# Spring 2010

 Math 1A - Section 1 - Calculus Instructor: Arthur Ogus Lectures: MWF 12:00-1:00pm, Room 2050 Valley LSB Course Control Number: 53903 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Nicolai Reshetikhin Lectures: MWF 10:00-11:00am, Room 2050 Valley LSB Course Control Number: 53936 Office: 917 Evans Office Hours: TBA Prerequisites: Math 1A, or its equivalent. Required Text: Stewart, Single Variable Essential Calculus, Cengage, (Custom Berkeley edition 1A/1B). Recommended Reading: The textbook. Syllabus: Techniques of integration, sequences and series, differential equations. Course Webpage: The link to the webpage will be posted at http://math.berkeley.edu/~reshetik . Grading: TBA Homework: Homework will be assigned weekly and due once a week. Comments: The detailed syllabus will be posted on the course webpage. Math 1B - Section 2 - Calculus Instructor: Per-Olof Persson Lectures: MWF 1:00-2:00pm, Room 155 Dwinelle Course Control Number: 53969 Office: 1089 Evans Office Hours: TBA Prerequisites: Math 1A Required Text: James Stewart, Single variable calculus: Early Transcendentals for University of California, (special Berkeley edition), ISBN 978-1-4240-5500-5 or 1-4240-5500-8, Cengage Learning. Recommended Reading: Syllabus: Chapters 7-17: Techniques and Applications of Integration, First- and Second-Order Differential Equations, Infinite Sequences and Series. Course Webpage: http://persson.berkeley.edu/1B Grading: Homework assignments and weekly quizzes (20%), Midterm Exam 1 (15%), Midterm Exam 2 (20%), Final Exam (45%). Homework: Weekly homework assignments will be posted on the course web page. Comments: Second part of the introduction to differential and integral calculus of functions of one variable, with applications. This course is intended for majors in engineering and the physical sciences. Math 1B - Section 3 - Calculus Instructor: Mina Aganagic Lectures: TuTh 12:30-2:00pm, Room 2050 Valley LSB Course Control Number: 54002 Office: Office Hours: Prerequisites: Math 1A Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Leo Harrington Lectures: MWF 11:00-12:00pm, Room 2050 Valley LSB Course Control Number: 54035 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Donald Sarason Lectures: MWF 9:00am-10:00am, Room 2050 Valley LSB Course Control Number: 54074 Office: 779 Evans Hall Office Hours: TBA Prerequisites: Math 16A or the equivalent Required Text: Goldstein, Lay, Schneider, Asmar, Calculus & Its Applications, Custom Edition for Math 16B, Volume 2, University of California, Berkeley. Recommended Reading: Syllabus: Functions of several variables, trigonometric functions, techniques of integration, differential equations, Taylor polynomials and infinite series, probability and calculus (Chapters 7-12 of the text-book). Course Webpage: TBA Grading: The course grade will be based on two midterm exams, the final exam, and section performance. Details will be provided at the first lecture. The final exam is scheduled for Monday, May 10, 7:00-10:00 PM. Do not enroll in the course if you have a conflict. There will be no make-up exams. Homework: Homework will be assigned weekly, except for week 1 and the weeks of midterm exams. Comments: The lectures will be fairly slow paced and will strive to get across the main ideas, often by means of examples. Students should expect to learn a lot on their own by studying the textbook and working homework exercises, and to solidify their understanding by attending discussion sections. The discussion sections meet on Tuesdays, and the first one meets before the first lecture. Do not skip it if you do not want to be dropped from the course. The course will be run much like Sarason's 16B in Sp 2006. Students can get an idea of what to expect from the webpage for that version of the course, which can be found on the Math Department's home page (except for homework solutions). Math 16B - Section 2 - Analytical Geometry and Calculus Instructor: Jon Wilkening Lectures: TuTh 9:30am-11:00am, Room 2050 Valley LSB Course Control Number: 54113 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - Freshman Seminar Instructor: Jenny Harrison Lectures: Tu 3:00pm-4:00pm, Room 891 Evans Course Control Number: 54149 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: In this seminar, we will discuss the latest developments in science and math. Students will present short oral reports from articles of their choice in the Science Times, Scientific American, Science News, or articles in What is Happening in the Mathematical Sciences. Discussion and debate are encouraged especially when controversial or challenging issues arise, e.g., cloning of organs, string theory, stem cell research, and geopolitics of global warming. Students are encouraged to think of applications and possibilities of new research projects. Brainstorming and creative thinking are encouraged! Students considering a major in math or science have found this seminar a useful resource to help clarify their choice. Jenny Harrison obtained her Ph.D. in mathematics in Warwick, England. She has taught at Oxford, Princeton, and Yale, as well as UC Berkeley. Her research interests include a new quantum calculus that applies equally to charged particles, fractals, smooth surfaces, and soap films. Applications of this theory to sciences may arise during this seminar. Course Webpage: Grading: Homework: Comments: Math 24 - Section 3 - Freshman Seminar Instructor: Maciej Zworski Lectures: Tu 4:00pm-5:00pm, Room 736 Evans Course Control Number: 54151 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: In this freshman seminar we will exploit the basis of mathematical quantum mechanics and linear algebra without assuming any prior knowledge of either. Although it sounds intimidating we will start with systems of linear equations with two unknowns and build simple models from that. By the end of the semester we will hopefully see some aspects of the classical/quantum correspondence. This should elucidate the fact that our macroscopic world is "classical" (that is the way it is) despite the fact that it is governed by mysterious quantum principles. Maciej Zworski is a Professor of Mathematics at UC Berkeley. His research interests include partial differential equations and mathematical physics. For more information regarding Professor Zworski, visit his faculty web page at http://math.berkeley.edu/~zworski/ . Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: The Staff Lectures: MWF 8:00-9:00am, Room 60 Evans Course Control Number: 54152 Office: Office Hours: 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: MW 2:00-4:00pm, Room 31 Evans Course Control Number: 54167 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: John Steel Lectures: TuTh 11:00am-12:30pm, Room 100 Lewis Course Control Number: 54191 Office: Office Hours: Prerequisites: Math 1B Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: Fraydoun Rezakhanlou Lectures: MWF 3:00-4:00pm, Room 105 Stanley Course Control Number: 54224 Office: 803 Evans Office Hours: MWF 11-12 am Prerequisites: Math 1B Required Text: Stewart, Multivariable Calculus: Early Transcendentals for UC Berkeley. Recommended Reading: Syllabus: Course Webpage: Grading: Homework and quizzes, 50 points. 3 midterms, the best two counting, worth 75 points each, totaling 150 points. Final Exam, 200 points. Total: 400 points possible. The first midterm will be in class on Wednesday, Feb. 17. The second midterm will be on Wednesday, Mar. 17. The third midterm will be on Friday, Apr. 23. The Final Exam will be on WEDNESDAY, MAY 12, 7-10 pm. Make sure you can make the midterms and the final exam check the schedule now to see that it is acceptable to you. It is not possible to have make-up exams. Homework: Homework will be assigned weekly. This semester we do not have readers, so your homework should be self-corrected, based on the solutions provided weekly by your TA. Nevertheless, homework must be handed in every Tuesday in your TA section for recording. There will be three quizzes (given in section) that count; with homework and quizzes totaling 50 points; quizzes will vary with the TA section. The first assignment is due in your TA section on Tuesday, Jan. 26. Comments: Incompletes: Official University policy states that an Incomplete can be given only for valid medical excuses with a doctor's certificate, and only if at the point the grade is given the student has a passing grade (C or better). If you are behind in the course, Incomplete is not an option! Enrollment: For enrollment matters, see Barbara Peavy. Her office is 967 Evans and students can see her most days 9-12 and 1-4. Students wishing to switch discussion sections will have to do this themselves on TeleBears. (They will only be able to do this if there is room in the section.) Also, please note that students MUST attend the discussion section they are registered for. Math H53 - Section 1 - Multivariable Calculus Instructor: The Staff Lectures: TBA 0:00am-0:00pm, Room TBA Course Control Number: 54256 Office: Office Hours: Prerequisites: Math 1B Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Ole Hald Lectures: MWF 4:00-5:00pm, Room 1 Pimentel Course Control Number: 54257 Office: Office Hours: Prerequisites: Math 1B Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: John Lott Lectures: TuTh 3:30-5:00pm, Room 1 Pimentel Course Control Number: 54296 Office: Office Hours: Prerequisites: Math 1B 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: 54335 Office: 925 Evans Office Hours: Tu 9-11, We 11-12 Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B is recommended but not required. Freshmen with solid high school math background and a possible interest in majoring in mathematics are strongly 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 C103 - Section 1 - Introduction to Mathematical Economics Instructor: Lectures: TuTh 2:00-3:30pm, Room 3 Evans Course Control Number: 54422 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Jenny Harrison Lectures: MWF 3:00-4:00pm, Room 51 Evans Course Control Number: 54425 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Joshua Sussan Lectures: MWF 9:00-10:00am, Room 71 Evans Course Control Number: 54428 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Paul Vojta Lectures: TuTh 3:30-5:00pm, Room 75 Evans Course Control Number: 54431 Office: 883 Evans Office Hours: TBA Prerequisites: Math 53 and 54. Required Text: Protter and Morrey, A First Course in Real Analysis, (Springer-Verlag). Recommended Reading: None. Syllabus: The course will cover the first six chapters of the book, minus some material towards the end of Chapter 5, plus some material on uniform convergence in Chapter 9. Course Webpage: http://math.berkeley.edu/~vojta/104.html Grading: Homeworks, 30%; midterms, 15% and 20%; final exam, 35%. Homework: Assigned weekly. Comments: I tend to follow the book rather closely, but try to give interesting examples. Math 104 - Section 4 - Introduction to Analysis Instructor: Marco Aldi Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54434 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Lek-Heng Lim Lectures: MWF 4:00-5:00pm, Room 75 Evans Course Control Number: 54437 Office: 873 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 105 - Section 1 - Second Course in Analysis Instructor: Atilla Yilmaz Lectures: TuTh 3:30-5:00pm, Room 87 Evans Course Control Number: 54440 Office: 796 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: (1) Spivak, Calculus on Manifolds, Westview Press; and (2) Stroock, A Concise Introduction to the Theory of Integration, Birkhauser, Third Edition. Recommended Reading: Syllabus: The course will consist of two parts. In the first part, we will cover the topics in Chapters 1 and 2 of Spivak's book. (Differentiation; chain rule; inverse and implicit function theorems.) In the second part of the course, we will follow Stroock's book. (Lebesgue measure and integration; product of measures; changes of variable; some basic inequalities; Fourier analysis if time permits.) Course Webpage: http://math.berkeley.edu/~atilla/ Grading: Homework 1/8, first midterm 1/8, second midterm 1/4, final 1/2. Homework: Weekly problem sets. Comments: Math 110 - Section 1 - Linear Algebra Instructor: Ken Ribet Lectures: TuTh 2:00-3:30pm, Room 10 Evans Course Control Number: 54443 Office: 885 Evans Hall Office Hours: To Be Announced Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: Linear Algebra, 4th edition by Friedberg, Insel and Spence. Recommended Reading: Syllabus: Please refer to my page of pages for my Math 110 course web pages in previous semester. Basically, we will follow the textbook closely through Chapter 6. The book's final chapter concerns the Jordan and other canonical forms. Experience suggests that we are unlikely to be able to discuss this chapter, especially now that there are fewer teaching days this spring than in previous spring semesters. Course Webpage: http://math.berkeley.edu/~ribet/110/; note that this URL will take you to my Fall, 2008 Math 110 web page until the new page goes live early in 2010. Grading: Roughly 25% homework