# Fall 2008

 Math 1A - Section 1 - Calculus Instructor: Ian Agol Lectures: TuTh 8:00-9:30am, Room 155 Dwinelle Course Control Number: 54103 Office: 921 Evans Office Hours: TBA Prerequisites: 3.5 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 Math 32. There is an on-line exam you can take to help you decide if you are ready for this course. Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~ianagol/1A.F08/ Grading: Homework: Comments: Math 1A - Section 2 - Calculus Instructor: Ole Hald Lectures: MWF 1:00-2:00pm, Room 2050 Valley LSB Course Control Number: 54142 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1A - Section 3 - Calculus Instructor: Martin Olsson Lectures: MWF 12:00-1:00pm, Room 155 Dwinelle Course Control Number: 54184 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Jon Wilkening Lectures: TuTh 11:00am-12:30pm, Room 2050 Valley LSB Course Control Number: 54223 Office: 1091 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Second Semester Calculus Instructor: George Bergman Lectures: MWF 3:00-4:00pm, Room 155 Dwinelle Course Control Number: 54262 Office: 865 Evans Office Hours: Tu 10:30-11:30, W 4:15-5:15, F 10:30-11:30 Prerequisites: Math 1A or equivalent background. (If you have taken the Math AP exams, there is advice on which math course you are ready for at http://math.berkeley.edu/courses_AP.html.) Required Text: Stewart, Single Variable Essential Calculus, Thomson Learning Syllabus: Chapters 6, 7, 8 and 17 of the text. Grading: Grades will be based on two midterms (15% + 20%), a final (35%), and weekly quizzes in section (30%). Homework: Homework will be assigned every week and discussed in section. It will not be graded, but section quizzes will be modeled on the homework problems, so you should do it. Comments: This course continues where Math 1A leaves off, developing techniques of integration, and further applications and techniques of calculus, including 4 weeks of differential equations. I hope to show you some of the beauty of these topics, along with the facts and techniques. I will give out a schedule of readings. My lecture each day will assume that you have studied the reading for the day, but that you may need to see things clarified or explained from another point of view, more examples worked, etc.. In lower-division math courses, proofs are not the main topic, but I will assign a certain number, typically one on each exam and one or two per homework assignment, and discuss some of the proofs from the text in lecture, to help get you ready for upper division math, and introduce you to mathematical thinking. Despite my best intentions, I am not a well-organized lecturer. I will do my best, as always; but if you want something more polished, you might take the other lecture. Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: James Demmel Lectures: TuTh 12:30-2:00pm, Room 105 Stanley Course Control Number: 54298 Office: 737 Soda Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and Calculus Instructor: Tsit-Yuen Lam Lectures: MWF 10:00-11:00am, Room 1 Pimental Course Control Number: 54337 Office: 871 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Jenny Harrison Lectures: MWF 9:00-10:00am, Room 105 Stanley Course Control Number: 54379 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman Seminars Instructor: Alberto Grünbaum Lectures: Tu 11:00am-12:30pm, Room 939 Evans Course Control Number: 54418 Office: 903 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - Freshman Seminars Instructor: Jenny Harrison Lectures: F 3:00-4:00pm, Room 891 Evans Course Control Number: 54421 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: The Staff Lectures: MWF 8:00-9:00am, Room 2060 Valley LSB Course Control Number: 54424 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Michael Hutchings Lectures: MWF 11:00am-12:00pm, Room 2050 Valley LSB Course Control Number: 54472 Office: 923 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: Constantin Teleman Lectures: TuTh 3:30-5:00pm, Room 100 Lewis Course Control Number: 54514 Office: 905 Evans Office Hours: W 12:00-1:30pm, Th 5:00-6:30pm Prerequisites: Required Text: Stewart, Multivariable Essential Calculus, Thomson Recommended Reading: Syllabus: Standard Multivarible calculus Course Webpage: http://math.berkeley.edu/~teleman/53f08 Grading: 20% Homework + quizzes, 20% each of two midterms, 40% final Homework: Assigned for every lecture (see the web schedule), collected in Section. Comments: Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Alberto Grünbaum Lectures: TuTh 8:00-9:30am, Room 150 Wheeler Course Control Number: 54550 Office: 903 Evans Office Hours: TBA Prerequisites: Math 1B Required Text: David Lay, Linear Algebra and Its Applications, 3rd edition Nagle, Saff & Snider, Fundamentals of Differential Equations and Boundary Value Problems For both you can get the paperback Berkeley editions. 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; second-order differential equations with constant coefficients. Fourier series and partial differential equations. Course Webpage: http://math.berkeley.edu/~grunbaum/54.html Grading: Homework 20%, midterms 20% each, and final exam 40%. Homework: Homework will be assigned weekly. Comments: Math H54 - Section 1 - Honors Linear Algebra and Differential Equations Instructor: Alexander Paulin Lectures: TuTh 3:30-5:00pm, Room 85 Evans Course Control Number: 54616 Office: 1053 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: Mark Haiman Lectures: MWF 12:00-1:00pm, Room 2060 Valley LSB Course Control Number: 54622 Office: 855 Evans Office Hours: WF 1:30-3:00pm Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B recommended. Freshmen with strong high school math background and a possible interest in majoring in mathematics may also wish to consider taking this course. Required Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th Edition Recommended Reading: Syllabus: Logic and proof techniques, basics of set theory, algorithms, elementary number theory, combinatorial enumeration, discrete probability, graphs and trees, with applications to coding theory. Course Webpage: http://math.berkeley.edu/~mhaiman/math55-fall08 Grading: Based on weekly homework, two midterm exams, and final exam. Homework: Comments: Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: The Staff Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54637 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: The Staff Lectures: TuTh 3:30-5:00pm, Room 75 Evans Course Control Number: 54640 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Jan Reimann Lectures: TuTh 2:00-3:30pm, Room 241 Cory Course Control Number: 54706 Office: 705 Evans Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: C. Pugh, Real Mathematical Analysis, Springer, 2002 Recommended Reading: Syllabus: Roughly Chapters 1 to 4: The real number system, cardinalities, metric spaces, convergence, compactness and connectedness, continuous functions on metric spaces, uniform convergence, power series, differentiation and integration. (We will leave out some rather advanced material in Chapters 2 and 4.) Course Webpage: Will be set up on bSpace. Grading: 20% homework, 20% each midterm, 40% final Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Ole Hald Lectures: MWF 11:00am-12:00pm, Room 71 Evans Course Control Number: 54709 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Michael Klass Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54712 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Joshua Sussan Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54715 Office: 761 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Brett Parker Lectures: TuTh 3:30-5:00pm, Room 87 Evans Course Control Number: 54718 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 6 - Introduction to Analysis Instructor: Robert Coleman Lectures: MWF 2:00-3:00pm, Room 4 Evans Course Control Number: 54721 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: In this course we will construct the real numbers, define differentiation and integration, prove the fundamental theorem of calculus and Taylor's theorem and make the gamma function. Course Webpage: Grading: Homework: Comments: Math H104 - Section 1 - Honors Introduction to Analysis Instructor: Alexander Givental Lectures: TuTh 3:30-5:00pm, Room 81 Evans Course Control Number: 54724 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Shamgar Gurevich Lectures: MWF 3:00-4:00pm, Room 4 Evans Course Control Number: 54727 Office: 867 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 2 - Linear Algebra Instructor: Marco Aldi Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54730 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 3 - Linear Algebra Instructor: Arthur Ogus Lectures: MWF 11:00am-12:00pm, Room 3113 Etcheverry Course Control Number: 54733 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 4 - Linear Algebra Instructor: Sebastian Herr Lectures: TuTh 12:30-2:00pm, Room 70 Evans Course Control Number: 54736 Office: 837 Evans Office Hours: TBA Prerequisites: 54 or a course with equivalent linear algebra content. Required Text: S. Friedberg, A. Insel, and L. Spence, Linear Algebra, Prentice Hall, 2002. Recommended Reading: You may find the following textbook helpful as supplementary reading (optional): S. Axler, Linear Algebra Done Right, Springer, 2004. Syllabus: Vector spaces, linear independence, bases, dimension. Linear transformations, matrices, change of bases, linear functionals. Systems of linear equations. Determinants, eigenvalues and eigenvectors, diagonalization. Inner products, orthonormalization and QR factorization, quadratic forms, spectral theorem, Rayleigh's principle. Jordan canonical form and applications. Course Webpage: http://math.berkeley.edu/~herr/110S4Fall08.html Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam. Homework: Homework will be assigned once a week, and will be due the following week. Comments: For more information, please take a look at the course webpage. Math 110 - Section 5 - Linear Algebra Instructor: Kenneth Ribet Lectures: TuTh 3:50-5:00pm, Room 3 Evans Course Control Number: 54739 Office: 885 Evans Office Hours: TBA Prerequisites: 54 or a course with equivalent linear algebra content Required Text: TBA Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~ribet/110/ Grading: Determined by a numerical composite grade that weights the three exams and the homework scores in some logical manner. Homework: Assigned weekly Comments: This course has the latest possible final exam slot: Saturday, December 20, 2008 at 12:30PM. Sign up for another section if you need to start your vacation before then. Math 110 - Section 6 - Linear Algebra Instructor: Christian Zickert Lectures: TuTh 2:00-3:30pm, Room 70 Evans Course Control Number: 54741 Office: 1053 Evans Office Hours: TBA Prerequisites: Required Text: Friedberg, Insel & Spence, Linear Algebra, Prentice-Hall, 2002 Recommended Reading: Syllabus: Vector spaces and linear maps, eigenvalues and eigenvectors, diagonalization, inner products, Jordan form, polar decomposition. Course Webpage: http://math.berkeley.edu/~zickert/ Grading: Homework: Comments: Math H110 - Section 1 - Honors Linear Algebra Instructor: George Bergman Lectures: MWF 1:00-2:00pm, Room 4 Evans Course Control Number: 54742 Office: 865 Evans Office Hours: Tu 10:30-11:30, W 4:15-5:15, F 10:30-11:30 Prerequisites: Math 54 or a course with equivalent linear algebra content, and a GPA of at least 3.3 in math courses taken over past year; or consent of the instructor. The course is aimed at mathematics majors and other students with a strong interest in mathematics. Required Text: S. H. Friedberg, A. J. Insel and L. E. Spence, Linear Algebra, 4th Edition, Prentice-Hall. Recommended Reading: None. Syllabus: We will cover most of the text, and possibly some additional topics. Course Webpage: None. Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam, 35%; regular submission of the daily question (see below), 5%. Homework: 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 briefly treated. Math 110 focuses on further development of the properties of abstract vector spaces and linear maps among them. After several days looking through texts that might give a more advanced approach to the material, and not finding one that I liked, I have ended up falling back on the text most commonly used in regular 110. This is well written, and has the advantage that students should be able to move between H110 and the majority of the regular 110 sections without too much difficulty. In H110, however, we will look into the ideas more deeply than in regular 110, we will include one or two topics that are not usually covered, and the exercises assigned will be more challenging. I am not a fan of the conventional lecture system, where students spend the hour copying the contents of the course from the blackboard into their notebooks. Hence I assign readings in the text, and conduct the class on the assumption that you have done the assigned reading and thought about 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.. If you are unbreakably attached to learning first from the lecture, and only then turning to the book, then my course is not for you. On each day for which there is an assigned reading, each student is required to submit, preferably by e-mail, 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 usually answer by e-mail. 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 113 - Section 1 - Introduction to Abstract Algebra Instructor: David Hill Lectures: MWF 10:00-11:00am, Room 70 Evans Course Control Number: 54745 Office: 757 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Alvaro Pelayo Lectures: TuTh 8:00-9:30am, Room 2 Evans Course Control Number: 54748 Office: Office Hours: TBA Prerequisites: Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th ed. Recommended Reading: Syllabus: Course Webpage: Grading: 2 midterm exams, a final exam and weekly homework. Homework: Weekly. Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Mauricio Velasco Lectures: MWF 8:00-9:00am, Room 71 Evans Course Control Number: 54751 Office: 1063 Evans Office Hours: TBA Prerequisites: Math 54 Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th edition Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Alvaro Pelayo Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54754 Office: Office Hours: TBA Prerequisites: Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th ed. Recommended Reading: Syllabus: Course Webpage: Grading: 2 midterm exams, a final exam and weekly homework. Homework: Weekly. Comments: Math 113 - Section 5 - Introduction to Abstract Algebra Instructor: Irwin Kra Lectures: TuTh 2:00-3:30pm, Room 4 Evans Course Control Number: 54756 Office: Office Hours: TuW 4:00-5:00 Prerequisites: Math 54 or a course with equivalent linear algebra content Required Text: John Stilwell, Elements of Algebra, Springer-Verlag, 2001 Recommended Reading: (1) John B. Fraleigh and Victor J. Katz, A First Course in Abstract Algebra, Addison-Wesley, 2003 (2) J.F. Humphreys and M.Y. Prest, Numbers, Groups and Codes, Cambridge University Press, 2004 Syllabus: This is an introductory algebra course designed specifically for students interested in secondary school mathematics teaching. It covers "the usual topics:" groups, rings, fields that all math majors must know. The emphasis will be on connecting abstract concepts to practical problems such as public key cryptograhy and error correcting codes and to topics appearing in the high school math curriculum such as solutions of equations. More details will be found on the Course Webpage. Course Webpage: Grading: quizzes 20% (there will be 4 quizzes), midterm examinations 40% (there will be two midterm tests), final examination 40% Homework: About 7 homework sets will be posted on the Course Webpage. Each will be due approximately two weeks after it is posted. Comments: Math 115 - Section 1 - Introduction to Number Theory Instructor: Chung Pang Mok Lectures: MWF 12:00-1:00pm, Room 241 Cory Course Control Number: 54757 Office: 889 Evans Office Hours: TBA Prerequisites: Required Text: Niven, Zuckerman and Montgomery, An Introduction to the Theory of Numbers, Wiley, 5th edition Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~mok/115.html Grading: 20% homework, 30% for two mid-terms, 50% final Homework: Assigned and due weekly. Comments: Math 121A - Section 1 - Mathematics for the Physical Sciences Instructor: John Neu Lectures: TuTh 9:30-11:00am, Room 85 Evans Course Control Number: 54760 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Boa, Mathematical Methods for Physical Sciences Recommended Reading: Syllabus: This course begins with subjects from math 1b, 53 and 54 that many do not get the first time around. That is, Taylor series and applications (from 1b), differential calculus in several variables (from math 53) and complex exponential and its applications to ODE and PDE (math 54) What's different is the maturity level, and that you are strongly encouraged to get it this time. Next, is Fourier series (a math 54 topic too) but now using the full power of complex numbers and the complex exponential. Fourier transform is introduced as the limit of Fourier series as the period interval goes to infinity. Applications of Fourier series and transforms to solutions of ODE and PDE lead naturally to delta functions and Green's functions. That's where the course finishes. In summary, this course is a basic survival kit for students getting slammed by their first serious upper division courses in physics, chemistry, ME, EE, etc. Course Webpage: Grading: Course has 2 midterms, 5th and 10th week (no delay) and a final. Problem set scores make a small contribution to grade. But bottom line is you gotta get it done on the exams. Homework: Comments: Math 121A - Section 2 - Mathematical Tools for the Physical Sciences Instructor: Vera Serganova Lectures: MWF 10:00-11:00am, Room 85 Evans Course Control Number: 54763 Office: 709 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 123 - Section 1 - Ordinary Differential Equations Instructor: Alexander Givental Lectures: TuTh 11:00am-12:30pm, Room 87 Evans Course Control Number: 54766 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Jan Reimann Lectures: TuTh 12:30-2:00pm, Room 3 Evans Course Control Number: 54769 Office: 705 Evans Office Hours: TBA Prerequisites: One upper division math course or consent of instructor. Required Text: Lectures Notes by Slaman and Woodin, free of charge will be provided to registered students. Recommended Reading: Syllabus: Propositional logic, first order logic - syntax and semantics, first order structures, the Gödel completeness theorem, compacntess, basic model theory, undecidability and