaborate Hilbert axioms which are the main concern of the second half of the course. The Greenberg text will be used to critically examine Euclid's original work and then develop plane geometry from Hilbert's axioms. At the end of the semester, it is hoped that there will be time for at least a short introduction to hyperbolic geometry. Course Webpage: TBA Grading: Homework 20%, First midterm 10%, Second midterm 20%, Final 50%. Homework: Weekly assignments, due every Monday. Comments: Students are required to form study groups to work on the homework problems but not to copy from each other. There will be a Yahoo "groups" chat room for communications to form study groups. THERE WILL BE A PROBLEM SESSION EVERY MONDAY TO DISCUSS THE SOLUTIONS OF THE PROBLEMS *after* THE PROBLEM SET HAS BEEN HANDED IN. Math 135 - Section 1 - Introduction to Theory Sets Instructor: Jack Silver Lectures: TuTh 9:30-11:00am, Room 6 Evans Course Control Number: 55044 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 140 - Section 1 - Metric Differential Geometry Instructor: Dan Geba Lectures: MWF 8:00-9:00am, Room 81 Evans Course Control Number: 55046 Office: 837 Evans Office Hours: MWF 9:00-10:00am Prerequisites: 104 or 121B Required Text: M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976 Recommended Reading: D.J. Struik, Lectures on Classical Differential Geometry, 2nd edition, Dover Publications, 1988 Syllabus: Curves, Regular Surfaces, The Geometry of the Gauss Map, The Intrinsic Geometry of Surfaces Course Webpage: http://math.berkeley.edu/~dangeba/140F05 Grading: Homework 25%, Midterm 25%, Final 50% Homework: Homework is due by the end of the Friday lecture, one week after it was assigned. Late homework will not be accepted. Worst 3 grades do not count. Comments: I plan to cover roughly the first 4 chapters of do Carmo's book. Math 160 - Section 1 - History of Mathematics Instructor: Mariusz Wodzicki Lectures: MWF 3:00-4:00pm, Room 241 Cory Course Control Number: 55050 Office: 995 Evans Office Hours: TBA Prerequisites: Math 104, 110 and 113 (or my consent) Required Text: Richard Gillings, Mathematics in the Time of the Pharaohs, Dover Publications Otto Neugebauer, The Exact Sciences in Antiquity, Dover Publications Thomas Ivor (editor), Greek Mathematical Works I/II, Loeb Classical Library, Nos. 335 & 362, Harvard University Press Recommended Reading: Carl B. Boyer, A History of Mathematics, John Wiley & Sons Syllabus: In an introductory course on History of Mathematics nothing can replace a first hand experience of working with original texts. We will focus on a number of such texts from various historical epochs. This will be supplemented by my lectures in which I will be presenting a panoramic overview of the development of Mathematics in its cultural perspective. Course Webpage: http://math.berkeley.edu/~wodzicki/160 Grading: Midterm 15%, Final 30%, 2 term papers (15% each), quizzes, homework & class participation 25% Homework: Homework assignments will take various forms; reading assignments will be given after every class. Comments: Students are expected to attend the class regularly. 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 Midterm. Math 172 - Section 1 - Combinatorics Instructor: Kevin Woods Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 55053 Office: 867 Evans Office Hours: TBA Prerequisites: It is NOT at all necessary to have taken Math 55 (Discrete Mathematics), even though the catalog lists it as a prerequisite. The only prerequisite is the readiness to take an upper-divisional, proof-oriented course. Required Text: Bogart, Introductory Combinatorics, 3rd Edition, Brooks/Cole. Recommended Reading: None. Syllabus: This will be an introduction to various topics in combinatorics, which is, loosely, the mathematics of examining discrete objects and doing things like counting them, constructing them, and finding algorithms to analyze them. We will definitely cover some enumeration and graph theory, and then we will sample a few topics which might include generating functions, polyhedral geometry, coding theory, and combinatorial games. Course Webpage: http://math.berkeley.edu/~kwoods/Math172.html Grading: TBA. Probably will include problem sets, a project, and a final exam. Homework: Problem sets will be assigned periodically throughout the semester, approximately every 2 weeks. Comments: How many different 8-bead pearl necklaces can be made using black and white pearls? If 50 people each bring one gift to a Christmas party and exchange them at random, what is the chance that no one ends up with their own gift? Are there any 3-dimensional shapes with exactly 10 faces, 18 edges, and 10 vertices? Given a network of roads, what is the shortest way from my house to my Aunt Susie’s? How should I encode music onto a CD so that, even if it gets a scratch, I can still play it? These are the sorts of questions we will look at in this class. Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Michael Klass Lectures: MWF 12:00-1:00pm, Room 71 Evans Course Control Number: 55056 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Michael Christ Lectures: TuTh 2:00-3:30pm, Room 289 Cory Course Control Number: 55059 Office: 809 Evans 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: TuTh 3:30-5:00pm, Room 75 Evans Course Control Number: 55062 Office: 873 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, 7th edition, the McGraw-Hill companies. Recommended Reading: Syllabus: Complex Numbers, Analytic Function, Complex Integral, Cauchy Theorem, Cauchy Formula, Power Series, Laurent Series, Residues, Residue Formula, Linear Transformation, Conformal Mapping, Harmonic Functions, and etc. Course Webpage: TBA Grading: 20% homeworks, 20% each midterm, 40% final Homework: Homework will be assigned on Tuesday and due next Tuesday. Comments: Math 191 - Section 1 - High School Mathematics from an Advanced Perspective Instructor: Emiliano Gomez Lectures: MW 4:30-6:30pm, Room 230-D Stephens Hall Course Control Number: 55065 Office: 985 Evans Office Hours: TBA Prerequisites: One year of Calculus and one upper-level math course, or permission of the instructor. Also, interest in teaching. Required Text: Usiskin, Peressini, Marchisotto and Stanley, Mathematics for High School Teachers: an Advanced Perspective, Prentice Hall, 2003. Recommended Reading: Journals like NCTM's Mathematics Teacher Syllabus: Content to be selected from the following topics: elementary functions and their properties; equations; rings of integers and polynomials; divisibility, fundamental theorem of arithmetic; induction and well ordering; modular arithmetic; fields of rational, real, and complex numbers; ordered and complete fields; geometry from synthetic, analytic, and transformational approaches; isometries and similarity; axioms of Euclidean geometry; area and volume; and historical perspectives on results from algebra and geometry. Course Webpage: Grading: Based on weekly homework, one or two midterms, and a final project and presentation. Homework: Weekly assignments. Comments: Be prepared to work in small groups and to participate actively in class. There will be more problem solving and discussion than lecturing. Math 202A - Section 1 - Introduction to Topology and Analysis Instructor: Donald Sarason Lectures: MWF 12:00-1:00pm, Room 3 LeConte Course Control Number: 55137 Office: 779 Evans Office Hours: TBA Prerequisites: Math 104 or the equivalent, plus familiarity with basic set theory, including Zorn's lemma. Required Text: Gerald B. Folland, Real Analysis, Second Edition, Wiley-Interscience, 1999 Recommended Reading: Syllabus: POINT-SET TOPOLOGY. Fundamentals (such as open and closed sets, convergence, continuity, connectedness, boundary, closure, interior, etc.), metric spaces, product spaces, compactness, separation axioms, theorems of Urysohn and Tietze, locally compact spaces, quotient spaces, spaces of continuous functions, Stone-Weierstrass theorem, Arzela-Ascoli theorem, metrization. MEASURE AND INTEGRATION. Sigma-rings and sigma-algebras, measures and outer measures, extensions of measures, Lebesgue measure in Euclidean spaces, integration, convergence theorems. Course Webpage: Grading: The course grade will be based on homework. There will be no exams. Homework: Homework will be assigned weekly and will be carefully graded. Comments: The lectures will be self-contained except for routine details. While the textbook contains most of the course material, the lectures will deviate from the book in the order in which the material is covered and, frequently, in the approach to the material. Math 204A - Section 1 - Ordinary and Partial Differential Equations Instructor: Fraydoun Rezakhanlou Lectures: TuTh 11:00am-12:30pm, Room 5 Evans Course Control Number: 55140 Office: 815 Evans Office Hours: MTuTh 3:00-4:00pm Prerequisites: Math 104 Required Text: Recommended Reading: Syllabus: This course reviews some fundamental concepts and results in the theory of ordinary differential equations and dynamical systems. Here is an outline of the course: 1. Fundamental existence theorem for ordinary differential equations. 2. Properties of linear systems with constant and periodic coefficients. 3. Sturm-Liouville theory. 