Spring 2007
| Math 1A - Section 1 - Calculus Instructor: Mina Aganagic Lectures: TuTh 11:00am-12:30pm, Room 155 Dwinelle Course Control Number: 54103 Office: 715 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Ole Hald Lectures: MWF 10:00-11:00am, Room 155 Dwinelle Course Control Number: 54145 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Calculus Instructor: Marina Ratner Lectures: MWF 12:00-1:00pm, Room 2050 Valley Life Science Course Control Number: 54184 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 3 - Calculus Instructor: James Sethian Lectures: TuTh 11:00am-12:30pm, Room 10 Evans Course Control Number: 54235 Office: 725 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Tsit-Yuen Lam Lectures: MWF 9:00-10:00am, Room 100 Lewis Course Control Number: 54277 Office: 871 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and Calculus Instructor: Zachary Judson Lectures: MWF 9:00-10:00am, Room 60 Evans Course Control Number: 54324 Office: 814 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Jack Wagoner Lectures: MWF 10:00-11:00am, Room 100 Lewis Course Control Number: 54325 Office: 899 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 2 - Analytical Geometry and Calculus Instructor: Jack Silver Lectures: TuTh 11:00am-12:30pm, Room 2050 Valley Life Science Course Control Number: 54373 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman Seminars Instructor: Jenny Harrison Lectures: F 3:00-4:00pm, Room 891 Evans Course Control Number: 54409 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - Freshman Seminars Instructor: Theodore Slaman & Jan Reimann Lectures: W 11:00am-12:00pm, Room 39 Evans Course Control Number: 54411 Office: 719 Evans & 705 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 3 - The Geometry of Relativity Instructor: Alan Weinstein Lectures: Tu 2:00-3:30pm, Room 891 Evans Course Control Number: 55672 Office: 825 Evans Office Hours: TBA Prerequisites: Math 1A or equivalent Required Text: TBA Recommended Reading: TBA Syllabus: This seminar will meet in the first week of classes and nine more Tuesdays, with precise dates to be arranged. This seminar is meant to fill in some of the mathematical background behind Hawking's "A Briefer History of Time." We will study some of the geometry underlying Einstein's special and general theories of relativity. Topics will include the geometry of Lorentz transformations in flat space time (for special relativity) and an introduction to riemannian geometry (for general relativity). The seminar activities will be a mix of reading, discussion, and presentations by students and the instructor. The math which will be taught in the seminar will give students a head start (or a review) for more advanced courses. Students should have had Math 1A or the equivalent. This seminar is part of the On the Same Page initiative: http://onthesamepage.berkeley.edu. Course Webpage: http://math.berkeley.edu/~alanw Grading: P/NP based on class participation and some written work. Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: Martin Vito-Cruz Lectures: MWF 8:00-9:00am, Room 9 Lewis Course Control Number: 54412 Office: 835 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 4:00-6:00pm, Room 71 Evans Course Control Number: 54423 Office: 985 Evans Office Hours: TBA Prerequisites: Math 1A Required Text: None Recommended Reading: To be handed out in class. Syllabus: We will discuss mathematics topics that are difficult for students in K-12, interesting mathematics problems from K-12, and issues pertaining to the practice of teaching. Course Webpage: Grading: P/NP based on homework, journal and final project. Homework: There will be weekly homework assigned during class. Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Vaughan Jones Lectures: MWF 2:00-3:00pm, Room 1 Pimental Course Control Number: 54445 Office: 929 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: Michael Hutchings Lectures: TuTh 3:30-5:00pm, Room F0295 Haas Course Control Number: 54484 Office: 923 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: Robion Kirby Lectures: MWF 8:10-9:00am, Room 155 Dwinelle Course Control Number: 54532 Office: 919 Evans Office Hours: Tu 10:00am-12:00pm, Th 10:30-11:30am Prerequisites: Math 1B Required Text: Richard Hill, Elementary Linear Algebra Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems Both in special editions for Math 54 at Berkeley. Recommended Reading: Syllabus: Linear equations and matrices, vector spaces, linear transformations, determinants, second order differential equations, systems of ordinary differential equations, Fourier series and partial differential equations. Course Webpage: http://math.berkeley.edu/~kirby/math54.html Grading: There will be 3 midterms worth 100 points each, a final worth 200 points, and these will constitute most of the final grade. Homework: Homework will be assigned on the web and due once a week. Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Kenneth Ribet Lectures: TuTh 3:30-5:00pm, Room 1 Pimental Course Control Number: 54580 Office: 885 Evans Office Hours: TBA in January Prerequisites: Math 1B Required Text: Hill, Elementary Linear Algebra; Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems Recommended Reading: Syllabus: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. Course Webpage: http://math.berkeley.edu/~ribet/54/; the current version of this page is left over from the Math 54 that I taught in Fall, 2005. Grading: Based on two midterms, the final, homework, and quizzes. The exact weights will be similar to the weights used in other lower-division math courses. In 2005, I declared that the midterms would be worth 15% each and that homework and quizzes would count 25% all together. That left 45% for the final exam. Homework: Homework will be due in discussion section twice each week. Comments: When you sign up for the course, please join the google discussion group Math 54. As you can see, the group proved to be a useful forum for students to ask questions and make comments. Questions received replies from me, the GSIs and other students. In 2005, I set up Math 54 lunches. I hope to be able to do the same thing again. Math 55 - Section 1 - Discrete Mathematics Instructor: Paul Vojta Lectures: MWF 2:00-3:00pm, Room 277 Cory Course Control Number: 54631 Office: 883 Evans Office Hours: TBA Prerequisites: Math 1A-1B, or consent of instructor. Required Text: Kenneth H. Rosen, Discrete Mathematics and its Applications, 6th edition, McGraw-Hill Recommended Reading: None Syllabus: A paper copy will be distributed on the first day of classes; see also the course web page. Course Webpage: http://math.berkeley.edu/~vojta/55.html Grading: Grading will be based on a first midterm (10%), a second midterm (20%), the final exam (45%), and a component stemming from the discussion sections (25%). This latter component is left to the discretion of the section leader, but it is likely to be determined primarily by homework assignments and biweekly quizzes. Homework: Homework will consist of weekly assignments, to be given on the syllabus. Comments: Math 1A-1B and (if you've had them) 53 and 54 are about smooth functions of one or more real variables; this course is about some very different topics. The main reason 1A-1B are prerequisites is to be sure students have enough familiarity with mathematical thinking; it also means that I will be free to occasionally make connections with topics from that sequence. Section 6.4 is related to a topic in Math 1B (power series), so students who have had 1B may find that section easier than those who have not. Nevertheless, the author's aim was to write the book so as not to assume calculus. If you haven't had calculus and want to take this course, come see me and we will discuss whether you are ready. Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: Patrick Barrow Lectures: MWF 3:00-4:00pm, Room 70 Evans Course Control Number: 54649 Office: 937 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: Dennis Courtney Lectures: MWF 3:00-4:00pm, Room 87 Evans Course Control Number: 54651 Office: 1008 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Giulio Caviglia Lectures: TuTh 2:00-3:30pm, Room 71 Evans Course Control Number: 54709 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Michael Klass Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54712 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Marina Ratner Lectures: MWF 10:00-11:00am, Room 75 Evans Course Control Number: 54715 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Rudin, Principles of Mathematical Analysis Recommended Reading: Syllabus: Completeness of real numbers, metric spaces, convergence, compactness, connectedness. Continuous functions, uniform convergence, series. Differentiation. Riemann integral. Course Webpage: Grading: The grade will be based 40% on the final examination, 25% on a midterm, 20% on quizzes, and 15% on weekly homework. Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: John Krueger Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54718 Office: 751 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~jkrueger/math104.html Grading: Homework: Comments: Math 105 - Section 1 - Analysis II Instructor: John Krueger Lectures: MWF 12:00-1:00pm, Room 85 Evans Course Control Number: 54721 Office: 751 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~jkrueger/math105.html Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Arthur Ogus Lectures: TuTh 3:30-5:00pm, Room 100 Lewis Course Control Number: 54724 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Paul Vojta Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54748 Office: 883 Evans Office Hours: TBA Prerequisites: 53 and 54 Required Text: John A. Beachy and William D. Blair, Abstract Algebra, Third Edition, Waveland Press, Long Grove, Ill. Recommended Reading: Syllabus: This course will cover the basics of groups, rings, and fields, as given in Chapters 1-7 and 9 of the textbook, omitting some sections of the higher-numbered chapters. Details will be announced at the beginning of the course. Course Webpage: http://math.berkeley.edu/~vojta/113.html Grading: Homeworks, 30%; midterms, 15% and 20%; final exam, 35%. Homework: Assigned weekly. Comments: I tend to follow the book rather closely, but will try to give more examples this time. Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Shamgar Gurevitch Lectures: TuTh 8:00-9:30am, Room 70 Evans Course Control Number: 54751 Office: 867 Evans Office Hours: TuW 1:00-2:00pm Prerequisites: Required Text: M. Artin, Algebra Recommended Reading: Syllabus: Topics from Linear Algebra, Groups, Symmetry, Linear Groups, Rings, Modules, Fields. Course Webpage: http://math.berkeley.edu/~shamgar/113S07.html Grading: There will be weekly assignments which will be due in one week, a midterm exam and a final. They will count toward the grade as follows: Assignments 30% Midterm 30% Final 40% Homework: Comments: Attitude: In our course we will study basic algebraic structures. The attitude will be to help you to develop your way on how to think about some mathematical objects that appears in the formulations and solutions of various problems. Moreover, I expect you to be an integral part of the course, i.e., to attend lectures, to submit homework, and to visit me during my office hours. Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Jack Wagoner Lectures: MWF 1:00-2:00pm, Room 3105 Etcheverry Course Control Number: 54754 Office: 899 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: George Bergman Lectures: TuTh 2:00-3:30pm, Room 75 Evans Course Control Number: 54757 Office: 865 Evans Office Hours: M 1:30-2:30pm, WTh 10:30-11:30am Prerequisites: Math 54 or a course with similar linear algebra content, and mathematical maturity appropriate to upper-division status. Required Text: John A. Beachy and William D. Blair, Abstract Algebra, third edition, Waveland Press, Long Grove, Illinois, 60047. Recommended Reading: Syllabus: 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 familiar 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. The parts of the book we will cover will be: Chapters 1, 2, 3 (Integers, Functions, Groups) followed by parts of 7 (Structures of Groups), 4 and 5 (Polynomials and Commutative Rings) and parts of 6 (Fields) and of 9 (Unique Factorization). Course Webpage: 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 Thursdays. Comments: 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.. On each day, each student will be required to submit, in writing or 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 often incorporate answers to students' questions into my lectures; other times I will answer your question by e-mail. More details on this and other matters will be given on the course handout (to be distributed in class the first day, and available on the door to my office thereafter). Math H113 - Section 1 - Honors Introduction to Abstract Algebra Instructor: Dagan Karp Lectures: TuTh 8:00-9:30am, Room 85 Evans Course Control Number: 54760 Office: 1053 Evans Office Hours: Tu 9:30-10:30am, W 3:00-4:00pm Prerequisites: 54 or a course with equivalent linear algebra content Required Text: I. N. Herstein, Topics in Algebra, Wiley & Sons Recommended Reading: Syllabus: Honors section corresponding to 113, which covers: Sets and relations. The integers, congruences and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions. Course Webpage: http://math.berkeley.edu/~dkarp/courses/113/ Grading: 40% homework, 15% each midterm, 30% final Homework: Homework will be assigned and collected roughly once a week. Comments: Math 114 - Section 1 - Abstract Algebra II Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54763 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Shamgar Gurevitch Lectures: TuTh 11:00am-12:30pm, Room 71 Evans Course Control Number: 54766 Office: 867 Evans Office Hours: TuW 1:00-2:00pm Prerequisites: Required Text: Mary L. Boas, Mathematical Methods in the Physical Sciences Recommended Reading: Syllabus: Linear algebra, complex numbers, complex functions, Harmonic Analysis, Discrete Harmonic Analysis, other topics and applications. Let me elaborate on some of the topics that will be covered 1. Linear Algebra. Probably the most important notions of mathematics are the notions of abstract vector spaces and Linear operators between them. 2. Complex numbers. We will extend our linear algebra notions to the language of vector spaces over the field of complex numbers. 3. Theory of complex functions. The notion of analytic function will be presented. A central theorem in complex analysis, known as Cauchy's theorem, will be formulated and proved. Using the language of complex functions you will be able to understand the calculations of difficult integrals of real functions. 4. Harmonic Analysis. Here the main question is how to think on a function defined on the circle T or on the real line R? Is it really defined by its values? This will lead us to the definition of the L2 spaces and in particular we will introduce one of the most important transforms in mathematics called the Fourier transform. We will learn about a nice application of Harmonic analysis to applied mathematics called Shannoni's Sampling Theorem. This is a theorem which is formulated in terms of the Fourier transform and is one of the corner stones of modern information theory and its applications. 5. Discrete Harmonic Analysis. Here you will see that one can define all the notions of Harmonic analysis in the case of the "discrete line" ZN = {0,1,...,N-1}. In particular we will introduce the discrete Fourier transform (DFT). This will help us to solve a model problem in the application of mathematics to the digital world. Namely, we will learn how to multiply two polynomials in a fast way. The solution will use the Cooley-Tukey Fast Fourier Transform algorithm (FFT). Course Webpage: http://math.berkeley.edu/~shamgar/121aS07.html Grading: There will be weekly assignments (handout by the TA) which will be due in one week, a midterm exam and a final. They will count toward the grade as follows: Assignments 30% Midterm 30% Final 40% Homework: Comments: Attitude: In our course we will study some fundamental tools of mathematics. The attitude will be to help you to develop your way on how to think on some mathematical objects that you will encounter during your undergraduate studies. Moreover, I expect from you to be an integral part of the course, i.e., I expect from you to attend lectures, to participate in the discussion, to submit home works, and to visit me during my office hours. Math 121B - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Jason Metcalfe Lectures: TuTh 12:30-2:00pm, Room 241 Cory Course Control Number: 54769 Office: 837 Evans Office Hours: TBA Prerequisites: Math 53 and Math 54 Required Text: M. Boas, Mathematical Methods in the Physical Sciences, 3rd edition (Wiley) Recommended Reading: Syllabus: Mains topics: Special functions (Ch. 11); Series solutions of ODE and more special functions (Ch. 12); Partial differential equations (Ch. 13); Probability and Statistics (Ch. 16). Please see the webpage for a detailed syllabus. Course Webpage: http://math.berkeley.edu/~metcalfe/teaching/math121b/ Grading: 15% homework, 25% each for two midterm exams, 35% final Homework: There will be an assignment corresponding to each lecture which is due one week later. Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Jack Silver Lectures: TuTh 2:00-3:30pm, Room 289 Cory Course Control Number: 54772 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 126 - Section 1 - Introduction to Partial Differential Equations Instructor: Ole Hald Lectures: MWF 1:00-2:00pm, Room 70 Evans Course Control Number: 54775 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 127 - Section 1 - Mathematics for Computational Biology Instructor: Bernd Sturmfels Lectures: TuTh 12:30-2:00pm, Room 70 Evans Course Control Number: 54777 Office: 925 Evans Office Hours: W 9:00-11:00am or by appt. Prerequisites: Some basics of Discrete Mathematics, Statistics and Abstract Algebra. An interest in Molecular Biology. Required Text: Lior Pachter & Bernd Sturmfels, Algebraic Statistics for Computational Biology, Cambridge University Press, 2005 Recommended Reading: Will be announced in class. Syllabus: This course offers an introduction to mathematical foundations which are relevant for computational biology, in particular, for biological sequence analysis. The emphasis lies on algebraic statistics (e.g. hidden Markov models) and discrete algorithms (e.g. neighbor-joining for tree construction). Occasional guest speakers will discuss biological problems and applications. Course Webpage: http://math.berkeley.edu/~bernd/math127.html Grading: Will be based on homework and a course project. Homework: Comments: The expected participants will be a mix of undergraduate students and graduate students, both from mathematics and from other departments (MCB, IB, Stat, EECS, etc....). This is a truly interdisciplinary opportunity. All of us will greatly benefit from working with each other. Math 128A - Section 1 - Numerical Analysis Instructor: Marc Rieffel Lectures: MWF 8:10-9:00am, Room 4 LeConte Course Control Number: 54778 Office: 811 Evans Office Hours: To be arranged in January. Prerequisites: Math 53 and 54 or equivalent. No prior knowledge of computer programming is expected. Required Text: K. Atkinson and W. Han, Elementary Numerical Analysis, 3rd ed., John Wiley Pub. 2004 Recommended Reading: The MATLAB Student Version, if you have your own computer. Syllabus: Solution of nonlinear equations, interpolation and polynomial approximation, numerical differentiation, numerical integration, numerical solution of ordinary differential equations. Course Webpage: There will eventually be a Course Webpage, reachable from my personal home page at http://math.berkeley.edu/~rieffel/ Grading: There will be homework, which will count for 10% of the course grade, and there will be programming exercises which will count for 20% of the course grade.. There will be 2 midterm exams, which will each count for 15% of the course grade. There will be a final examination, which will count for 40% of the course grade. Homework: Homework will be assigned at almost every lecture, due the next section meeting. Comments: This is a mathematics course, and so the emphasis will be on how to obtain effective methods for computation, and on analysing when methods will, and will not, work well (in contrast to just learning methods and applying them). You will have an easier time with the course if you review Taylor's theorem and ordinary differential equations before the course begins. The programming exercises are to be done in MATLAB, but no prior knowledge of MATLAB will be assumed, and help will be provided for learning the relatively small amount of MATLAB which will be needed for the course. (But if you can learn a bit of MATLAB before the course begins, that will make the course easier. See Appendix D of the text.) Math 128B - Section 1 - Numerical Analysis Instructor: William Kahan Lectures: TuTh 8:00-9:30am, Room 81 Evans Course Control Number: 54799 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory Sets Instructor: Leo Harrington Lectures: TuTh 12:30-2:00pm, Room 75 Evans Course Control Number: 54805 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 142 - Section 1 - Elementary Algebraic Topology Instructor: Robion Kirby Lectures: MWF 2:00-3:00pm, Room 70 Evans Course Control Number: 54808 Office: 919 Evans Office Hours: Tu 10:00am-12:00pm, Th 10:30-11:30am Prerequisites: Math 104 and 113 Required Text: M. A. Armstrong, Basic Topology Recommended Reading: Syllabus: Continuity, compactness, connectedness for topological spaces, surfaces, homotopy type, fundamental group, covering spaces, knots and links. Course Webpage: http://math.berkeley.edu/~kirby/math142.html Grading: There will be 2 or 3 midterms worth 100 points each, a final worth 200 points, and these will constitute most of the final grade. Homework: Homework will be assigned on the web and due once a week. Comments: Math 151 - Section 1 - School Curriculum I Instructor: Emiliano Gomez Lectures: TuTh 3:30-5:00pm, Room 41 Evans Course Control Number: 54810 Office: 985 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 152 - Section 1 - School Curriculum II Instructor: Hung-Hsi Wu Lectures: TuTh 2:00-3:30pm, Room 85 Evans Course Control Number: 54811 Office: 733 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 160 - Section 1 - History of Mathematics Instructor: Mariusz Wodzicki Lectures: TuTh 11:00am-12:30pm, Room 9 Evans Course Control Number: 54814 Office: 995 Evans Office Hours: TBA Prerequisites: Math 104, 110 and 113 (or my consent) Required Text: We will begin from the following texts: Richard Gillings, Mathematics in the Time of the Pharaohs, Dover Publications Otto Neugebauer, The Exact Sciences in Antiquity, Dover Publications Ivor Thomas (editor), Greek Mathematical Works I/II, Loeb Classical Library, Nos. 335 & 362, Harvard University Press Recommended Reading: Carl B. Boyer, A History of Mathematics, John Wiley & Sons Syllabus: In an introductory course on History of Mathematics nothing can replace a first hand experience of working with original texts. We will focus on a number of such texts from various historical epochs. This will be supplemented by my lectures in which I will be presenting a panoramic overview of the development of Mathematics in its cultural perspective. Course Webpage: http://math.berkeley.edu/~wodzicki/160 Grading: Midterm 20%, Final 30%, a term paper (25% each), quizzes, homework & class participation 25% Homework: Homework assignemens will take various forms; reading assignments will be given after every class. Comments: Students are expected to attend the class regularly. Math 170 - Section 1 - Mathematical Method Optimization Instructor: Ming Gu Lectures: MWF 12:00-1:00pm, Room 3 Evans Course Control Number: 54817 Office: 861 Evans Office Hours: MF 11:00am-12:00pm, W 1:00-2:00pm Prerequisites: Math 53, Math 54 Required Text: Joel Franklin, Methods of Mathematical Economics, SIAM Recommended Reading: Syllabus: Introduction to linear programs and their duals; the simplex method; Separating planes for convex sets; the Farkas Alternative; the revised simplex algorithm; multiobjective linear programming; zero-sum, two-person games; integer programming; Wolfe's method for Quadratic Programming; Kuhn-Tucker Theory. Course Webpage: http://math.berkeley.edu/~mgu/MA170 Grading: 25% homework, 25% midterm, 20% project, 30% final Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 172 - Section 1 - Combinatorics Instructor: Joel Kamnitzer Lectures: TuTh 3:30-5:00pm, Room 85 Evans Course Control Number: 54820 Office: 1067 Evans Office Hours: TBA Prerequisites: Math 1B, 54 or consent of instructor Required Text: Miklos Bona, Enumerative Combinatorics Recommended Reading: Syllabus: Combinatorics is the study of discrete objects, such as graphs, permutations, and partially ordered sets. It has applications both to pure mathematics and computer science. In this course, we will focus mainly on enumerative combinatorics, that is, the art of counting. We will go from simple questions, like how many words can be made by rearranging ABRACADABRA? to more complicated ones such as, how many rooted unlabeled trees are there on n vertices? We will first study generating functions, both ordinary and exponential, as these are the basic tools of enumerative combinatorics. We will then apply our techniques to counting permutations and graphs. Along the way, other concepts such as partially ordered sets will be introduced and explored. Students will also explore a topic of their own choosing through a project. Course Webpage: http://math.berkeley.edu/~jkamnitz/math172 Grading: 40% homework, 30% project, 30% final Homework: There will be homework assignments every two weeks. These will be difficult problems and you will not be expected to solve all of them. You are encouraged to work in groups, but must write up your solutions individually. Comments: Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Dapeng Zhan Lectures: TuTh 8:00-9:30am, Room 75 Evans Course Control Number: 54823 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: James Ward Brown and Ruel V. Churchill, Complex Variables and Applications Recommended Reading: Syllabus: This course will cover the content of the textbook from Chapter 1 to Chapter 9. They include complex numbers, analytic functions, elementary functions, integerals, Cauchy integral formula, series, residues and poles, application of residues, etc. Course Webpage: http://math.berkeley.edu/~dapeng/ma185.html Grading: 20% homework, 20% each midterm, 40% final Homework: Homework will be assigned on the web every class, and due once a week. Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: David Cimasoni Lectures: TuTh 3:30-5:00pm, Room 141 Giannini Course Control Number: 54826 Office: 749 Evans Office Hours: W 10:00am-12:00pm, Th 11:00am-12:00pm Prerequisites: Math 104 Required Text: Freitag and Busam, Complex Analysis, Springer Recommended Reading: Syllabus: We shall cover the first three chapters of the textbook, without following it too closely. They include: complex numbers, complex derivation, the Cauchy-Riemann equations, analytic functions, complex line integrals, the Cauchy integral theorem, the Cauchy integral formula, the fundamental theorem of algebra, the maximum principal, power series, singularities, Laurent decomposition, the residue theorem and its applications. Course Webpage: http://math.berkeley.edu/~cimasoni/Math185.html Grading: 20% homework, 20% each midterm, 40% final Homework: Homework will be posted on the web every Tuesday, and due one week later. Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Jan Reimann Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54829 Office: 705 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Freitag and Busam, Complex Analysis, Springer Recommended Reading: Syllabus: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. If time permits some additional topics such as the Riemann mapping theorem. Course Webpage: http://math.berkeley.edu/~reimann/Spring_07/185.html Grading: 20% Homework, 20% each Midterm, 40% Final Homework: Comments: Math H185 - Section 1 - Honors Introduction to Complex Analysis Instructor: Xuemin Tu Lectures: TuTh 3:30-5:00pm, Room 87 Evans Course Control Number: 54832 Office: 1055 Evans Hall Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 189 - Section 1 - Math/Met Class/Quan Instructor: Dan Voiculescu Lectures: TuTh 12:30-2:00pm, Room 3102 Etcheverry Course Control Number: 54835 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 202B - Section 1 - Introduction to Topology and Analysis Instructor: Justin Holmer Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54940 Office: 849 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 209 - Section 1 - Von Neumann Algebra Instructor: Richard Borcherds Lectures: TuTh 3:30-5:00am, Room 75 Evans Course Control Number: 54946 Office: 927 Evans Office Hours: TuTh 11:00am-12:00pm Prerequisites: Math 206 Banach algebras and spectral theory (this will be reviewed in the course) Required Text: Notes by Vaughan Jones, available on the course home page. Recommended Reading: See course home page. Syllabus: Basic theory of von Neumann algebras. Density theorems, topologies and normal maps, traces, comparison of projections, type classification, examples of factors. Additional topics, for example, Tomita Takasaki theory, subfactors, group actions, and noncommutative probability. Course Webpage: http://math.berkeley.edu/~reb/209/ Grading: Homework: Homework will be assigned on the web every week. Comments: Math 214 - Section 1 - Differential Manifolds Instructor: Alexander Givental Lectures: MWF 10:00-11:00AM, Room 81 Evans Course Control Number: 54949 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Robion Kirby Lectures: MWF 11:00am-12:00pm, Room 6 Evans Course Control Number: 54951 Office: 919 Evans Office Hours: Tu 10:00am-12:00pm, Th 10:30-11:30am Prerequisites: Math 215A or the equivalent. Required Text: Allen Hatcher, Algebraic Topology Milnor and Stasheff, Characteristic Classes Recommended Reading: Syllabus: More topics in homotopy and homology theory not covered in 215A, followed by characteristic classes, with many examples from low dimensional topology. Course Webpage: http://math.berkeley.edu/~kirby/math215B.html Grading: Hard and interesting homework problems will provide the basis for the grade. Homework: Homework will be assigned on the web and due periodically. Comments: Math C218B - Section 1 - Probability Theory Instructor: Jim Pitman Lectures: TuTh 9:30-11:00am, Room 330 Evans Course Control Number: 54952 Office: 303 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 219 - Section 1 - O.D.E. and Flows Instructor: Fraydoun Rezakhanlou Lectures: TuTh 11:00am-12:30pm, Room 39 Evans Course Control Number: 54955 Office: 815 Evans Office Hours: TuTh 1:30-3:00pm Prerequisites: Some analysis and measure theory Required Text: No required text. Handwritten notes will be distributed in class. 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. 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. Thermodynamic formalism. Perron-Frobenius operator. Bowen-Ruelle-Sinai measures. 4. Pesin’s theorem. Ruelle’s inequality. 5. Small perturbations of integrable Hamiltonian systems. Invariant tori. Kolmogorov-Arnold-Moser Theory. Course Webpage: Grading: There will be some homework assignments. Homework: Comments: Math 220 - Section 1 - Methods of Applied Mathematics Instructor: Alexandre Chorin Lectures: MWF 11:00am-12:00pm, Room 85 Evans Course Control Number: 54958 Office: 911 Evans Office Hours: MWF 12:00-1:00pm Prerequisites: Required Text: None Recommended Reading: Lecture notes from a previous time I taught this class will be made available, as well as reading material for topics not covered in the previous class. Syllabus: Introductory probability, solution of differential equations by Brownian motion, introduction to stochastic processes, Markov chains and Markov chain Monte Carlo, renormalization, scaling, the Langevin and Fokker-Planck equations, the Barenblatt equation, many coupled oscillators, irreversible processes, applications. Course Webpage: http://math.berkeley.edu/~chorin/math220 Grading: Based on homework sets. Homework: Weekly assignments, some may involve computation and due once a week) Comments: I'll try to make the course self-contained and there are no formal prerequisites; previous experience with the applications of mathematics to a science would make things easier. Math 222B - Section 1 - Partial Differential Equations Instructor: Daniel Tataru Lectures: TuTh 12:30-2:00pm, Room 39 Evans Course Control Number: 54961 Office: 841 Evans Office Hours: By appt. Prerequisites: 222A or equivalent Required Text: Recommended Reading: L. C. Evans, Partial Differential Equations M. E. Taylor, Partial Differential Equations I L. Hormander, Partial Differential Equations I Syllabus: The theory of initial value and boundary value problems for hyperbolic, parabolic, and elliptic partial differential equations, with emphasis on nonlinear equations. (Continues 222A) Course Webpage: Grading: Homework + final project. Homework: Homework will be assigned periodically. Comments: Math 225B - Section 1 - Metamathematics Instructor: Theodore Slaman Lectures: TuTh 9:30-11:00am, Room 72 Evans Course Control Number: 54964 Office: 719 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228B - Section 1 - Numerical Solution of Differential Equations Instructor: Jon Wilkening Lectures: TuTh 11:00am-12:30pm, Room 7 Evans Course Control Number: 54967 Office: 1091 Evans Office Hours: M 11:00am-1:00pm Prerequisites: Math 128A or equivalent knowledge of basic numerical analysis. Some programming experience (e.g., Matlab, Fortran, C, or C++) Required Text: Morton & Mayers, Numerical Solution of Partial Differential Equations Dietrich Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics Recommended Reading: Syllabus: In the first half of the course, we will study finite difference methods for solving hyperbolic and parabolic partial differential equations. I will describe von Neumann stability analysis, CFL conditions, the Lax-Richtmeyer equivalence theorem (consistency + stability = convergence), dissipation and dispersion. We will use these tools to analyze several popular schemes (Lax-Wendroff, Lax-Friedrichs, leapfrog, Crank-Nicolson, ADI, etc.) The second half of the course will be devoted to finite element methods for elliptic equations (Poisson, Lamé, Stokes). We will discuss Sobolev spaces, functional analysis, the Lax-Milgram theorem, Cea's lemma, the Bramble-Hilbert lemma, variational calculus, mixed methods for saddle point problems, and the Babuska-Brezzi inf-sup condition. If time permits, I'll also talk about hyperbolic conservation laws in the first part of the course and least squares finite elements in the second part. Course Webpage: http://math.berkeley.edu/~wilken/228B.F06 Grading: Grades will be based entirely on homework. Homework: 8 assignments Comments: Homework problems will be graded Right/Wrong, but you may resubmit the problems you get Wrong within two weeks of getting them back to convert them to Right. (If you turn in a homework late, you forfeit this possibility). Math 235A - Section 1 - Theory of Sets Instructor: John Steel Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54970 Office: 717 Evans Office Hours: TBA Prerequisites: This course will be an introduction to forcing. We shall assume familiarity with basic set theory (the axions of ZFC, cardinal arithmetic, definitions and proofs by transfinite recursion). It would also be good, though not essential, to be familiar with the basic theory of Gödel’s universe L of constructible sets. Required Text: Recommended Reading: Syllabus: Cohen’s method of forcing is a powerful tool for producing models of Zeumelo–Fraenkel Set Theory (ZFC), and thereby showing that many natural mathematical statements are neither provable nor refutable in ZFC. Besides its metamathematical use, forcing is also useful in obtaining consequences of ZFC, and more broadly, descriptive set theory, recursion theory, and model theory as well. Every logician should know the basics of forcing. Here is a rough course outline: 1. Transitive models, the Levy hierarchy of formulae, truth in transitive models. A short discussion of Gödel’s L. 2. The basic forcing theorem: the generic extension M[G] satisfies ZFC. 3. The independence of CH. Chain conditions and closure. Possible behavior of the function κ → Zκ in models of ZFC (Easton’s Theorem). 4. Models of ZF where the Axiom of Choice fails. 5. Forcing theory: complete Boolean algebras. Subalgebras versus submodels of M[G]. Characterization of the Levy collapse algebra. Vopenka’s theorem. 6. Solovay’s model of ZF + “All sets of reals are Lebesgue measurable”. 7. Iterated forcing and Martin’s Axiom. 8. Forcing and large cardinals. Prikry forcing. Forcing the failure of the Singular Cardinals Hypothesis. Course Webpage: Grading: Homework: Comments: Math 240 - Section 1 - Riemannian Geometry Instructor: John Lott Lectures: TuTh 2:00-3:30pm, Room 7 Evans Course Control Number: 54973 Office: 895 Evans Office Hours: TBA Prerequisites: 214 or equivalent Required Text: John Lee, Riemannian Manifolds 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. In particular, we will prove Perelman's no local collapsing theorem. Course Webpage: Grading: Based on homework. Homework: Weekly homework assignments will be given. Comments: Math 250B - Section 1 - Multilinear Algebra Instructor: Giulio Caviglia Lectures: TuTh 9:30-11:00am, Room 5 Evans Course Control Number: 54976 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 254B - Section 1 - Number Theory Instructor: Kenneth Ribet Lectures: TuTh 11:00am-12:30pm, Room 5 Evans Course Control Number: 54979 Office: 885 Evans Office Hours: TBA and by appointment Prerequisites: Math 254A or some basic knowledge of algebraic number fields and their completions. Required Text: Number Theory, edited by Cassels and Fröhlich Recommended Reading: Notes of an analogous course this year at Harvard. Syllabus: We will study local classfield theory and then global classfield theory, following the lectures by Serre and Tate (respectively) in Cassels-Fröhlich. We will pause frequently for background lectures on cohomolgy and other relevant topics. Course Webpage: Grading: Generous. Homework: Homework will be assigned occasionally. Comments: Most of us know the bare statements of classfield theory but have never bothered to learn the proofs and techniques that were developed 50 odd years ago to bring order into the subject. Now is our chance to fill in the gaps in our understanding! Math 256B - Section 1 - Algebraic Geometry Instructor: Brian Osserman Lectures: TuTh 2:00-3:30pm, Room 41 Evans Course Control Number: 54982 Office: 767 Evans Office Hours: Tu 1:00-2:00, W 2:00-3:00 Prerequisites: 256A Required Text: Hartshorne, Algebraic Geometry Recommended Reading: Eisenbud and Harris, the Geometry of Schemes Syllabus: This is the second semester of an integrated, year-long course in algebraic geometry. The primary source text will be Hartshorne's Algebraic Geometry. We will have already covered most of Chapter II in the fall. We will begin with the basic properties of sheaf cohomology and the statement of the Riemann-Roch theorem, and classical applications to the study of curves. This will focus as motivation for the development of cohomology in Chapter III. Finally, we will conclude with some discussion of special topics, most likely involving moduli spaces. Course Webpage: http://math.berkeley.edu/~osserman/classes/256B/ Grading: 75% homework, 25% final paper Homework: Homework will be assigned roughly weekly. Comments: Math 257 - Section 1 - Group Theory Instructor: Mariusz Wodzicki Lectures: TuTh 3:30-5:00pm, Room 7 Evans Course Control Number: 54985 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra - Stacks Instructor: Martin Olsson Lectures: MWF 10:00-11:00am, Room 385 LeConte Course Control Number: 54987 Office: 887 Evans Office Hours: TBA Prerequisites: Math 256A or equivalent course on schemes Required Text: None Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Algebraic stacks were originally introduced by Grothendieck, Artin, Deligne, and Mumford as the natural setting for the study of moduli spaces. In recent years stacks have found much broader applications and are now a standard tool of the modern algebraic geometer. Stacks are generalizations of schemes, which enable one to handle geometric objects with symmetries which cannot be studied adequately using schemes. For example, many moduli spaces are stacks (for example moduli spaces for curves), and quotients of varieties by group actions are stacks. In this course I will discuss the foundations of algebraic stacks, and time permitting some more recent applications towards the end of the class. I aim to make the course accessible to students familiar with schemes as taught for example in 256A though of course more background will be helpful (in particular a course in algebraic topology would be helpful). In light of these limited prerequisites, I will spend some time at the beginning of the course to develop the foundations necessary for the basic definitions in the theory of stacks (Grothendieck topologies, descent, groupoids, ...). I will then discuss the basic theory of quasi-coherent and coherent sheaves on stacks, separated and proper morphisms, Chow's lemma, and other generalizations of standard scheme theory to stacks. Throughout I will discuss in detail examples to illustrate the theory. At the end of the course I hope to discuss Artin's method for proving representability by an algebraic stack, as well as other more advanced topics (to be chosen based on the interests of the participants). Math 275 - Section 1 - Topics in Applied Mathematics: Flow, Deformation and Fracture Instructor: Grigory Barenblatt Lectures: TuTh 9:30-11:00am, Room 41 Evans Course Control Number: 54988 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. 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 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, and damage accumulation. 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. 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 - Chainlet Theory - New Geometric Methods in Analysis Instructor: Jenny Harrison Lectures: MWF 1:00-2:00pm, Room 39 Evans Course Control Number: 54991 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: In the first half of this course we present a class of objects called ‘chainlets’, a particularly well-behaved subspace of de Rham currents. Chainlets are a generalization of k-surfaces in n-space, but with algebraic information encoded both locally and globally. Equipped with a new, ‘natural’ norm, we discard many cumbersome methods used in geometric measure theory, instead building an elegant calculus from the ground up on domains that include, but are not limited to, discrete and continuous domains, soap films, fractals, and particle fields. The second half of the course will cover a wide array of applications, from analysis to differential and algebraic topology, calculus of variations, PDEs, and physics, as time permits. Course Webpage: Grading: Homework: Comments: Math 278 - Section 2 - Topics in Random Matrices Instructor: Alice Guionnet Lectures: MWF 12:00-1:00pm, Room 55 Evans Course Control Number: 54993 Office: 757 Evans Office Hours: W 2:00-3:00pm, F 2:00-4:00pm Prerequisites: Basic probability theory Required Text: No textbook will be required but lecture notes (from a course I gave in Saint Flour) will be posted on my web page http://www.umpa.ens-lyon.fr/~aguionne/ . Recommended Reading: Syllabus: Random matrices appeared first in statistics in the work of Wishart in the thirties and then in quantum mechanics when Wigner introduced them as a model to the Hamiltonian of highly excited nuclei. Since then, random matrices appeared in many different branches of physics (e.g. theoretical physics, string theory, quantum field theory) and mathematics (e.g. number theory, combinatorics, free probability and operator algebras, hydrodynamics via the totally asymmetric simple exclusion process). The goal of the course is to give an introduction to the rapidly developing theory of random matrices. In the first part of the course I will focus on properties of random matrices which are 'universal' in the sense that they do not depend much on the distribution of the entries. In the second part, I will focus on properties more closely related with Gaussian entries. Most results and proofs will be given for the so-called Wigner's matrices which are self-adjoint matrices with independent entries modulo the symmetry constraints, but generalizations to other classical ensembles will be pointed out. The following is a possible list of topics forthis course. Ideally, we would like to cover all of them, but adjustments may have to be made because of time constraints.
Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor: Jenny Harrison Lectures: W 5:00-7:00pm, Room 47 Evans Course Control Number: 55603 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: |