and quizzes, 15% each midterm, 45% final exam. Homework: Lots of homework! (Homework will be turned in to your GSI in section at each section meeting.) Comments: Math H110 - Section 1 - Linear Algebra Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54461 Office: 901 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Linear Algebra is the mathematics associated with linear equations, alternatively, it is the algebra needed to understand the geometry of lines, planes and their higher dimensional generalizations. It is the algebra of “ﬁrst approximations.” In general, things in the real world are not linear but if they were they would be a lot simpler. The geometry of lines and planes is much easier to understand than the geometry of ellipses and ellipsoids. As you learned in calculus, when you look real close things look linear; the derivative is the slope of the tangent line at a point. In this course, we will begin the systematic study of all things linear. Once you know how lines work you can start tampering with more complicated things, like groups, algebraic geometry, differential equations and physics. Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Calder Daenzer Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54464 Office: 1083 Evans Office Hours: TBA Prerequisites: Math 53 and 54 or equivalent. Required Text: Algebra, by Michael Artin Recommended Reading: Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~cdaenzer/Math113Spring2010.html Grading: See course webpage. Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Konrad Waldorf Lectures: TuTh 12:30-2:00pm, Room 71 Evans Course Control Number: 54467 Office: 833 Evans Office Hours: will be announced on the course webpage Prerequisites: Multivariable Calculus (Math 53) and Linear Algebra (Math 54) Required Text: The course follows J. B. Fraleigh, A first course in Abstract Algebra, Addison-Wesley, 2002. Recommended Reading: see the course webpage Syllabus: Sets and relations. Groups and factor groups. Commutative rings, ideals and quotient fields. Polynomials: Euclidean algorithm and unique factorizations. Fields and field extensions. Categories and Functors. Course Webpage: http://math.berkeley.edu/~waldorf/abstractalgebra Grading: 25% each midterm, 50% final Homework: Homework will be assigned on the course webpage and due once a week. Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Denis Auroux Lectures: TuTh 9:30-11:00am, Room 75 Evans Course Control Number: 54470 Office: 817 Evans Office Hours: TBA Prerequisites: Required Text: John Fraleigh, A First Course in Abstract Algebra, 7th edition, Addison-Wesley. Recommended Reading: Syllabus: Groups, rings, and fields. Course Webpage: http://math.berkeley.edu/~auroux/113s10 Grading: Homework, two midterms, and final exam. Homework: Weekly Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Christian Zickert Lectures: MWF 12:00-1:00pm, Room 71 Evans Course Control Number: 54473 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H113 - Section 1 - Honors Introduction to Abstract Algebra Instructor: Mariusz Wodzicki Lectures: TuTh 3:30-5:00pm, Room 85 Evans Course Control Number: 54476 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 114 - Section 1 - Second Course in Abstract Algebra Instructor: David Hill Lectures: MWF 3:00-4:00pm, Room 6 Evans Course Control Number: 54479 Office: 785 Evans Office Hours: TBA Prerequisites: Math 113 Required Text: Beachy/Blair, Abstract Algebra, 3rd Ed. Recommended Reading: Syllabus: See website. Course Webpage: http://www.math.berkeley.edu/~dhill1 Grading: 30% Homework, 30% Midterms, 40% Final. Homework: Homework assigned daily and collected each week. Comments: Math 116 - Section 1 - Cryptography Instructor: Kenneth A. Ribet Lectures: TuTh 11:00am-12:30pm, Room 3109 Etcheverry Course Control Number: 54482 Office: 885 Evans Office Hours: To Be Announced Prerequisites: Math 55 Required Text: An Introduction to Mathematical Cryptography. See the note below about online access and the availability of paperbound copies for $24.95. Recommended Reading: Syllabus: It might help to explain what the course is not about: We will spend only a tiny amount of time on classical ciphers like the Vigenère cipher. Also, we will treat only occasionally the sort of complexity questions that intervene in computer science texts on cryptography. Instead, we will study problems involving factoring, discrete logs, perfect secrecy, entropy, elliptic curves and lattices. Our emphasis on the mathematics that underlies modern cryptography and potential attacks on the security of cryptosystems. Course Webpage: href="https://math.berkeley.edu/~ribet/116/">http://math.berkeley.edu/~ribet/116/, though the URL currently points to the web page for Spring, 2009. Grading: 25% homework, 15% each midterm, 45% final exam. Homework: Homework will be due once per week. Comments: First of all, please consult the SpringerLink web page for our text. If you are inside berkeley.edu (or please yourself inside this domain via the library proxy server or the Campus VPN Service, you can download the book's chapters electronically and order a MyCopy paperbound version of the book for only$24.95, including shipping. Second, although the textbook claims to have no upper-division prerequisites, experience shows that some experience with Math 115 and/or Math 113 is very helpful. If you have taken these courses before, be prepared to review your notes as needed. If not, please consider signing up for Math 113 at the same time that you take the crypto course. If you have had no experience with abstract algebra and don't plan to take Math 113 in the spring, try to spend some time with an abstract algebra textbook before the start of the semester. Math 118 - Section 1 - Fourier Analysis, Wavelets, and Signal Processing Instructor: John Strain Lectures: TuTh 12:30-2:00pm, Room 75 Evans Course Control Number: 54485 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Vera Serganova Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54488 Office: 709 Evabs Office Hours: M 4:00-5:30, W 11:00-12:30 Prerequisites: Math 1A, 1B, 53, 54 Required Text: M.L. Boas, Mathematical Methods in Physical Sciences, (third edition). Recommended Reading: Syllabus: Review of series and power series (Chapter 1); Complex numbers (Chapter 2); Partial Differentiation (Chapter 4); Functions of a complex variable (Chapter 14); Fourier series and transforms (Chapter 7); Laplace transform and Green functions (Chapter 8); Calculus of variations (Chapter 9) (if time permits). Course Webpage: Grading: 20% homework, 20% each midterm and 40% for the final. Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 121B - Section 1 - Mathematical Tools for the Physical Sciences Instructor: John Neu Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54491 Office: Office Hours: Prerequisites: Required Text: M. Boas, Mathematical Methods in the Physical Sciences Recommended Reading: Syllabus: 1) Basic PDE (starting with chapter 10 in Boas, incorporating some special functions from chapter 12. Further handouts and problem sets for the spirited and brave.) 2) Calculus of variations (starting with chapter 9 in Boas, handouts by professor on variational principles and conservation laws for PDE.) 3) Basic probability (chapter 15: counting, basic distributions, binomial, poisson. Sum of random variables and diffusion. Einstein and Avagadro's number.) Course Webpage: Grading: Homework = 20% of total Midterm I (5th week) = 20% of total Midterm II (10th week) = 20% of total Final = 40% of total Homework: Weekly problem sets Comments: Learn to use the Dark Side of the Math. Math 126 - Section 1 - Introduction to Partial Differential Equations Instructor: Fraydoun Rezakhanlou Lectures: MWF 12:00-1:00am, Room 75 Evans Course Control Number: 54494 Office: 803 Evans Office Hours: MWF 11-12am Prerequisites: Math 54 and 53 Required Text: W. A. Strauss, Partial Differential Equations, An Introduction, Wiley. Recommended Reading: Syllabus: This is a basic course in partial differential equations. The main topics are: 1. Waves and diffusion. 2. Green's function and maximum principle. 3. Calculus of variation, Dirichlet principle and eigenvalue problem. 4. Shock waves and conservation laws. 5. Scattering and solitons. Course Webpage: Grading: Homework 30 points, Midterm 30 points, Final exam 40 points. Homework: Comments: Math 127 - Section 1 - Mathematical/Computational Methods in Molecular Bio. Instructor: Lior Pachter Lectures: TuTh 9:30-11:00am, Room 4 Evans Course Control Number: 54497 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Alexander Chorin Lectures: MWF 1:00-2:00pm, Room 277 Cory Course Control Number: 54500 Office: 911 Evans Hall Office Hours: MWF 2:15-3:15 Prerequisites: Math 53 and Math 54 Required Text: Burden/Faires, Numerical Anlaysis Recommended Reading: Syllabus: Approximation of functions, numerical differentiation and integration, solution of ordinary differential equations, introduction to numerical linear algebra. Course Webpage: math.berkeley.edu/~chorin/math128.html Grading: 10% theory homework, 20% computer homework, 25% midterm, 45% final; an F in the computer homework is an F in the course. Homework: Homework will be assigned on the web each Monday; the theory homework will be due 9 days later, the computer homework will be due at the end of the semester. Comments: My lecturing style is informal and I enjoy class discussion. Math 128B - Section 1 - Numerical Analysis Instructor: Ming Gu Lectures: MWF 10:00-11:00am, Room 71 Evans Course Control Number: 54521 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory Sets Instructor: Jack Silver Lectures: TuTh 2:00-3:30pm, Room 71 Evans Course Control Number: 54527 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 136 - Section 1 - Incompleteness and Undecidability Instructor: Jan Reimann Lectures: MWF 3:00-4:00pm, Room 5 Evans Course Control Number: 54530 Office: 705 Evans Office Hours: TBA Prerequisites: 53, 54, and 55. Required Text: N. Cutland, Computability - An Introduction to Recursive Function Theory, Cambridge University Press, 1980. Recommended Reading: Syllabus: Functions computable by algorithm, Turing machines, Church's thesis. Unsolvability of the halting problem, Rice's theorem. Recursively enumerable sets, creative sets, many-one reductions. Self-referential programs. Gödel's incompleteness theorems, undecidability of validity, decidable and undecidable theories. Course Webpage: Will be set up on bSpace. Grading: 20% homework, 20% each midterm, 40% final. Homework: Homework will be assigned once a week, due the following week. Comments: Math 140 - Section 1 - Metric Differential Geometry Instructor: Nicolai Reshetikhin Lectures: MWF 1:00-2:00pm, Room 3 Evans Course Control Number: 54533 Office: 917 Evans Office Hours: TBA Prerequisites: Math 53, math 54, math 104 is not necessary but could be helpful. Required Text: R. Millman and G. Parker, Elements of Differential Geometry, Prentice Hall. Recommended Reading: The textbook. Syllabus: Theory of curves in the plane and in space, surfaces in space, first and second fundamental forms, Gauss and mean curvature, Gauss-Bonnet Theorem, introduction to higher dimensional Riemannian geometry. Course Webpage: The link to the webpage will be posted at the end of the semester, see http://math.berkeley.edu/~reshetik . Grading: Tentatively 15% quizzes, 25% each midterm, 35%, to be confirmed. Homework: Homework will be assigned every class, and due once a week. Comments: Math 141 - Section 1 - Elementary Differential Topology Instructor: Rob Kirby Lectures: MWF 8:00-9:00am, Room 5 Evans Course Control Number: 54536 Office: 919 Evans Office Hours: MW 10:00-11:00am, Th 11-12am Prerequisites: Math 104 and linear algebra. Required Text: Guillemin and Pollack, Differential Topology, Prentice-Hall. Recommended Reading: 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: 25% each midterm, 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: Nate Ackerman Lectures: TuTh 9:30-11:00am, Room 3 Evans Course Control Number: 54539 Office: 898 Evans Office Hours: TBA Prerequisites: Required Text: Math 151 Lecture Notes, available from Copy Central. Recommended Reading: None. Syllabus: This course is the first part of a three-semester sequence, Math 151-152-153, whose purpose is to give a complete mathematical development of all the main topics of school mathematics in grades 8-12, except probability and statistics. The first half of the course will consist of a thorough development of fractions and the rational numbers followed a discussion of Euclid's algorithm. The second half of the course will cover basic properties of Euclidian geometry followed by a study of symbolic expression and linear equations. Course Webpage: Grading: Homework 40%, First midterm 15%, Second midterm 15%, Final 30%. Homework: Homework will be assigned every week, and due once a week. Comments: Math 153 - Section 1 - Mathematics of the Secondary School Curriculum III Instructor: Hung-Hsi Wu Lectures: MWF 11:00am-12:30pm, Room 9 Evans Course Control Number: 54545 Office: 733 Evans Office Hours: TBA Prerequisites: Math 152, Math 113 Required Text: Math 153 Lecture Notes, available from Copy Central. Recommended Reading: None. Syllabus: *This course is the last part of a three-semester sequence, Math 151-152-153, whose purpose is to give a complete mathematical development of all the main topics of school mathematics in grades 8-12, except probability and statistics. A key feature of this presentation is that it would be directly applicable to the classroom of grades 8-12, and in fact, to middle school as well. *The main topics covered are: Trigonometric functions and their extensions to the number line, the addition theorems, and relations with complex numbers; the concept of limit, basic theorems, and the Least Upper Bound Axiom; the decimal expansion of a number, the equivalence of fractions with repeating decimals, and fractions equal to finite decimals; the concept of geometric measurements, standard formulas of length, area and volume; a second proof of The Pythagorean Theorem using Area; continuity, derivatives, and integrals; the Fundamental Theorem of Calculus, and characterization of the exponential and logarithmic functions. General laws of exponents. Study group encouraged. A fair amount of reading assignments will also be made throughout the semester. Discussion section on Tuesday, 2-3:30 pm (110 Wheeler). Its main purpose is to discuss solutions of problems in the homework assignment, but it will inevitably touch on other issues related to the lectures. Course Webpage: Grading: Homework 30%, First midterm 10%, Second midterm 20%, Final 40%. Homework: Homework will be assigned every week, and due once a week. Comments: Math 160 - Section 1 - History of Mathematics Instructor: Ole Hald Lectures: MWF 1:00-2:00pm, Room 45 Evans Course Control Number: 54551 Office: 875 Evans Hall Office Hours: MWF 2-3pm in 875 Evans Prerequisites: Math 104 Required Text: C.H. Edwards, Jr. The Historical Development of the Calculus, Springer Verlag. Recommended Reading: Syllabus: A serious study of the history of calculus would require knowledge of Greek, Latin, Arabic, Italian, French, English, German and Russian. The book chosen for this course drags the reader through the original arguments, but uses English and modern notation. The work will consist of filling in the gaps and solving the exercises. The grade will be based on homework, essays, and bi-weekly oral presentations. Course Webpage: Grading: Homework: Comments: Math 172 - Section 1 - Combinatorics Instructor: Mark Haiman Lectures: MWF 11:00am-12:00pm, Room 71 Evans Course Control Number: 54557 Office: 855 Evans Office Hours: TBA Prerequisites: Math 55 Required Text: Miklos Bona, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, Second Edition (World Scientific, 2006). Recommended Reading: Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~mhaiman/math172-spring10/ Grading: Based on homework, 2 midterms and final exam. Homework: Weekly problem sets posted on course web page. Comments: Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Michael Rose Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54560 Office: 849 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: J. Brown and R. Churchill, Complex Variables and Applications, 8th edition. Recommended Reading: Syllabus: Course Webpage: Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam. Homework: Homework will be assigned on bSpace and due once a week. Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Michael Klass Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54563 Office: Office Hours: Prerequisites: Math 104 Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Christian Zickert Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54566 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H185 - Section 1 - Honors Introduction to Complex Analysis Instructor: Alberto Grünbaum Lectures: TuTh 8:00-9:30am, Room 81 Evans Course Control Number: 54569 Office: 903 Evans Office Hours: Prerequisites: Required Text: L. Ahlfors, Complex Analysis Recommended Reading: Syllabus: Complex analysis is a fundamental tool in all branches of mathematics. This course is intended to give a solid foundation and has as prerequisite a class such as Math 104. The material includes important tools such as integrals by residues, Taylor and Laurent expansions, harmonic functions, etc. as well as detailed proofs of many of the basic facts. There are several regular versions of this honor class, and every student should consider all the options. I will spend a good part of the class doing explicit examples and some of the proofs. Students are expected to read the book very carefully to fill in material that I may not have time to cover. Course Webpage: Grading: Grades will be based on Homework 30%, Midterms 30% and 30% and a project 10%. There will be two midterms: the first one on Feb 9th, the second one on April 13th. Homework: There will be weekly homework problems, mostly from the book. Comments: Math 191 - Section 1 - Experimental Courses in Mathematics Instructor: Robert Coleman Lectures: MWF 2:00-3:00pm, Room 4 Evans Course Control Number: 54572 Office: 901 Evans Office Hours: MF 3:00-4:00pm Prerequisites: Math 113 or 115. Required Text: Fernando Gouvea, p-adic Numbers, Springer. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: André Weil (a famous mathematician) once said, if a thousand years from now, creatures from another planet try to reconstruct the history of mathematics on earth, they may decide that humans discovered p-adic Numbers before real numbers. Math 191 - Section 2 - Experimental Courses in Mathematics: Cross-Cultural History of Mathematics Instructor: Robin Hartshorne and David Mumford Lectures: MW 2:00-3:30pm, Room 740 Evans Course Control Number: 54575 Office: 881 Evans Office Hours: TBA Prerequisites: Mastery of high school mathematics. Required Text: V.J. Katz, The Mathematics of Egypt, Mesopotamia, China, India, and Islam, Princeton Univ. Press, 2007. Recommended Reading: Euclid, The Elements; Archimedes, Works, (both edited by T. L. Heath, Dover); Jacques Sesiano, An Introduction to the History of Algebra, AMS, 2009 Syllabus: We will study primary sources in the mathematics of Babylon, India, Greece, China, Islam and European Renaissance, with special attention to topics that flow through several of these cultures, such as the Pythagorean theorem, development of algebra, and the origins of integration in calculations of areas and volumes. Students will give oral presentations and write a term paper. Students with reading