Spring 2005
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Math 1A - Section 1 - Calculus Instructor: Hung-Hsi Wu Lectures: MWF 1:00-2:00pm, Room 10 Evans Course Control Number: 54303 Office: 733 Evans Office Hours: TBA Prerequisites: Trigonometry and Analytic Geometry Required Text: Stewart, Calculus: Early Transcendentals, 5th edition, Brooks/Cole Recommended Reading: None Syllabus: Essentially the first six chapters of the text will be covered. A precise syllabus, including the weekly homework assignments, will be given in http://groups.yahoo.com/group/Math1AWu/ and in https://courseweb.berkeley.edu/courseweb/index.jsp AFTER January 10, 2005. Course Webpage: http://groups.yahoo.com/group/Math1AWu/ and https://courseweb.berkeley.edu/courseweb/index.jsp (valid only AFTER January 10, 2005) Grading: 20% homework and quizzes, 10% First Midterm, 20% Second Midterm, 50% final. Homework: Assigned weekly. Group work among students is encouraged, but note that "group work" does not mean "copy each other". Comments: This is not a cookbook course. It is a regular course in college mathematics. Mathematical reasoning and problem solving techniques are equally emphasized, and exam questions will include some that require explanations, which are sometimes called "proofs". Here are a few additional things you need to know: (A) About 80% of the exam questions will be close to the assigned homework problems, but no exam question will ever be exactly the same as a homework problem. (B) The lectures will generally follow the text; on the few occasions that they don't, it would be made explicit. (C) The course syllabus gives the sections of the textbook to be covered each week. It is important that you know ahead of time what to expect in each lecture. For this purpose, read the book ahead of the lecture. (D) The pace of the course is relentless. This is not like in high school when you can afford to goof off for a few days and catch up again. Don't goof off, ever. Math 1B - Section 1 - Calculus Instructor: Marina Ratner Lectures: MWF 2:00-3:00pm, Room 100 Lewis Course Control Number: 54336 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Calculus Instructor: Marina Ratner Lectures: MWF 12:00-1:00pm, Room 155 Dwinelle Course Control Number: 54375 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 3 - Calculus Instructor: Nicolai Reshetikhin Lectures: TuTh 2:00-3:30pm, Room 155 Dwinelle Course Control Number: 54408 Office: 917 Evans Office Hours: WTh 1:00-2:00pm Prerequisites: Prerequisites Math 1A or an equivalent course. Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Recommended Reading: Syllabus: Syllabus is available on my web-site (see below). Course Webpage: http://math.berkeley.edu/~reshetik/math1b.html Grading: See syllabus. Homework: The schedule of homeworks is in the syllabus. Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Alan Weinstein Lectures: TuTh 3:30-5:00pm, Room 155 Dwinelle Course Control Number: 54453 Office: 825 Evans Office Hours: Th 11:00am-12:00pm & 1:45-3:30pm (1st week of classes: W 11:15am-2:00pm) Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Required Text: Goldstein, Lay and Schneider, Calculus and its Applications, 10th edition, Prentice-Hall (Chapters 1-6) Recommended Reading: Syllabus: This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions. Course Webpage: http://math.berkeley.edu/~alanw/ Grading: The course grade will based on weekly homework and quizzes in section meetings, two midterm exams, and a final exam. Homework: There will be weekly problem sets. Comments: I expect students to come out of Math 16A as "informed consumers" rather than "professional producers" of calculus as used in the social and biological sciences. This means that there will be significant emphasis on understanding the concepts of calculus, not just methods of calculation, though the latter will not be ignored either. Students who expect to make extensive use of calculus in their further study and careers should take Math 1A instead. My lecture style tends to involve leaving some material for students to learn on their own from reading, saying more than I write on the board, and encouraging active participation by the class. Thus, students are expected to prepare for each lecture by attempting the reading assignment in advance. A course website (see http://www.math.berkeley.edu/~alanw) will contain homework assignments, solutions to homework problems, and a "bulletin board" for online discussion of questions relating to the course. Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Tom Graber Lectures: MWF 11:00am-12:00pm, Room 100 Lewis Course Control Number: 54492 Office: 833 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 2 - Analytical Geometry and Calculus Instructor: Vera Serganova Lectures: TuTh 3:30-5:00pm, Room 2050 Valley Life Science Course Control Number: 54525 Office: 709 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman Seminars Instructor: Jenny Harrison Lectures: F 3:00-4:00pm, Room 891 Evans Course Control Number: 54570 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - Freshman Seminars Instructor: Hung-Hsi Wu Lectures: W 2:00-3:30pm, Room 961 Evans Course Control Number: 54573 Office: 733 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 100 GPB Course Control Number: 54576 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Maciej Zworski Lectures: MWF 2:00-3:00pm, Room 2050 Valley Life Science Course Control Number: 54606 Office: 897 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: Mariusz Wodzicki Lectures: TuTh 12:30-2:00pm, Room 100 Lewis Course Control Number: 54645 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Craig Evans Lectures: MWF 3:00-4:00pm, Room 2050 Valley Life Science (plus discussion sections on TuTh) Course Control Number: 54684 Office: 907 Evans Office Hours: TBA Prerequisites: Math 1B Required Text: Special UCB paperback student editions of R. Hill, Elementary Linear Algebra and W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems Recommended Reading: Syllabus: Main topics: Linear equations and matrices Vector spaces Linear transformations Determinants and diagonalization Homogeneous ODE, Wronskians Systems of ODE Fourier series, solutions of PDE Course Webpage: TBA Grading: 20% quizzes and homework in sections, 20% each for the two midterms, 40% final Homework: Homework will be due twice a week, in the discussion sections. Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Arthur Ogus Lectures: TuTh 11:00am-12:30pm, Room 2050 Valley Life Science Course Control Number: 54729 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: Michael Christ Lectures: MWF 9:00-10:00am, Room 145 Dwinelle Course Control Number: 54768 Office: 809 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: The Staff Lectures: MWF 3:00-4:00pm, Room 6 Evans Course Control Number: 54789 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Robert Anderson Lectures: TuTh 11:00am-12:30pm, Room 71 Evans Course Control Number: 54843 Office: 501 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Dan Geba Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54846 Office: 837 Evans Office Hours: MWF 2:00-3:00pm Prerequisites: Math 53 and 54 Required Text: K.A. Ross, Elementary Analysis Recommended Reading: W. Rudin, Principles of Mathematical Analysis Syllabus: Real number system. Sequences. Series. Metric spaces. Continuous functions. Differentiation in one variable. Riemann integral. Course Webpage: Grading: Homework (25%), Midterm (25%), Final (50%) Homework: Assigned on Friday, due next Friday. Worst 3 homeworks not counted. No late homeworks. Comments: No make-up exams. Math 104 - Section 3 - Introduction to Analysis Instructor: Michael Klass Lectures: MWF 12:00-1:00pm, Room 332 Evans Course Control Number: 54849 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://socrates.berkeley.edu/~novello/104 Grading: Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Justin Holmer Lectures: MWF 10:00-11:00am, Room 75 Evans Course Control Number: 54852 Office: 849 Evans Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: Davidson & Donsig, Real Analysis with Real Applications, Prentice Hall Recommended Reading: For background, Spivak, Calculus or Ross, Elementary Analysis: The Theory of Calculus. For course companion material, Rudin, Principles of Mathematical Analysis. For follow-up material, Haaser & Sullivan, Real Analysis, or Royden, Real Analysis. Syllabus: The real number system. Sequences, limits, and continuous functions in R and Rn. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral. Course Webpage: http://math.berkeley.edu/~holmer/courses/s10404/ Grading: 25% homework/quizzes, 30% midterm, 45% final Homework: Homework will be assigned on the web every Wednesday, and due the following Wednesday. Comments: We will concentrate on Part A of the text, and perhaps cover some pieces of Part B on applications. I will leave the remainder of Part B as recommended follow-up reading. It introduces several areas of analysis that are active areas of modern research. Feel free to e-mail me with questions. Math 104 - Section 5 - Introduction to Analysis Instructor: Dapeng Zhan Lectures: TuTh 3:30-5:00pm, Room 285 Cory Course Control Number: 54855 Office: 873 Evans Office Hours: TBA Prerequisites: Math 53 and Math 54 Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer Recommended Reading: Syllabus: Real number system, Sequences, Series, Metric spaces, Continuous functions, Differentiation in one variable, Riemann integral, and etc. Course Webpage: http://math.berkeley.edu/~dapeng/ma104.html Grading: 20% homeworks, 20% each midterm, 40% final Homework: Homework will be assigned on Tuesday, and due next Tuesday. Comments: Math 105 - Section 1 - Analysis II Instructor: Paul Chernoff Lectures: MWF 10:00-11:00am, Room 85 Evans Course Control Number: 54858 Office: 933 Evans Office Hours: MWF 1:45-2:45pm Prerequisites: Math 104 Required Text: H.S. Bear, A Primer of Lebesgue Integration, second edition (2002), Academic Press. M. Rosenlicht, Introduction to Analysis, (paperback), Dover. Recommended Reading: Syllabus: Theory of solutions of ordinary differential equations. Implicit function theorem. Most of course: Lebesgue measure and integral. I welcome and encourage questions and comments. Course Webpage: Grading: 15% homework, 40% midterms and quizzes, 45% final. Homework: Weekly assignments. Comments: Math 110 - Section 1 - Linear Algebra Instructor: Kenneth A. Ribet Lectures: TuTh 12:30-2:00am, Room 10 Evans Course Control Number: 54861 Office: 885 Evans Office Hours: TBA Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: Friedberg, Insel and Spence, Linear Algebra, 4th edition (Prentice Hall, 2003). Recommended Reading: Syllabus: Matrices, vector spaces, linear transformations, linear functionals, inner products, determinants, eigenvectors, symmetric and orthogonal matrices, diagonalizability. Course Webpage: http://math.berkeley.edu/~ribet/110/; this page currently shows H110 from Fall, 2003 but will be updated for Spring, 2005. Grading: Based on two midterms, homework, quizzes and the final exam. Homework: Homework will be due weekly and is an essential part of the course. Comments: I hope to get to know you even though this will be a large class. Come to office hours; raise your hand during the lecture; speak to me before class begins; introduce yourself if you see me on campus. Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Leo Harrington Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54888 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Martin Weissman Lectures: TuTh 3:30-5:00pm, Room 75 Evans Course Control Number: 54894 Office: 1067 Evans Office Hours: TBA Prerequisites: Math 54 or Math 74 or Math 110 or Permission of Instructor. Required Text: Michael Artin, Algebra Recommended Reading: TBA Syllabus: A full syllabus will be given out on the first day of class. The course will cover the basic theory of groups and group actions, rings and fields. A focus will be on learning about these abstract algebraic objects by studying numerous concrete examples, especially in geometry, combinatorics, linear algebra, and number theory. Course Webpage: TBA Grading: 50% homework, 20% midterm, 30% final Homework: There will be weekly problem sets. Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Jack Wagoner Lectures: MWF 9:00-11:00am, Room 71 Evans Course Control Number: 54897 Office: 899 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 5 - Introduction to Abstract Algebra Instructor: Marc Rieffel Lectures: MWF 11:00am-12:00pm, Room 71 Evans Course Control Number: 54900 Office: 811 Evans Office Hours: TBA Prerequisites: Math 54 or equivalent linear algebra content. Required Text: Algebra, Abstract and Concrete, 2nd ed., F. M. Goodman, Prentice Hall. Recommended Reading: Syllabus: Groups and symmetry; Commutative rings, polynomials, factorization, fields. Some emphasis on writing proofs. Course Webpage: Grading: There will be homework, 2 midterm exams, and a final exam. Homework: Comments: Math H113 - Section 1 - Introduction to Abstract Algebra Instructor: Ai-Ko Liu Lectures: TuTh 11:00am-12:30pm, Room 85 Evans Course Control Number: 54903 Office: 905 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 114 - Section 1 - Abstract Algebra II Instructor: George M. Bergman Lectures: MWF 1:00-2:00pm, Room 75 Evans Course Control Number: 54906 Office: 865 Evans Office Hours: TuW 10:30-11:30am, F 4:15-5:15pm Prerequisites: Math 113 or consent of the instructor. The course is aimed at mathematics majors and others with a strong interest in mathematics. Required Text: Ian Stewart, Galois Theory, 3rd edition, Chapman and Hall/CRC, 2004. Recommended Reading: Syllabus: I hope we can cover the whole book, though it is a bit fatter than the Second Edition that I've taught the course from in the past. We'll see. Course Webpage: Grades: will be based on weekly homework (25%), two Midterms (15% and 20%), a Final (35%) and regular submission of the daily question (see Course Structure below) (5%). Subject matter: It is easy to see that a complex number z is real if and only if it is fixed (unmoved) by the operation of complex conjugation. This course develops a vast and beautiful generalization of that result, showing how questions of when an element of a field F belongs to a given subfield E can, in a large class of cases, be reduced to questions of which automorphisms of F the element is fixed by. The set of automorphisms of F that fix all elements of E forms a subgroup of the group G of all automorphisms of F, and we get a correspondence between subgroups of G and subfields of F, in which properties of the one can be related to properties of the other. This theory is the key to the solution of the famous problem of determining what regular polygons can be constructed by ruler and compass, and the demonstration that though one can give general formulas for the solution of a quadratic, cubic or quartic equation, one cannot do the same for quintic or higher-degree equations. Course structure: 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 will go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, and discuss points to watch out for in the next reading. A question a day: On each day for which there is assigned reading, each student is required to submit, preferably by e-mail before class, 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 will try to incorporate answers to students' questions into my lectures, though I may instead answer a question with a note to the student. 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. If you go to my web page of undergraduate handouts, http://math.berkeley.edu/~gbergman/ug.hndts, you will find at the bottom of that page my answers to selected questions submitted by students in a number of past courses, including Math 114 taught from the previous edition of this book. Math 118 - Section 1 - Wavelets and Signal Processing Instructor: Olga Holtz Lectures: MWF 1:00-2:00pm, Room 85 Evans Course Control Number: 54909 Office: 821 Evans Office Hours: MF 11:00am-12:00pm and by appt. Prerequisites: 53 and 54 Required Text: None Recommended Reading: Strang and Nguyen, Wavelets and Filter Banks Syllabus: data representation, Fourier series and orthogonal systems, Fourier transform, multiresolution analysis (MRA), construction of wavelets via MRA, properties of wavelets and scaling functions, splines, good representation systems, signal analysis, filter banks, applications to denoising, feature detection, and image compression Course Webpage: http://www.cs.berkeley.edu/~oholtz/118/index.html Grading: 30% homework, 30% first midterm, 40% final Homework: Assigned weekly, includes programming in MATLAB Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Paul Chernoff Lectures: MWF 3:00-4:00pm, Room 4 Evans Course Control Number: 54912 Office: 933 Evans Office Hours: MWF 1:45-2:45pm Prerequisites: Math 53 and 54 Required Text: Mary L. Boas, Mathematical Methods in the Physical Sciences, (second edition), Wiley. Recommended Reading: Syllabus: Review of series and partial differentiation. Functions of a complex variable. Laplace and Fourier transforms. Fourier series. Calculus of variations. Course Webpage: Grading: Based on homework, two midterms, and final. Homework: Weekly assignments. Comments: I welcome and encourage students' questions. Math 121B - Section 1 - Mathematical Tools for the Physical Sciences Instructor: F. Alberto Grünbaum Lectures: TuTh 8:00-9:30am, Room 9 Evans Course Control Number: 54915 Office: 903 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Jack Silver Lectures: TuTh 3:30-5:00pm, Room 9 Evans Course Control Number: 54918 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 126 - Section 1 - Introduction to Partial Differential Equations Instructor: L. Craig Evans Lectures: MWF 12:00-1:00pm, Room 247 Cory Course Control Number: 54921 Office: 907 Evans Office Hours: TBA Prerequisites: It would be good for students to have had Math 104, but this is not absolutely necessary. Required Text: Strauss, Partial Differential Equations: An Introduction, Wiley Recommended Reading: Syllabus: Main topics: Introduction Waves and diffusion Reflections and sources Boundary problems Laplace's equation, Green's functions More on wave propagation Nonlinear PDE Course Webpage: TBA Grading: 25% homework, 25% midterm, 50% final Homework: Homework will be assigned during every class, and each assignment is due in one week) Comments: Math 128A - Section 1 - Numerical Analysis Instructor: John Neu Lectures: TuTh 8:00-9:30am, Room 120 Latimer Course Control Number: 54924 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: No textbook. Set of notes will be available at Copy Central on Euclid. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128B - Section 1 - Numerical Analysis Instructor: Olga Holtz Lectures: MWF 3:00-4:00pm, Room 85 Evans Course Control Number: 54945 Office: 821 Evans Office Hours: MF 11:00am-12:00pm and by appt. Prerequisites: 110 and 128A Required Text: Mathews and Fink, Numerical Methods Using MATLAB Recommended Reading: Burden and Faires, Numerical Analysis Syllabus: introduction to MATLAB, iterative techniques in matrix algebra, finding eigenvalues and eigenvectors, boundary-value problems for ODEs, numerical solutions to PDEs Course Webpage: http://www.cs.berkeley.edu/~oholtz/128B/index.html Grading: 30% homework, 20% each midterm, 30% final Homework: Assigned weekly, includes programming in MATLAB Comments: Math 135 - Section 1 - Introduction to Theory Sets Instructor: Marina Ratner Lectures: MWF 10:00-11:00am, Room 6 Evans Course Control Number: 54951 Office: 827 Evans Office Hours: TBA Prerequisites: None, but an ability to understand proofs. Required Text: Enderton, Elements of Set Theory Recommended Reading: Syllabus: Zermelo-Frankel axiom system, relations and functions, the theory of natural numbers, cardinal numbers and the Axiom of Choice, well orderings and ordinals, transfinite induction, alephs. Course Webpage: Grading: The grade will be based 10% on the homework, 20% on quizzes, 30% on a midterm and 40% on the final. Homework: Comments: Math 140 - Section 1 - Metric Differential Geometry Instructor: Alexander Givental Lectures: TuTh 3:30-5:00pm, Room 433 Latimer Course Control Number: 54954 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 160 - Section 1 - History of Mathematics Instructor: Bjorn Poonen Lectures: MWF 8:00-9:00am, Room 3 Evans Course Control Number: 54957 Office: 879 Evans Office Hours: (starting 1/14/05) MWF 9:30-10:30am (tentative), or by appointment Prerequisites: Math 53, 54, and 113, or permission of instructor. Familiarity with other upper-division math courses (such as Math 104) may be helpful. Required Text: John Stillwell, Mathematics and its history, second edition, Springer, 2002. Recommended Reading: Syllabus: This course will be an overview of mathematics as a whole. It will focus on mathematical ideas, not the lives of the mathematicians. Most other upper-division courses offer a complete development of a particular subject, with all results proved, but because the list of topics for this course is so broad, we will omit many proofs and instead focus on the statements of the results and their interrelations. For specifics about the topics to be covered, see the table of contents of the text. We will cover most of the book. The text's "biographical notes" will not be covered in class, though you are welcome to read them on your own (they are interesting). Course Webpage: http://math.berkeley.edu/~poonen/math160.html Exams: There will be two in-class midterm exams and a 3-hour final exam. Grading: 35% homework, 15% first midterm, 15% second midterm, 35% final. Each homework grade below the weighted average of your final and midterm grades will be boosted up to that average. The course grade will be curved. Click here for an example. Homework: There will be weekly assignments posted on the web and due at the beginning of class each Monday. Late homework will not be accepted, but see the grading policy. You should not expect to be able to solve every single problem on your own; instead you are encouraged to discuss questions with each other or to come to office hours for help. If you meet with a study group, please think about the problems in advance and try to do as many as you can on your own before meeting. After discussion with others, write-ups must be done separately. (In practice, this means that you should not be looking at other students' solutions as you write your own.) Write in complete sentences whenever reasonable. Staple loose sheets! Comments: Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Daniel Geba Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54960 Office: 837 Evans Office Hours: MWF 2:00-3:00pm Prerequisites: Math 104 Required Text: J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th edition, 2004 Recommended Reading: Syllabus: Complex numbers. Analytic functions. Elementary functions. Integrals. Series. Residues and poles. Application of residues. Mapping by elementary functions. Course Webpage: Grading: Homework (25%), Midterm (25%), Final (50%) Homework: Assigned on Friday, due next Friday. Worst 3 homeworks not counted. No late homeworks. Comments: No make-up exams. Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Justin Holmer Lectures: MWF 8:00-9:00am, Room 71 Evans Course Control Number: 54963 Office: 849 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Stein & Shakarchi, Complex Analysis (Princeton Lectures in Analysis), Princeton University Press Recommended Reading: For background, Brown & Churchill, Complex Variables and Applications. For companion material, or a bit more advanced, see Ahlfors, Complex Analysis, or Conway, Functions of One Complex Variable I, or Ablowitz & Fokas, Complex Variables : Introduction and Applications (Cambridge Texts in Applied Mathematics). A quite different approach to the subject is Needham, Visual Complex Analysis. Syllabus: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping. Course Webpage: http://math.berkeley.edu/~holmer/courses/s18502/ Grading: 25% homework/quizzes, 30% midterm, 45% final Homework: Homework will be assigned on the web every Wednesday, and due the following Wednesday. Comments: We will aim to cover Chapters 1-7 of the text. The basic topics in the course are those listed in the syllabus description, although there should be time in a 15 week course to address some additional topics, such as Fourier transforms (Ch 4) and the gamma and zeta functions (Ch 5-6). Please feel free to e-mail me with questions. Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Dapeng Zhan Lectures: TuTh 11:00am-12:30pm, Room 75 Evans Course Control Number: 54966 Office: 873 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, 7th edition, the McGraw-Hill companies. Recommended Reading: Syllabus: Complex Numbers, Analytic Function, Complex Integral, Cauchy Theorem, Cauchy Formula, Power Series, Laurent Series, Residues, Residue Formula, Linear Transformation, Conformal Mapping, Harmonic Functions, and etc. Course Webpage: http://math.berkeley.edu/~dapeng/ma185.html Grading: 20% homeworks, 20% each midterm, 40% final Homework: Homework will be assigned on Tuesday and due next Tuesday. Comments: Math H185 - Section 1 - Introduction to Complex Analysis Instructor: Donald Sarason Lectures: MWF 8:00-9:00am, Room 5 Evans Course Control Number: 54969 Office: 779 Evans Office Hours: M 9:30-11:30am, Tu 10:00am-12:00pm Prerequisites: Math 104 Required Text: Donald Sarason, Notes on Complex Function Theory, published by Henry Helson Recommended Reading: James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, McGraw-Hill, 1996 Syllabus: The field of complex numbers, differentiation of functions of a complex variable, holomorphic functions, elementary functions, power series, complex integration, Cauchy's theorem and consequences, Laurent series, additional topics (including possibly the Riemann mapping theorem) Course Webpage: Grading: The course grade will be based on homework, two midterm examinations, and the final examination. Exams will most likely be open book. More details will be provided at the first class meeting. Homework: Homework will be assigned weekly and will be carefully graded. Comments: Complex analysis can be described as calculus with complex numbers, but that description does not do the subject justice. While complex analysis is in a sense a subdiscipline within the theory of maps between Euclidean spaces (in this case two-dimensional spaces), it has a character and an elegance of its own. The notion of complex differentiability, for instance, has remarkable implications one would not expect from the study of real analysis. The elegance of the subject is typified by its main theorem, Cauchy's theorem, which devotees regard as the portal to paradise. Besides being intrinsically beautiful, complex analysis is useful - its results and ideas permeate much of modern mathematics, including applied areas. The goal of Math H185 will be to provide students with a solid grounding in the subject so that they can continue its study at a higher level or use it in other areas. Math 187 - Section 1 - Senior Analysis Instructor: Daniel Tataru Lectures: TuTh 9:30-11:00am, Room 85 Evans Course Control Number: 54972 Office: 841 Evans Office Hours: TBA Prerequisites: Math 104 and 185 Required Text: E. Stein and R. Shakarchi, Fourier Analysis Recommended Reading: Syllabus: The course provides a more elementary yet rigorous introduction to Fourier Analysis. We begin with Fourier series and their summability, and continue with the study of the Fourier transform. Both as a motivation and as an application we consider along the way for many examples in partial differential equations. Additional topics will be covered as time permits. Course Webpage: http://math.berkeley.edu/~tataru Grading: Homework: Homework will be assigned on the web every class, and due once a week. Comments: Math 189 - Section 1 - Mathematical Methods in Classical and Quantum Mechanics Instructor: Remus Floricel Lectures: TuTh 9:30-11:00am, Room 4 Evans Course Control Number: 54975 Office: 759 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: The purpose of this course is to provide an introduction to spectral theory with applications in quantum mechanics. Topics will include: Hilbert spaces, Fock spaces, special classes of linear operators (compact operators, Hilbert-Schmidt and trace class operators, creation and annihilation operators), spectral theory of self-adjoint and normal operators. Course Webpage: Grading: Homework: Comments: Math 191 - Section 1 - Experimental Course in Cryptography Instructor: Kenneth A. Ribet Lectures: Class meetings will be at a time to be determined. I propose to meet on Wednesdays from 11:10 to 12:30. Please let me know if you are seriously interested in this course but have a conflict with this time slot. Course Control Number: 54978 Office: 885 Evans Office Hours: TBA Prerequisites: Math 113 and/or Math 115; a love of algebra. Some inclination to do machine computations would be a plus. Required Text: Johannes Buchmann, Introduction to Cryptography, 2nd edition by (Springer, 2004). Recommended Reading: William A. Stein, Elementary Number Theory and Victor Shoup, A Computational Introduction to Number Theory and Algebra Syllabus: We will study some common techniques in cryptography and investigate the mathematics behind them. Course Webpage: http://math.berkeley.edu/~ribet/191/; this page will be built before the semester starts. Grading: Based on some homework and especially on students' lectures in class. Homework: Homework will be assigned at irregular intervals and may include some simple programming projects. Comments: I know number theory pretty well but don't know cryptography. We will be learning the material together. Math 191 - Section 2 - Unsolvability, Undecidability, and Incompleteness Instructor: John Steel Lectures: TuTh 12:30-2:00pm, Room 85 Evans Course Control Number: 54981 Office: 717 Evans Office Hours: TBA Prerequisites: There is no pre-requisite for the course other than a general readiness to take upper division math. This will indeed be a rigorous math course, stressing exact definitions and honest proofs. It might be helpful to have taken 125A, or even just 110 or 113, but it is not necessary. Required Text: Nigel Cutland, Computabiity: An Introduction to Recursive Function Theory, Cambridge University Press Recommended Reading: Syllabus: The course title sounds a bit negative, doesn't it? Actually, we'll cover some of the most beautiful theorems in Logic, results of Church, Turing, Kleene, and Godel from the 1930's. These theorems established basic limitations on what can be computed by algorithm, and what is provable in axiomatic systems. The most famous of these results are probably Kurt Godel's incompleteness theorems, which we will cover toward the end of the semester. We shall follow Cutland's book, supplemented with handouts later in the course. Course Webpage: Grading: Homework: Comments: Math 191 - Section 3 - Research Seminar in Mathematical Modeling Instructor: TBA. For questions contact Anand Kulkarni, anandk [at] berkeley [dot] edu Lectures: TuTh 12:30-2:00pm, Room 321 Haviland Course Control Number: 54983 Office: Office Hours: TBA Prerequisites: No formal prerequisites; however, students who have not taken 53 and 54 will need to put in additional effort to acquire the necessary background. The class is designed to be accessible to students with some technical background. Lower-division students and non-math majors are encouraged to consider enrolling. Required Text: Recommended Reading: Syllabus: This seminar facilitates the development and execution of high-quality student research projects in mathematical modeling. Over the course of the semester, students will be introduced to general methods of applied mathematics and modeling techniques, with the goal of producing original applied mathematics research on problems of their choosing. Students will carry out three smaller team modeling projects along with a final independent research project, learning and designing the necessary mathematics as they go. The class will culminate in students' submission of an original mathematics research paper for publication in an academic journal. Coursework within the classroom will be complemented by the inclusion of visits to MSRI, guest lectures from practicing industry mathematicians, and field studies. The course will also prepare interested students for competition in the 2006 Mathematical Contest in Modeling. Course Webpage: TBA Grading: Grading will be based on three research projects and a final research paper, each on problems of the student's choosing. There may also be smaller assignments throughout the semester, such as student talks on specific mathematical topics. Homework: Comments: Math 202B - Section 1 - Introduction to Topology and Analysis Instructor: Marc Rieffel Lectures: MWF 10:00-11:00am, Room 71 Evans Course Control Number: 55071 Office: 811 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 205 - Section 1 - Theory of Functions of a Complex Variable Instructor: Maciej Zworski Lectures: MWF 1:00-2:00pm, Room 3109 Etcheverry Course Control Number: 55074 Office: 897 Evans Office Hours: TBA Prerequisites: Math 104, Math 185 or equivalent Required Text: L. Ahlfors, Complex Analysis Recommended Reading: L. Carleson and T. W. Gamelin, Complex Dynamics Syllabus: Review of basic complex analysis: linear fractional transformations, Cauchy’s theorem, calculus