4. Poincare-Bendixson Theorem 5. Rotations numbers, twist maps. Course Webpage: Grading: Weekly homework assignments and a final take-home exam. Homework: Comments: Math 206 - Section 1 - Banach Algebras and Spectral Theory Instructor: Marc Rieffel Lectures: MWF 10:00-11:00am, Room 51 Evans Course Control Number: 55143 Office: 811 Evans Office Hours: TBA Prerequisites: Math 202AB or equivalent. Student who have studied only part of the material of Math 202AB and wish to enroll in Math 206 should discuss this with me. Required Text: John B. Conway, A Course in Functional Analysis, 2nd ed., Springer-Verlag Syllabus: I will be teaching Math 208, C*-algebras, in the Spring, and I will organize Math 206 and Math 208 as a year-long course, but I will do so in such a way that Math 206 still works well as a stand-alone course too. Math 208 will be an introduction to the exciting ideas of Alain Connes concerning non-commutative differential geometry and its many applications. Essentially all of the material of Math 206 is important for Connes' program, and in Math 206 I will try to indicate briefly how the various topics may find use in Math 208. The theory of Banach algebras is a very elegant blend of algebra and topology which provides unifying principles for a number of different parts of mathematics, notably operator theory, commutative and non-commutative harmonic analysis and the theory of group representations, and the theory of functions of one and several complex variables. But at the present time its most extensive use is as a foundation for non-commutative measure theory (von Neumann algebras, Math 209) and non-commutative topology and geometry (C*-algebras, Math 208). These in turn provide a foundation for quantum physics, but they also have myriad applications in many other directions, including group representations and harmonic analysis, ordinary topology and geometry, and even number theory. (For a vast panorama of the applications see Connes' book "Noncommutative Geometry".) In Math 206 I will cover the standard topics as listed in the catalog. Beyond the basic general theory of Banach algebras this will include several forms of the spectral theorem for self-adjoint operators on Hilbert space, Hilbert-Schmidt and Fredholm operators, and group algebras and the Fourier transform. Grading: I will give out almost weekly problem sets. There will be no final examination. Math 215A - Section 1 - Algebraic Topology Instructor: Michael Hutchings Lectures: TuTh 9:30-11:00am, Room 9 Evans Course Control Number: 55146 Office: 923 Evans Office Hours: TBA Prerequisites: The only formal requirements are some basic algebra, point-set topology, and "mathematical maturity". However, the more familiarity you have with algebra and topology, the easier this course will be. Required Text: Hatcher, Algebraic Topology Recommended Reading: Bredon, Topology and Geometry Syllabus: Algebraic topology seeks to capture the essence of a topological space in terms of various algebraic and combinatorial objects. We will construct and apply three such gadgets: the fundamental group, homology groups, and the cohomology ring. Much but by no means all of the course content is in the book by Hatcher. I will place somewhat more emphasis on the topology of manifolds. Course Webpage: Will be linked from http://math.berkeley.edu/~hutching Grading: A reasonable effort on homework will result in a good grade. Homework: There will be some homework. Comments: Math C218A - Section 2 - Probability Theory Instructor: James Pitman Lectures: TuTh 2:00-3:30pm, Room 332 Evans Course Control Number: 55151 Office: 303 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 221 - Section 1 - Advanced Matrix Computation Instructor: William Kahan Lectures: MWF 3:00-4:00pm, Room 5 Evans Course Control Number: 55152 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 222A - Section 1 - Partial Differential Equations Instructor: Maciej Zworski Lectures: TuTh 12:30-2:00pm, Room 7 Evans Course Control Number: 55155 Office: 897 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 224A - Section 1 - Mathematical Methods for the Physical Sciences Instructor: Fraydoun Rezakhanlou Lectures: TuTh 12:30-2:00pm, Room 5 Evans Course Control Number: 55158 Office: 815 Evans Office Hours: MTuTh 3:00-4:00pm Prerequisites: Math 104 Required Text: None Recommended Reading: Syllabus: The majority of the fundamental processes of our natural world are described by differential equations. Some examples are the vibration of solids, the flow of fluids, the formation of crystals, the spread of infections, the diffusion of chemicals, the structure of molecules, etc. These examples are responsible for our interest in partial differential equations such as Hamilton-Jacobi equation, Euler equation, Navier-Stokes equation, Diffusion equation, Wave equation and Korteweg-deVries equation. As the primary goal of the course, I discuss some of the above equations and explain some mathematicals tools that are needed to solve them. I also use these equation as an excuse to introduce students to some basic questions in fluid mechanics and statistical physics. Some of the topics are: 1. Advection, diffusion, Brownian motion, sources, Green's function. 2. Fluid mechanics, Euler equation, incompressible limit, shallow water equation. 3. Shock waves, Rarefaction waves, Riemann invariants. 4. Similarity methods. 5. Scattering theory, Korteweg-deVries equation. There is no required text and I will distribute handwritten notes in the class. Course Webpage: Grading: There will be weekly homework assignments (due Tuesdays) and one take-home exam. Homework: Comments: Math 225A - Section 1 - Metamathematics Instructor: Jack Silver Lectures: TuTh 12:30-2:00pm, Room 51 Evans Course Control Number: 55161 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 227A - Section 1 - Theory of Recursive Functions Instructor: Leo Harrington Lectures: MWF 11:00am-12:00pm, Room 71 Evans Course Control Number: 55164 Office: 711 Evans 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 9:30-11:00am, Room 85 Evans Course Control Number: 55167 Office: 1099 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 242 - Section 1 - Symplectic Geometry Instructor: Alan Weinstein Lectures: TuTh 11:10am-12:30pm, Room 81 Evans Course Control Number: 55170 Office: 825 Evans Office Hours: Tu 12:40-2:00pm, Th 9:40-11:00am Prerequisites: Math 214 or equivalent familiarity with basic material on differentiable manifolds, including vector fields, differential forms, and Lie groups. I will occasionally use results and ideas from other areas of mathematics, such as functional analysis and algebraic topology. When I do, I will give references for the required background material. Required Text: Cannas da Silva, Lectures on Symplectic Geometry, Springer Lecture Notes in Mathematics Recommended Reading: Syllabus: Course Webpage: See http://math.berkeley.edu/~alanw. Grading: The grade will be based on homework, class participation, and an expository paper on some aspect of symplectic geometry or its applications. Homework: Comments: This course is meant to equip the student with a knowledge of the essential definitions, methods, and results in symplectic geometry, either for the further study of symplectic geometry itself, or for applications to other fields of mathematics and mathematical physics (e.g. topology, representation theory, algebraic geometry, partial differential equations, classical and quantum mechanics and field theory). As per the catalog, I will discuss symplectic linear algebra, symplectic manifolds, Darboux's theorem, cotangent bundles, variational problems and Legendre transform, hamiltonian systems, lagrangian submanifolds, Poisson brackets, symmetry groups and momentum mappings, coadjoint orbits and Kahler manifolds. If time remains at the end, I will go further into Poisson geometry or, perhaps, supermanifolds and their symplectic geometry. Math 249 - Section 1 - Algebraic Combinatorics Instructor: Lior Pachter Lectures: TuTh 3:30-5:00pm, Room 85 Evans Course Control Number: 55173 Office: 1081 Evans Office Hours: W 1:00-3:00pm Prerequisites: Basic knowledge of abstract algebra and linear algebra is essential. An undergraduate course in combinatorics would be helpful, but is not required. Required Text: Recommended Reading: Gian-Carlo Rota, Combinatorial Theory (1999) and Richard P. Stanley, Enumerative Combinatorics (1986,1997,1999) Syllabus: Course Webpage: http://math.berkeley.edu/~lpachter/249/ About the Course: In 1963 Gian Carlo Rota taught his first course on combinatorics at Harvard University. With his course, he began a tradition of algebraic combinatorics that draws on, and continues to inspire, a wide range of mathematics. At the the same time, his style combined an intuitive approach to the subject with a delightful sense of humor. He also emphasized applications ranging from algebraic geometry to probability theory. The last time his course was offered was in the Fall of 1998 at MIT. In the 35 years that had elapsed since the course had been developed the field and its scope had changed enormously. There had also been a proliferation of new textbooks, such as the excellent "Enumerative Combinatorics" by Richard Stanley (who took the course in 1967). Starting with his favorite companion to combinatorics, lattice theory, Rota proceeded to highlight many of the classic (often forgotten) results that are routinely omitted from textbooks and courses. Fortunately, a student in the class, John N. Guidi, preserved his lectures and wit in a carefully compiled series of lecture notes. Our own course will be based on this material, supplemented by other texts and recent research papers. We will begin by reviewing sets and relations, and basic enumeration. We will then study lattices and projective space, followed by matching and matroid theory. Time permitting, we will discuss other topics such as geometric probability, tropical mathematics, and applications of algebraic combinatorics in biology. Grading: Exercises will be assigned during the lectures, and will be due a week or two after being assigned. The final grade will be based solely on the homework. Homework: Comments: Math 250A - Section 1 - Groups, Rings, and Fields Instructor: Paul Vojta Lectures: MWF 1:00-2:00pm, Room 70 Evans Course Control Number: 55176 Office: 883 Evans Office Hours: TBA Prerequisites: 114 or consent of instructor Required Text: Lang, Algebra, Springer Recommended Reading: None Syllabus: Current plans call for covering the first four chapters of the book, plus material from Chapters V, VI, VIII, and X. For a current list, see the course web page. Course Webpage: http://math.berkeley.edu/~vojta/250a.html Grading: 15% midterm, 35% final exam, 50% homework Homework: Homework will be due every week or two Comments: Although the basic definitions of groups, etc., will be introduced from scratch, they will be covered at a pace that requires knowledge of the material already from an undergraduate-level course. The second semester of this course will be taught by Prof. Sturmfels and is likely to emphasize commutative algebra, in preparation for algebraic geometry. Math 252A - Section 1 - Representation Theory Instructor: Vera Serganova Lectures: MWF 12:00-1:00pm, Room 5 Evans Course Control Number: 55179 Office: 709 Evans Office Hours: WF 10:00-11:30am Prerequisites: Math 250A Required Text: No required text, lecture notes will be posted on the web. Recommended Reading: Syllabus: Serre, Linear representations of finite groups, Gabriel, Roiter, Representations of finite-dimensional algebras, Fulton, Harris, Representation theory. The course will have two parts. First, we study representations of finite groups. Topics included: characters, complete reducibility, induced representations, Artin's and Brauer's theorems. I plan to do many examples and cover representations of symmetric groups and Schur-Weyl duality. Then we discuss representations of semi-simple algebras and Wedderburn-Artin's theorem. The second part of the course concerns the case when category of representations is not semi-simple. The notions of projective and indecomposable modules and extensions will be introduced. We will discuss representation theory of quivers as a main example. Hopefully I will have time to prove the Gabriel's theorem about tame quivers. Course Webpage: http://math.berkeley.edu/~serganov Grading: 50% homework, 50% take home final Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 254A - Section 1 - Number Theory Instructor: Brian Osserman Lectures: MWF 11:00am-12:00pm, Room 65 Evans Course Control Number: 55182 Office: 767 Evans Office Hours: TBA Prerequisites: Math 250A required, 115 and 250B recommended Required Text: Lang, Algebraic Number Theory Recommended Reading: Cox, Primes of the form x^{2}+ny^{2} Syllabus: Roughly, we will cover algebraic number theory from scratch, using Lang's book with examples and motivation from other sources. Advanced topics such as class field theory and Tchebotarev density will be discussed with an emphasis on the statements and applications, so proofs of these will be omitted, and they will be treated in the classical language of ideals rather than ideles and group cohomology. Course Webpage: http://math.berkeley.edu/~osserman/classes/254a Grading: TBA Homework: Homework will most likely be assigned weekly. Math 256A - Section 1 - Algebraic Geometry Instructor: Mark Haiman Lectures: MWF 2:00-3:00pm, Room 5 Evans Course Control Number: 55185 Office: 771 Evans Office Hours: TBA Prerequisites: Math 250A Required Text: Qing Liu, Algebraic Geometry and Arithmetic Curves, Oxford University Press, 2002. Recommended Reading: A. Grothendieck, Éléments de géométrie algébrique, I-IV, Publications Mathématiques de l'IHES, vols. 4, 11, 17, 20, 24, 28, 32; A. Grothendieck and collaborators, Séminaire de Géométrie Algébrique, 1-7. Syllabus: See course web page. Course Webpage: Math 256AB Web Page Grading: Based on homework. Homework: Problems assigned on the web approximately weekly. Comments: Math 257 - Section 1 - Geometric Group Theory Instructor: John Stallings Lectures: MWF 10:00-11:00am, Room 39 Evans Course Control Number: 55188 Office: 801 Evans Office Hours: Possibly 11:00-12:00 MWF, but other times are possible depending on the needs of the audience. Prerequisites: Required Text: Recommended Reading: Syllabus: This course will be devoted to items about free groups and presentations of groups, and some other items, such as basic category theory. As far as I can tell now, I won't prove the Poincare Conjecture. Course Webpage: www.math.berkeley.edu/~stall/math257 Grading: Homework: Comments: There are items of notes on my web page that are related to this course. Some of these will be expanded and changed a bit. Various items of more recent work, especially on free groups, may be taken up. I also like several books, such as "Combinatorial Group Theory", one book by Magnus et al., another one by Lyndon et al., a more recent one by de la Harpe. Math 275 - Section 1 - Topics in Applied Mathematics Instructor: Jon Wilkening Lectures: MWF 12:00-1:00pm, Room 75 Evans Course Control Number: 55193 Office: 1091 Evans Office Hours: TBA Prerequisites: There are no formal prerequisites, although familiarity with at least Laplace's equation and some form of numerical computation (e.g. numerical linear algebra or ODE's) will be assumed. Required Text: Recommended Reading: Syllabus: In this course, we will study fundamental aspects of the finite element and boundary integral methods for solving elliptic equations, especially the Poisson equation, the equations of elasticity, and the Stokes equations. I will also cover more advanced topics including mixed finite element methods, corner singularities, least squares finite elements, the calculus of variations, shape optimization, the Navier-Stokes equations (in the velocity-pressure and vorticity-stream formulations), fast linear solvers, grid generation, and various competing methods such as the immersed interface and immersed boundary methods. My goal is to present a wide array of interesting numerical methods for solving partial differential equations which aren't normally covered in Math 228b so the students won't immediately default to using finite differences when faced with new computational problems. Course Webpage: http://math.berkeley.edu/~wilken/teaching/fall05.html Grading: Homework: Comments: Math 276 - Section 1 - Topics in Topology Instructor: Peter Teichner Lectures: TuTh 12:30-2:00pm, Room 65 Evans Course Control Number: 55194 Office: 703 Evans Office Hours: TBA Prerequisites: Basic algebraic and differential topology Required Text: Recommended Reading: What is an elliptic object? with Stephan Stolz, available on my homepage http://math.berkeley.edu/~teichner/ Syllabus: In this topics course we'll study one particular extra-ordinary cohomology theory, elliptic cohomology, from a geometrical point of view, namely via conformal field theory. During the previous semester we looked at elliptic cohomology from a purely homotopy theoretical point of view using formal group laws. Most material from that course is not required and those parts that are will be reviewed carefully. Course Webpage: Grading: Homework: Comments: Math 279 - Section 1 - Topics in Nonlinear Elliptic Equations Instructor: Neil Trudinger Lectures: TuTh 2:00-3:30pm, Room 39 Evans Course Control Number: 55196 Office: Office Hours: TBA Prerequisites: Required Text: Gilbard & Trudinger, Elliptic Partial Differential Equations of the Second Order, Springer, 2001 Recommended Reading: Syllabus: In recent decades there has been a phenomenal increase in the applications of the theory of nonlinear elliptic partial differential equations. Contemporary applications lie within mathematics itself, notably in geometry, and throughout science and technology in the wake of applications to the resurgent theory of optimal transportation. This course will treat the basic theory necessary for applications. Topics will include the Schauder theory of linear equations, the DeGiorgi-Nash estimates and their applications to the calculus of variations, the Krylov-Safonov estimates and their application to the theory of fully nonlinear equations, equations of Monge-Ampere type and their application to optimal transportation. Course Webpage: Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor: Hung-Hsi Wu Lectures: W 4:00-6:00pm, Room 247 Cory Course Control Number: 55869 Office: 733 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: |