incompleteness. Course Webpage: Will be set up on bSpace. Grading: TBA Homework: Homework will be assigned once a week, due the following week. Comments: Math 127 - Section 1 - Mathematical and Computational Methods in Molecular Biology Instructor: Lior Pachter Lectures: TuTh 9:30-11:00am, Room 75 Evans Course Control Number: 54772 Office: 1081 Evans Office Hours: TuTh 11:00am-12:30pm Prerequisites: Math 55 or permission of instructor Required Text: Durbin, Eddy, Krogh and Mitchison, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~lpachter/127/ Grading: homework 50%, midterm 20%, final presentation/project 30% Homework: Weekly Comments: This course provides an introduction to the mathematical aspects of computational genomics with an emphasis on evolutionary biology. Math 128A - Section 1 - Numerical Analysis Instructor: Ming Gu Lectures: MWF 2:00-3:00pm, Room 60 Evans Course Control Number: 54775 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: R. L. Burden and J. D. Faires, Numerical Analysis, 8th edition Recommended Reading: Syllabus: In this course, we will learn some of the most basic concepts and methods in scientific computing. Many physical phenomena are governed by differential equations. Newton's second law of motion is in general a set of second order time-dependent differential equations. In this course our main goal is to develop a number of tools for solving these and other equations numerically. Our main focus is in developing numerical methods for such purposes. Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to the Theory of Sets Instructor: John Krueger Lectures: MWF 3:00-4:00pm, Room 85 Evans Course Control Number: 54790 Office: 751 Evans Office Hours: TBA Prerequisites: 113 and 104 Required Text: Yiannis Moschovakis, Notes on Set Theory Recommended Reading: Syllabus: Cardinality of sets, axioms of set theory, well-orderings, axiom of choice and its consequences, ordinal and cardinal numbers. Course Webpage: http://math.berkeley.edu/~jkrueger/math135.html Grading: Homework: Comments: The course, while primarily aimed at students interested in mathematical logic, will also benefit students in any area of pure mathematics, including abstract algebra and analysis. The course will help improve skills in abstract thinking and reading and writing of proofs, and also assist in developing a general perspective of mathematics from the foundational point of view. Math 142 - Section 1 - Elementary Algebraic Topology Instructor: Mauricio Velasco Lectures: MWF 9:00-10:00am, Room 71 Evans Course Control Number: 54793 Office: 1063 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 143 - Section 1 - Elementary Algebraic Geometry Instructor: David Eisenbud Lectures: TuTh 11:00am-12:30pm, Room 3102 Etcheverry Course Control Number: 54795 Office: 909 Evans Office Hours: Tu-Th 2:00-3:00pm (tentative) Prerequisites: Math 113 or the equivalent Required Text: Hassett, Introduction to Algebraic Geometry, (softcover), Cambridge U. Press Recommended Reading: Syllabus: Topics to be covered include affine and projective varieties, elimination theory, Groebner bases, Bezout's theorem, Grassmann varieties and the theory of algebraic curves, especially plane curves. Course Webpage: https://bspace.berkeley.edu Grading: Homework, two in-class tests, and a take-home final or project. Homework: Homework will be assigned every week. Comments: The course is suitable both for those interested in pure mathematics and for those interested in applications, as constructive and computational aspects of the subject will also be treated. Math 152 - Section 1 - School Curriculum Instructor: Emiliano Gomez Lectures: MWF 11:00am-12:00pm, Room 5 Evans Course Control Number: 54796 Office: 985 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 160 - Section 1 - History of Mathematics Instructor: Hung-Hsi Wu Lectures: TuTh 12:30-2:00pm, Room 85 Evans Course Control Number: 54802 Office: 733 Evans Office Hours: TBA Prerequisites: Math 53, 54, 113 Required Text: C.B. Boyer and U.C. Merzbach, A History of Mathematics, 2nd edition, Wiley, 1991 Recommended Reading: To be given throughout the course. Syllabus: After a very short chronological overview (two or three lectures) of the main events in the development of mathematics, we will trace the evolution of geometry, algebra, analysis, and number theory from the time of the Babylonians to the nineteenth century. The discussion of geometry and algebra will be intentionally brief, so that we can concentrate more on analysis and number theory. The Boyer-Merzbach text will be a main reference, but will not be followed chapter by chapter. Course Webpage: See b-space. Grading: Homework 30%, Midterm 20%, Final 50% Homework: Homework will be assigned every week, and due once a week. Students are expected to consult the web. Comments: The assignments and the exams will both involve writing short essays about historical or biographical information. Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Lek-Heng Lim Lectures: MWF 2:00-3:00pm, Room 70 Evans Course Control Number: 54805 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Marco Aldi Lectures: TuTh 11:00am-12:30pm, Room 75 Evans Course Control Number: 54808 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Michael Rose Lectures: MWF 8:00-9:00am, Room 75 Evans Course Control Number: 54811 Office: 849 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: J. Brown and R. Churchill, Complex Variables and Applications, 8th edition Recommended Reading: Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~rose/math185 Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam. Homework: Homework will be assigned once a week, and will be due on Wednesdays. Comments: Math 191 - Section 1 - Advanced Problem Solving Instructor: Olga Holtz Lectures: TuTh 3:30-5:00pm, Room 5 Evans Course Control Number: 54814 Office: 821 Evans Office Hours: TuTh 10:00-11:00am & by appt. Prerequisites: Math 16A-B, 53, 54, 55, or equivalent background Required Text: None: some reading material will be posted on the web. Recommended Reading: Gleason, A. M.; Greenwood, R. E.; and Kelly, L. M.; The William Lowell Putnam Mathematical Competition. Problems and solutions: 1938--1964. Mathematical Association of America, Washington, D.C., 