Fall 2003
Math 1A  Section 1  Calculus Instructor: Garth Dales Lectures: TuTh 12:302:00pm, Room 2050 Valley Life Science Course Control Number: 54303 Office: Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 1A  Section 2  Calculus Instructor: HungHsi Wu Lectures: MWF 10:0011:00am, Room 1 Pimental Course Control Number: 54354 Office: 733 Evans, email: wu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Trigonometry and analytic geometry Syllabus: Essentially the first six chapters of the text will be covered. Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Grading: 20% homework and quizzes, 10% Midterm 1, 20% Midterm 2, 50% final. Homework: Weekly assignments given on the web. Group work among students is encouraged. Comments: The lectures will generally follow the text, but there will be minor deviations. A course schedule giving the sections of the text that will be covered each week will be made available on the web. Students are required to read the text in advance of the lectures. Both mathematical reasoning and techniques for solving problems will be emphasized. This is emphatically not a cookbook course. For the exams, students will be responsible for a small number of proofs in the text, e.g., the proof of the Fundamental Theorem of Calculus, but about 80% of the exam question will be close to the assigned homework problems. This means that each student has almost complete control over his/her grades: just work hard at the homework problems week in and week out. The course progresses very rapidly by high school standards. Good work habits are required for survival in this course. Math 1A  Section 3  Calculus Instructor: Jenny Harrison Lectures: MWF 3:004:00pm, Room 115 Dwinelle Course Control Number: 54405 Office: 851 Evans, email: harrison [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 1B  Section 1  Calculus Instructor: Ole Hald Lectures: MWF 9:0010:00am, Room 155 Dwinelle Course Control Number: 54438 Office: 875 Evans, email: hald [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 1B  Section 2  Calculus Instructor: Charles Pugh Lectures: TuTh 2:003:30pm, Room 155 Dwinelle Course Control Number: 54489 Office: 829 Evans, email: pugh [at] math [dot] berkeley [dot] edu Office Hours: TBA Comments: There is a course webpage here. Math 16A  Section 1  Analytical Geometry and Calculus Instructor: Leo Harrington Lectures: TuTh 3:305:00pm, Room 1 Pimental Course Control Number: 54525 Office: 711 Evans, email: leo [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 16A  Section 2  Analytical Geometry and Calculus Instructor: John Wagoner Lectures: MWF 11:00am12:00pm, Room 155 Dwinelle Course Control Number: 54567 Office: 899 Evans, email: wagoner [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 16B  Analytical Geometry and Calculus Instructor: Robin Hartshorne Lectures: MWF 8:009:00am, Room 10 Evans Course Control Number: 54612 Office: 881 Evans, email: robin [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 24  Section 1  Freshman Seminars Instructor: Jenny Harrison Lectures: F 4:00pm5:00pm, Room 72 Evans Course Control Number: 54651 Office: 851 Evans, email: harrison [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 24  Section 2  Freshman Seminars Instructor: Nicolai Reshetikhin Lectures: M 3:00pm5:00pm, Room 891 Evans Course Control Number: 54653 Office: 945 Evans, email: reshetik [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 32  Precalculus Instructor: GSI  TBA Lectures: MWF 8:009:00am, Room 2060 Valley Life Science Course Control Number: 54654 Office: Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 53  Multivariable Calculus Instructor: Michael Hutchings Lectures: TuTh 8:009:30am, Room 155 Dwinelle Course Control Number: 54702 Office: 923 Evans, email: hutching [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 53M  Multivariable Calculus With Computers Instructor: Mariusz Wodzicki Lectures: MWF 12:001:00pm, Room 390 Hearst Mining Course Control Number: 54759 Office: 995 Evans, email: wodzicki [at] math [dot] berkeley [dot] edu Office Hours: F 1:102:30pm Prerequisites: Math 1B with a grade B or better. Syllabus: In this course, I will introduce students to the elements of Theory of Differential Forms. Familiarity with differential forms is a necessity for students of Mathematics, Physics and Engineering, yet the subject is rarely taught at the (non Honors) undergraduate level. An added bonus is that topics that are complicated and cumbersome in the traditional approach become clear and transparent when one uses the language of differential forms. The students should be advised that Multivariable Calculus is a serious course, much harder than Math 1A/B, which rewards dedication and discipline. Regular lecture attendance is practically a requirement. My intention is to make lectures an exciting experience which opens "windows onto previously unknown worlds". I will not be using a third party's textbook. My own text will be available on the course web page to students enrolled in the class. Prior familiarity with at least basics of Linear Algebra is a clear advantage in learning Multivariable Calculus. Therefore, it makes sense to take this course either in parallel with Math54, or Math54M, or to take Math54, or Math54M, before taking Math53M. Computers will be used mostly for visualization purposes. Previous programming experience is not essential, though helpful. Since I am expecting a certain minimum level of preparation for this course, I require grade B, or better, on Math1B (or an equivalent) from prospective students. Before enrolling, any student should work through a 12 page document entitled Preliminaries. If you struggle with the material it contains, then this course is probably not for you and you should not enroll in it. All students will be tested in the second week of the class on this material. By enrolling in this class you consent to the fact that you can take the Final Exam at the date and time prescribed by the University. No makeup finals will be given. Required Text: See above. Recommended Reading: Harley Flanders, Differential Forms with Applications to the Physical Sciences, Dover Publications, 1989 (originally, Academic Press, 1963). Grading: Based on two midterms (20 percent) whose dates will be announced during the first week of classes, the final (30 percent), homework (20 percent), and the work in discussion sections (10 percent). Homework: Weekly; collected in your discussion section every Thursday. Math H53  Multivariable Calculus  Honors Instructor: Kevin Hare Lectures: MWF 12:001:00pm, Room 71 Evans Course Control Number: 54753 Office: 767 Evans, email: kghare [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 1B Recommended Prerequisite: Math 1B with a grade of B or higher. Syllabus: I plan to cover Chapters 10 through 16 of the book (except for Chapter 11), plus additional material that I think is interesting. Chapter 10. Parametric equations and polar coordinates. Chapter 12. Vectors in R^{2} and R^{3} Chapter 13. Vector functions Chapter 14. Partial derivatives Chapter 15. Multiple integrals Chapter 16. Vectors calculus Required Text: Stewart, Calculus: Early Transcendentals, 4th ed. Grading: Grades will be based on weekly quizzes (ten of which count) (20%), two inclass midterm (40%), and the Final Exam (40%) Homework: There will be homework assigned weekly. The homework will not be due, but quizes will be based on the homework questions. Comments: There will be a webpage for the Course maintained at http://www.math.berkeley.edu/~kghare/Courses/MathH53.html Math 54  Linear Algebra and Differential Equations Instructor: Allen Knutson Lectures: TuTh 11:00am12:30pm, Room 2050 Valley Life Science Course Control Number: 54780 Office: 1033 Evans, email: allenk [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 54M  Linear Algebra and Differential Equations Instructor: Ming Gu Lectures: MWF 3:004:00pm, Room 10 Evans Course Control Number: 54831 Office: 861 Evans, email: mgu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 55  Discrete Mathematics Instructor: John Strain Lectures: TuTh 2:003:30pm, Room 2050 Valley Life Science Course Control Number: 54849 Office: 1099 Evans, email: strain [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 1AB strongly recommended. Some knowledge of computer science helpful. Syllabus: Chapters 17 of the text will be covered thoroughly, plus supplementary notes on probability theory by Prof. Lenstra. Required Text: K.H. Rosen, Discrete Mathematics and Its Applications, 5th edition, McGrawHill, 2003. Recommended Reading: Student Solutions Guide for Rosen's text. Grading: Homework 10%, Quizzes 10%, Midterms 20% each, Final 40%. Math 74  Transition to Upper Division Mathematics Instructor: GSI  TBA Lectures: MWF 3:004:00pm, Room 277 Cory Course Control Number: 54873 Office: Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math H90  Honors Problem Solving Instructor: Staff Lectures: M 4:006:00pm, Room 31 Evans Course Control Number: 54876 Office: Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 104  Section 1  Introduction to Analysis Instructor: Laurent Bartholdi Lectures: TuTh 9:3011:00am, Room 75 Evans Course Control Number: 54936 Office: 1073 Evans, email: laurent [at] math [dot] berkeley [dot] edu Office Hours: Tu(Th) 1:002:00pm at Cafe Strada, Bancroft @ Telegraph Prerequisites: Math 53 and 54 Syllabus: 1. Introduction: Basic concepts of logic and set theory. Functions. Natural numbers and induction. Field axioms and real numbers. Completeness axiom. 2. Sequences: Limit theorems. Cauchy sequences. Metric space topology. Compactness. HeineBorel Theorem. Series. 3. Continuity: Basic properties of continuous functions. Uniform continuity. Limits of functions. Continuity and connectedness in metric spaces. 4. Sequences and series of functions: Power series. Uniform convergence. Convergence tests. Weierstrass' Approximation Theorem. 5. Differentiation: Basic properties of differentiation. The Mean Value Theorem. Taylor's Theorem. 6. Integration: The Rieman Integral. Fundamental Theorem of Calculus. RiemanStieltjes Integral. Required Text: Kenneth A. Ross, The Elementary Theory of Calculus Recommended Reading: Walter Rudin, Principles of Mathematical Analysis Grading: 20% min(MID,HW), 40% max(MID,HW), 40% final Homework: Weekly, graded. Comments: This is usually a difficult class, that requires substantial personal effort from students. More information can be found on the class website Math 104  Section 2  Introduction to Analysis Instructor: George M. Bergman Lectures: MWF 11:00am12:00pm, Room 71 Evans Course Control Number: 54939 Office: 865 Evans, email: gbergman [at] stat [dot] berkeley [dot] edu Office Hours: Tu 1:302:30pm, Th 10:3011:30am, F 4:155:15pm Prerequisites: Math 53 and 54. (Math 74, which may be taken simultaneously, is also strongly recommended for students not familiar with proofs.) Syllabus: We will cover Chapters 17 of the text. Required Text: W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGrawHill Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam, 35%; regular submission of the daily question (see below), 5%. Homework: Weekly, generally due Wednesdays. Comments: This is the course in which the material you saw in calculus is put on a solid mathematical basis. It begins with the properties of the real numbers that underlie these results. It will be for some of you the first course in which you are expected, not to calculate answers, but to give proofs. This transition, though intellectually exciting, is difficult for many students. I will bear in mind that the function of the course is not just to teach you Real Analysis, but also to introduce you to mathematical reasoning, and that it is my job to help you with the one as much as the other. Students who think they will have particular difficulty with proofs are advised to take Math 74 simultaneously. I don't like the conventional lecture system, where students spend the hour copying the contents of the course from the blackboard into their notebooks. Hence I will assign readings in the text, and conduct the class on the assumption that you have done this reading and thought about the what you've read. In lecture I may go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, discuss points to watch out for in the next reading, etc.. On each day for which there is assigned reading (usually Mondays and Fridays), each student is required to submit, in writing or (preferably) by email, a question on the reading. (If there is nothing in the reading that you don't understand, you can submit a question marked "pro forma", together with its answer.) I try to incorporate answers to students' questions into my lectures; when I can't do this I may instead answer your question by email. More details on this and other matters will be given on the course handout distributed in class the first day, and available on the door to my office thereafter. Many students find Rudin a difficult text. If your response to this would be to put it aside and try to learn from the lectures alone, I advise you not to take my section. The author writes clearly, but writes as a mathematician, and in lecture I will try to help you understand him, not replace him. Math 104  Section 3  Introduction to Analysis Instructor: Dan Geba Lectures: MWF 2:003:00pm, Room 75 Evans Course Control Number: 54942 Office: 837 Evans, email: dangeba [at] math [dot] berkeley [dot] edu Office Hours: MW 3:004:30pm Prerequisites: Math 53 and 54 Syllabus: Real number system. Sequences. Series. Metric spaces. Continuous functions. Differentiation in one variable. Riemann integral. Required Text: K.A. Ross, Elementary Analysis Recommended Reading: W. Rudin, Principles of Mathematical Analysis Grading: Homework (30%), Midterm (30%), Final (40%) Homework: Assigned on Friday, due next Friday. The worst 3 homeworks will not be included in the final grade. No late homeworks. No makeup exams. Math 104  Section 4  Introduction to Analysis Instructor: Keith Miller Lectures: TuTh 12:302:00pm, Room 75 Evans Course Control Number: 54945 Office: 803 Evans, email: kmiller [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 104  Section 5  Introduction to Analysis Instructor: Daniel Tataru Lectures: TuTh 2:003:30pm, Room 75 Evans Course Control Number: 54948 Office: 841 Evans, email: tataru [at] math [dot] berkeley [dot] edu Office Hours: Th 9:3010:30am, F 10:0011:00am Prerequisites: Math 53 and 54 Syllabus: Chapters 17 of the text. Required Text: W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGrawHill Grading: 25% homeworks, 25% the midterm, 50% the final Homework: Homework is assigned on the course web page, and due once a week. Comments: For many students this is the first course in which you learn mathematics in a rigurous way. This means that the emphasis now is not on computational abilities but instead on giving proofs and using mathematical reasoning. To ease this transition the course will start slowly and pick up the pace later on. The textbook I chose is quite demanding, but it also has the advantage of being one of the best around. Math 104  Section 6  Introduction to Analysis Instructor: Donald Sarason Lectures: MWF 3:00pm4:00pm, Room 3 Evans Course Control Number: 54951 Office: 779 Evans, email: sarason [at] math [dot] berkeley [dot] edu (Do not contact me by email except in a dire emergency. If you have a question about the course, see me in my office, preferably during office hours or by appointment, or try to reach me by phone (6423521).) Office Hours: MW 9:3011:30am Prerequisites: Math 53 and 54 Syllabus: Most of the textbook and a certain amount of supplementary material will be covered. The aim of the course is to develop rigorously the basic ideas underlying calculus (and much of the rest of mathematics). This will start with a detailed study of the system of real numbers. The notions of convergence and continuity will be examined, and will be shown to apply in a very general setting, that of metric spaces. The two fundamental operations of calculus, differentiation and integration, will be developed from scratch. Along the way one encounters surprises: a continuous functions that is nowhere differentiable, a spacefilling curve, the Cantor ternary set (the original fractal). Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, SpringerVerlag, 1980 Grading: Homework, 20%; two midterm examinations, 20% each; final examination, 40% Homework: Homework will be due most Wednesdays. It should be handed in at the beginning of class. Late papers will not be accepted. Exams: The final exam is scheduled for Friday, December 12, 12:303:30 p.m. (Exam Group 8). The schedule for the midterm exams is to be decided. There will be no makeup exams. Accordingly, do not register for this section if you have a conflict. Comments: A tutor for Math 104 will be available in 891 Evans each Monday and Tuesday, for five hours each day. The identity of the tutor and the precise hours will be announced shortly. There is a class website at http://www.math.berkeley.edu/~sarason/Class_Webpages/Math104_S6.html. Math H104  Introduction to Analysis  Honors Instructor: Vaughan Jones Lectures: MWF 3:004:00pm, Room 51 Evans Course Control Number: 54954 Office: 929 Evans, email: vfr [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and 54 and an enjoyment of challenging problems. According to a departmental policy that began in January, 2003, students who take this course should normally be math majors with a 3.5 GPA in upperdivision mathematics courses. Exceptions may be made by the instructor. Instead of signing up for this course, students put themselves on the waitlist. Department staff members will move students into the class incrementally. If you absolutely wish to take this class but haven't yet been admitted, you may need to speak with the instructor to plead your case. Syllabus: I will cover Chapters 14 of the book. Required Text: Charles Pugh, Real Mathematical Analysis, Springer UTM Series. Grading: Homework 25%, two midterms, each 15%. Final exam 45%. Homework: Weekly. Mostly, but not always, taken from the book. Comments: Math 104 is the defining math course in the undergraduate curriculum. It is here that one makes rigorous the concepts underlying calculus. It is here especially that one learns to think and write carefully about mathematics. It is a difficult course even for the best students, but the rewards are great. The emphasis in the honors section will be on more difficult problems, but only once the basic ideas have been properly assimilated. Math 110  Section 1  Linear Algebra Instructor: George M. Bergman Lectures: MWF 3:004:00pm, Room 75 Evans Course Control Number: 54957 Office: 865 Evans, email: gbergman [at] math [dot] berkeley [dot] edu Office Hours: Tu 1:302:30pm, Th 10:3011:30am, F 4:155:15pm Prerequisites: Math 54, or a course with equivalent linear algebra content. (Math 74 is also recommended for students not familiar with proofs.) Syllabus: Approximate list of sections of the text that we will cover: Appendices A, B, D, 1.11.6, 2.12.6, 4.44.5, 5.1, 5.2, 5.4, 6.16.6, 6.9, 7.17.3. Required Text: S. H. Friedberg, A. J. Insel and L. E. Spense, Linear Algebra, 4th Edition, PrenticeHall. Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam, 35%; regular submission of the daily question (see below), 5%. Homework: Weekly, generally due Fridays. Comments: In Math 54 you saw elementary linear algebra, with an emphasis on solving linear equations, and with the abstract concept of a vector space rather briefly treated. In this course, the emphasis will be on further development of the properties of abstract vector spaces, and linear maps among them. It will be for many of you the first course in which you are expected not just to calculate, but to give proofs. This transition, though intellectually exciting, is difficult for some students. I will bear in mind that the function of the course is not just to teach you linear algebra, but also to introduce you to mathematical reasoning. For students who think they will have particular difficulty with proofs, Math 74 is recommended. Unfortunately, this is scheduled for the same hour as my section this Fall; so students who need it should either take it during Summer Session, or take it this Fall but take a different section of Math 110. I don't like the conventional lecture system, where students spend the hour copying the contents of the course from the blackboard into their notebooks. Hence I will assign readings in the text, and conduct the class on the assumption that you have done this reading and thought about the what you've read. In lecture I may go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, discuss points to watch out for in the next reading, etc.. On each day for which there is assigned reading (usually Mondays and Wednesdays), each student in my class is required to submit, in writing or (preferably) by email, a question on the reading. (If there is nothing in the reading that you don't understand, you can submit a question marked "pro forma", together with its answer.) I try to incorporate answers to students' questions into my lectures. When I can't do this, I may instead answer your questions by email. More details on this and other matters will be given on the course handout distributed in class the first day, and available on the door to my office thereafter. Math 110  Section 2  Linear Algebra Instructor: AiKo Liu Lectures: TuTh 2:003:00pm, Room 71 Evans Course Control Number: 54960 Office: 905 Evans, email: akliu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 110  Section 3  Linear Algebra Instructor: Arthur Ogus Lectures: TuTh 11:00am12:30pm, Room 71 Evans Course Control Number: 54963 Office: 877 Evans, email: ogus [at] math [dot] berkeley [dot] edu Office Hours: MWF 2:003:00pm, subject to change. Grading: The grading will be approximately weighted as follows: 25% homeowrk, 30% midterms, 40% final, 5% quizzes. I try to assign grades as follows:
Webpage: http://www.math.berkeley.edu/~ogus/Math_110/index.html Comments: In concrete terms, linear algebra is the study of systems of linear equations in several variables. Such systems arise in a vast number of situations in mathematics and other fields, and it is absolutely crucial to understand them as thoroughly and conceptually as possible. The solution set to such a system has a rich geometric structure which is a fundamental part of linear algebra. The concepts of vector and inner product spaces reveal both the geometric and algebraic points of view, and a key theme of the course will be the interplay between the "abstract" linear algebra and the geometric intuition that it expresses. In the end (and in fact even in the beginning) this theme will be more important to us than the algorithmic methods for solving equations covered in math 54. An important goal of the course is for students to learn to read and write mathematical proofs, as well as to become comfortable with the interplay between abstraction and intuition. There will be a graduate student instructor assigned to help answer questions, especially with the homework. His office hours will be: Wednesday: 911, 12, 46 Thursday: 912, 46, in 891 Evans. For information on how to reach me, see my home page. Math 110  Section 4  Linear Algebra Instructor: John Steel Lectures: TuTh 12:302:00pm, Room 2 Evans Course Control Number: 54966 Office: 717 Evans, email: steel [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 110  Section 5  Linear Algebra Instructor: Tara Holm Lectures: MWF 9:0011:00am, Room 75 Evans Course Control Number: 54969 Office: 813 Evans, email: tsh [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 54, or a course with equivalent linear algebra content. (Math 74, which may be taken simultaneously, is also recommended for students not familiar with proofs.) Syllabus: TBA Required Text: S. Axler, Linear Algebra Done Right Grading: TBA Homework: Weekly, generally due Wednesdays. Math 110  Section 6  Linear Algebra Instructor: Ming Gu Lectures: MWF 12:001:00pm, Room 75 Evans Course Control Number: 54972 Office: 861 Evans, email: mgu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 110  Section 7  Linear Algebra Instructor: Donald Sarason Lectures: MWF 8:009:00am, Room 75 Evans Course Control Number: 54975 Office: 779 Evans, email: sarason [at] math [dot] berkeley [dot] edu (Do not contact me by email except in a dire emergency. If you have questions about the course, see me in my office, preferably during office hours or by appointment, or try to reach me by phone (6423521).) Office Hours: MW 9:3011:30am Prerequisites: Math 53 and 54 Syllabus: It is hoped we can cover the whole book together with occasional supplementary material. The basic objects of study will be finitedimensional vector spaces over the real and complex numbers, and the linear transformations between them. Of special concern will be linear transformations from a space to itself, socalled operators. The deepest theorems in the subject, the spectral theorem and the Jordan decomposition, describe the structure of operators. Required Text: Sheldon Axler, Linear Algebra Done Right, Second Edition, Springer, 1997. Grading: Homework, 20%; two midterm examinations, 20% each; final examination, 40%. Homework: Homework will be due most Fridays. It should be handed in at the beginning of class. Late papers will not be accepted. Exams: The final exam is scheduled for Thursday, December 11, 8:0011:00 a.m. (Exam Group 4). The schedule for the midterm exams is to be decided. There will be no makeup exams. Accordingly, do not register for this section if you have a conflict. Comments: A tutor for Math 110 will be available in 891 Evans every Wednesday and Thursday, five hours each day. The identity of the tutor and the precise hours will be available shortly. There is a class webpage at http://www.math.berkeley.edu/~sarason/Class_Webpages/Math110_S7.html. Math 110  Section 8  Linear Algebra Instructor: Ilan Hirshberg Lectures: TuTh 3:305:00pm, Room 6 Evans Course Control Number: 54978 Office: 1055 Evans, email: ilan [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: High school AP math, including a working knowledge of complex numbers (Math 1B,53 and 54 are not necessary). Students will be expected to understand and produce proofs. Students who have a lot of trouble with proofs are advised to take Math 74 before taking this class. To help you decide if this course is for you, the first suggested reading will be posted on the course website (see below). Students who are unsure if they are prepared to take the course are advised to try working through the first reading before classes start; that should give you an idea of what to expect. Feel free to contact me (by email) if you have any further questions. Syllabus: Scalars, vector spaces, linear transformations, determinants, Eigenvalues, characteristic and minimal polynomials, Jordan form, inner product spaces. Recommended Reading: P. R. Halmos, Linear Algebra Problem Book. Before most lectures, I'll give a list of suggested readings from the book, which may help you understand the lecture if you do them ahead of time. The readings are purely optional, and I will not assume that you have done them. Grading: Homework, two optional midterms and a final. Those will count as 40% Final, 20% max(Final, Midterm #1), 20% max(Final, Midterm #2), 20% max(Final,Homework), and will be converted to a letter grade by: 85100: A, 7084: B, 5569: C (adjusted by +'s and 's). The grades will not be `curved'. Homework: Typically 67 problems, due each Thursday. The problems will mostly be theoretical, and may be quite different from what you have seen in lower division. It is OK if you can't figure out how to do some of the problems, as long as you make a serious effort, learn from your mistakes, study the solutions, and eventually (before the exam) understand how to do those problems. Comments: Different instructors have different styles and emphases, and you should choose the one best for you. Here's some more information on my approach. The course will be rigorous and rather abstract. The focus will be on giving students a good grasp of the theory. I will not discuss any applications. My lectures tend to be organized, and I'll write (almost) everything on the board. The lectures will be selfcontained, except for some things which will be left as exercises or homework. I will not follow a textbook. Students are expected to attend lecture regularly and take good notes. The course will have a webpage: http://www.math.berkeley.edu/~ilan/110/ Math H110  Linear Algebra  Honors Instructor: Kenneth Ribet Lectures: MWF 12:001:00pm, Room 7 Evans Course Control Number: 54981 Office: 885 Evans, email: ribet [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 54 required, Math 53 and experience with proofs highly recommended. According to a departmental policy that began in January, 2003, students who take this course should normally be math majors with a 3.5 GPA in upperdivision mathematics courses. Exceptions may be made by the instructor. Instead of signing up for this course, students put themselves on the waitlist. Department staff members will move students into the class incrementally. If you absolutely wish to take this class but haven't yet been admitted, you may need to speak with the instructor to plead your case. Syllabus: The catalog proposes description reads as follows: "Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QF factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals." We will discuss most, but not all, of the topics on that intimidating list. Because this is an honors course, lectures will approach linear algebra from an abstract point of view, stressing theorems and their proofs. Required Text: Stephen H. Friedberg, Arnold J. Insel and Lawrence E. Spence, Linear Algebra, Fourth Edition. Recommended Reading: There are quite a few good linear algebra books in circulation; see the textbook lists for some examples. You might want to work problems in other books when studying for exams or to test your own understanding. Also, whenever you feel stuck when reading our text, feel free to consult alternative treatments. Reading several discussions of one topic is often illuminating. Grading: Homework 25%, midterms 15% each, final 45%. Homework: See the course web page for weekly assignments. (This page was begun in Fall, 2002 but will be updated for Fall, 2003 over the summer.) Math 113  Section 1  Introduction to Abstract Algebra Instructor: John Wagoner Lectures: MWF 1:002:00pm, Room 75 Evans Course Control Number: 54984 Office: 899 Evans, email: wagoner [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 113  Section 2  Introduction to Abstract Algebra Instructor: Alexander Givental Lectures: TuTh 11:00am12:30pm, Room 2 Evans Course Control Number: 54987 Office: 701 Evans, email: givental [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 113  Section 3  Introduction to Abstract Algebra Instructor: Tom Graber Lectures: MWF 8:009:00am, Room 71 Evans Course Control Number: 54990 Office: 833 Evans, email: graber [at] math [dot] berkeley [dot] edu Office Hours: MWTh 10:00am11:00am Prerequisites: Math 54 or equivalent knowledge of linear algebra. Syllabus: We will cover the basic theory of groups, rings, and fields. Required Text: Beachy and Blair, Abstract Algebra Grading: Homework, 30%; Midterms 15% each; Final 40%. Homework: Assigned weekly. Math 113  Section 4  Introduction to Abstract Algebra Instructor: Mark Haiman Lectures: TuTh 9:3011:00am, Room 4 Evans Course Control Number: 54993 Office: 771 Evans, email: Office Hours: TuTh 1:002:00pm (starting Fall 2003) Prerequisites: Math 54 or equivalent knowledge of linear algebra. Syllabus: Abstract algebra is a method of studying diverse mathematical concepts, to do with geometry, symmetry, numbers, and arithmetic, by discovering general axiomatic systems that describe properties they have in common. In this course we will study the three most important types of these axiomatic systems: groups, rings and fields. We will see how they can be used to solve some classical problems dating back to antiquity, such as the impossibilty of trisecting an arbitrary angle or constructing the cube root of 2 using only a straightedge and compass, and why there are formulas for the roots of a polynomial of degree 2, 3 and 4 but not 5. Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th edition, AddisonWesley, 2003. Grading: Grading policy to be announced. Homework: Homework assignments will be posted weekly on the course web page. Web Page: www.math.berkeley.edu/~mhaiman/math113 Math 113  Section 5  Introduction to Abstract Algebra Instructor: Paul Vojta Lectures: MWF 3:004:00pm, Room 9 Evans Course Control Number: 54996 Office: 883 Evans, email: vojta [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: 53 and 54 Syllabus: This course will cover the basics of groups, rings, and fields, as given in (parts of) Chapters 0, 1, 2, 3, 5, 6, 7, and 8 of the textbook. Details will be announced at the beginning of the course. Required Text: Fraleigh, A first course in abstract algebra Grading: Homeworks, 30%; midterms, 15% and 20%; final exam, 35%. Homework: Assigned weekly Web page: Comments: I tend to follow the book rather closely, but will try to give more examples this time. Math 113  Section 6  Introduction to Abstract Algebra Instructor: A. Yong Lectures: TuTh 3:305:00pm, Room 75 Evans Course Control Number: 54999 Office: 1035 Evans, email: ayong [at] math [dot] berkeley [dot] edu Office Hours: TuTh 5:006:00pm, Reader's office hours to be posted. Prerequisites: Math 54 or equivalent knowledge of linear algebra. Syllabus: (From the course catalog): "Sets and relations. The integers, congruences and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions."  as given in (parts of) chapters 010 of the textbook. Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th edition, AddisonWesley, 2003 Recommended Reading: Joseph J. Rotman, A First Course in Abstract Algebra, 2nd edition, Prentice Hall, 2000 Michel Artin, Algebra, Prentice Hall, 1991 I. N. Herstein, Abstract Algebra, 3rd edition, Prentice Hall, 1996 Grading: Homework (30%), Two midterms (15% each), Final exam (40%) Homework: Assignments will be posted weekly starting September 2nd on the course webpage and are due in class the following week. Webpage: http://math.berkeley.edu/~ayong/teaching.html Exams: There will be two in class midterms; the first will be on October 14th, covering group theory and some ring theory), the second on Thursday November 27 covering more ring theory and some field theory. The final exam will be cumulative, and the date will be set by the registrar. Comments: I will spend 1 week on "preliminaries" (chapter 0), 5.5 weeks on "group theory" (chapters 13,7), 4.5 weeks on "rings and polynomials" (chapters 45) and 4 weeks on "elements of field theory" (chapters 6,910). Of course there will not be time to cover **every** aspect of these chapters! Math 115  Introduction to Number Theory Instructor: Richard Borcherds Lectures: TuTh 3:305:00pm, Room 85 Evans Course Control Number: 55002 Office: 927 Evans, email: reb [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and 54. Syllabus: Divisibility, congruences, numerical functions, theory of primes, Diophantine analysis, continued fractions, partitions, quadratic fields. Required Text: Niven, Zuckerman, and Montgomery, The Theory of Numbers Grading: 40% homework, 15% each midterm, 30% final. Homework: Homework will be assigned on the web every week. Comments: See the course home page www.math.berkeley.edu/~reb/115 for more details. Math 121A  Section 1  Mathematical Tools for the Physical Sciences Instructor: Vera Serganova Lectures: MWF 11:00am12:00pm, Room 3 Evans Course Control Number: 55005 Office: 709 Evans, email: serganova [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 121A  Section 2  Mathematical Tools for the Physical Sciences Instructor: Dan Voiculescu Lectures: TuTh 12:302:00pm, Room 6 Evans Course Control Number: 55008 Office: 783 Evans, email: dvv [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 123  Ordinary Differential Equations Instructor: Mehmet Erdogan Lectures: TuTh 11:00am12:30pm, Room 3 Evans Course Control Number: 55011 Office: 805 Evans, email: burak [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 125A  Mathematical Logic Instructor: Leo Harrington Lectures: TuTh 12:302:00pm, Room 70 Evans Course Control Number: 55014 Office: 711 Evans, email: leo [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 128A  Section 1  Numerical Analysis Instructor: Alexandre Chorin Lectures: MWF 10:0011:00am, Room 3 Evans Course Control Number: 55020 Office: 911 Evans, email: chorin [at] math [dot] berkeley [dot] edu Office Hours: TBA Syllabus: I will cover the syllabus as it is announced in the catalog, and follow the book loosely. Grading: Grading will be based on a midterm, a final, and homework, with emphasis on computing assignments. Comments: My lecturing style is informal and I enjoy class discussion. Math 128A  Section 2  Numerical Analysis Instructor: Kevin Hare Lectures: MWF 3:004:00pm, Room 85 Evans Course Control Number: 55026 Office: 767 Evans, email: kghare [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and Math 54 Syllabus: I plan to cover the first six chapters in the text. 1. Number systems and errors: Representation of numbers; error propagation and error estimation. 2. Solution of nonlinear equations: Bisection, secant method, Newton's method; fixed point iteration and acceleration. 3. Systems of linear equations: Elimination method  factorization, pivoting, inverse calculation; iterative methods; eigenvalue problems. 4. Interpolation and Approximation: Interpolating polynomial, Lagrange form, error formula; spline interpolation; trigonometric interpolation and Fourier Series. 5. Differentiation and Integration: Numerical differentiation; numerical quadratureRomberg scheme, composite rules, Gaussian quadrature. 6. Initial Value Problems: Euler's method, Taylor and RungeKutta methods; convergence, stability, trapezoid method; stiff equations. Required Text: Richard L. Burden and J. Douglas Faires, Numerical Analysis, 7th ed. Grading: Grades will be based on six Homework assignments (30%), two inclass midterm (30%), and the Final Exam (40%). Homework: There will be six assignments. These will be based on questions from the text, plus occasionally additional questions. There may be a small number of minor programing questions. Comments: There will be a webpage for the Course maintained at http://www.math.berkeley.edu/~kghare/Courses/Math128a.html Math 128A  Section 3  Numerical Analysis Instructor: John Neu Lectures: TuTh 8:009:30am, Room 85 Evans Course Control Number: 55032 Office: 1051 Evans, email: neu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 130  Classical Geometries Instructor: Robin Hartshorne Lectures: MWF 10:0011:00am, Room 9 Evans Course Control Number: 55038 Office: 881 Evans, email: robin [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 135  Introduction to Theory Sets Instructor: Jack Silver Lectures: TuTh 2:003:30pm, Room 85 Evans Course Control Number: 55041 Office: 753 Evans, email: silver [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 141  Elementary Differential Topology Instructor: Allen Knutson Lectures: TuTh 8:009:30am, Room 3 Evans Course Control Number: 55044 Office: 1033 Evans, email: allenk [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 160  History of Mathematics Instructor: HungHsi Wu Lectures: MWF 1:002:00pm, Room 6 Evans Course Control Number: 55047 Office: 733 Evans, email: wu [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53, 54, and 113 Syllabus: The first four weeks on the history of mathematics from Babylonia (circa 1800 B.C.) to Descartes, the remainder of the semester on the period 16001900. Required Text: John Stillwell, Mathematics and Its History, Second Edition, SpringerVerlag, 2002. Recommended Reading: D. J. Struik, A Concise Histroy of Mathematics, Dover, 1987. Grading: Homework 20%, Midterm I 15%, Midterm II 25%, Term paper 40%. Homework: Weekly, problems will be about mathematics AND history. Working in groups will be encouraged. Comments: The first thing to make clear is that this is an upper division course on mathematics. The official prerequisites of second year calculus and introductory algebra (Math 113) will not be enough, and new mathematics will have to be introduced. This is because the course will try to explore the mathematics of the nineteenth century, which would also overtax the capability of the instructor. This course is a lot of work, and if past experience is any guide, students generally do not consider this to be an acceptable way of learning the history of mathematics. But work it will be, so please consider carefully before enrolling. For those who want to learn something about MATHEMATICS, instead of about calculus or algebra or geometry or complex functions, this course should be rewarding. You will get to learn about the evolution of mathematical ideas, for example, the line of thought from Eudoxus to Euclid, to Abel and Cauchy, to Dedekind, Cantor and Weierstrass. A term paper will replace the final; a suggested list of topics will be handed out during the first week. The two midterms will be about both mathematics and history. Math 170  Mathematical Methods for Optimization Instructor: L. Craig Evans Lectures: TuTh 3:305:00pm, Room 81 Evans Course Control Number: 55050 Office: 907 Evans, email: evans [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 53 and 54 Syllabus: Topics will include: 1. Linear programming 2. Nonlinear programming 3. Game theory 4. The calculus of variations 5. Control theory (if time permits) Required Text: Joel Franklin, Methods of Mathematical Economics (SIAM) Grading: 25% homework, 25% midterm, 50% final Homework: I will assign a homework problem, due in one week, at the start of each class. Math 185  Section 1  Introduction to Complex Analysis Instructor: Mehmet Erdogan Lectures: TuTh 8:009:30am, Room 71 Evans Course Control Number: 55053 Office: 805 Evans, email: burak [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 185  Section 2  Introduction to Complex Analysis Instructor: Dan Geba Lectures: MWF 1:002:00pm, Room 71 Evans Course Control Number: 55056 Office: 837 Evans, email: dangeba [at] math [dot] berkeley [dot] edu Office Hours: MW 3:004:30pm Prerequisites: Math 104 Syllabus: Complex numbers. Analytic functions. Elementary functions. Integrals. Series. Residues and poles. Application of residues. Mapping by elementary functions. Conformal mapping. Required Text: J.W. Brown and R.V. Churchill, Complex Variables and Applications Recommended Reading: L.V. Ahlfors, Complex Analysis Grading: Homework (30%), Midterm (30%), Final (40%) Homework: Assigned on Friday, due next Friday. The worst 3 homeworks will not be included in the final grade. No late homeworks. No makeup exams. Math 185  Section 3  Introduction to Complex Analysis Instructor: Dan Voiculescu Lectures: TuTh 9:3011:00am, Room 71 Evans Course Control Number: 55059 Office: 783 Evans, email: dvv [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 187  Fourier Analysis and Applications Instructor: Michael Christ Lectures: MWF 2:003:00pm, Room 71 Evans Course Control Number: 55062 Office: 809 Evans, email: mchrist [at] math [dot] berkeley [dot] edu Office Hours: Tu 1:302:30pm, W 1:102:00pm Prerequisites: Math 104 and 185. Syllabus: Most undergraduate courses are introductions to particular branches of mathematics, or to particular subsubjects. In this course we seek to link together some of these diverse subsubjects. We will begin with a solid introduction to Fourier analysis, but will thereafter focus on its interconnections with topics throughout mathematics and science. In the title, ``Applications'' refers especially to applications within mathematics; this will not be a course in ``applied mathematics'' per se. Topics will include:
Required Text: T. W. Korner, Fourier Analysis Recommended Reading: E. M. Sein and R. Shakarchi, Fourier Analysis: An Introduction H. Dym and H. P. McKean, Fourier Series and Integrals Y. Katznelson, An Introduction to Harmonic Analysis Homework: Problem sets will be assigned weekly. Comments: There will be two inclass midterm exams (dates TBA) and a written final exam. Math 191  Section 1  Experimental Courses in Mathematics Instructor: Emiliano Gomez Lectures: MW 4:306:00pm, Room 35 Evans Hall Course Control Number: 55065 Office: 985 Evans, email: emgomez [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 191  Section 2  Undergraduate Seminar in Applied Mathematics Instructor: L. C. Evans/Frances Hammock (For questions, contact Frances at hammockf [at] hotmail [dot] com.) Lectures: M 4:005:00pm, Room 9 Evans Hall Course Control Number: 55068 Prerequisites: Math 1A, 1B, 53, 54 Syllabus: Seminar in applied math. There will be an hour of lecture by a speaker once a week on some topic in applied math. Grading: P/NP Homework: One twopage paper due at the end of the semester. Comments: Ever wondered what you can do with a background in applied mathematics? Come find out from some of the leading minds in biotechnology, computer science, economics, astrophysics....the list goes on! Math is used everywhere  to learn more about it come check out this seminar. Speakers from around campus and from LBL will be giving undergraduate level talks about their work. Some speakers include: List some names James Demmel, Computer Science Stefano Dellavi, Economics Richard Plant, Agriculture Richard Muller, Physics Math 191  Section 3  Experimental Mathematical Modeling Instructor: Nathaniel Singer Lectures: MW 8:30am10:00am, Room 262 Dwinelle Course Control Number: 55070 Office: email: nathanielsinger [at] yahoo [dot] com Office Hours: TBA Prerequisites: Math 53 and 54 Syllabus: This course will operate with one clearly defined goal: To have students understand how to build mathematical models. A very relevant question is how would one most effectively learn to do this? First you might want to start out by asking why you want to learn about mathematical models in the first place. Before approaching that you might want to know what a mathematical model is and how it fits in to your understanding of the world. You will have to do that initial inquiry on your own, but to get you started you might try going to this website: http://www.mathmodeling.com/UMAPissues/2002MCM.pdf. This class will be taught in a manner that differs from conventional mathematics classes. Differences include:
Required Text: Ned's will stock the following books: John Holland, Hidden Order: How Adaptation Builds Complexity; Edward Bender, An Introduction to Mathematical Modeling. Grading: Class participation and presentations (30%), Homework (40%), Final Project (30%). Comments: For more information I suggest that you go to the course website, www.mathmodeling.com. Math 191  Section 4  Topics in Discrete and Computational Geometry Instructor: Jesus De Loera and Francis Su Lectures: Th 3:305:00pm, Room 72 Evans Hall Course Control Number: 55917 Office: MSRI, email: fsu [at] msri [dot] org Office Hours: TBA Prerequisites: A first course in linear algebra, and an excitement for discrete mathematics as well as geometry. Grading: Attendance and participation will be crucial. Each student will be expected to produce a nice detailed set of notes for a topic of his/her choice at least once in the semester. Credit: 2 units of passfail credit. Comments: This course will cover a selection of topics in discrete and computational geometry with the aim to introduce undergraduates to some of the exciting ideas at the heart of the "Discrete and Computational Geometry" Fall program at the Mathematical Sciences Research Institute (MSRI) at UCBerkeley. The general format of the seminar each week will be to explore an attractive problem in the areas of discrete geometry and computational geometry. We will facilitate a fun environment in which active participation will be valued and encouraged. Here is a tentative sample of topics: 1) Guarding art galleries and polygons. 2) Who are the Platonic and Archimedean solids? 3) Combinatorial fixed points and splitting the rent with roommates. 4) Computing volumes and areas. 5) Zonotopes and hyperplane arrangements. 6) Computational origami. 7) Cash registers, coin exchanges, and geometry. 8) Pick's theorem, areas, and polygons. 9) A taste of the Geometry of Numbers. 10) Euler's formula and its generalizations. Math 191  Section 5  Undergraduate Research Seminar Instructor: Kenneth A. Ribet Lectures: Th 11:10am12:30pm, Room 939 Evans Hall Course Control Number: 55920 Office: 885 Evans, email: ribet [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: The goal of the seminar will be to study rational points on elliptic curves. Required Text: Joseph H. Silverman and John Tate, Rational Points on Elliptic Curves, SpringerVerlag Credit: 2 units; Letter grade or P/NP Comments: Our textbook will be "Rational Points on Elliptic Curves" by Joseph H. Silverman and John Tate (SpringerVerlag Undergraduate Texts in Mathematics). Students may enjoy reading the review of this book by William R. Hearst III and Kenneth A. Ribet that was published in the April, 1994 issue of the Bulletin of the American Mathematical Society. (The review is available as http://modular.fas.harvard.edu/edu/Spring2003/21n/papers/hearst.pdf.) The textbook is based loosely on lectures that Tate gave to undergraduates at Haverford College in 1961. What is this subject about? Take a cubic equation like y^2 + y = x^3 x^2 and look for solutions in which x and y are rational numbers. As has been known for at least 100 years, the set of solutions acquires the structure of an abelian group after one adds in the extra "point at infinity" that one sees when looking at solution in the projective (rather than affine) plane. This abelian group is "finitely generated" in the sense that there exists a finite set of solutions from which one can obtain all other solutions. The finite generation is a theorem that L. E. J. Mordell proved in 1923. Incredibly, there are still a host of open problems that have been on the table since Mordell's work. For example, the conjecture of Birch and SwinnertonDyer, which posits an analytic formula for the number of independent rational solutions, is one of the milliondollar Millenium Prize Problems that were stated by the Clay Mathematics Institute three years ago. On the other hand, it is quite easy to compute with elliptic curves using the software package "gp" (and some other symbolic manipulation programs). One can get gp from http://www.parigphome.de/, by the way. Elliptic curves occur prominently in the proof of Fermat's Last Theorem. Students may wish to read Ribet's article on FLT that appeared in the Bulletin of the AMS in October, 1995. This article can be downloaded as http://www.ams.org/journals/bull/pre1996data/199510/199510001.pdf. Math 202A  Topology and Analysis Instructor: Charles Pugh Lectures: TuTh 11:00am12:30pm, Room 102 Moffitt Course Control Number: 55131 Office: 829 Evans, email: pugh [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Webpage: http://math.berkeley.edu/~robmyers/math202a.html Grading: Homework: Comments: Math 204A  Ordinary and Partial Differential Equations Instructor: Alberto Grunbaum Lectures: MWF 9:0010:00am, Room 31 Evans Course Control Number: 55134 Office: 903 Evans, email: grunbaum [at] math [dot] berkeley [dot] edu Office Hours: TBA Syllabus: This is a one semester graduate level class on ODEs. The emphasis will be on analytical treatment of differential equations with a heavy emphasis at the beginning on linear systems, including the standard material on constant coefficients, periodic coefficients, the theory of regular and irregular singular points, etc. We will make a rather detailed study of Gauss' hypergeometric equation with 3 regular singular points as well as its confluent versions, leading to Bessel's equation. We will have some discussion of the important notion (due to Poincare) of asymptotic solutions as well as the notion of the monodromy group associated to a linear equation with meromorphic coefficients in the Riemann sphere. Very important nonlinear equations like those of Painleve will appear in the latter part of the course in the study of the "isomonodromic deformations". I will use a very classical text, Coddington and Levinson to insure a solid foundation for the basic material. The latter part of the material is not covered in the book and I will attempt to prepare lecture notes based in some cases on recent literature in connection with integrable systems. This class provides a solid bridge between very classical and very current topics in analysis, mathematical physics, combinatorics, probability, etc. The main prerequisites are linear algebra (eigenvalues, eigenvectors, Jordan form, etc) and complex variables (meromorphic functions, analytic continuation) at the undergraduate level. Required Text: Coddington and Levinson, Theory of Ordinary Differential Equations, McGraw Hill. Recommended Reading: Einar Hille, Ordinary Differential Equations in Complex Domain, Wiley. Math 207  Unbounded Operators Instructor: Paul Chernoff Lectures: MWF 10:0011:00am, Room 65 Evans Course Control Number: 55140 Office: 933 Evans, email: chernoff [at] math [dot] berkeley [dot] edu Office Hours: MWF 10:10am12:00pm Prerequisites: Math 202AB Syllabus: Spectral theorem for unbounded selfadjoint operators; symmetric operators; one parameter groups and semigroups, generation of oneparameter unitary groups by selfadjoint operators; applications to quantum mechanics, including the Stonevon Neumann theorem on the Heisenberg commutation relations; Schrodinger operators. Grading: Based on homework assignments. Math 214  Differentiable Manifolds Instructor: Alan Weinstein Lectures: TuTh 9:3011:00am, Room 85 Evans Course Control Number: 55143 Office: 825 Evans, email: alanw [at] math [dot] berkeley [dot] edu Office Hours: Tu 11:15am12:30pm and 2:153:30pm Prerequisites: Math 202A or equivalent Required Text: John M. Lee, Introduction to Smooth Manifolds, Springer, 2003 Grading: The grade will be based on weekly homework assignments and a takehome final exam. Comments: I will cover the basic theory of differentiable manifolds, mappings, vector fields, differential forms, Lie groups, etc., as preparation for further study of differential geometry, topology, geometric analysis, and applications. My lectures tend to be on the informal side, with students referred to the text and other references for details of some proofs. Since my research interests center around symplectic geometry and its physical applications, some of the examples in lecture will come from these fields. Math 215A  Algebraic Topology Instructor: Michael Hutchings Lectures: TuTh 11:00am12:30pm, Room 85 Evans Course Control Number: 55146 Office: 923 Evans, email: hutching [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 219  Ordinary Differential Equations and Flows Instructor: Fraydoun Rezakhanlou Lectures: MWF 1:002:00pm, Room 85 Evans Course Control Number: 55149 Office: 815 Evans, email: rezakhan [at] math [dot] berkeley [dot] edu Office Hours: MWF, 2:003:00pm Prerequisites: Some analysis and measure theory. Syllabus: The main goal of the theory of dynamical system is the study of the global orbit structure of maps and flows. This course reviews some fundamental concepts and results in the theory of dynamical systems with an emphasis on differentiable dynamics. Several important notions in the theory of dynamical systems have their roots in the work of Maxwell, Boltzmann and Gibbs who tried to explain the macroscopic behavior of fluids and gases on the basic of the classical dynamics of many particle systems. The notion of ergodicity was introduced by Boltzmann as a property satisfied by a Hamiltonian flow on its constant energy surfaces. Boltzmann also initiated a mathematical expression for the entropy and the entropy production to derive Maxwell's description for the equilibrium states. Gibbs introduced the notion of mixing systems to explain how reversible mechanical systems could approach equilibrium states. The ergodicity and mixing are only two possible properties in the hierarchy of stochastic behavior of a dynamical system. Hopf invented a versatile method for proving the ergodicity of geodesic flows. The key role in Hopf's approach is the hyperbolic behavior of dynamical systems. Lyapunov exponents and KolmogorovSinai entropy are used to measure the hyperbolicity of a system. Here is an outline of the course: 1. Existence and uniquesness of solutions to ODEs. PoincareBendixon Theorem. 2. Examples: Linear systems. Translations on Tori. Arnold can map. Baker's transformation. Geodesic flows. Sinai's billiard. Lorentz gas. 3. Invariant measures. Ergodic theory. KolmogorovSinai Entropy. Lyapunov exponents. Hyperbolic systems. Smale horseshoe. 4.Thermodynamic formalism. PerronFrobenius operator. BowenRuelleSinai measures. 5. Pesin's theorem. Ruelle's inequality. Escape rates. GallavotiCohen fluctuation formula. Homework: There will be some homework assignments. Math 221  Applied Numerical Linear Algebra Instructor: Keith Miller Lectures: TuTh 9:3011:00am, Room 5 Evans Course Control Number: 55152 Office: 803 Evans, email: kmiller [at] math [dot] berkeley [dot] edu Office Hours: TBA Teaching Assistant: Jiang Zhu, email: zhujiang [at] math [dot] berkeley [dot] edu Prerequisites: Good knowledge of linear algebra (such as Math 110), coding experience, numerics equivalent to the level of Math 128AB. Syllabus: The standard problems we will consider are linear systems of equations, least squares problems, eigenvalue problems, and singular value problems  for full and sparse matrices and by direct and iterative methods. General concepts emphasized include (1) matrix factorizations, (2) perturbation theory and condition numbers, (3) effects of roundoff errors, (4) the speed of an algoritm, (5) choosing the best algorithm for your problem, and (6) engineering numerical software. Required Text: James Demmel, Applied Numerical Linear Algebra, SIAM, 1997 Recommended Reading: L. N. Trefethen, Numerical Linear Algebra, SIAM, 1997. This book is more purely mathematical in flavor than Demmel, but its exposition is sometimes more easily readable. Grading: Homework (about 25%), Programs (about 25%), Final (about 50%). Programs will be of two kinds  those in Fortran or C, and those in Matlab. Homework: Homework will be due every 1 or 2 weeks. Exams: 3hour final (Exam Group 7). Math 222A  Partial Differential Equations Instructor: L. Craig Evans Lectures: TuTh 12:302:00pm, Room 7 Evans Course Control Number: 55155 Office: 907 Evans, email: evans [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 105 or Math 202A Syllabus: 1. Introduction 2. Four important linear PDE 3. Nonlinear firstorder PDE 4. Sobolev spaces 5. Introduction to secondorder linear elliptic PDE Required Text: Lawrence C. Evans, Partial Differential Equations (American Math Society) Grading: 25% homework, 25% midterm, 50% final Homework: I will assign a homework problem, due in one week, at the start of each class. Math 224A  Methods of Mathematical Physics Instructor: Alberto Grunbaum Lectures: MWF 8:009:00am, Room 5 Evans Course Control Number: 55158 Office: 903 Evans, email: grunbaum [at] math [dot] berkeley [dot] edu Office Hours: TBA Syllabus: The beauty and the challenge of this class is that of presenting material that has been around in one form or another for a long time in a way that is fresh and attractive to students. I will try hard to walk this narrow line. In the first semester I will try to stick to the material in the book: intuitive ideas about Green functions, Fourier analysis and distribution theory, one dimensional boundary value problems, Hilbert spaces, Operator theory and integral equations. Spectral theory of second order differential operators. In the second semester, I will have to do some unfinished material from the first one, and then we will see how this classical stuff plays a crucial role in problems of current interest. Among the topics that I would like to touch upon, either during the main part of the course or towards the end are Tridiagonal matrices, i.e., discrete versions of second order differential operators. The classical orthogonal polynomials: Hermite, Laguerre, Bessel and Jacobi. Spectral theory for finite, semiinfinite and doubly infinite tridiagonal matrices. The Toda equation for coupled unharmonic oscillators. Beyond orthogonal polynomials. The relativistic Toda chain and Laurent orthogonal polynomials. Birth and death processes. Uses of the spectral theorem in examples. The Schroedinger equation, including the main examples: the free particle, the harmonic oscillator, the hydrogen atom etc. to give a concrete discussion of H. Weyl's limit pointlimit circle classification of separated boundary conditions. Regular and irregular singular points for linear differential equations in the complex plane. Gauss' linear second order hypergeometric equation. The Bessel equation. Sampling, aliasing and all that. The relation between the Fourier transform, the Fourier series and the DFT. Heisenberg's principle. The problem of double concentration. Some basic ideas behind the construction of "wavelet basis". Random walks on integer lattices, discrete time and continuous time. The issue of recurrence in different dimensions. Brownian motion. Integration in function space, the FeynmanKac formula. Paul Levy's arcsine law. The scattering transform as an important nonlinear version of the Fourier transform. Reflectionless potentials, solitons, recovering a potential from scattering data, the Kortewegde Vries equation. Some matrix valued versions of the Schroedinger equation. Required Text: I. Stakgold, Green's functions and boundary value problems. (I consider this book as required, since it contains a lot of the basic material.) Recommended Reading: The following is a partial list of recommended books, covering different aspects of the class. G. Lamb, Elements of soliton theory. M. Toda, Theory of nonlinear lattices. S. Karlin and H. Studden, A second course in Stochastic Processes. Grading: It will be based solely on homework. Homework: A weekly assignment. Math 225A  Metamathematics Instructor: Jack Silver Lectures: TuTh 11:00am12:30pm, Room 31 Evans Course Control Number: 55161 Office: 753 Evans, email: silver [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 228A  Numerical Solution of Differential Equations Instructor: John Strain Lectures: TuTh 11:00am12:30pm, Room 5 Evans Course Control Number: 55164 Office: 1099 Evans, email: strain [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 128A, or equivalent knowledge of elementary numerical analysis. Previous or concurrent experience with Matlab, C or Fortran programming will be helpful. Syllabus: The course will cover theory and practical methods for solving onedimensional differential and integral equations. 1. Methods for solving initial value problems for systems of ordinary differential equations: construction, convergence and implementation. 1.1 Classical multistep (Adams and BDF) and RungeKutta methods. 1.2 Stable highorder deferred correction methods. 2. Solution of boundary value problems for systems of ordinary differential equations. 2.1 Classical shooting and finite difference techniques. 2.2 Divide and conquer algorithms for integral equations. Required Text: 1. E Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations I and II (2 vols). Second edition, Springer, 1993 and 1996. 2. U.M. Ascher, R.M.M. Mattheij, and R.D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM Publications, 1995. Grading: Grades will be based on regular homework assignments. Math 229  Theory of Models Instructor: Thomas Scanlon Lectures: MWF 3:004:00pm, Room 5 Evans Hall Course Control Number: 55166 Office: 723 Evans, email: scanlon [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 240  Riemannian Geometry Instructor: Alan Weinstein Lectures: TuTh 12:302:00pm, Room 5 Evans Course Control Number: 55167 Office: 825 Evans, email: alanw [at] math [dot] berkeley [dot] edu Office Hours: Tu 9:4011:00am and 2:103:30pm Prerequisites: Math 214 or equivalent Required Text: John M. Lee, Riemannian Manifolds, An Introduction to Curvature, Springer, 1997 Grading: The grade will be based on homework and an expository paper on some aspect of riemannian geometry and its applications. Comments: Riemannian geometry, besides being a subject of great intrinsic interest, is an essential tool in all areas of differential geometry, as well as in topology and other areas of mathematics and its applications. (Even in probability theory, riemannian manifolds of probability distributions have made their appearance; riemannian geometry is also turning out to be a useful tool in the study of some aspects of computer vision.) The textbook covers the basics, and I will lecture on additional topics, such as the theory of connections on is the gauge theory of connections on principal bundles. Math 250A  Groups, Rings and Fields Instructor: Bjorn Poonen Lectures: TuTh 8:009:30am, Room 70 Evans Course Control Number: 55170 Office: 703 Evans, email: poonen [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 114 (or equivalent undergraduate abstract algebra) or consent of instructor. Syllabus: We will cover most of Chapters IVI in Lang's text: groups (including the Sylow theorems and the JordanHolder Theorem), rings, modules, polynomials, algebraic field extensions, Galois theory (including infinite Galois theory, and an introduction to Galois cohomology, if there is time). There is a lot of material, so students will be expected to read the text for definitions and topics not covered in class. Class time will serve to emphasize important points, to clarify difficult topics, and to supplement the text as needed. Required Text: Lang, Algebra (revised third edition, Springer, 2002) Grading: There will be no exams. Grades will be based on weekly homework. Homework: Assignments will be due in class on Tuesdays. Late homeworks will not be accepted. Comments: The uptodate course website is at http://math.berkeley.edu/~poonen/math250a.html Math 252  Representation Theory Instructor: Vera Serganova Lectures: MWF 1:002:00pm, Room 4 Evans Course Control Number: 55173 Office: 709 Evans, email: serganova [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 254A  Number Theory Instructor: CheeWhye Chin Lectures: MWF 2:003:00pm, Room 9 Evans Course Control Number: 55176 Office: 705 Evans, email: cheewhye [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Strong foundation in abstract algebra (250A) and commutative algebra (250B). Syllabus: The goal of this course is to present the key results in class field theory for number fields, using the tools of Galois cohomology. The course can be roughly divided into three parts. The first part covers the basics of local fields and global fields: valuations, completions, extensions, ramification, adeles, ideles, approximation theorems, etc. The second part will be about cohomology: of finite groups, of profinite groups, of Galois groups. The final part will be focused on class field theory: both for local fields and for global (number) fields. Recommended Reading: Algebraic number theory, edited by J. W. S. Cassels and A. Frohlich, Academic Press, Inc., London, 1986. J. Neukirch, Algebraic number theory, SpringerVerlag, Berlin, 1999. The proceedings edited by Cassels and Fr–hlich is an excellent source of study material; the first seven chapters of the book will be especially relevant for this course. Neukirch's book will be used as a reference from time to time. Grading: There will be no exams. Grades will be based on weekly homework. Math 255  Algebraic Curves Instructor: Robert Coleman Lectures: MWF 12:001:00pm, Room 9 Evans Course Control Number: 55179 Office: 901 Evans, email: coleman [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 256A  Algebraic Geometry Instructor: Arthur Ogus Lectures: TuTh 2:003:30pm, Room 51 Evans Course Control Number: 55182 Office: 877 Evans, email: ogus [at] math [dot] berkeley [dot] edu Office Hours: MWF 2:003:00pm, subject to change. Prerequisites: Students will need some background in commutative algebra, in particular with localization and tensor products. Some experience with the methods of global geometry (e.g. differential or algebraic topology), and the language of category theory, will also be helpful. Recommended Reading: Qing Liu, Algebraic Geometry and Arithmetic Curves, Oxford University Press Grothendieck's EGA Webpage: http://www.math.berkeley.edu/~ogus/Math_256A/index.html Comments: There are many foundations on which algebraic geometry can be built. Probably the most natural is Grothendieck's theory of schemes, which provides a uniform framework for calculus, geometry and arithmetic and has led to spectacular advances in all of these fields. My main goal is to introduce students to the basic ideas and techniques of schemes in a way that is general enough to apply to arithmetic and number theory, without neglecting the geometry that comes from studying varieties over algebraic closed fields. In the course of the two semesters I hope to cover the main parts of chapters II and III of Hartshorne's classic text, as well as selected topics from chapters IV and V, although I will not follow the text closely. Hartshorne's book and this course are notorious for their difficult and timeconsuming homework, which is absolutely essential for mastery of the subject. Math 257  Group Theory Instructor: Laurent Bartholdi Lectures: TuTh 2:003:30pm, Room 5 Evans Course Control Number: 55185 Office: 1073 Evans, email: laurent [at] math [dot] berkeley [dot] edu Office Hours: (Tu)Th 1:002:00pm at Cafe Strada, Bancroft @ Telegraph Prerequisites: Math 250A (Groups, Rings and Fields) Syllabus: 1. The theory of groups acting on trees with "small" stabilizers, with as model the celebrated theorem "A group acting freely on a tree is free" 2. The theory of groups acting on rooted trees, with a special emphasis on closed (profinite) groups and groups generated by automata 3. The connection between these topics, and in particular the construction of lattices in products of simple Lie groups due to Marc Burger and Shahar Mozes Required Text: None  notes will be handed out. Recommended Reading: JeanPierre Serre, Trees, Amalgams, SL2 Hyman Bass and Alex Lubotzky, Tree lattices Laurent Bartholdi, Rostislav I. Grigorchuk and Zoran Sunik, Branch groups Grading: A or A+, I haven't decided yet Homework: Exercises will be handed out; because of the amount of material to cover, I will expect students to read some selected papers so that they can be discussed in class. Comments: There is a class website. Math 261A  Lie Groups and Lie Algebras Instructor: Nicolai Reshetikhin Lectures: MWF 10:0011:00am, Room 85 Evans Course Control Number: 55188 Office: 945 Evans, email: reshetik [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: Math 274  Rational Curves in Algebraic Varieties Instructor: Tom Graber Lectures: MWF 9:0010:00am, Room 51 Evans Course Control Number: 55191 Office: 833 Evans, email: graber [at] math [dot] berkeley [dot] edu Office Hours: MWTh 10:00am11:00am Prerequisites: Math 256 Syllabus: The ostensible goal of the course will be to study the geometry of rational curves in projective varieties, with an emphasis on those varietiesw which contain many rational curves. This will also serve as a pretext for introducing representable functors (especially the Hilbert scheme and close relatives) and their infinitesimal study via deformation theory. The core material of the course will be roughly what is covered in chapters 25 of Debarre's text, HigherDimensional Algebraic Geometry. Recommended Reading: O. Debarre, HigherDimensional Algebraic Geometry. J. Koll'ar, Rational Curves on Algebraic Varieties. Math 275  Combinatorial Game Theory Instructor: Elwyn Berlekamp Lectures: TuTh 2:003:30pm, Room 81 Evans Course Control Number: 55193 Office: 847 Evans, email: berlekamp [at] math [dot] berkeley [dot] edu Office Hours: TBA Syllabus: We will study combinatorial game theory, according to the first volume of "Winning Ways." The theory makes powerful use of recursion, although there are no formal prerequisites beyond an understanding of proof by induction and an interest in working through a few sequences of specific examples. We will use this theory to find explicit winning strategies for many positions in a wide variety of playable games, including Hackenbush, Domineering, Toads & Frogs, Ski Jumps, Konane, Kayles, Dawson, DotsandBoxes, Amazons, and Clobber. We will investigate some operators which map games into games, and extensions of this theory which extend the original group into a monoid and now provide rigorous and precise solutions to many hard endgame problems in a variety of games, including the classical Asian board game of Go, and some rare applications of chess and checkers. We will encounter several "NP" and "PSPACE" complexity results. We will also study the relationships between these mathematical theorems and the heuristic search methods of artificial intelligence used by many computer gameplaying programs. There will be at least two quizzes and probably three midterms (one oral and two written) and a written final exam. This is a subject in which it is possible for graduate students rather quickly to acquire sufficient background to tackle some unsolved but relatively tractable research problems. Extra credit for original work. For examples of significant original contributions which originated when they were students in earlier versions of this course, see papers by the following authors in "Games of No Chance": David Wolfe, David Moews, Dan Garcia, Mike Zieve, Jeff Erickson and Yonghoan Kim, and in "More Games of No Chance" by Alice Chan and Alice Tsai. Required Text: Berlekamp, Conway and Guy, Winning Ways, Vol. 1, AKPeters, Ltd, 2001 Recommended Reading: Don Knuth, Surreal Numbers, 1974, Addison Wesley R. Nowakowski (Editor), Games of No Chance, 1996, 1999, Cambridge University Press R. Nowakowski (Editor), More Games of No Chance, 2002, which is available online at msri.org. Math 279  Topics in Partial Differential Equations Instructor: Daniel Tataru Lectures: TuTh 11:00am12:30pm, Room 7 Evans Course Control Number: 55194 Office: 841 Evans, email: tataru [at] math [dot] berkeley [dot] edu Office Hours: By appointment Prerequisites: Real analysis. Some pde background would also be useful. Syllabus: The aim of the course is to provide an overview of microlocal analysis, oriented toward problems in nonlinear partial differential equations. Following are some topics I have in mind: The Fourier transform Phase space transforms (i.e. Bargman and FBI) LittlewoodPaley theory Pseudodifferential operators, The Garding and FeffermanPhong inequalities Fourier integral operators (following Bony) Paradifferential calculus Coherent states and wave packets All this will be interwoven with applications to problems in linear and then nonlinear partial differential equations. References: Jean Marc Delort, FBI Transformation Charles Fefferman, The Uncertainty Principle (AMS Bulletin) Gerard Folland, Harmonic Analysis in Phase Space Lars Hormander, The Analysis of Linear Partial Differential Operators Elias Stein, Harmonic Analysis Michael Taylor, Pseudodifferential operators and Nonlinear PDE's Math 300  Teaching Workshop Instructor: Ole Hald Lectures: Course Control Number: 55845 Office: 875 Evans, email: hald [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Syllabus: Required Text: Recommended Reading: Grading: Homework: Comments: 