of residues, entire functions; Riemann mapping theorem, conformal and quasi-conformal mappings, classification of fixed points of holomorphic funtions; Rational iteration, Julia and Fatou sets; Classification of periodic components. Course Webpage: Grading: Homework: Comments: Math 209 - Section 1 - Von Neumann Algebras Instructor: Dan Voiculescu Lectures: MWF 12:00-1:00pm, Room 5 Evans Course Control Number: 55077 Office: 783 Evans Office Hours: TBA Prerequisites: From 206 commutative C*-algebras and spectral theory for normal operators. Required Text: Recommended Reading: Syllabus: The course will give an introduction to the basics of the theory of von Neumann algebras. Depending on how much time will be left after discussing the general theory, I would like to emphasize II1 factors, examples and probabilistic aspects. Course Webpage: Grading: Homework: Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Michael Hutchings Lectures: TuTh 8:00-9:30am, Room 31 Evans Course Control Number: 55080 Office: 923 Evans Office Hours: TBA Prerequisites: Math 215A or equivalent. Required Text: Milnor and Stasheff, Characteristic classes Recommended Reading: Bredon, Topology and geometry, plus assorted references to be given as we go along. Syllabus: Depending on where Math 215A ends, we will do something approximating the following: higher homotopy groups and obstruction theory, bundles and characteristic classes, spectral sequences, Morse theory and applications to differential topology. Course Webpage: http://math.berkeley.edu/~hutching/teach/215b/ Grading: The only official requirement is to write a term paper; please see the course webpage for details. Homework: Some exercises will be assigned but not graded. Comments: Math 220 - Section 1 - Methods of Applied Mathematics Instructor: Alexandre Chorin Lectures: MWF 1:00-2:00pm, Room 285 Cory Course Control Number: 55083 Office: 911 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: I expect to cover a variety of methods in stochastic analysis: Monte Carlo methods, sampling, filtering, stochastic ODEs, Langevin formalisms, path integrals, Feynman diagrams, and the like. A good account of some of these topics can be found in my lecture notes "Stochastic methods in applied mathematics and physics" available on my website. Course Webpage: http://math.berkeley.edu/~chorin/ Grading: Homework: There will be weekly homework sets. Comments: My lecturing style is informal and I enjoy class discussion. Math 222B - Section 1 - Partial Differential Equations Instructor: Fraydoun Rezakhanlou Lectures: MWF 11:00am-12:00pm, Room 31 Evans Course Control Number: 55086 Office: 815 Evans Office Hours: MWF 1:00-2:00pm Prerequisites: Required Text: Recommended Reading: Syllabus: The course starts with the Sobolev spaces. For this part of the course some knowledge of Lp spaces is helpful. We then discuss the existence and uniqueness of solutions to linear elliptic and parabolic PDEs. The nonlinear parabolic and elliptic PDEs will be treated using several approaches including variational techniques, monotonicity method, and the fixed point methods. We then develope the viscosity method for the general Hamilton-Jacobi Equations. The rest of the semester will be devoted to the systems of conservation laws and nonlinear wave equations. Course Webpage: Grading: Homework: There will be weekly homework assignments and one take-home exam. Comments: Math 224B - Section 1 - Mathematical Methods for the Physical Sciences Instructor: John Neu Lectures: TuTh 11:00am-12:30pm, Room 31 Evans Course Control Number: 55089 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 225B - Section 1 - Metamathematics Instructor: Jack Silver Lectures: TuTh 12:30-2:00pm, Room 72 Evans Course Control Number: 55092 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228B - Section 1 - Numerical Solution of Differential Equations Instructor: John Strain Lectures: TuTh 9:30-11:00am, Room 31 Evans Course Control Number: 55095 Office: 1099 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 245A - Section 1 - General Theory of Algebraic Structures Instructor: George M. Bergman Lectures: MWF 3:00-4:00pm, Room 7 Evans Course Control Number: 55098 Office: 865 Evans Office Hours: TuW 10:30-11:30am, F 4:15-5:15pm Prerequisites: The equivalent of one of Math H113, 114, or 250A, or consent of the instructor. Math 135 can also be helpful if you have not seen basic set theory in other contexts. Required Text: George M. Bergman, An Invitation to General Algebra and Universal Constructions (but see end of this announcement). Recommended Reading: Syllabus: The theme of Math 245A, as I teach it, is universal constructions. We begin with a well known case, the construction of free groups. We will develop this in three quite different ways, and show why they come to the same thing. We then examine a smorgasbord of other important universal constructions, noting similarities, differences, and general patterns. After that, we settle down to developing the tools needed to study the subject: Ordered sets and the axiom of choice, closure operators, category theory, and the general concept of a variety of algebras. (We in fact treat most of these, not merely as means to this goal, but as interesting landscapes worth lingering over.) We find that the free group construction is a particular example of an adjoint functor (it is left adjoint to the underlying set functor on groups), and eventually develop a magnificent result of Peter Freyd, characterizing those functors between varieties of algebras that have left adjoints, and determine, in several cases, all such examples. Course Webpage: Homework and grading: The text contains more interesting exercises than anyone could do; I will ask you to think briefly about each exercise, and select a few to hand in each week. Grades will be based mainly on this homework. Students wishing a reduced homework-load can enroll S/U. Comments: My philosophy is that it does not make sense to spend the classroom time using the instructor and students as an animated copying machine. Rather, the material that is typically delivered in a lecture should be put in duplicated notes which the students study, and class time should be devoted to the more human activities of discussing and clarifying the material, introducing some topics by the Socratic method, etc.. Such notes for Math 245, begun about 25 years ago and reworked each time I have taught the course, have developed into the text we will use. There are difficulties with this way of teaching if a textbook leaves out motivation, examples, etc., that might be included in a lecture; but I have made it a point to include these in the notes. Another problem is that doing the reading before class runs counter to the habits many students have acquired. To get around this, I require each student to hand in on each class day a question about the day's reading, preferably by e-mail at least an hour before class, so that I can prepare to address some of these questions in class. You can view the text online, and see how to purchase it, by clicking on the title above. However, I hope to get a somewhat revised version ready by January, so if you plan to take the course this Spring, don't buy your own copy before then. Math 250B - Section 1 - Commutative Algebra Instructor: Richard Borcherds Lectures: TuTh 2:00-3:30pm, Room 7 Evans Course Control Number: 55101 Office: 927 Evans Office Hours: TuTh 3:30-5:00pm Prerequisites: Math 250A Required Text: David Eisenbud, Commutative Algebra Recommended Reading: Syllabus: I intend to cover most of the first half of the book and possibly selected topics from the second half. Course Webpage: http://math.berkeley.edu/~reb/courses/250B/ Grading: Homework: Homework will be assigned on the web every week. Comments: Math 256B - Section 1 - Algebraic Geometry Instructor: Paul Vojta Lectures: TuTh 11:00am-12:30pm, Room 5 Evans Course Control Number: 55107 Office: 883 Evans Office Hours: TuTh 11:30am-1:00pm Prerequisites: Math 256A Required Text: Hartshorne, Algebraic Geometry, Springer Recommended Reading: Syllabus: The course will pick up where 256A left off and finish Chapter II (if necessary). After that, we will proceed on to do much of Chapter III (Cohomology), plus possibly a few sections of Chapter IV (Curves). Course Webpage: http://math.berkeley.edu/~vojta/256b.html Grading: Grades will be based on homework assignments. There will be no final exam, but the last problem set will be due about a week after the last day of classes. Homework: Weekly or biweekly, assigned in class. Comments: Math 258 - Section 1 - Classical Harmonic Analysis Instructor: Daniel Tataru Lectures: TuTh 12:30-2:00pm, Room 81 Evans Course Control Number: 55110 Office: 841 Evans Office Hours: TBA Prerequisites: Graduate real analysis, some complex analysis and some pde's Required Text: Recommended Reading: E. Stein, Harmonic Analysis Syllabus: The course will provide an overview of the major topics in harmonic analysis. This includes maximal functions, Hardy spaces, Calderon-Zygmund theory, oscillatory integrals and applications. As time permits we may explore additional topics of current interest. Course Webpage: http://math.berkeley.edu/~tataru Grading: Homework: Comments: Math 271 - Section 1 - Topics in Foundations Instructor: John Steel Lectures: TuTh 9:30-11:00am, Room 7 Evans Course Control Number: 55113 Office: 717 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Deformation Theory Instructor: Robin Hartshorne Lectures: TuTh 2:00-3:30pm, Room 6 Evans Course Control Number: 55116 Office: 881 Evans Office Hours: TBA Prerequisites: Basic familiarity with methods of algebraic geometry and schemes. 256A will be a good start, though I will also have to use some cohomology from time to time. Required Text: Lecture notes will be available. Recommended Reading: See references in notes. Syllabus: See comments below. Course Webpage: Grading: Any reasonable participation earns an A. Homework: By mutual agreement. Comments: The basic problem of deformation theory in algebraic geometry is when you have a family of objects (varieties, or subschemes in a fixed space, or line bundles or vector bundles on a fixed scheme, etc) to see what happens in a small deformation of one member of the family. Using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck, we study first what happens over small infinitesimal deformations, and then gradually build up to more global situations. There is no satisfactory reference for this material, because existing sources are either too elementary or impossible to understand. Therefore I will be using my own notes for the course. Basic topics will include *deformations over the dual numbers *smoothness and the infinitesimal lifting property *Zariski tangent space and obstructions to deformation problems. *prorepresentable functors of Schlessinger *infinitesimal study of moduli spaces such as the Hilbert scheme, Picard scheme, moduli of curves, and moduli of stable vector bundles. I expect to include important examples illustrating various aspects of the theory along the way. For example, when I first started thinking about teaching this course long ago, one of my goals was to understand the classical statement that every irreducible componene of the Hilbert scheme of curves of degree d in P^3 has dimension >= 4d. For the curious I will also try to say something about algebraic spaces and stacks if I can understand them well enough myself to say anything intelligent. Finally, I am open to suggestions and requests for topics to include, time permitting. Math 275 - Section 1 - Topics in Applied Mathematics - Scaling, Physical Similarity: Dimensional Analysis and the Renormalization Group Instructor: Grigori Barenblatt Lectures: TuTh 9:30-11:00am, Room 51 Evans Course Control Number: 55119 Office: 735 Evans Office Hours: TuTh 11:15am-12:50pm Prerequisites: No special knowledge of advanced mathematics and/or continuum mechanics will be assumed -- all needed concepts and methods will be explained on the spot. Syllabus: Similarity methods play an important and ever growing role in applied mathematics, including computing, and engineering science. Sometimes a simple application of dimensional analysis leads to results of extreme importance (e.g., Taylor-von Neumann scaling laws for intense blast waves; Kolmogorov scaling laws in turbulence). More recent concepts such as the renormalization group, fractals, etc., are in fact closely related to dimensional analysis and physical similarity. The proposed course will give a systematic presentation of similarity methods, including dimensional analysis, physical similarity, complete and incomplete similarity, intermediate asymptotics, the renormalization group and various types of self-similar solutions and scaling laws. The presentation will be illustrated by many examples, including the examples from turbulence and fracture. The typical difficulties arising in using similarity methods will be illustrated by examples. Required Text: Barenblatt, G. I., Scaling (Cambridge University Press, 2003) Recommended Reading: 1. Barenblatt, G. I., Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge University Press, 1996) 2. Goldenfeld, N. D., Lectures on Phase Transitions and Renormalization Group (Addison-Wesley, 1992) 3. Chorin, A. J., and Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (Springer, 1990) 4. Landau, L.D. and Lifsh itz, E.M., Theory of Elasticity (Pergamon Press, London, New York, 1986) 5. Landau, L.D. and Lifsh itz, E.M., Fluid Mechanics (Pergamon Press, London, New York, 1987) Homework: There will be no systematic homework. Comments: In the end of the course the instructor will give a list of 10 topics. Students are expected to come to the exam having an essay (5-6 pages) concerning one of these topics which they have chosen. They have to answer the detailed questions concerning this topic. After that general questions without details concerning the course will be asked. Math 275 - Section 2 - Duality and String Theory Instructor: Mina Aganagic Lectures: W 3:00-4:00pm, Room 2 Evans F 3:00-5:00pm, Room 9 Evans Course Control Number: 55121 Office: 715 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: The course will provide an introduction to exciting recent developments at the intersection of physics and mathematics. The main emphasis will be on duality relations between apparently unrelated physical and mathematical theories, which follow from string theory. We will begin with some physics and mathematics preliminaries. Topics discussed will include mirror symmetry, dualities of open and closed string theories which relate, e.g. Chern-Simons theory and Gromov-Witten theory or random matrix models and B-type topological string theory, and mathematics of black holes in string theory. Course Webpage: Grading: Homework: Comments: Math 276 - Section 1 - Topics in Topology Instructor: Peter Ozsvath Lectures: TuTh 5:00-6:30pm, Room 81 Evans Course Control Number: 55122 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 276 - Section 2 - Elliptic Cohomology Instructor: Peter Teichner Lectures: TuTh 11:00am-12:30pm, Room 285 Cory Course Control Number: 55125 Office: 703 Evans Office Hours: Tu 2:00-4:00pm Prerequisites: Some algebraic and differential topology. Required Text: Recommended Reading: Stephan Stolz and Peter Teichner, What is an elliptic object? Syllabus: In this topics course we'll explain one particular extra-ordinary cohomology theory, elliptic cohomology, from various points of view. One is purely homotopy theoretical and goes back to Hopkins-Miller. A different approach, using conformal field theory, will be explained in more detail, including the necessary preliminaries on von Neumann algebras and spin geometry. Course Webpage: http://math.berkeley.edu/~teichner/Courses/Elliptic.html Grading: Homework: Homework will be assigned regularly in class. Comments: Math 278 - Section 1 - New Topological Methods in Geometric Measure Theory Instructor: Jenny Harrison Lectures: MWF 11:00am-12:00pm, Room 51 Evans Course Control Number: 55128 Office: 851 Evans Office Hours: MWF 1:00-2:00pm Prerequisites: Linear Algebra, Vector Calculus Required Text: Recommended Reading: Harrison, Ravello Lecture Notes, New Topological Methods in Geometric Measure Theory Part I (draft). Flanders, Differential Forms with Applications to the Physical Sciences Syllabus: Geometric Measure Theory (GMT) is the study of domains, called currents, defined by deRham as dual spaces to differential forms. In this topics course we study an important subspace of currents, called chainlets, that are especially amenable to direct topological methods, without resorting to duality with differential forms. These methods lead to both simplifications and extensions of major results in GMT as well as entirely new results. Three celebrated results of GMT will be discussed from this viewpoint:
Grading: Homework: Comments: These lectures will extend the six lectures given by Professor Harrison at the Ravello Summer School for Mathematical Physics in October, 2004. The first half of the course will be devoted to fundamental mathematical principles related to the exterior calculus and Banach spaces. We will assume a background in linear algebra and vector calculus. There will be basic, instructional homework, optional challenge questions, and research problems in the second half of the course. In the second half, we will discuss theoretical implications and applications. At times, there will be brief excursions into applications that assume some knowledge of measure theory, topology, geometry, analysis, fractals, or physics, but the emphasis will be upon building the theory from first principles. Math 290 - Section 1 - Non-Axiomatic Quantum Field Theory Instructor: Peter Teichner Lectures: Th 12:30-2:00pm, Room 35 Evans Course Control Number: 55131 Office: 703 Evans Office Hours: Tu 2:00-4:00pm Prerequisites: Required Text: Recommended Reading: Syllabus: In this course we will go through parts of Steve Weinberg's book on quantum field theory in an attempt to understand some of the physicists motivation to introduce quantum fields. The book is written with an emphasis on discussing "why" this is a good formalism to describe the physical world. Participants will be giving one hour lectures on particular sections of the book, and there will be a discussion session after every lecture. Course Webpage: http://math.berkeley.edu/~teichner/Courses/QFT.html Grading: Homework: Comments: Math 290 - Section 2 - The Ising Model: From Statistical Physics to Asymptotic Combinatorics Instructor: Senya Shlosman Lectures: M 2:00-4:00pm, Room 1011 Evans Course Control Number: 55134 Office: TBA Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Barry Simon, The Statistical Mechanics of Lattice Gases, Vol. I, Princeton University Press, 1993. Sinai, Y. A., Theory of phase transitions: rigorous results, Pergamon Press, New York, 1982. S. Shlosman, The Method of Reflection Positivity in the Mathematical Theory of First-Order Phase Transitions, Russian Math. Surveys, 41:3, 83-134, 1986. Syllabus: In my course I am going to cover some rigorous results about the Ising model and other lattice models of statistical mechanics, as well as related results from combinatorics. To follow the course the needed prerequisites are basic facts of probability theory and measure theory, basic calculus, basic variation calculus. All the necessary concepts from these fields will be introduced as needed. The following topics will be discussed: Gibbs random fields (as natural analogs of Markov Chains). Phase transitions. Coexistence of phases and the geometry of interfaces. Reflection Positivity (application of methods of quantum field theory to rigorous statistical mechanics). Geometry of random droplets and random crystals, Wulff construction. Number partitions, Young diagrams, mausoleums, MacMahon formula, quantum hook formula. Planar and spatial tilings, asymptotic combinatorics. Course Webpage: Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor: Ole Hald Lectures: TBA Course Control Number: 55719 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: |