1980. ISBN 0-88385-428-7 The William Lowell Putnam mathematical competition. Problems and solutions: 1965--1984. Edited by Gerald L. Alexanderson, Leonard F. Klosinski and Loren C. Larson. Mathematical Association of America, Washington, DC, 1985. ISBN 0-88385-441-4 Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi; The William Lowell Putnam Mathematical Competition, 1985--2000. Problems, solutions, and commentary. MAA Problem Books Series. ISBN 0-88385-807-X Syllabus: Mathematical induction. Integer and prime numbers. Congruence. Rational and irrational numbers. Complex numbers. Progressions and sums. Diophantine equations. Quadratic reciprocity. Basic theorems and techniques from algebra. Polynomials. Inequalities. Extremal problems. Limits. Integrals. Series. Differential equations. Combinatorial counting. Recurrence relations. Generating functions. The inclusion-exclusion principle. The pigeonhole principle. Combinatorial averaging. Course Webpage: http://www.cs.berkeley.edu/~oholtz/191/ Grading: Based on homework and class participation. Homework: Homework will be assigned on the web every week, due next week. Comments: This is an advanced class intended to improve students' problem solving skills. A sub-goal of this class is to prepare UC-Berkeley competitors for the Putnam competition. The class will be taught in an informal, problem-oriented way. Homework problems will require hard work, ingenuity, and good mathematical writing. Math 191 - Section 2 - Cryptography Instructor: Robert Coleman Lectures: MWF 11:00am-12:00pm, Room 4 Evans Course Control Number: 54817 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: In 1757, Cassanova could say: Five or six weeks later, she [Madame d'Urfé] asked me if I had deciphered the manuscript which had the transmutation procedure. I told her that I had. "Without the key, sir, excuse me if I believe the thing impossible." "Do you wish me to name your key, madame?" "If you please." I then told her the key-word, which belongs to no language, and I saw her surprise. She told me that it was impossible, for she believed herself the only possessor of that word which she kept in her memory and which she had never written down. I could have told her the truth -- that the same calculation which had served me for deciphering the manuscript had enabled me to learn the word -- but on a caprice it struck me to tell her that a genie had revealed it to me. This false disclosure fettered Madame d'Urfé to me. That day I became the master of her soul, and I abused my power. Every time I think of it, I am distressed and ashamed, and I do penance now in the obligation under which I place myself of telling the truth in writing my memoirs. In this course we'll see why he couldn't get away with it today. Course Webpage: Grading: Homework: Comments: Math 202A - Section 1 - Introduction to Topology and Analysis Instructor: Donald Sarason Lectures: MWF 8:00-9:00am, Room 60 Evans Course Control Number: 54910 Office: 779 Evans Office Hours: TBA Prerequisites: Math 104 or the equivalent, plus familiarity with basic set theory. There will be a handout on the axiom of choice and Zorn's lemma for those who want it. Required Text: None. See below for suggested references. Syllabus: POINT-SET TOPOLOGY. Fundamentals (such as open and closed sets, convergence, continuity, connectedness, boundary, closure, interior, etc.), metric spaces, product spaces, compactness, separationaxioms, theorems of Urysohn and Tietze, locally compact spaces, quotientspaces, 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. On average there will be 3-4 HW problems per week, many of them challenging. Comments: The lectures will be self-contained except for routine details. The basic approach will be abstract, but moderated by frequent examples. No textbook will be followed in detail. The following references are suggested. G. B. Folland, Real Analysis, Second Edition, Wiley Interscience, 1999 H. L. Royden, Real Analysis, Third Edition, Prentice Hall, 1988 J. L. Kelley, General Topology, Springer-Verlag, 1975 The books of Folland and Royden cover most of the material in Math 202AB, in some cases more thoroughly, in some cases less thoroughly, than in the courses. The classic of Kelley contains the material on topology in Math 202A, i.e., the first half of the course. Math 204 - Section 1 - Ordinary Differential Equations Instructor: Richard Borcherds Lectures: TuTh 9:30-11:00am, Room 81 Evans Course Control Number: 54913 Office: 927 Evans Office Hours: TuTh 11:00am-12:00pm Prerequisites: Math 104 Required Text: E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, ISBN-13:978-0898747553 (This is not the same as "Introduction to Ordinary Differential Equations" by Coddington.) Recommended Reading: Syllabus: Rigorous theory of ordinary differential equations. Fundamental existence theorems for initial and boundary value problems, variational equilibria, periodic coefficients and Floquet Theory, Green's functions, eigenvalue problems, Sturm-Liouville theory, phase plane analysis, Poincare-Bendixon Theorem, bifurcation, chaos. Course Webpage: http://math.berkeley.edu/~reb/204 Grading: Based on homework and possibly a final exam. Homework: To be assigned each week. Comments: Math 214 - Section 1 - Differentiable Manifolds Instructor: Mariusz Wodzicki Lectures: MWF 11:00am-12:00pm, Room 47 Evans Course Control Number: 54916 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 215A - Section 1 - Algebraic Topology Instructor: Christian Zickert Lectures: TuTh 11:00am-12:30pm, Room 3 Evans Course Control Number: 54919 Office: 1053 Evans Office Hours: TBA Prerequisites: Required Text: Glen E. Bredon, Topology and Geometry, GTM 139, Springer Recommended Reading: Allen Hatcher, Algebraic Topology, available at http://www.math.cornell.edu/~hatcher/AT/ATpage.html Syllabus: Fundamental group, covering spaces, homology and cohomology, homotopy groups. Course Webpage: http://math.berkeley.edu/~zickert/ Grading: Homework: Comments: Math C218A - Section 1 - Probability Theory Instructor: James Pitman Lectures: TuTh 12:30-2:00pm, Room 334 Evans Course Control Number: 54922 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: Ming Gu Lectures: MWF 10:00-11:00am, Room 5 Evans Course Control