knowledge of Sanskrit, Arabic, Greek or Chinese are encouraged to enroll! Course Webpage: Grading: Based on class participation, oral reports and term papers. Homework: Homework will be assigned readings and occasional problem sets. Comments: Admission by permission of the instructors. Math 191 - Section 3 - Experimental Courses in Mathematics Instructor: Daniel Berwick Evans Lectures: Th 12:30-2:00pm, Room 740 Evans Course Control Number: 54577 Office: Office Hours: Prerequisites: Math 54 or equivalent, although some problems may necessitate background in algebra, linear algebra, real analysis, and/or complex analysis (113, 110, 104, and/or 185 respectively). Required Text: Recommended Reading: Syllabus: Students will work in teams on two 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: Grading: Homework: Comments: Math 202B - Section 1 - Introduction to Topology and Analysis Instructor: Marc Rieffel Lectures: MWF 11:00am-12:00pm, Room 70 Evans Course Control Number: 54695 Office: 811 Evans Office Hours: TBA Prerequisites: Math 202A or equivalent preparation in analysis. Notice that some measure and integration will have been covered in Math 202A. Required Text: Basic Real Analysis, by Anthony Knapp. Through an agreement between UC and Springer, chapters of the text are available for free download by students. You can find the chapters here. You may need to use campus computers to authenticate yourself to gain access. Recommended Reading: Advanced Real Analysis, by Anthony Knapp. It is my impression that, at least on-line, one can purchase the two Knapp books together as a package at a more attractive price than if they are purchased singly. You can find chapters to download here. Syllabus: We will continue the study of measure and integration begun in Math 202A. This will include product measures and Fubini theorems, signed measures, Radon-Nikodym theorem, measure and integration on locally compact spaces. This will be followed by an introduction to functional analysis. Banach spaces, closed-graph theorem, Hahn-Banach theorem and duality, duals of classical Banach spaces, weak topologies, Alaoglu theorem, convexity and Krein-Milman theorem. In my lectures I will try to give well-motivated careful presentations of the material. Course Webpage: Grading: I plan to assign roughly-weekly problem sets. Collectively they will count for 50% of the course grade. Students are strongly encouraged to discuss the problem sets and the course content with each other, but each student should write up their own solutions, reflecting their own understanding, to turn in. There will be a final examination on Tuesday May 11, 7-10 PM, which will count for 35% of the course grade. There will be a midterm exam. It will count for 15% of the course grade. There will be no early or make-up final examination. Nor will a make-up midterm exam be given; instead, if you tell me ahead of time that you must miss the midterm exam, then the final exam will count for 50% of your course grade. If you miss the midterm exam but do not tell me ahead of time, then you will need to bring me a doctor's note or equivalent in order to have the final exam count for 50% of your course grade. Homework: They will be posted at Homework as they are assigned. Comments: Students who need special accommodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance what specific accommodation they need, so that I will have enough time to arrange it. The above procedures are subject to change. (Last updated 10/23/09) Math 203 - Section 1 - Singular Perturbation Methods in Applied ODE and PDE Instructor: John Neu Lectures: MWF 3:00-4:00pm, Room 81 Evans Course Control Number: 54698 Office: 1051 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: 1. Prototype singular perturbations - examples of matched inner and outer approximations and multiple scales. Theme of examples - distinguished limits by scaling. 2. Minicourse on asymptotic expansion (as opposed to convergent series). Asymptotic evaluation of integrals from Laplace method to steepest descents in complex plane. Primer on linear waves. 3. Matched asymptotic expansions - beyond leading order, boundary layers, internal layers, and derivative layers in nonlinear problems. Singularly perturbed eigenfunctions of the Laplacian. Phase fronts and motion by mean curvature. Classic boundary layer theory for Navier-Stokes equations. 4. Multiple scales - portfolio of definitive elementary examples. Modulation theory of nonlinear resonance, nonlinear waves and averaged Langrangian. Primer on homogenization theory. 5. Scary special topic - JBK smoothing method of waves in random media in real space and time. Course Webpage: Grading: Based on problem sets. Honorable rules of engagement. Homework: Problem sets (many, hard). Comments: Learn to use the Dark Side of the Math. Math 205 - Section 1 - Theory & Functions of a Complex Variable Instructor: Alberto Grünbaum Lectures: TuTh 9:30-11:00am, Room 55 Evans Course Control Number: 54701 Office: 903 Evans Office Hours: Prerequisites: This is a graduate level class that assumes knowledge of the material usually covered in Math 185. I will start with a quick review. Required Text: There is no one book that covers all the material, but a good selection of books is: L. Ahlfors, Complex Analysis. W. Rudin, Real and Complex analysis. H.P. McKean and V. Moll, Elliptic curves. K. Chandrasekharan, Elliptic functions. Recommended Reading: Syllabus: I have in mind covering four areas that are spelled out below, keeping in mind that there are substantial overlaps among these areas: I intend to review at the beginning some material on multivalued functions and then move on to the presentation of material that leads to the Riemman mapping theorem and Picard's theoreom. I will cover the material from Ahlfors on Riemann's approach to the hypergeometric equation of Euler and Gauss. I will give a discussion of Elliptic function theory including Weierstrass' and Jacobi' versions. Hardy spaces, factorization problems. The Wiener-Hopf method and applications to prediction theory. Riemann-Hilbert problems and applications to mathematical physics. Course Webpage: Grading: Homework: There will be biweekly homework assignments and the grade will be based on this work. Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Constantin Teleman Lectures: TuTh 9:30-11:00am, Room 61 Evans Course Control Number: 54704 Office: 905 Evans Office Hours: TuTh 11-12 Prerequisites: Math 215A Required Text: Hatcher, Algebraic Topology, Cambridge; Hatcher, Vector Bundles, available on the web. Recommended Reading: Milnor-Stasheff, Characteristic Classes. Syllabus: Basics of homotopy theory, fibrations, Postnikov towers, relations between homology and homotopy. Vector bundles, basics of K-theory and characteristic classes. Course Webpage: math.berkeley.edu/~teleman/classes/215S10 Grading: Homework and a final paper. Homework: Assigned periodically. Comments: Math C218B - Section 1 - Probability Theory Instructor: Lectures: TuTh 9:30-11:00am, Room 330 Evans Course Control Number: 54707 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 220 - Section 1 - Stochastic Methods of Applied Mathematics Instructor: Alberto Grünbaum Lectures: TuTh 2:00-3:30pm, Room 85 Evans Course Control Number: 54710 Office: 903 Evans Office Hours: Prerequisites: It is hard to describe exactly what are the prerequisites for this class besides a genuine interest in learning the material. You may want to try it for a few lectures and then decide if this is worth your effort. I will make every reasonable effort to start from scratch as we begin any new subject. Required Text: Recommended Reading: There is no required text but I will give pointers to the literature as we go along. Syllabus: The purpose of this class is to present some topics that play in important role in several areas of "applied mathematics". Each of these subjects can be presented in a very detailed and technical fashion, but this is exactly what I will try to avoid. My aim will be to give an ab-initio presentation of several subjects and try to emphasize their connections to each other. These topics include: Random walks and Brownian motion. Birth and death processes. Recurrence, reversibility, the Ehrenfest urn model. Differential equations, coupled harmonic oscillators, some basic harmonic analysis. Evolution equations, semigroups of operators, the Feynman-Kac formula. Some prediction theory for stationary stochastic processes, the Ornstein-Uhlenbeck process. Some Hamiltonian systems. Some important nonlinear equations exhibiting solitons, such as Korteweg de-Vries, non linear Schroedinger etc. The scattering transform as a nonlinear Fourier transform. Isospectral evolutions, the Toda equations. Course Webpage: Grading: Homework: There will be biweekly homework assignments and the grade will be based on the homework. Comments: Math 222B - Section 1 - Partial Differential Equations Instructor: Maciej Zworski Lectures: TuTh 12:30-2:00pm, Room 35 Evans Course Control Number: 54713 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C223B - Section 1 - Stochastic Processes Instructor: Steve Evans Lectures: MW 5:00-6:30pm, Room 332 Evans Course Control Number: 54716 Office: 329 Evans Office Hours: By appointment. Prerequisites: Math C218A or Statistics C205A. Required Reading: None. Recommended Reading: None. Syllabus: Coupling, metric structures on spaces of probability measures, optimal transport, mixing of Markov chains, correlation inequalities and statistical mechanics, Palm theory. Course Webpage: See bSpace -- course crosslisted as Stat C206A. Grading: Final project. Homework: None. Comments: Math 225B - Section 1 - Metamathematics Instructor: John Steel Lectures: TuTh 2:00-3:30pm, Room 7 Evans Course Control Number: 54719 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228B - Section 1 - Numerical Solution of Differential Equations Instructor: James Sethian Lectures: TuTh 8:00-9:30am, Room 3 Evans Course Control Number: 54722 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~sethian/math228b-2010.html Grading: Homework: Comments: Math 229 - Section 1 - Theory of Models Instructor: Thomas Scanlon Lectures: MWF 3:00-4:00pm, Room 3 Evans Course Control Number: 54725 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 240 - Section 1 - Riemannian Geometry Instructor: John Lott Lectures: TuTh 11:00am-12:30pm, Room 81 Evans Course Control Number: 54728 Office: 897 Evans Office Hours: TBA Prerequisites: 214 or equivalent. Required Text: John Lee, Riemannian Manifolds, Springer Graduate Texts in Mathematics. Recommended Reading: Syllabus: The first 2/3 of the semester will be devoted to basic topics of Riemannian geometry, such as Riemannian metrics, connections, geodesics, Riemannian curvature and relations to topology. The last few weeks will be an introduction to Ricci flow. Course Webpage: http://math.berkeley.edu/~lott/teaching.html Grading: Based on homemwork. Homework: Weekly homework assignments will be given. Comments: Math 241 - Section 1 - Complex Manifolds Instructor: Denis Auroux Lectures: TuTh 2:00-3:30pm, Room 5 Evans Course Control Number: 54731 Office: 817 Evans Office Hours: TBA Prerequisites: Math 214 (Differentiable Manifolds) and 215A (Algebraic Topology) Required Text: Huybrechts, Complex geometry: an introduction, Springer Forster, Lectures on Riemann surfaces, Springer Recommended Reading: Syllabus: The course will begin with Riemann surfaces, then proceed with higher-dimensional complex manifolds. The topics include: differential forms, Cech and Dolbeault cohomology, divisors and line bundles, Riemann-Roch, vector bundles, connections and curvature, Kahler-Hodge theory, Lefschetz theorems, Kodaira theorems. Course Webpage: http://math.berkeley.edu/~auroux/241s10 Grading: Homework: Will be assigned periodically. Comments: Math 249 - Section 1 - Algebraic Combinatorics Instructor: Lauren Williams Lectures: TuTh 11:00-12:30pm, Room 5 Evans Course Control Number: 54734 Office: 913 Evans Office Hours: W 11am-12:30pm or by appointment. Prerequisites: Math 250A, or equivalent algebraic background. Required Text: Richard Stanley, Enumerative Combinatorics I and II. Recommended Reading: William Fulton, Young tableaux. Bruce Sagan, The symmetric group. Gunter Ziegler, Lectures on polytopes. Syllabus:Introduction to combinatorics at the graduate level, covering four general areas: (I) enumeration (ordinary and exponential generating functions) (II) order (posets, lattices, incidence algebras) (III) geometric combinatorics (hyperplane arrangements, simplicial complexes, polytopes) (IV) symmetric functions, tableaux, and representation theory. Course Webpage: http://math.berkeley.edu/~williams/249-spring10.html Grading: 100% homework Homework: Homework will be assigned every two weeks. Comments: Math 250B - Section 1 - Multilinear Algebra and Further Topics Instructor: Arthur Ogus Lectures: MWF 10:00-11:00am, Room 81 Evans Course Control Number: 54737 Office: 877 Evans Office Hours: TBA Prerequisites: Math 250A or equivalent Required Text: Lang's Algebra Recommended Reading: Eisenbud's Commutative Algebra with view toward algebraic geometry Syllabus: This will be a course in commutative algebra, with a view towards algebraic number theory and algebraic geometry. I will cover a combination of topics from Lang's Algebra(chapters VII--X) and Eisenbud's Commutative Algebra with a view toward Algebraic Geometry. I will continue in with the functorial spirit of Math 250A. Course Webpage: See my home page. Grading: Homework and oral office conversations. Homework: Comments: Math 254B - Section 1 - Number Theory Instructor: Chung Pang Mok Lectures: TuTh 11:00-12:30pm, Room 7 Evans Course Control Number: 54740 Office: 889 Evans Office Hours: TBA Prerequisites: Math254A or equivalent Required Text: None Recommended Reading: J.Coates, R.Sujatha, Cyclotomic Fields and Zeta Values. L.Washington, Introduction to Cyclotomic Fields. S.Lang, Cyclotomic Fields I and II. Syllabus: This is an introduction to Iwasawa theory. Hopefully we can cover the proof of the main conjecture. Course Webpage: Grading: Homework: Comments: Math 256B - Section 1 - Algebraic Geometry Instructor: Martin Olsson Lectures: MWF 9:00-10:00am, Room 31 Evans Course Control Number: 54743 Office: 879 Evans Office Hours: TBA Prerequisites: Math 256A or equivalent. Required Text: Hartshorne, Algebraic Geometry. Recommended Reading: Syllabus: This will be a continuation of Math 256 A, following Hartshorne's book. I will continue the discussion of schemes, then discuss cohomology, and finally time permitting some curve theory. Course Webpage: A webpage for the course will be maintained in bSpace. Grading: Course grades will be based on weekly homework. Homework: There will be weekly homework assignments. Comments: Math 261B - Section 1 - Quantum Groups Instructor: Vera Serganova Lectures: MWF 1:00-2:00pm, Room 81 Evans Course Control Number: 54746 Office: 709 Evans Office Hours: M 4-5:30, W 11:00-12:30 Prerequisites: 261 A Required Text: Recommended Reading: Fulton-Harris: Representation Theory (a first course); Lusztig: Introduction to Quantum Groups; Chari-Pressley: A Guide to Quantum Groups; Dixmier: Enveloping Algebras. Syllabus: Finite-dimensional representations of Lie groups and Weyl character formuala, Flag varieties, Bruhat decomposition, Borel-Weil-Bott theorem, Schur-Weyl duality, Gelfand-Tsetlin basis, cohomology of Lie algebras, Harish-Chandra theorem, Verma modules and category O, nilpotent cone and Kostant theorem, Hopf algebras, quantum groups, canonical bases, real Lie groups and symmetric spaces, infinite-dimensional Lie algebras (if time permits). Course Webpage: Grading: Homework and take-home final exam. Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 270 - Section 1 - Hot Topics Course in Mathematics Instructor: Peter Teichner Lectures: Tu 3:30-5:00pm, Room 122 Latimer Course Control Number: 54749 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra - Intersection Theory Instructor: David Eisenbud Lectures: TuTh 12:30-2:00pm, Room 9 Evans Course Control Number: 54752 Office: 909 Evans Office Hours: Friday 1-3 Prerequisites: Basic Algebraic Geometry: Varieties, Divisors, Differentials, Bertini's Theorem, .... Required Text: The manuscript of a new book on Intersection Theoryby Eisenbud and Harris will be distributed. Recommended Reading: Fulton, Intersection Theory. Syllabus: Construction of Chow Groups, Intersection Products, Chern Classes, Schubert Calculus, and applications. Course Webpage: Grading: Based on participation. Homework: Groups will work on homework problems together, present them occasionally in class. Comments: This course will emphasize the examples of intersection theory, and the construction of parameter/moduli spaces. Math 275 - Section 1 - Topics in Applied Mathematics - Flow, Deformation, Fracture and Turbulence Instructor: Grigory Barenblatt Lectures: TuTh 9:30-11:00am, Room 736 Evans Course Control Number: 54755 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. The course may be continued in the Fall Semester as Math 275B for those who were enrolled in the present course. 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 276 - Section 1 - Topics in Topology Instructor: Ian Agol Lectures: TuTh 9:30-11:00am, Room 51 Evans Course Control Number: 54758 Office: 921 Evans Office Hours: TBA Prerequisites: Algebraic Topology, Riemannian Geometry, would be helpful to have attended Math 277 fall 2009. Required Text: There will be notes made available over the course of the semester. Recommended Reading: William Thurston, Three-dimensional Geometry and Topology, Vol. 1. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, NJ, 1997. x+311 pp. ISBN 0-691-08304-5. Cooper, Daryl; Hodgson, Craig D.; Kerckhoff, Steven P. Three-dimensional Orbifolds and Cone-manifolds. With a Postface by Sadayoshi Kojima, MSJ Memoirs, 5. Mathematical Society of Japan, Tokyo, 2000. x+170 pp. ISBN 4-931469-05-1. Syllabus: This seminar will focus on topics in 3-manifold topology which are consequences of the Geometrization Theorem and Orbifold Theorem, which we will take for the most part as a black box. Some topics may include: - review of Thurston's 8 geometries and the geometrization and orbifold theorems - classification of universal covers of closed 3-manifolds - homotopy rigidity of aspherical 3-manifolds - geometric proofs of Dehn's lemma, the loop theorem, and sphere theorem - solution to the word and conjugacy problems in 3-manifold fundamental groups - algorithmic classification of compact 3-manifolds If there is time, we may survey some other topics such as the classification of covers of compact 3-manifolds with finitely generated fundamental group, the generalized Smale conjecture, Dehn surgery results, and volume estimates for Haken hyperbolic 3-manifolds. Course Webpage: http://math.berkeley.edu/~ianagol/ Grading: Homework: Comments: Math 278 - Section 1 - Topics in Analysis - Additive Combinatorics With a Sprinkling of Fourier Analysis Instructor: Michael Christ Lectures: MWF 2:00-3:00pm, Room 51 Evans Course Control Number: 54761 Office: 809 Evans Office Hours: TBA Prerequisites: Graduate level mathematical maturity. Required Text: Additive Combinatorics, by Terence Tao and Van H. Vu, Cambridge University Press, (2009 paperback edition). Recommended Reading: Syllabus: Course Webpage: TBA Grading: Homework: Problem Sets. Comments: See more detailed announcement on instructor's web page. Math 300 - Section 1 - Teaching Workshop Instructor: The Staff Lectures: TBA Course Control Number: 55379 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: