Spring 2009
| Math 1A - Section 1 - Calculus Instructor: Zvezdelina Stankova Lectures: TuTh 3:30-5:00pm, Room 105 Stanley Course Control Number: 53903 Office: 713 Evans Office Hours: TuTh 2:00-3:30pm Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Recommended Reading: Syllabus: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. Course Webpage: The following course webpage will be updated in the beginning of the spring'09 term: http://math.berkeley.edu/~stankova/ Grading: 15% quizzes, 25% each midterm, 35% final Homework: Homework will be assigned on the web every class, and due once a week. Comments: Math 1B - Section 1 - Calculus Instructor: Marina Ratner Lectures: MWF 12:00-1:00pm, Room 2050 Valley LSB Course Control Number: 53942 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 2:00-3:00pm, Room 155 Dwinelle Course Control Number: 53981 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 3 - Calculus Instructor: Richard Borcherds Lectures: TuTh 12:30-2:00pm, Room 2050 Valley LSB Course Control Number: 54026 Office: 927 Evans Office Hours: TuTh 2:00-3:30pm Prerequisites: Math 1A Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Recommended Reading: Syllabus: Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. Course Webpage: http://math.berkeley.edu/~reb/1B/index.html Grading: 20% homework, 20% quizzes, 15% each midterm, 30% final Homework: Homework will be assigned on the web every week, and is due once a week. Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Hugh Woodin Lectures: TuTh 2:00-3:30pm, Room 155 Dwinelle Course Control Number: 54062 Office: 721 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Leo Harrington Lectures: MWF 11:00am-12:00pm, Room 1 Pimental Course Control Number: 54107 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 2 - Analytical Geometry and Calculus Instructor: Thomas Scanlon Lectures: TuTh 11:00am-12:30pm, Room 105 Stanley Course Control Number: 54152 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - The Mathematics of Gambling Instructor: Alberto Grünbaum Lectures: Tu 11:00am-12:30pm, Room 939 Evans Course Control Number: 54182 Office: 903 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - What is Happening in Math and Science? Instructor: Jenny Harrison Lectures: F 3:00-4:00pm, Room 891 Evans Course Control Number: 54185 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 3 - Flipping Coins and Other Fun Problems in Probability Theory Instructor: Nicolai Reshetikhin Lectures: Tu 1:00-3:00pm, Room 740 Evans Course Control Number: 54187 Office: 915 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: The goal of this course is an introduction to probability and its applications. Flipping a coin and estimating how many times it will land on one side and how many times it will land on the other side is a good illustration to how determinism enters into randomness. We will start with this example (after a short recollection of basic principles of probability). We will compute the probability of a coin landing n times on one side after N flipping. Then we will discuss random processes and an important class known as Markov processes. We will also discuss the question known in probability theory as large deviations and will see that some times there is an element of determinism in randomness. We will consider some simple combinatorial examples such as pile of squares to illustrate this phenomenon. The seminar will start with a series of introductory lectures, and then, towards the end of the seminar, students will give presentations. Knowledge of elements of probability theory is desirable but not required. The list of suggested reading will be given on the first seminar and will be posted at the seminar's web site before the beginning of the semester. Course Webpage: Grading: Homework: Comments: The class is P/NP. The class will meet for the first 10 weeks of the semester. Math 32 - Section 1 - Precalculus Instructor: Michael Rose Lectures: MWF 8:00-9:00am, Room 101 Valley LSA Course Control Number: 54188 Office: 849 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 39A - Section 1 - Seminar for Teaching Math in Schools Instructor: Emiliano Gomez Lectures: M 2:00-4:00pm, Room 45 Evans Course Control Number: 54202 Office: 985 Evans Office Hours: TBA Prerequisites: Math 1A Required Text: None Recommended Reading: To be handed out in class. Syllabus: We will discuss important mathematics topics for students in K-12, interesting mathematics problems for collaborative group work, and issues pertaining to the practice of teaching. The course includes a field placement in a local school. Course Webpage: Grading: Based on homework, journal of field placement observations, and a final project. Homework: There will be weekly homework assigned during class. Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: James Sethian Lectures: TuTh 8:00-9:30am, Room Wheeler Auditorium Course Control Number: 54224 Office: 725 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: Paul Vojta Lectures: TuTh 9:30-11:00am, Room 2050 Valley LSB Course Control Number: 54281 Office: 883 Evans Office Hours: MTuTh 2:00-3:00pm (subject to change) 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: The topics for the course will be:
Course Webpage: http://math.berkeley.edu/~vojta/54.html Grading: Grading will be based on:
The component of the grade coming from discussion sections is left to the discretion of the section leader, but it is likely to be determined primarily by weekly quizzes and homework assignments. Homework: Weekly homework will be assigned; the exact problems will be made available closer to the start of the semester. Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Jack Wagoner Lectures: MWF 10:00-11:00am, Room 1 Pimentel Course Control Number: 54320 Office: 899 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: Bernd Sturmfels Lectures: TuTh 8:00-9:30am, Room 145 Dwinelle Course Control Number: 54359 Office: 925 Evans Office Hours: W 8:00-11:00am Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B is recommended but not required. Freshmen with strong high school math background and a possible interest in majoring in mathematics are encouraged to take this course. Required Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th Edition Recommended Reading: Syllabus: This course provides an introduction to logic and proof techniques, basics of set theory, algorithms, elementary number theory, combinatorial enumeration, discrete probability, graphs and trees, with a view towards applications in engineering and the life sciences. It is designed for majors in mathematics, computer science, statistics, and other related science and engineering disciplines. Course Webpage: http://math.berkeley.edu/~bernd/math55.html Grading: 5% quizzes, 15% homework, 20% each of two midterm exams, 40% final exam Homework: Weekly homework will be due on Mondays and returned in discussion sections on Wednesdays. Comments: Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: Daniel Berwick-Evans Lectures: MWF 3:00-4:00pm, Room 87 Evans Course Control Number: 54374 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C103 - Section 1 - Introduction to Mathematical Economics Instructor: David Ahn Lectures: TuTh 2:00-3:30pm, Room 101 Wurster Course Control Number: 54434 Office: 549 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Shamgar Gurevitch Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54437 Office: 867 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Brett Parker Lectures: TuTh 3:30-5:00pm, Room 4 Evans Course Control Number: 54440 Office: 796 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Sebastian Herr Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54443 Office: 837 Evans Office Hours: TBA Prerequisites: Math 53 and Math 54 Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer (latest edition). Recommended Reading: You may find the following book helpful (optional): Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill. Syllabus: This course provides an introduction to Mathematical Analysis with a focus on rigorous theory and mathematical reasoning. The main topics are the following: The real numbers, countable and uncountable sets. Sequences and limits, Cauchy sequences, subsequences, infinite series. Metric spaces, compactness. Limits of functions, continuous functions, uniform continuity. Power series, exponential and trigonometric functions, uniform convergence of sequences of functions, interchange of limit operations. Differentiation, the mean value theorem and applications. The Riemann integral, the fundamental theorem of calculus, Taylor's theorem. Course Webpage: http://math.berkeley.edu/~herr/104S3Spring09.html Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam Homework: Homework will be assigned every Tuesday and will be due on the following Tuesday, 9:30am in class. Comments: For more information, please take a look at the course webpage. Math 104 - Section 4 - Introduction to Analysis Instructor: Michael Klass Lectures: MWF 1:00-2:00pm, Room 332 Evans Course Control Number: 54446 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Lek-Heng Lim Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54449 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 105 - Section 1 - Second Course in Analysis Instructor: John Krueger Lectures: MWF 4:00-5:00pm, Room 85 Evans Course Control Number: 54452 Office: 751 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: James R. Munkres, Analysis on Manifolds and Howard Wilcox and David Meyers, An Introduction to Lebesgue Integration and Fourier Series Recommended Reading: Syllabus: Differential calculus in Rn: the derivative as a linear map; the chain rule; inverse and implicit function theorems. Lebesgue integration on the line; comparison of Lebesgue and Riemann integrals. Convergence theorems. Fourier series, L2 theory. Fubini's theorem, change of variable. Course Webpage: http://math.berkeley.edu/~jkrueger/math105.html Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Ole Hald Lectures: MWF 2:00-3:00pm, Room 71 Evans Course Control Number: 54455 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 2 - Linear Algebra Instructor: Joshua Sussan Lectures: MWF 11:00am-12:00pm, Room 2 Evans Course Control Number: 54458 Office: 761 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 3 - Linear Algebra Instructor: Mariusz Wodzicki Lectures: TuTh 9:30-11:00am, Room 200 Wheeler Course Control Number: 54461 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 4 - Linear Algebra Instructor: Chung Pang Mok Lectures: TuTh 11:00am-12:30pm, Room B51 Hildebrand Course Control Number: 54464 Office: 889 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~mok/110.html Grading: Homework: Comments: Math 110 - Section 5 - Linear Algebra Instructor: Alexander Givental Lectures: MWF 9:00-10:00am, Room 110 Barker Course Control Number: 54467 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Alexander Paulin Lectures: MWF 12:00-1:00pm, Room 71 Evans Course Control Number: 54470 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Chung Pang Mok Lectures: TuTh 2:00-3:30pm, Room 3107 Etcheverry Course Control Number: 54473 Office: 889 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~mok/113.html Grading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Alexander Paulin Lectures: MWF 3:00-4:00pm, Room 2 Evans Course Control Number: 54476 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: < Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Brett Parker Lectures: TuTh 12:30-2:00pm, Room 71 Evans Course Control Number: 54479 Office: 796 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H113 - Section 1 - Honors Introduction to Abstract Algebra Instructor: George Bergman Lectures: MWF 3:00-4:00pm, Room 85 Evans Course Control Number: 54482 Office: 865 Evans Office Hours: Tu 10:30-11:30am, W 4:15-5:15pm, F 10:30-11:30am 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: David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd edition, Wiley (2004) Recommended Reading: None. Syllabus: I expect to cover most of Chapters 1-9 and sections 13.1-13.2, and possibly a few other topics. Course Webpage: None. Grading: Homework (25%), two Midterms (15% and 20%), a Final (35%), and regular submission of the daily question (see below) (5%). Homework: An important part of the learning process! Will generally be due on Wednesdays. Comments: Abstract algebra is the study of sets of elements on which one or more operations are defined, which satisfy specified laws. The most familiar examples are various systems of numbers, under the usual operations of addition, multiplication, etc.. But you have already had a taste of the exotic: In Math 54 you saw matrices, and the fact that their multiplication operation does not satisfy the commutative law xy = yx. This course will mainly study two sorts of algebraic structures: groups, and commutative rings (including fields). I am not happy with 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 this reading and have thought about the what you've read. In lecture I go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, motivate ideas in the next reading, discuss points to watch out for in that 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 114 - Section 1 - Second Course in Abstract Algebra Instructor: Lek-Heng Lim Lectures: MWF 12:00-1:00pm, Room 6 Evans Course Control Number: 54485 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 116 - Section 1 - Cryptography Instructor: Kenneth A. Ribet Lectures: TuTh 11:00am-12:30pm, Room 3 Evans Course Control Number: 54488 Office: 885 Evans Office Hours: TBA Prerequisites: Math 55 is the official prerequisite. In addition, it would be helpful to have had one or more of Math 110, Math 113, Math 115. If you have had a couple of these upper-division courses but have never taken Math 55, that should be fine. Required Text: An introduction to mathematical cryptography (Springer link) by Hoffstein, Pipher and Silverman Recommended Reading: There are lots of interesting books that have been written about cryptography. During the winter break, you might want to borrow one or more from your public library. Perhaps Simon Singh's The Code Book is a good place to start. Syllabus: The catalog description is very terse: "Construction and analysis of simple cryptosystems, public key cryptography, RSA, signature schemes, key distribution, hash functions, elliptic curves, and applications". The book covers these topics and more. We'll start on page 1 and see how far we can get. Course Webpage: http://math.berkeley.edu/~ribet/116/, but it doesn't exist yet. Look for it in December. Grading: Something like 20% homework, 15% each midterm, 50% final. That's my standard mix. Homework: A fair amount, assigned weekly. Comments: The book claims to be self-contained, but it includes compact summaries of material from and abstract and linear algebra and from number theory. If you haven't had courses in these subjects, be prepared for moments when you will need to digest a lot of material in a short amount of time. I would recommend purchasing the book well ahead of time and looking over the contents to see whether there are passages that will be problematic for you. If there are such passages, devote some time to mastering them before the start of the semester. Math 118 - Section 1 - Fourier Analysis, Wavelets, and Signal Processing Instructor: Jon Wilkening Lectures: TuTh 11:00am-12:30pm, Room 71 Evans Course Control Number: 54491 Office: 1091 Evans Office Hours: TBA Prerequisites: Math 53 and 54 or equivalent Required Text: Boggess & Narcowich, A First Course in Wavelets with Fourier Analysis Recommended Reading: Yves Nievergelt, Wavelets Made Easy Stephane Mallat, A Wavelet Tour of Signal Processing Syllabus: This course will cover the basic mathematical theory and practical applications of Fourier analysis and wavelets, including one-dimensional signal processing and multi-dimensional image processing:
Grading: 30% homework, 30% midterm, 40% final Homework: 8-10 assignments, some involving programming in Matlab Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Shamgar Gurevitch Lectures: MWF 12:00-1:00pm, Room 75 Evans Course Control Number: 54494 Office: 867 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121B - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Vera Serganova Lectures: MWF 1:00-2:00pm, Room 75 Evans Course Control Number: 54497 Office: 709 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: John Neu Lectures: TuTh 9:30-11:00am, Room 75 Evans Course Control Number: 54500 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Per-Olof Persson Lectures: MWF 10:00-11:00am, Room 160 Kroeber Course Control Number: 54503 Office: 1089 Evans Office Hours: TBA Prerequisites: Math 53 and 54, basic programming skills Required Text: R. L. Burden and J. D. Faires, Numerical Analysis, 8th edition, Brooks-Cole, 2005. Recommended Reading: J. Dorfman, Introduction to MATLAB Programming, Decagon Press, Inc. Syllabus: Basic concepts and methods in numerical analysis: Solution of equations in one variable; Polynomial interpolation and approximation; Numerical differentiation and integration; Initial-value problems for ordinary differential equations; Direct methods for solving linear system; Least square approximation. Course Webpage: http://math.berkeley.edu/~persson/128A Grading: Homework (30%), midterm exams (20% + 20%), final exam (30%). Homework: Assigned weekly. Comments: Math 128B - Section 1 - Numerical Analysis Instructor: Ming Gu Lectures: MWF 2:00-3:00pm, Room 9 Evans Course Control Number: 54521 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 130 - Section 1 - The Classical Geometries Instructor: Vera Serganova Lectures: MWF 10:00-11:00am, Room 85 Evans Course Control Number: 54527 Office: 709 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory Sets Instructor: Thomas Scanlon Lectures: TuTh 12:30-2:00pm, Room 75 Evans Course Control Number: 54530 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 136 - Section 1 - Incompleteness and Undecidability Instructor: John Steel Lectures: TuTh 11:00am-12:30pm, Room 5 Evans Course Control Number: 54533 Office: 717 Evans Office Hours: TBA Prerequisites: Math 55 would help. Math 125A might help a little. Math 113, or some equivalent experience with abstract mathematics (definitions, theorems, and proofs), might help. Nevertheless, the course will be self-contained. Required Text: Nigel Cutland, Compatibility: 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. Among these results are Kurt Godel's famous incompleteness theorems, which we will cover toward the end of the semester. Course Webpage: http://math.berkeley.edu/~steel/courses/Courses.html Grading: Homework: Homework will be assigned weekly. The assignments will be announced at lecture and posted on the web at http://math.berkeley.edu/~steel/courses/Courses.html Comments: There will be two midterms, the first in late February or early March, after we have covered Chapter 5, and the second in late April. I will announce the exact date for each midterm at least 2 weeks in advance of it. There will be a written final exam as well. Math 140 - Section 1 - Metric Differential Geometry Instructor: Fraydoun Rezakhanlou Lectures: MWF 3:00-4:00pm, Room 6 Evans Course Control Number: 54536 Office: 815 Evans Office Hours: MWF 2:00-3:00pm Prerequisites: Math 140 Required Text: Richard S. Millman and George D. Parker, Elements of Diff erential Geometry, Prentice-Hall Inc. Recommended Reading: Syllabus: This class will be an introduction to the mathematical theory of curves and surfaces. The main topics are: 1. Frenet-Serret formula, isoperimetric inequality. 2. Local theory of surfaces in Euclidean space, first and second fundamental forms, Gaussian and mean curvature. 3. Gauss's Theorema Egregium, geodesics, parallelism, the Gauss-Bonnet Theorem. 3. Manifolds and linear connections. Course Webpage: Grading: Homework 30 points, Midterm 30 points, Final exam 40 points. Homework: Comments: Math 141 - Section 1 - Elementary Differential Topology Instructor: Rob Kirby Lectures: MWF 9:00-10:00am, Room 81 Evans Course Control Number: 54539 Office: 919 Evans Office Hours: MW 10:00-11:00am, Th 11:00am-12:00pm Prerequisites: Math 104 and Linear algebra. Required Text: J. Munkres, Analysis on Manifolds Recommended Reading: Michael Spivak, Calculus on Manifolds Syllabus: Inverse and implicit function theorems, Sard's Theorem, transversality, manifolds, differential forms, integration on manifolds, de Rham cohomology. Course Webpage: http://math.berkeley.edu/~kirby/math141.html Grading: 10% homework, 20% each of two midterms, 50% final. Homework: Homework will be assigned and due once a week. Comments: Math 151 - Section 1 - Mathematics of the Secondary School Curriculum I Instructor: Hung-Hsi Wu Lectures: MWF 2:00-3:00pm, Room 3 Evans Course Control Number: 54542 Office: 733 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 153 - Section 1 - Mathematics of the Secondary School Curriculum III Instructor: Hung-Hsi Wu Lectures: MWF 11:00am-12:00pm, Room 75 Evans Course Control Number: 54548 Office: 733 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 170 - Section 1 - Mathematical Methods for Optimization Instructor: John Strain Lectures: TuTh 3:30-5:00pm, Room 85 Evans Course Control Number: 54554 Office: 1099 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 172 - Section 1 - Combinatorics Instructor: Mauricio Velasco Lectures: TuTh 2:00-3:30pm, Room 75 Evans Course Control Number: 54557 Office: 1063 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 1 - Introduction to Complex Analysis Instructor: John Lott Lectures: MWF 10:00-11:00am, Room 71 Evans Course Control Number: 54560 Office: Office Hours: MWF 11:00am-12:00pm Prerequisites: Math 104 Required Text: Brown and Churchill, Complex Variables and Applications, McGraw-Hill, 8th Edition Recommended Reading: Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~lott/185.html Grading: Final 30%, Midterms 30%, Homework 40% Homework: Weekly Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Sebastian Herr Lectures: TuTh 2:00-3:30pm, Room 71 Evans Course Control Number: 54563 Office: 837 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Donald Sarason, Complex Function Theory, American Mathematical Society (latest edition). Recommended Reading: You may find the following textbook helpful (optional): J.W. Brown and R.V. Churchill, Complex Variables and Applications, McGraw Hill. Syllabus: The main topics are the following: 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, conformal maps. We will discuss futher topics if time permits. Course Webpage: http://math.berkeley.edu/~herr/185S2Spring09.html Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam Homework: Homework will be assigned every Tuesday and will be due on the following Tuesday, 2:00pm in class. Comments: For more information, please take a look at the course webpage. Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Marco Aldi Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54566 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H185 - Section 1 - Honors Introduction to Complex Analysis Instructor: Marina Ratner Lectures: MWF 10:00-11:00am, Room 81 Evans Course Control Number: 54569 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: John Conway, Functions of one complex variable, Springer, 2nd ed. Recommended Reading: Syllabus: Analytic functions, Cauchy's Integral Theorem, Power Series, Laurent Series, singularities of analytic functions, the Residue Theorem with applications to definite integrals. Identity Theorem, Maximum Modulus Theorem, Open Mapping Theorem. Harmonic Functions. Course Webpage: Grading: The grade will be based: 15% on a weekly homework, 20% on quizzes, 25% on a mid-term, 40% on a final exam. Homework: Weekly. Comments: Math 191 - Section 1 - Experimental Courses in Mathematics Instructor: Alberto Grünbaum Lectures: MWF 4:00-5:30pm, Room 3107 Etcheverry Course Control Number: 54572 Office: 903 Evans Office Hours: TBA Prerequisites: The official prerequisites are Math 53 and Math 54. Having taken Math 55 or an upper division class or two will be useful. Required Text: None. Recommended Reading: All books in the Math/Stat library. Syllabus: Students will work in teams on three open-ended projects over the course of the semester, using any means they choose. They will write reports and give presentations for the other teams. The objective is to gain research experience by working on interesting, tractable problems. Course Webpage: TBA Grading: Approximately 50% written reports and 50% presentations. Homework: The three projects. Comments: Math 202B - Section 1 - Introduction to Topology and Analysis Instructor: Don Sarason Lectures: MWF 8:00-9:00am, Room 70 Evans Course Control Number: 54683 Office: 779 Evans Office Hours: TBA Prerequisites: Math 202A or the equivalent Required Text: No text will be followed in detail. Recommended Reading: Folland's Real Analysis and Rudin's Functional Analysis could be helpful references. Syllabus: CONTINUATION OF MEASURE THEORY. Product measures, Fubini's theorem, Tonelli's theorem, the distribution function, convolution. Signed measures, Hahn decomposition. Absolute continuity, Radon-Nikodym theorem, Lebesgue decomposition, differentiation of measures in N-space. Measure theory in locally compact spaces. FUNCTIONAL ANALYSIS. Banach spaces and their duals, Hahn-Banach theorem, biduals, quotient spaces. Bounded linear transformations, principle of uniform boundedness, open mapping theorem,. Topological vector spaces, dual pairs, separation theorem, locally convex spaces, polar sets, bipolar theorem. Weak and weak-* topologies, Banach-Alaoglu theorem, Banach-Krein-Smulyan theorem. Extreme points, Krein-Milman theorem. Possible additional topics. Applications of most of the main theorems will be given. Course Webpage: Grading: The course grade will be based on weekly homework assignments, which will be carefully graded. No exam. Homework: See above. Comments: Except for routine details and an occasional handout, the lectures will be self-contained. Math 203 - Section 1 - Singular Perturbation Methods in Applied ODE and PDE Instructor: John Neu Lectures: TuTh 12:30-2:00pm, Room 7 Evans Course Control Number: 54686 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus:
Course Webpage: Grading: 50% problem sets, 20% midterm, 30% final Homework: Lots. Comments: May the force be with you. Math 206 - Section 1 - Banach Algebras and Spectral Theory Instructor: Marc Rieffel Lectures: MWF 8:00-9:00am, Room 31 Evans Course Control Number: 54692 Office: 811 Evans Office Hours: TBA Prerequisites: Math 202AB or equivalent. Students who have studied only part of the material of Math 202AB and wish to enroll in Math 206 should discuss this with me. Required Text: John B. Conway, A Course in Functional Analysis, 2nd ed., Springer-Verlag. Recommended Reading: Syllabus: I will also be teaching Math 208, C*-algebras, this Spring semester, and in Math 206 I will try to discuss first the material that is most important for Math 208, so that it will be feasible to take both of these courses concurrently. This will probably also make it feasible to take Math 206 and Math 209 (von Neumann algebras) concurrently, but students who would like to do that should consult Professor Voiculescu. The theory of Banach algebras is a very elegant blend of algebra and topology which provides unifying principles for a number of different parts of mathematics, notably operator theory, commutative and non-commutative harmonic analysis and the theory of group representations, and the theory of functions of one and several complex variables. But at the present time probably its most extensive use is as a foundation for non-commutative topology and geometry (C*-algebras, Math 208) and non-commutative measure theory (von Neumann algebras, Math 209). These in turn provide a foundation for quantum physics, but they also have myriad applications in many other directions, including group representations and harmonic analysis, ordinary topology and geometry, and even number theory. (For a vast panorama of the applications see Connes' book "Noncommutative Geometry", available on the web for free download.) In Math 206 I will cover the standard topics as listed in the catalog. Beyond the basic general theory of Banach algebras this will include several forms of the spectral theorem for self-adjoint operators on Hilbert space, Hilbert-Schmidt and Fredholm operators, and group algebras and the Fourier transform. Course Webpage: Grading: Most weeks I will give out a problem set, and the course grade will be based on the work done on these. There will be no final examination. Homework: Comments: Math 208 - Section 1 - C*-Algebras Instructor: Marc Rieffel Lectures: MWF 9:00-10:00am, Room 9 Evans Course Control Number: 54695 Office: 811 Evans Office Hours: TBA Prerequisites: The basic theory of bounded operators on Hilbert space and of Banach algebras, especially commutative ones. Math 206 is more than sufficient. I will be teaching Math 206 this semester, and I will try to discuss first the material that is most important for Math 208, so that it will be feasible to take both of these courses concurrently. As another alternative, self-study of sections 3.1-2, 4.1-4 of "Analysis Now" by G. K. Pedersen would be sufficient. Required Text: Recommended Reading: None of the available textbooks follows closely the path that I will take through the material. The closest is probably: K. R. Davidson, C*-algebras by Example, Fields Institute Monographs, A.M.S. I strongly recommend this text for its wealth of examples (and attractive exposition). Syllabus: The theory of operator algebras grew out of the needs of quantum mechanics, but by now it also has strong interactions with many other areas of mathematics. Operator algebras are very profitably viewed as "non-commutative (algebras "of functions" on) spaces", thus "quantum spaces". As a rough outline, we will first develop the basic facts about C*-algebras ("non-commutative locally compact spaces") We will then briefly look at "non-commutative vector bundles" and K-theory ("noncommutative algebraic topology"). Finally we will glance at "non-commutative differential geometry" (e.g. cyclic homology as "noncomutative deRham cohomology"). But I will not assume prior knowledge of algebraic topology or differential geometry, and we are unlikely to have time to go into these last topics in any depth. I will discuss a variety of examples, drawn from dynamical systems, group representations and mathematical physics. But I will somewhat emphasize examples which go in the directions of my current research interests, which involve certain mathematical issues that arise in string theory and related parts of high-energy physics. Thus one thread that will run through the course will be to see what the various concepts look like for quantum tori, which are the most accessible non-commutative differential manifolds. In spite of what is written above, the style of my lectures will be to give motivational discussion and complete proofs for the central topics, rather than just a rapid survey of a large amount of material. Course Webpage: Grading: I plan to assign several problem sets. Grades for the course will be based on the work done on these. But students who would like a different arrangement are very welcome to discuss this with me. Homework: Comments: Math 209 - Section 1 - Von Neumann Algebras Instructor: Dan Voiculescu Lectures: MWF 11:00am-12:00pm, Room 5 Evans Course Control Number: 54698 Office: 783 Evans Office Hours: F 2:30-4:00pm Prerequisites: From Math 206: commutative C*-algebras and spectral theory for normal operators. Required Text: Recommended Reading: For the general theory part: Vaughan Jones Notes for Math 209 Kadison and Ringrose, Fundamentals of the theory of operator algebras Stratila and Zsido, Lectures on von Neumann algebras Takesaki, Theory of operator algebras For the free probability part: Voiculescu, Dykema and Nica, Free random variables Syllabus: The course will be an introduction to von Neumann algebras emphasizing II1 factors. The last part of the course will deal with free probability and the random matrix model it provides for the II1 factors of free groups (depending on how much time will be left). Course Webpage: Grading: Homework: Homework assigned during classes will be collected once a week. Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Ian Agol Lectures: TuTh 8:00-9:30am, Room 81 Evans Course Control Number: 54701 Office: 921 Evans Office Hours: TBA Prerequisites: Math 215A Required Text: Hatcher, Algebraic Topology Milnor & Stasheff, Characteristic Classes Recommended Reading: Greenberg & Harper Syllabus: Homotopy Theory (Chapter 4 of Hatcher), Characteristic Classes Course Webpage: Grading: Based on homework. Homework: Weekly homework. Comments: Math C218B - Section 1 - Probability Theory Instructor: David Aldous Lectures: TuTh 9:30-11:00am, Room 330 Evans Course Control Number: 54704 Office: 351 Evans Office Hours: TBA Prerequisites: Math C218A or similar Required Text: Durrett, Probability, Duxbury Recommended Reading: Syllabus: For more information see course webpage. Course Webpage: http://www.stat.berkeley.edu/~aldous/205B/index.html Grading: Homework: Comments: Math 219 - Section 1 - Dynamical Systems Instructor: Fraydoun Rezakhanlou Lectures: MWF 1:00-2:00pm, Room 81 Evans Course Control Number: 54707 Office: 815 Evans Office Hours: MTuTh 2:00-3:00pm Prerequisites: Some measure theory Required Text: Recommended Reading: Syllabus: The main goal of the theory of dynamical system is the study of the global orbit structure of maps and flows. This course reviews some fundamental concepts and results in the theory of dynamical systems with an emphasis on differentiable dynamics. Several important notions in the theory of dynamical systems have their roots in the work of Maxwell, Boltzmann and Gibbs who tried to explain the macroscopic behavior of fluids and gases on the basic of the classical dynamics of many particle systems. The notion of ergodicity was introduced by Boltzmann as a property satisfied by a Hamiltonian flow on its constant energy surfaces. Boltzmann also initiated a mathematical expression for the entropy and the entropy production to derive Maxwell's description for the equilibrium states. Gibbs introduced the notion of mixing systems to explain how reversible mechanical systems could approach equilibrium states. The ergodicity and mixing are only two possible properties in the hierarchy of stochastic behavior of a dynamical system. Hopf invented a versatile method for proving the ergodicity of geodesic flows. The key role in Hopf's approach is played by the hyperbolicity. Lyapunov exponents and Kolmogorov-Sinai entropy are used to measure the hyperbolicity of a system. There is no required text and I will distribute typed notes in the class. Here is an outline of the course: 1. Examples: Linear systems. Translations on Tori. Arnold can map. Baker's transformation. Geodesic flows. Sinai's billiard. Lorentz gas. 2. Invariant measures. Ergodic theory. Kolmogorov-Sinai Entropy. Lyapunov exponents. Hyperbolic systems. Smale horseshoe. 3. Perron-Frobenius operator. Bowen-Ruelle-Sinai measures. 4. Pesin's theorem. Ruelle's inequality. 5. Billiards. 6. Aubry-Mather theory. Course Webpage: Grading: There will be some homework assignments. Homework: Comments: Math 220 - Section 1 - Stochastic Methods of Applied Mathematics Instructor: Alexandre Chorin Lectures: MWF 9:00-10:00am, Room 85 Evans Course Control Number: 54710 Office: 911 Evans Office Hours: TBA Prerequisites: Some familiarity with the applications of mathematics or with PDEs Required Text: Chorin/Hald, Stochastic tools in mathematics and science, copies will be distributed without charge Recommended Reading: Syllabus: Some probability, conditional averaging, Brownian motion, Langevin and Fokker-Planck equations, path integrals, Feynman diagrams, time series, Monte Carlo methods, renormalization and scaling, an introduction to statistical mechanics, optimal prediction, filtering. Course Webpage: http://math.berkeley.edu/~chorin/math220 Grading: Based on homework assignments. Homework: Homework will be assigned on the web every week. Comments: Math 222B - Section 1 - Partial Differential Equations Instructor: L. Craig Evans Lectures: MWF 12:00-1:00pm, Room 31 Evans Course Control Number: 54713 Office: 1033 Evans Office Hours: TBA Prerequisites: Math 222A 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. Second-order elliptic equations, parabolic and hyperbolic equations, calculus of variations methods, additional topics selected by instructor. 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 C223B - Section 1 - Statistical Mechanics and the (Ferromagnetic) Ising Model Instructor: Nick Crawford Lectures: TuTh 11:00am-12:30pm, Room 340 Evans Course Control Number: 54716 Office: Office Hours: TBA Prerequisites: References: Will give complete list during the first class, o/w email me at crawford [at] stat [dot] berkeley [dot] edu Syllabus: The Ising model was originally introduced (in the 1920’s) as a caricature of the physical phenomenon of ferromagnetism. It has become a paradigm for the study of emergent macroscopic behavior from microscopic interactions and appears in various forms in an array of different fields from computer science and phylogenetics to statistical mechanics. In this course, we will provide an introduction to this model, with a particular emphasis on the issues which arise in its formulation on Zd. Topics to be Covered (not nesc. in this order): Classical Theory: (1) Finite Volume Gibbs States (2) Correlation inequalities I; FKG, GKS. (3) Thermodynamics: the free energy. (4) Rigorous definition of phase transition. (5) Infinite volume Gibbs states and the DLR conditions. (6) Gibbs variational principle. (7) Occurrence of phase transition in d ≥ 2: the High and Low Temperature Expansions. (8) Lee Yang Circle theorem. (9) Uniqueness of ∞ volume Gibbs States with non-zero external field. (10) Relationship to Potts models and the random cluster representation/domination of measures/percolation signature of the phase transition. Advanced Topics: (Some selection of these, depending on interest): (1) The random field Ising model: absence of phase transition in dimension d = 2. (2) The random field Ising model: existence of phase transition in dimension d ≥ 3. (3) Critical Behavior of the Ising model: d ≥ 5 (1980’s, follows Aizenman and coauthors). (4) Conformal Invariance in the Ising model: d = 2 (2006-2008, follows Smirnov). (5) An introduction to the roughening transition in d = 3. Finally, we hope that this class will be interactive in the sense that students will give presentations for credit. These presentations can take on a number of forms, from original research related to this subject to the presentation of a paper relevant to the field (perhaps on one of the topics not covered in the second set). Math 224B - Section 1 - Mathematical Methods for the Physical Sciences Instructor: Alberto Grünbaum Lectures: TuTh 9:30-11:00am, Room 5 Evans Course Control Number: 54719 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 second 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. This second semester will cover mostly the spectral theory of operators in infinite dimensional space, with particular emphasis on selfadjoint and unitary operators. I will make a fresh beginning for those students that are not too familiar with the infinite dimensional setup. The issue of the importance of Boundary conditions will be discussed in detail in terms of H. Weyl's classification in limit point-limit circle cases. We will illustrate all this material with applications taken from the physical sciences. Course Webpage: Grading: Homework: There will be weekly assignments, mainly from the book. Comments: The grade will be based on the homework. Math 225B - Section 1 - Metamathematics Instructor: Jan Reimann Lectures: TuTh 2:00-3:30pm, Room 81 Evans Course Control Number: 54722 Office: 705 Evans Office Hours: TBA Prerequisites: 225A Required Text: I will provide my own notes. Recommended Reading: Rautenberg, A Concise Introduction to Mathematical Logic; Shoenfield, Mathematical Logic; Soare, Recursively Enumerable Sets and Degrees; Kaye, Models of Peano Arithmetic Syllabus: Metamathematics of number theory, models of Peano Arithmetic, recursive functions, computability, Turing machines, undecidable problems, the arithmetical hierarchy, coding and arithmetization, the Goedel incompleteness theorems, Theorems of Tarski and Church, the Paris-Harrington theorem, examples of undecidable theories. Course Webpage: Will be set up on bSpace Grading: Homework: Homework will be assigned every week. Comments: Math 228B - Section 1 - Numerical Solution of Differential Equations Instructor: John Strain Lectures: TuTh 11:00am-12:30pm, Room 30 Wheeler Course Control Number: 54725 Office: 1099 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 236 - Section 1 - Metamathematics of Set Theory Instructor: John Krueger Lectures: MWF 12:00-1:00pm, Room 81 Evans Course Control Number: 54728 Office: 751 Evans Office Hours: TBA Prerequisites: 225B, 235A, or permission of instructor Required Text: None Recommended Reading: Syllabus: Basics of forcing. Chain conditions and closure. Consistency results. Iterated forcing. Course Webpage: http://math.berkeley.edu/~jkrueger/math236.html Grading: Homework: Comments: Math 242 - Section 1 - Symplectic Geometry Instructor: Michael Hutchings Lectures: TuTh 12:30-2:00pm, Room 81 Evans Course Control Number: 54731 Office: 923 Evans Office Hours: TBA Prerequisites: 214 and 215a or equivalent required; 215b helpful Required Text: McDuff and Salamon, Introduction to Symplectic Topology, 2nd edition, Oxford Univ Press Recommended Reading: Geiges, An Introduction to Contact Topology, Cambridge Univ Press Syllabus: We will introduce some of the fundamental ideas that underlie current research in symplectic geometry (and also contact geometry, its odd-dimensional sibling). Although holomorphic curves play a major role in this area, we will emphasize more basic concepts which are less technically demanding but still essential. Course Webpage: Will be linked from math.berkeley.edu/~hutching Grading: Each student will be expected to investigate a particular topic of interest and either write a 5-10 page expository article about it or give a 40 minute presentation to the class. The books by McDuff-Salamon and Geiges suggest a number of good starting points for this. Homework: Comments: Math 249 - Section 1 - Algebraic Combinatorics Instructor: Lior Pachter Lectures: TuTh 9:30-11:00am, Room 101 Wheeler Course Control Number: 54734 Office: 1081 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 250B - Section 1 - Multilinear Algebra and Further Topics Instructor: Paul Vojta Lectures: TuTh 12:30-2:00pm, Room 3105 Etcheverry Course Control Number: 54737 Office: 883 Evans Office Hours: MTuTh 2:00-3:00pm (subject to change) Prerequisites: Math 250A Required Text: Eisenbud, Commutative algebra with a view toward algebraic geometry, Springer Recommended Reading: Syllabus: The course will cover the following chapters or parts of the text:
Course Webpage: http://math.berkeley.edu/~vojta/250b.html Grading: Grades will be based on homework assignments, including a final problem set in place of a final exam. Homework: Homework will be assigned approximately every two weeks. Comments:
Math 252 - Section 1 - Representation Theory Instructor: Brendon Rhoades Lectures: MWF 3:00-4:00pm, Room 81 Evans Course Control Number: 54740 Office: 851 Evans Office Hours: MWF 2:00-3:00pm Prerequisites: Linear algebra, abstract algebra Required Text: None Recommended Reading: Syllabus: This will be an introductory course inrepresentation theory. Topics will include representations of finite-dimensional algebras and, in particular, representations of finite groups in characteristic zero with special emphasis on the case of symmetric groups. I hope to conclude with an introduction to Hecke algebras and Kazhdan-Lusztig theory. Course Webpage: Grading: Homework: Several homeworks. Comments: Math 254B - Section 1 - Number Theory Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54743 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Serre, Local Fields Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: When doing arithmetic or geometry it is usually helpful, if not essential, to look closely at what is happening near a point (or prime ideal). Fortunately points are simpler than global spaces and easier to study, but the closer one looks the more interesting things get and in the end one can learn deep information about the global space by really understanding its points. We will begin to investigate this local perspective in this course. Math 255 - Section 1 - Algebraic Curves Instructor: Konrad Waldorf Lectures: TuTh 3:30-5:00pm, Room 81 Evans Course Control Number: 54746 Office: 833 Evans (could possibly change) Office Hours: TuTh 5:00-6:30pm Prerequisites: Point-set topology (202A), groups, rings and fields (the basics of 250A, or 114), complex analysis (185). Required Text: Recommended Reading: Available on the course webpage. Syllabus: Riemann surfaces, projective curves, curves with nodes, meromorphic functions and holomorphic maps, divisors, Bezout's theorem, algebraic curves, the Riemann-Roch theorem, Jacobians, Abel's Theorem, elliptic curves, possibly further topics. Course Webpage: http://math.berkeley.edu/~waldorf/algebraiccurves Grading: Based on homework. Homework: TBA Comments: Math 256B - Section 1 - Algebraic Geometry Instructor: Arthur Ogus Lectures: MWF 11:00am-12:00pm, Room 31 Evans Course Control Number: 54749 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 257 - Section 1 - Group Theory Instructor: David Hill Lectures: MWF 2:00-3:00pm, Room 81 Evans Course Control Number: 54752 Office: 785 Evans Office Hours: TBA Prerequisites: Math 250A Required Text: Recommended Reading: Kleshchev, Linear and Projective Representations of Symmetric Groups Syllabus: In this course, we will study the representation theory of the affine Hecke algebra of type A. This algebra has a family of remarkable finite dimensional quotients, including the group algebra of the symmetric group. We will approach this subject from various points of view. We will review classical Schur-Weyl duality and its affinization. Next, we will go on to investigate how this representation theory can be understood by studying highest weight representations of affine Kac-Moody algebras of type A. Time permitting, we will also explore connections to a new diagram calculus introduced by Khovanov and Lauda. Course Webpage: http://math.berkeley.edu/~dhill1/ Grading: Homework: Comments: Math 261B - Section 1 - Quantum Groups Instructor: Nicolai Reshetikhin Lectures: MWF 10:00-11:00am, Room 5 Evans Course Control Number: 54755 Office: 915 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: The goal of this part of the Lie groups and Lie algebras course is an introduction to quantum groups. The subject was developed over the last 20 years. Many ideas and techniques are natural extensions of those in Lie groups, Lie algebras, and their representation theory. The main hero of this course (at least in the first part of it) will be quantum sl2. Elements of symplectic geometry will be used in parts of this course. A symplectic geometry course as a pre-requisite is desirable, but not necessary. Here is a tentative outline of the course: 1. Lie bialgebras and Poisson Lie groups. Standard Poisson Lie structure for SL2 in details. Standard Poisson Lie structures on simple Lie groups. 2. Deformation quantization of Poisson-Lie groups and of universal enveloping algebras of Lie bialgebras. Hopf algebras and basic constructions with Hopf algebras. Monoidal categories. Category of vector spaces. Category of modules over a Hopf algebra. Duality in a monoidal category (dual vector spaces for the category of vector spaces) 3. Braiding in monoidal categories. The Drinfeld double construction. Braiding for quantized universal enveloping algebras of simple Lie algebras. 4. Integral forms of quantized universal enveloping algebras. 5. Elements of the representation theory of quantized universal enveloping algebras. Finite dimensional irreducible representations. The category of finite dimensional modules as a braided monoidal category. 6. Elements of harmonic analysis on quantum groups. 7. Specializations at roots of unity and corresponding representation theories. There are several books on the subject. They all can be used as a supplementary reading material. The list of reading material will be posted at the web-site of the course before the beginning of the semester. Course Webpage: Grading: Homework: Comments: Math 270 - Section 1 - Hot Topics Course in Mathematics Instructor: Peter Teichner Lectures: Tu 11:00am-12:30pm, Room 736 Evans Course Control Number: 54758 Office: 703 Evans Office Hours: TBA Prerequisites: Required Text: Lurie, On the Classification of Topological Field Theories Recommended Reading: Other papers by Lurie at http://www-math.mit.edu/~lurie/ Syllabus: Course Webpage: Check at http://web.me.com/teichner/Math/Hot_Topics.html Grading: Homework: Comments: Math 270 - Section 2 - Hot Topics Course in Mathematics Instructor: Leo Harrington Lectures: M 4:00-5:30pm, Room 35 Evans Course Control Number: 54761 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra - Tropical Geometry Instructor: Bernd Sturmfels Lectures: TuTh 11:00am-12:30pm, Room 3107 Etcheverry Course Control Number: 54764 Office: 925 Evans Office Hours: W 8:00-11:00am Prerequisites: Commutative algebra (250B), an interest in geometric combinatorics and algebraic geometry, and willingness to work hard in a team. Required Text: I will post some lecture notes and pointers to research articles on the course webpage. Recommended Reading: Syllabus: Tropical geometry is the algebraic geometry over the min-plus algebra. It is a young subject that in recent years has both established itself as an area of its own right and unveiled its deep connections to numerous branches of pure and applied mathematics. From an algebraic geometric point of view, algebraic varieties over a field with non-archimedean valuation are replaced by polyhedral complexes, thereby retaining much of the information about the original varieties. This course offers an introduction to tropical geometry, with emphasis on algebraic, computational and combinatorial aspects. One concrete goal is to prepare the students for possible participation in activities of the Fall 2009 research program on Tropical Geometry at MSRI. Course Webpage: http://math.berkeley.edu/~bernd/math274.html Grading: The course grade will be based on both the homework and the course projects. Homework: There will be regular assignments during the first eight weeks of the course. Comments: After spring break students will work on a term project in tropical geometry. Math 274 - Section 2 - Infinitesimal Geometry (Topics in Algebra) Instructor: Mariusz Wodzicki Lectures: TuTh 5:00-6:30pm, Room 72 Evans Course Control Number: 54767 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: This course will describe the current state of our knowledge in what I like to call “Infinitesimal Geometry”. One of the great achievements of 20th Century Mathematics was the realization that de Rham theory provided an adequate, "analytic" means of understanding geometry of smooth C∞ manifolds, smooth complex manifolds, and smooth algebraic varieties over fields of characteristic zero. When singularities appear, or the ring of coefficients is not a field of characteristic zero, it has been known since 1950-ies that de Rham theory is not adequate at all. Yet, the concepts of Infinitesimal Geometry, infinitesimal invariants, infinitesimal cohomology groups, make perfect sense in all situations. The following is the tentative list of topics:
Course Webpage: Grading: Homework: Math 275 - Section 1 - Topics in Applied Mathematics - Flow, Deformation, Fracture and Turbulence Instructor: Grigory Barenblatt Lectures: TuTh 9:30-11:00am, Room 61 Evans Course Control Number: 54770 Office: 735 Evans Office Hours: TuTh 11:15am-12:50pm Prerequisites: No special knowledge of advanced mathematics and continuum mechanics will be assumed - all needed concepts and methods will be explained on the spot, however the knowledge of the elements of vector analysis and ordinary differential equations will be useful. Required Texts: Landau, L. D. and Lifshits, E. M., Fluid Mechanics (Pergamon Press, London, New York 1987) Landau, L. D. and Lifshits, E. M., Theory of Elasticity (Pergamon Press, London, New York, 1986) Chorin, A. J. and Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (Springer, 1990) Barenblatt, G. I., Scaling (Cambridge University Press, 2003) Batchelor, G. K., An Introduction to Fluid Dynamics (Cambridge University Press, 1998) Recommended Reading: Syllabus: Fluid Mechanics, including Turbulence and Mechanics of Deformable Solids, including Fracture Mechanics are fundamental disciplines, playing an important and ever-growing role in applied mathematics, including computing, and also physics, and engineering science. The models of fluid flow, deformation and fracture of solids under various conditions appear in all branches of applied mathematics, engineering science and many branches of physical science. Among the problems of these sciences which are under current active study there are great scientific challenges of our time such as turbulence, fracture and fatigue of metals, damage accumulation and nanotechnology. The proposed course will present the basic ideas and methods of fluid mechanics, including turbulence, mechanics of deformable solids, including fracture as a unified mathematical, physical and engineering discipline. The possibility of such a unified presentation is based on the specific `intermediate-asymptotic approach’ which allows the explanation of the main ideas simultaneously for the problems of fluid mechanics and deformable solids. The basic distinction of this year course will have special emphasis on turbulence. The instructor expects to present the basic ideas and to evaluate the current state of the turbulence studies. In particular, scaling laws for the shear flows and local structure of the developed turbulent flows will be presented and discussed. Course Webpage: Grading: Homework: There will be no systematic homework. Some problems will be presented shortly at the lectures, their solutions will be outlined, and interested students will be offered the opportunity to finish the solutions. This will not be related to the final exams. 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 should be able to answer questions concerning the details of these topics. After that general questions (without details) will be asked concerning the other parts of the course. Math 278 - Section 1 - Topics in Analysis - Free Analysis Instructor: Dan Voiculescu Lectures: MWF 1:00-2:00pm, Room 31 Evans Course Control Number: 54776 Office: 783 Evans Office Hours: F 2:30-4:00pm Prerequisites: Basic notions from Math 206 Required Text: Recommended Reading: Syllabus: The course will be about analysis with variables having the highest degree of noncommutativity. The free difference quotient, a noncommutative extension of the difference quotient, replaces then the usual derivative. The analogue of the Fourier transform, in this context, is a noncommutative generalization of the Cauchy-Stieltjes transform. There are more entries in this dictionary which will be discussed. I plan also to cover some of the motivation for this development originating in free probability (random matrix and operator algebra questions, the free analogue of entropy). Course Webpage: Grading: Homework: There will be a few homeworks. Comments: Math 300 - Section 1 - Teaching Workshop Instructor: Anthony Varilly Lectures: TBA Course Control Number: 55388 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: |
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