Number: 54925 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Matrix computations are among the most basic of all scientific computations. A surprising number of scientific and engineering problems can be formulated and solved effectively using matrix tools and algorithms. In this course we will introduce numerical methods for solving the three basic problems in matrix computations: linear systems of equations, linear least squares problems, and eigenvalue problems. Along the way, we will also discuss the two most important issues concerning a numerical method, namely speed (or computational efficiency) and accuracy. Course Webpage: Grading: Homework: Comments: Math 222A - Section 1 - Partial Differential Equations Instructor: Lawrence C. Evans Lectures: MWF 12:00-1:00pm, Room 3 Evans Course Control Number: 54928 Office: 1033 Evans Office Hours: TBA Prerequisites: Math 105 or Math 202A Required Text: Lawrence C. Evans, Partial Differential Equations, American Math Society. Recommended Reading: Syllabus: The theory of boundary value and initial value problems for partial differential equations, with emphasis on nonlinear equations. Laplace's equation, heat equation, wave equation, nonlinear first-order equations, conservation laws, Hamilton-Jacobi equations, Fourier transform, Sobolev spaces. Course Webpage: Grading: 25% homework, 25% midterm, 50% final Homework: I will assign a homework problem, due in one week, at the start of each class. Comments: Math C223A - Section 1 - Stochastic Processes Instructor: Sourav Chatterjee Lectures: TuTh 2:00-3:30pm, Room 330 Evans Course Control Number: 54931 Office: 333 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Percolation is one of the deepest and most well-researched branches of probability theory, and yet a repository of a large number of important open questions. Advances in percolation were responsible, in part, for Wendelin Werner's Fields Medal in 2006. The purpose of this course is to serve as an introduction to this fascinating and beautiful area of mathematics to advanced graduate students. Course Webpage: http://www.stat.berkeley.edu/~sourav/stat206Afall08.html Grading: Homework: Comments: Math 224A - Section 1 - Mathematical Methods for the Physical Sciences Instructor: F. Alberto Grünbaum Lectures: TuTh 9:30-11:00am, Room 5 Evans Course Control Number: 54934 Office: 903 Evans Office Hours: TuWTh 11:00am-12:00pm Prerequisites: Required Text: Stakgold, Green's functions and boundary value problems Recommended Reading: Syllabus: This is the first semester of a two semester sequence. The main topic here is basic functional analysis, i.e. infinite dimensional linear algebra. I would like to think of this class as "Functional Analysis in action" In this class we will see how this subject arises naturally form the study of concrete problems in ordinary and partial differential equations, Fourier and other transforms, Green functions, perturbation theory, etc. and how this has always been a natural tool to study many linear problems in several areas of physics, chemistry and related sciences. We will see that in many cases these tools are well suited to study non-linear problems too. In the first semester I will try to cover most of the material in Stakgold's book "Green's functions and boundary value problems". This will give us the tools needed to go into many "applications". I will supplement the material in the book with a number of concrete physical models such as Brownian motion. Course Webpage: Grading: Homework: There will be weekly assignments, mainly from the book. Comments: The grade will be based on the homework. Math 225A - Section 1 - Metamathematics Instructor: Leo Harrington Lectures: MWF 12:00-1:00pm, Room 35 Evans Course Control Number: 54937 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 11:00am-12:30pm, Room 70 Evans Course Control Number: 54940 Office: 1099 Evans Office Hours: TBA Prerequisites: Math 128A or equivalent knowledge of basic numerical analysis. Sufficient computer skills and gumption to download, compile, modify and run numerical packages written in Fortran and C. Required Text: Recommended Reading: E. Hairer, S. P. Norsett and G. Wanner, Solving ordinary differential equations, Second Edition (2 vols.), Springer U. M. Ascher, R. M. M. Mattheij, and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, SIAM, 1995 P. Deuflhard and F. Bornemann, Scientific Computing with Ordinary Differential Equations, Springer, 2002 Syllabus: The course will cover theory and practical methods for solving systems of one-dimensional differential and integral equations. Methods for solving initial value problems for systems of ordinary differential equations: construction, convergence and implementation: Classical multistep (Adams and BDF) and Runge-Kutta methods. Stable high-order deferred correction methods. Solution of initial value problems for systems of ordinary differential-algebraic equations. Solution of boundary value problems for systems of ordinary differential equations: Classical shooting and finite difference techniques. Divide and conquer algorithms for integral equations. Solution of boundary value problems for elliptic systems of linear partial differential equations: Second-order finite difference methods. Derivation and fast solution of boundary integral equations. Course Webpage: http://math.berkeley.edu/~strain/228a.F08/ Grading: Grades will be based on weekly problem sets, some individualized. Homework: Comments: Class Notes available from the course webpage. Math 229 - Section 1 - Theory of Models Instructor: Thomas Scanlon Lectures: TuTh 12:30-2:00pm, Room 5 Evans Course Control Number: 54943 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 239 - Section 1 - Algebraic Statistics Instructor: Bernd Sturmfels Lectures: TuTh 8:00-9:30am, Room 81 Evans Course Control Number: 54946 Office: 925 Evans Office Hours: W 9:00-11:00 and by appointment Prerequisites: Fluency in discrete probability and a serious interest in statistics. Knowledge of undergraduate abstract algebra (at the level of Math 113) and computational algebra (at the level of the [Cox-Little-O'Shea]). Experience with mathematical software (Matlab, R, Maple, Magma, M2, etc.) will be helpful. Required Text: There is no required text book for this course. Lecture notes will be posted at this website. Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~bernd/stat260.html Grading: The course grade will be based on both the homework and the course projects. Homework: There will be weekly homework during the first eight weeks of the course. Comments: Math 240 - Section 1 - Riemannian Geometry Instructor: Ian Agol Lectures: TuTh 9:30-11:00am, Room 47 Evans Course Control Number: 54949 Office: 907 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 250A - Section 1 - Groups, Rings, and Fields Instructor: David Eisenbud Lectures: TuTh 8:00-9:30am, Room 70 Evans Course Control Number: 54952 Office: 909 Evans Office Hours: Tu-Th 2:00-3:00pm (tentative) Prerequisites: Math 114 or consent of instructor. Required Text: Lorenz, Algebra, Vols. 1,2, Springer-Verlag Recommended Reading: Freyd, Abelian Categories (on course website). Lang, Algebra Syllabus: This course will focus on the basic problems of solving polynomial equations as a unifying theme in the study of groups, rings and fields, following the new text "Algebra", by Falko Lorenz (Vols. 1 and 2, Springer Verlag "Universitext".) Basic ideas of Category Theory will be introduced as well. From the Catalogue Description: Group theory, including the Jordan-Hoolder theorem and the Sylow theorems. Basic theory of rings and their ideals. Unique factorization domains and principal ideal domains. Modules. Chain conditions. Fields, including fundamental theorem of Galois theory, theory of finite fields, and transcendence degree. Course Webpage: https://bspace.berkeley.edu Grading: 50% homework, 20% midterm, 30% final Homework: Homework will be assigned in class, and due once a week. Comments: This course treats many of the same topics as in Math 113-114, but much faster and at a higher level of abstraction. Students will be expected to read the text independently, with only some of the topics covered in class. There will be a lot of independent reading and homework. Math 254A - Section 1 - Number Theory Instructor: Martin Olsson Lectures: MWF 2:00-3:00pm, Room 85 Evans Course Control Number: 54958 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: S. Lang, Algebraic Number Theory. Recommended Reading: Syllabus: This will be an introduction to algebraic number theory. I intend to cover Part I of Lang's book (Chapters I-VIII), and time permitting some selected topics from Parts two and three. This includes the basic theory of algebraic integers, completions, ramification, cyclotomic fields, Minkowski bound, and some basic properties of zeta and L-functions. Course Webpage: Grading: Based on weekly (substantial) homeworks. Homework: Weekly. Comments: Math 256A - Section 1 - Algebraic Geometry Instructor: Arthur Ogus Lectures: MWF 9:00-10:00am, Room 81 Evans Course Control Number: 54961 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: R. Hartshorne, Algebraic Geometry Recommended Reading: Qing Liu, Algebraic Geometry and Algebraic Curves A. Grothendieck and J. Dieudonne, Elements de Geometrie Algebrique Syllabus: Grothendieck's theory of schemes has proved to be a spectacularly successful foundation for algebraic geometry, providing the framework for the understanding and solution of many classical problems. It has also established a unification between geometry and number theory--arithmetic geometry''--that has been equally, if not more, spectacular, leading to solutions of the Weil conjectures, the Mordell conjecture, and the proof of Fermat's Last Theorem. My goal in this course will be to provide an introduction to scheme theory, preparing both for work both in classical'' algebraic geometry over the complex numbers and in the arithmetic'' theory of schemes over rings of integers in numberfields. Hartshorne's classic text will be our main guide, but I plan to supplement it with other more arithmetic treatments, including Grothendieck's EGA. I will skip chapter I of Hartshorne's book, beginning instead by discussing affine algebraic sets and spaces; then I will go straight to chapter II. Students should have a good foundation in commutative algebra, as well as some experience with global techniques in geometry (e.g. differential or algebraic topology). Course Webpage: http://math.berkeley.edu/~ogus/Math%20_256A--08/index.html Grading: Yes. Homework: Lots and lots. Comments: Math 261A - Section 1 - Lie Groups Instructor: Mark Haiman Lectures: MWF 10:00-11:00am, Room 145 McCone Course Control Number: 54967 Office: 855 Evans Office Hours: WF 1:30-3:00pm Prerequisites: Background in algebra and topology equivalent to 202A and 250A. Although 214 (Differential Manifolds) is the official prerequisite, I will review in the lectures those bits of differential geometry that we will needed. Required Text: Anthony W. Knapp, Lie Groups Beyond an Introduction, 2nd Edition Recommended Reading: Armand Borel, Linear Algebraic Groups, 2nd Enlarged Edition Syllabus: General theory of real and complex Lie groups and their Lie algebras; classification of compact Lie groups and complex semisimple Lie groups and their representations. I will also give an introduction to algebraic groups and Hopf algebras, to serve as preparation for Reshetikhin covering quantum groups in 261B. Course Webpage: http://math.berkeley.edu/~mhaiman/math261A-fall08 Grading: Based on homework assignments. Homework: Comments: Math 265 - Section 1 - Differential Topology Instructor: Peter Teichner Lectures: TuTh 11:00am-12:30pm, Room 85 Evans Course Control Number: 54970 Office: 703 Evans Office Hours: TBA Prerequisites: 214, 215A Required Text: Recommended Reading: Davis-Kirk, Milnor-Stasheff, Stong, Switzer are good text books. Syllabus: The course will start with a short survey on Morse theory and the s-cobordism theorem. Then the Thom-Pontrjagin construction will be discussed in detail. It translates smooth manifolds (with additional structure) up to bordism into the homotopy groups of certain Thom spaces. This will lead to the notion of Thom spectra and the associated homology theories. In some cases, these can be computed using characteristic classes which form the next topic of the class. We will then use characteristic numbers to write down certain genera (e.g. Todd-genus, L-genus, A-genus, Witten-genus) that have an interpretation as the index of elliptic operators. If time permits, the heat equation proof of the index theorem will be sketched with an emphasis on its relation to super symmetry. Course Webpage: Will appear at http://math.berkeley.edu/~teichner Grading: Homework: Regular homework will be offered. Comments: Math 270 - Section 1 - Hot Topics Course in Mathematics Instructor: Peter Teichner Lectures: Tu 3:30-5:00pm, Room 51 Evans Course Control Number: 54973 Office: 703 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 273I - Section 1 - Numerical Functional Analysis Instructor: Olga Holtz Lectures: TuTh 12:30-2:00pm, Room 81 Evans Course Control Number: 54978 Office: 821 Office Hours: TuTh 10:00-11:00am & by appt. Prerequisites: Math 104 & Math 110 & Math 128A or equivalent background Required Text: Online lecture notes by Carl de Boor (see http://pages.cs.wisc.edu/~deboor/717/) Recommended Reading: Syllabus: Fundamentals of normed linear spaces and their duals. Linear and nonlinear operators acting on normed linear spaces. Applications to approximate solutions of operator equations by discretization and iteration. Perturbation and error. Variational problems. Basics of approximation theory. Chapter headings: 1. Linear algebra. 2. Advanced calculus. 3. Normed linear spaces. 4. The (continuous) dual. 5. Baire category and consequences. 6. Convexity. 7. Inner product spaces. 8. Compact perturbation of the identity. 9. The spectrum of a linear map. 10. Linearization and Newton's method. Course Webpage: http://www.cs.berkeley.edu/~oholtz/273I/ Grading: Based on homework and final presentation. Homework: Homework will be assigned on the web every week, due next week. Comments: Math 276 - Section 1 - Topics in Topology Instructor: Constantin Teleman Lectures: TuTh 12:30-2:00pm, Room 9 Evans Course Control Number: 54979 Office: 905 Evans Office Hours: W 1:00-2:00pm, Th 5:00-6:30pm Prerequisites: Algebraic Topology 215A,B Required Text: A list of papers (downloadable) Recommended Reading: Félix, Halperin and Thomas, Rational Homotopy Theory, Springer GTM, 2001. Griffiths and Morgan, Rational Homotopy Theory and Differential Forms, Birkhäuser, 1983. Syllabus: The first 2/3 of the course will cover the description of rational homotopy types by differential graded algebras (Sullivan) and differential graded Lie algebras (Quillen). Some highlights include Haefliger's computation of the rational homotopy of spaces of maps and the formality theorem for compact Kähler manifolds. We will start with concrete constructions for single spaces and move on to the categorical set-up, and the main theorems on equivalences of homotopy categories. The final third of the course will discuss the non-commutative theory: A-infinity algebras and topological conformal field theories (after Kontsevich, Costello etc). Course Webpage: http://math.berkeley.edu/~teleman/Rat Grading: There will be a thoroughly thought-out system. Homework: Assigned periodically. Comments: Math 276 - Section 2 - Topics in Analysis - Smooth Algebras of Operators and K-Theory Instructor: Richard Melrose Lectures: MWF 1:00-2:00pm, Room 45 Evans Course Control Number: 54981 Office: 895 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: In this course I plan to describe aspects of smooth K-theory. I will start with a discussion of the algebra of smoothing operators in its various forms and properties including finite-dimensional approximation, the Fredholm determinant, group of invertible perturbations of the identity and hence to definitions of odd and even K-theory. Subsequently I will discuss: 1. The loop group and delooping sequence and the Chern character. 2. Semiclassical quantization and Bott periodicity. Thom isomorphism and Atiyah-Singer theorem. 3. The quantization (looping) sequence and Quillen's line bundle. 4. Segal's representation of the loop group and the K-theory gerbe. As time (and the enthusiasm of the audience) permits I will discuss K-homology, twisting of K-theory and bordism (for which I will need some pseudodifferential machinery which I will acquire by fiat). Course Webpage: Grading: Homework: Comments: Math 279 - Section 1 - Topics in Partial Differential Equations Instructor: Maciej Zworski Lectures: TuTh 2:00-3:30pm, Room 2 Evans Course Control Number: 54982 Office: 897 Evans Office Hours: M 2:00-3:00pm or by appt. Prerequisites: Math 222A or equivalent Required Text: Recommended Reading: S.H. Tang and M. Zworski, Potential scattering on the real line, http://math.berkeley.edu/~zworski/tz1.pdf J. Sjöstrand, Lectures on resonances, http://www.math.polytechnique.fr/~sjoestrand/CoursgbgWeb.pdf Syllabus: The course will provide an introduction to mathematical scattering theory from the PDE point of view. A basic graduate course in real and functional analysis is the only prerequisite. Needed facts, such as analytic Fredholm theory, or properties of solutions to hyperbolic equations will be developed as we move along. The ﬁrst quarter of the course will be based on the notes by S.H. Tang and M. Zworski (available on line, see above). That will introduce basic concepts of scattering theory in the simplest setting. There will be no formal requirements. 1. Scattering theory in one dimension: scattering matrix, resolvent spectral decomposition. 2. Trace formulae in one dimension; the Maaß-Selberg relation, the Eisenbud-Wigner formula. 3. Resonances: asymptotic distribution, complex scaling in one dimension, the Breit-Wigner formula. 4. Scattering theory of the free Laplacian: the resolvent, spectral decomposition, generalized eigenfuctions, absolute scattering matrix. 5. Compactly supported potentials: distorted Fourier transform, scattering matrix, wave operators. 6. Resonances in higher dimensions: upper bounds on the number of resonances, the method of complex scaling, Poisson formula for resonances, lower bounds on the density of resonances. 7. Possible additional topics: obstacle scattering, “black box” formalism, long range perturbations, scattering on manifolds. Course Webpage: Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor: The Staff Lectures: W 4:00-6:00pm, Room 70 Evans Course Control Number: 55663 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: