# Fall 2007

 Math 1A - Section 1 - Calculus Instructor: Paul Vojta Lectures: MWF 2:00-3:00pm, Room 10 Evans Course Control Number: 54103 Office: 883 Evans Office Hours: TBD Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or Math 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: Stewart, Single Variable Essential Calculus - Early Transcendentals (custom edition for UCB), Brooks/Cole Note: This is not the same as Calculus - Early Transcendentals, which is being used for Math 1B and was used for Math 1A last semester and during the summer. If a book is the fifth or sixth edition of something, then it is the wrong book. For Math 1A, you can use the regular edition of Essential Calculus, Early Transcendentals (note the title change), since the early chapters of the custom edition are the same as the early chapters of the standard edition. However, the custom edition adds material on differential equations used in Math 1B, so the standard edition would not be suitable for students planning to continue on to Math 1B. Recommended Reading: None Syllabus: A paper copy will be distributed on the first day of class; it will also be available on the course web page shortly before classes begin. Course Webpage: http://math.berkeley.edu/~vojta/1a.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. See more details, below. Homework: Homework will consist of weekly assignments, given on the syllabus. Information on solutions will be available on the syllabus. Comments: This is the first semester of the year-long calculus sequence; this particular course is intended primarily for majors in engineering and the physical sciences. This semester's topics will include differentiation, transcendental functions, and integration. A detailed syllabus will be passed out during the first week of class. Math 1A - Section 2 - Calculus Instructor: Ole Hald Lectures: MWF 10:00-11:00am, Room 1 Pimentel Course Control Number: 54133 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1A - Section 3 - Calculus Instructor: Mariusz Wodzicki Lectures: TuTh 3:30-5:00pm, Room 2050 Valley Life Science Course Control Number: 54190 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Nicolai Reshetikhin Lectures: MWF 11:00am-12:00pm, Room 2050 Valley Life Science Course Control Number: 54245 Office: 917 Evans Office Hours: TBA Prerequisites: Calculus 1A or its equivalent Required Text: Stewart, Calculus: Early Transcendentals, 5th edition Recommended Reading: The same as the required text. Lecture notes will be available during the semester. Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~reshetik/math1B-Fall.html (with some omissions which will be completed before the end of the semester) Grading: See course webpage. Homework: See course webpage. Comments: See course webpage. Math 1B - Section 2 - Calculus Instructor: Maciej Zworski Lectures: TuTh 2:00-3:30pm, Room 2050 Valley Life Science Course Control Number: 54280 Office: 897 Evans Office Hours: Mon 1:30-3:00pm, Tu 3:45-5:00pm. Prerequisites: Math 1A or equivalent Required Text:Stewart, Calculus: Early Transcendentals, 5th edition Recommended Reading: The same as the required text. Lecture notes will be available during the semester. Syllabus: Course Webpage:http://math.berkeley.edu/~zworski/math1B.html Grading: See course webpage. Homework: See course webpage. Comments: See course webpage. Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: John Wagoner Lectures: MWF 1:00-2:00pm, Room 2050 Valley Life Science Course Control Number: 54328 Office: 899 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and Calculus Instructor: Zvezdelina Stankova Lectures: TuTh 12:30-2:00pm, Room 105 Stanley Course Control Number: 54367 Office: 713 Evans Office Hours: TuTh 2:00-3:30pm Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Consult the mathematics department for details. Required Text: Goldstein, Lay and Schneider, Calculus and Its Applications, Prentice Hall Recommended Reading: Syllabus: This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions. A detailed syllabus shall be posted on the course webpage. Course Webpage: http://math.berkeley.edu/~stankova Grading: 15% quizzes, 25% each midterm, 35% final Homework: Homework will be assigned on the web every class, and due once a week. Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Jack Silver Lectures: TuTh 11:00am-12:30pm, Room 105 Stanley Course Control Number: 54412 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman Seminars Instructor: Alberto Grünbaum Lectures: Tu 11:00am-12:30pm, Room 939 Evans Course Control Number: 54448 Office: 903 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - Freshman Seminars Instructor: Jenny Harrison Lectures: F 3:00-4:00pm, Room 891 Evans Course Control Number: 54450 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: Staff Lectures: MWF 8:00-9:00am, Room 10 Evans Course Control Number: 54451 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Alexander Givental Lectures: TuTh 12:30-2:00pm, Room 100 Lewis Course Control Number: 54499 Office: 701 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: MWF 3:00-4:00pm, Room 155 Dwinelle Course Control Number: 54544 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: Arthur Ogus Lectures: MWF 9:00-10:00am, Room 105 Stanley Course Control Number: 54595 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: The main topics in Math 54 are linear algebra and differential equations. We begin by studying how matrix algebra can be used to solve systems of linear equations. Then we see how to interpet these algebraic techniques geometrically in a more general and abstract context. This allows us to apply linear algebra to the theory of differential equations, one of its most important applications. An important goal of this course is to illustrate the interplay between algebra and geometry and between abstraction and applications. Course Webpage: http://math.berkeley.edu/~ogus/Math_54-07/index.html Grading: Grading will be based on the two miderms, final, and nearly daily quizzes (which will closely match the homework). Homework: Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Ming Gu Lectures: TuTh 3:30-5:00pm, Room 155 Dwinelle Course Control Number: 54646 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H54 - Section 1 - Honors Linear Algebra and Differential Equations Instructor: Dan Voiculescu Lectures: MWF 1:00-2:00pm, Room 70 Evans Course Control Number: 54696 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: James Demmel Lectures: MWF 12:00-1:00pm, Room 277 Cory Course Control Number: 54697 Office: 737 Soda Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: Dennis Courtney Lectures: MWF 3:00-4:00pm, Room 70 Evans Course Control Number: 54715 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: Santiago Canez Lectures: TuTh 3:30-5:00pm, Room 70 Evans Course Control Number: 54718 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 3 - Transition to Upper Division Mathematics Instructor: Staff Lectures: MWF 3:00-4:00pm, Room 87 Evans Course Control Number: 54720 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H90 - Section 1 - Honors Undergraduate Seminar in Mathematical Problem Solving Instructor: William Kahan Lectures: M 4:00-6:00pm, Room 71 Evans Course Control Number: 54721 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Jan Reimann Lectures: MWF 1:00-2:00pm, Room 3111 Etcheverry Course Control Number: 54787 Office: 705 Evans Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: C. Pugh, Real Mathematical Analysis, Springer, 2002. Recommended Reading: Syllabus: The real number system, cardinalities, metric spaces, convergence, compactness and connectedness, continuous functions on metric spaces, uniform convergence, power series, differentiation and integration. 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 104 - Section 2 - Introduction to Analysis Instructor: John Krueger Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54790 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 104 - Section 3 - Introduction to Analysis Instructor: Michael Klass Lectures: MWF 12:00-1:00pm, Room 70 Evans Course Control Number: 54793 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Dagan Karp Lectures: TuTh 2:00-3:30pm, Room 285 Cory Course Control Number: 54796 Office: 1053 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Shamgar Gurevich Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54799 Office: 867 Evans Office Hours: TuTh 5:00-6:00pm Prerequisites: Required Text: Walter Rudin, Principles of Mathematical Analysis Recommended Reading: Syllabus: Real and complex numbers, basic topology, sequences and series, continuity, differentiation, integration, sequences and series of functions, linear algebra, Fourier series and integrals. Course Webpage: http://math.berkeley.edu/~shamgar/104F07.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% Attitude: In our course we will study some basics of analysis. The attitude will be to help you to develop your way on how to think about some mathematical objects that you will encounter during your undergraduate studies. Moreover, I expect you to be an integral part of the course, i.e., to attend lectures, to participate in the discussions, to submit homework, and to visit me during my office hours. What: We intend to cover all the basic material so we can understand why a nice function on the circle can be written as a linear combination of exponential functions en(x) = e2πinx, n ∈ Z. In particular I hope to formulate, explain and prove the Stone-Weierstrass theorem. Math H104 - Section 1 - Honors Introduction to Analysis Instructor: Joshua Sussan Lectures: MWF 3:00-4:00pm, Room 81 Evans Course Control Number: 54802 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Calder Daenzer Lectures: TuTh 3:30-5:00pm, Room 75 Evans Course Control Number: 54805 Office: TBA Office Hours: TBA Prerequisites: Math 54 Required Text: Sheldon Axler, Linear Algebra Done Right, Springer, 2nd ed. Recommended Reading: Syllabus: Introduction to linear spaces and linear maps, inner product spaces and the spectral theorem, Jordan form, trace, determinant. Course Webpage: TBA Grading: 25% Homework, 20% Exam I, 20% Exam II, 35% Final Exam Homework: Homework will be due every week. Comments: Math 110 - Section 2 - Linear Algebra Instructor: Marco Aldi Lectures: MWF 8:00-9:00am, Room 71 Evans Course Control Number: 54808 Office: 805 Evans Office Hours: TBA Prerequisites: Math 54 Required Text: Friedberg, Insel, and Spence, Linear Algebra, 4th edition, Prentice Hall, 2003. Recommended Reading: Syllabus: Vector spaces, linear transformations and matrices, systems of linear equations, determinants, eigenvectors and eigenvalues, diagonalization, inner product spaces, Jordan canonical form. Course Webpage: http://math.berkeley.edu/~aldi/110.html Grading: 25% Homework, 20% First Midterm, 20% Second Midterm, 35% Final Exam. Homework: Each Friday I will assign a new homework set and collect your solutions to the previous one. Comments: Math 110 - Section 3 - Linear Algebra Instructor: Lek-Heng Lim Lectures: MWF 11:00am-12:00pm, Room 71 Evans Course Control Number: 54811 Office: 873 Evans Office Hours: M 12–2pm, W 2–4pm Prerequisites: Math 54 Required Text: Strang, Linear algebra & its applications, 4th edition, Thomson Learning, 2006. Recommended Reading: Strang, Introduction to linear algebra, 3rd edition, Wellesley-Cambridge, 2003. Syllabus: Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals. Course Webpage: http://math.berkeley.edu/~lekheng/courses/110 Grading: 40% Homework, 15% Midterm I, 15% Midterm II, 30% Final Homework: Assigned once a week, due the following week. Comments: Math 110 - Section 4 - Linear Algebra Instructor: Jan Reimann Lectures: MWF 3:00-4:00pm, Room 155 Donner Lab Course Control Number: 54814 Office: 705 Evans Office Hours: TBA Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: Friedberg, Insel, and Spence, Linear Algebra, 4th edition, Prentice Hall, 2003. Recommended Reading: Syllabus: Vector spaces, linear transformations and matrices, systems of linear equations, determinants, eigenvectors and eigenvalues, diagonalization, inner product spaces, Jordan canonical form. 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 110 - Section 5 - Linear Algebra Instructor: Chung Pang Mok Lectures: TuTh 8:00-9:30am, Room 9 Evans Course Control Number: 54817 Office: 889 Evans Office Hours: TBA Prerequisites: Math 54 Required Text: Friedberg, Insel and Spence, Linear Algebra, 4th edition, Prentice Hall, 2003. Recommended Reading: Syllabus: Vector spaces, linear transformations and their matrices, system of linear equations, determinant, diagonalization, inner product spaces. Course Webpage: http://math.berkeley.edu/~mok/math110.html Grading: 20% homework, 20% each midterm, 40% final Homework: Homework assigned weekly, due the following week. Comments: Math 110 - Section 6 - Linear Algebra Instructor: Benoit Dherin Lectures: MWF 11:00am-12:00pm, Room 3107 Etcheverry Course Control Number: 54819 Office: 879 Evans Office Hours: M 10:00am-11:00am, F 9:00am-11:00am Prerequisites: Math 54 Required Text: Sheldon Axler, Liner Algebra Done Right, Springer, 2nd ed. Recommended Reading: TBA Syllabus: On bspace. https://bspace.berkeley.edu/ Course Webpage: On bspace. https://bspace.berkeley.edu/ Grading: 20% homework, 20% each midterm, 40% final Homework: Homework will be due every week. Comments: On bspace. https://bspace.berkeley.edu/ Math H110 - Section 1 - Honors Linear Algebra Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54820 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Thomas Scanlon Lectures: TuTh 11:00am-12:30pm, Room 71 Evans Course Control Number: 54823 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Vera Serganova Lectures: MWF 3:00-4:00pm, Room 2 Evans Course Control Number: 54826 Office: 709 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: David Hill Lectures: MWF 12:00-1:00pm, Room 71 Evans Course Control Number: 54829 Office: 757 Evans Office Hours: TBA Prerequisites: Math 54 Required Text: Beachy/Blair, Abstract Algebra, 3rd edition Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Martin Olbermann Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54832 Office: 829 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 115 - Section 1 - Introduction to Number Theory Instructor: Chung Pang Mok Lectures: TuTh 12:30-2:00pm, Room 155 Donner Course Control Number: 54835 Office: 889 Evans Office Hours: TBA Prerequisites: Math 53, 54 Required Text: Niven, Zuckerman and Montgomery, An Introduction to the Theory of Numbers, Wiley, 5th edition. Recommended Reading: Syllabus: Divisibility, Congruences, Quadratic Reciprocity and Quadratic Forms Course Webpage: http://math.berkeley.edu/~mok/math115.html Grading: 20% homework, 20% each midterm, 40% final Homework: Homework assigned weekly, due the following week. Comments: Math 118 - Section 1 - Fourier Analysis, Wavelets and Signal Processing Instructor: L. Craig Evans Lectures: TuTh 9:30-11:00am, Room 87 Evans Course Control Number: 54838 Office: 1033 Evans Office Hours: TBA Prerequisites: Math 53 and 54 (Math 104 would be very helpful.) Required Text: Boggess and Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall Recommended Reading: None Syllabus: Inner product spaces, Fourier series, Fourier transform, discrete Fourier transform, Haar wavelets, general theory of wavelets, Daubechies wavelets, and discussion of some applications. Course Webpage: TBA Grading: 25% homework, 25% midterm, 50% final Homework: Homework will be assigned **every** class, and each assignment is due in one week. Comments: Math 121A - Section 1 - Mathematics for the Physical Sciences Instructor: John Neu Lectures: TuTh 11:00am-12:30pm, Room 85 Evans Course Control Number: 54841 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121A - Section 2 - Mathematical Tools for the Physical Sciences Instructor: Alberto Grünbaum Lectures: TuTh 8:00-9:30am, Room 87 Evans Course Control Number: 54844 Office: 903 Evans Office Hours: TuTh 9:30-11:00am Prerequisites: Math 53, 54. Required Text: Mary Boas, Mathematical Methods in the Physical Sciences, Wiley (3rd edition). Recommended Reading: Syllabus: Course Webpage: Grading: The grade will be based on your homework (25%), two midterms (20% and 20%) and a final (35%). The first midterm will take place pretty early, at the end of the third week of classes. Homework: There will be a weekly homework assignment, with problems from the book. Comments: This class is designed for students in the physical sciences and engineering who need to go from a lower division mathematical foundation into a more advanced level and cannot take a series of classes where this material is introduced at a slower and more detailed pace. The book does a very good job at covering a large amount of basic material that will be useful in a variety of science and engineering classes. Math 123 - Section 1 - Ordinary Differential Equations Instructor: Daniel Tataru Lectures: TuTh 12:30-2:00pm, Room 4 Evans Course Control Number: 54847 Office: 841 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Hirsch, Smale and Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos Recommended Reading: Ross (easier) Arnold (more interesting) Syllabus: Existence and uniqueness of solutions, linear systems, regular singular points. Other topics selected from analytic systems, autonomous systems, Sturm-Liouville Theory. Course Webpage: TBA Grading: Homework, midterm and final exam. Homework: Homework will be assigned periodically. Comments: Math 125A - Section 1 - Mathematical Logic Instructor: John Steel Lectures: TuTh 3:30-5:00pm, Room 241 Cory Course Control Number: 54850 Office: 717 Evans Office Hours: M 11:00am-12:30pm, W 12:00-1:30pm, and by appointment Prerequisites: Math 113, or some equivalent experience with abstract mathematics (definitions, theorems, and proofs). Required Text: H. Enderton, A mathematical introduction to logic, Academic Press, 2nd edition. Recommended Reading: Syllabus: Introduction. General description of the material to be covered, and especially of the Completeness theorem for first order logic, which is our main target. Background material from elementary set theory. Countable and uncountable sets. Approximately 1.5 weeks. Chapter 1. Sentential logic. Approximately 4 weeks. We shall omit 1.6. Chapter 2. First order logic. Approximately 9 weeks. We shall cover all of this chapter except perhaps section 2.8. My lectures will expand the material in sections 2.2 and 2.6 fairly substantially. We will also cover the material in a slightly different order than the book does, in that we will cover most of 2.6 before we cover 2.4 and 2.5. There will be two midterms, the first in early October , after we have covered chapter 1, and the second in November, after we have covered 2.0-2.3 and 2.6. I will announce the exact date for each midterm at least 2 weeks in advance of it. Course Webpage: Course information and homework assignments will be available online at http://math.berkeley.edu/~steel/courses/Courses.html Grading: There will be two midterms and a final. Each midterm is worth 20%, and the final exam is worth 40%. Homework accounts for the remaining 20%. Homework: Homework will be assigned weekly. The assignments will announced at lecture on Tuesdays, and posted on the web at http://math.berkeley.edu/~steel/courses/Courses.html. In general, homework will be due at lecture the Tuesday of the week following its assignment. Comments: In my lectures I shall give the main definitions, examples, theorems, and proofs, along with what I hope will be intuitive explanations which glue them all together. This is a course in “real”, rigorous mathematics; students will be asked to know the exact statements of the main definitions and theorems, how to prove the main theorems, and to be able to find and present simpler proofs on their own. The main difficulty 125 presents to students is the abstraction and unfamiliarity of its basic concepts. Once you are at home with the basic concepts, it is not hard to prove the main theorems of the course. The difficulty is that these concepts, formal language, interpretation, truth, validity, definability, provability..., are pretty abstract, and not treated in other math courses you have had. Of course, as a thinking person, you have some intuitions as to what valid might mean. Such intuitions are useful, and you should try to build on them, but they are not a substitute for learning the mathematically rigorous definitions we shall give! One important way to deal with abstract concepts is to generate lots of examples on your own. Another is to make sure you have memorized all the main definitions, theorems, and proofs, in an exact form. Math 127 - Section 1 - Mathematical and Computational Methods in Molecular Biology Instructor: Lior Pachter Lectures: TuTh 11:00am-12:30pm, Room 87 Evans (effective 9/13/07) Course Control Number: 54852 Office: 1081 Evans Office Hours: TuTh 12:30-2:00pm, Room 1081 Evans Prerequisites: Required Text: R. C. Donier, S. Tavare and M. S. Waterman, Computational Genome Analysis: An Introduction (3rd printing, 2006) Recommended Reading: Syllabus: An introduction to computational genomics, featuring topics such as sequence alignment and assembly, DNA signals, analysis of gene expression, and human genetic variation. Course Webpage: http://math.berkeley.edu/~lpachter/127/ Grading: 50% homework, 30% midterm, 20% final project Homework: Weekly Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Xuemin Tu Lectures: MWF 2:00-3:00pm, Room 60 Evans Course Control Number: 54853 Office: 1055 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 85 Evans Course Control Number: 54871 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 140 - Section 1 - Metric Differential Geometry Instructor: L. Craig Evans Lectures: TuTh 12:30-2:00pm, Room 70 Evans Course Control Number: 54874 Office: 1033 Evans Office Hours: TBA Prerequisites: Math 53 and 54 (Math 104 would be very helpful.) Required Text: R. Millman and G. Parker, Elements of Differential Geometry, Prentice Hall Recommended Reading: None 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: None Grading: 25% homework, 25% midterm, 50% final Homework: Homework will be assigned **every** class, and each assignment is due in one week. Comments: Math 153 - Section 1 - School Curriculum Instructor: Hung-Hsi Wu Lectures: TuTh 2:00-3:30pm, Room 5 Evans; W 4:00-5:00pm, Room 31 Evans Course Control Number: 54877 Office: 733 Evans Office Hours: TBA Prerequisites: Math 151, Math 113 or equivalent. Required Text: None. Lecture notes will be made available as the course progresses. Recommended Reading: Syllabus: This is an upper division course in mathematics. Therefore, like any other upper division mathematics course, the emphasis will be on precision and reasoning (i.e., proofs). The goal is to present school mathematics as part of mathematics proper, so that when it is your turn to teach in the schools, you will be able to teach your students honest mathematics rather than the mess that one often witnesses in most school classrooms. 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. A key feature of this presentation is that it would be directly applicable to the classroom of grades 8-12. The topics to be covered include: The trigonometric functions and similar triangles; basic identities. Periodic functions. The real line and the least upper bound axiom. The concept of limit. Existence of n-th root. Area and volume: basic definitions and formulas. Second proof of the Pythagorean theorem. Basic concepts from calculus: continuity, convergence of infinite series, decimal representation of a real number. Derivative and integral. Fundamental Theorem of Calculus; relationship with the concept of area and volume. Exponential and logarithmic functions and their basic properties. Proof of laws of exponents. Course Webpage: http://courseweb.berkeley.edu/courseweb/pub/courses/2007/FL/MATH/153/001 Grading: Homework: Weekly assignments, due every Wednesday. Comments: Students are welcome to form study groups to work on the homework problems but not to copy from each other. The purpose of the problem session, every Wednesday 4-5 pm, is to discuss the solutions of the problems *after* the problem set has been handed in. Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Lek-Heng Lim Lectures: MWF 4:00-5:00pm, Room 75 Evans Course Control Number: 54889 Office: 873 Evans Office Hours: M 12–2pm, W 2–4pm Prerequisites: Math 104 Required Text: Bak and Newman, Complex analysis, 2nd edition, Springer, 1997. Recommended Reading: Lang, Complex analysis, 4th edition, Springer, 1999. Syllabus: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping. Course Webpage: http://math.berkeley.edu/~lekheng/courses/185 Grading: 40% Homework, 15% Midterm I, 15% Midterm II, 30% Final Homework: Assigned once a week, due the following week. Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Paul Vojta Lectures: MWF 11:00am-12:00pm, Room 85 Evans Course Control Number: 54892 Office: 883 Evans Office Hours: TBD Prerequisites: Math 104 Required Text: Brown & Churchill, Complex variables and applications Recommended Reading: None Syllabus: The course will cover the first eight or nine chapters of the textbook. Course Webpage: http://math.berkeley.edu/~vojta/185.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 185 - Section 3 - Introduction to Complex Analysis Instructor: Mauricio Velasco Lectures: TuTh 12:30-2:00pm, Room 85 Evans Course Control Number: 54895 Office: 1063 Evans Office Hours: Tu 9:00-11:00am, Th 10:00-11:00am Prerequisites: Math 104 (Introduction to Analysis) Required Text: Brown and Churchill, Complex Variables and Applications, 7th edition. Recommended Reading: None Syllabus: This course is an introduction to the theory of functions of one complex variable. We will study functions f: C → C differentiable "in the complex sense" and explore some of the fundamental results of the theory: the Cauchy Integral formula, Liouville's theorem, the maximum modulus principle, analytic continuation, Taylor's theorem and the residue theorem. If time permits we will introduce elliptic functions. Course Webpage: http://math.berkeley.edu/~velasco/185.html Grading: Homework 20%, Midterms (x2) 20%, and Final 40% Homework: There will be weekly homework assignments. Comments: See webpage. Math 191 - Section 1 - Seminar on Cryptography Instructor: Kenneth A. Ribet Lectures: W 11:10am-12:30pm, Room 939 Evans Course Control Number: 54955 Office: 885 Evans Office Hours: To be announced Prerequisites: Lower-division mathematics (including Math 53 and Math 54), and a keen interest in number theory and/or cryptography. Math 115 (even if taken concurrently) would be a big help. Required Text: To be announced. People claim that there is no clear winner in this area. Syllabus: To some extent, this depends on the textbook. We want to discuss some of the standard crypto systems that depend on number theoretic issues for their security. It is likely that we will talk about elliptic curves at some point. Course Webpage: http://math.berkeley.edu/~ribet/191/; this is left over from a similar course that I taught long ago, but will be re-built for the fall. Grading: P/NP; everyone signs up for 2 units of credit. Homework: There will be some homework problems. I hope that there will be a grader. Comments: I'm no expert in the subject, but I learned a lot the last time I taught a course like this. I think that the book (by Buchmann) that we used last time is not optimal, so I'm looking for something better. You might think that it would be a challenge to get telebears to agree that this course exists, but I know that it has been done, so go ahead and sign up if you'd like to. Math 202A - Section 1 - Introduction to Topology and Analysis Instructor: Justin Holmer Lectures: MWF 3:00-4:00pm, Room 10 Evans Course Control Number: 54985 Office: 849 Evans Office Hours: TBA Prerequisites: An undergraduate "Intro. to Analysis" course (such as Math 104 here at Berkeley) with emphasis on writing rigorous mathematical proofs. Specifically, must have mastery of basic set theory (including countability vs. uncountability), the logic of quantifiers, supremum/infimum of sets of real numbers, convergence/divergence of sequences and series of real numbers and the epsilon-N definition of limit, liminf and limsup, definitions of continuity and derivatives of functions and associated theorems, the definition and properties of the Riemann integral and the fundamental theorem of calculus, uniform versus pointwise convergence of sequences and series of functions and associated theorems on interchange of limit operations under hypothesis of uniformity. Also, basic linear algebra (such as Math 110 here at Berkeley), especially concept of vector space, linear transformation, and matrix multiplication and diagonalization of hermitian matrices. Required Text: None Recommended Reading: Stein and Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Royden, Real Analysis. Munkres, Topology. Stein and Shakarchi is reasonably priced and beautifully written. It does not, however, cover the topology material. Munkres covers topology alone and is a very clearly written text. Royden is a standard text for this course and covers both topology and measure theory. A detailed syllabus will be provided so you can study from any book of your choice. Syllabus: During the first half of the course, we will cover general point-set topology and metric space theory. During the second half of the course, we will cover the Lesbesgue measure and integration theory in Rd. Math 202b in the spring will pick up on abstract measure and integration theory (includes the Lebesgue theory as a particular case, but also more exotic examples), and then launch into functional analysis: the study of Hilbert spaces, Banach spaces, their generalizations, and linear mappings between these spaces. Course Webpage: http://math.berkeley.edu/~holmer/teaching/f202a/ Grading: 50% homework, 50% final Homework: Homework will be assigned once a week and due the following week, and will consist of about a dozen problems. Plan to spend a full day preparing your solutions. All problems, even if taken from a textbook, will be retyped and posted on the web. Comments: This course is recommended for advanced undergraduate students planning to study math in graduate school, beginning graduate students who have not yet studied this material, or for students from other fields of science and engineering with the appropriate background and motivation. If you are a full time student, plan to devote 1/4 of your time to this course. Math 204A - Section 1 - Ordinary and Partial Differential Equations Instructor: John Neu Lectures: TuTh 2:00-3:30pm, Room 81 Evans Course Control Number: 54988 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 205 - Section 1 - Theory of Functions of a Complex Variable Instructor: Donald Sarason Lectures: MWF 8:00-9:00am, Room 81 Evans Course Control Number: 54991 Office: 779 Evans Office Hours: TBA Prerequisites: An introductory complex analysis course. Mastery of basic real analysis and basic topology. Required Text: No textbook will be followed closely. The classic book of L. V. Ahlfors, "Complex Analysis," contains most of the course material. Other possible references will be mentioned in the first lecture. Recommended Reading: Syllabus: Brief review centering on Cauchy's theorem and the argument principle; conformal mapping, including the Riemann mapping theorem and distortion theorems; analytic continuation; algebraic functions; entire functions and functions meromorphic in the entire plane, including the Weierstrass and Mittag-Leffler representations; elliptic functions; the modular function; Picard's theorems; Dirichlet series; Riemann zeta-function; prime number theorem. Course Webpage: Grading: The course grade will be based on homework. There will be no exams. Homework: There will be regular homework assignments, usually two or three problems per week, most of them challenging. The homework will be carefully graded. Comments: The lectures will be self-contained except for routine details. Math 206 - Section 1 - Banach Algebras and Spectral Theory Instructor: Dan Voiculescu Lectures: MWF 11:00am-12:00pm, Room 39 Evans Course Control Number: 54994 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 212 - Section 1 - Complex Analysis in Several Variables Instructor: Michael Christ Lectures: TuTh 11:00am-12:30pm, Room 31 Evans Course Control Number: 54997 Office: 809 Evans Office Hours: Tu 1:30-2:30pm, W 1:00-2:00pm (tentative) Prerequisites: 202AB (graduate real analysis) and 185 (undergraduate complex analysis) or equivalents, and comfort with differential forms. In the second half of the semester, familiarity with the definitions of differentiable manifolds and vector bundles will be assumed. Some concepts and facts from algebra (concerning UFDs, quotient fields, modules over a ring, Noetherian rings, prime ideals) will crop up, but only superficial knowledge will be required. Required Text: L. Hörmander, An Introduction to Complex Analysis in Several Variables (3rd edition) Recommended Reading: Other useful alternative sources include: From Holomorphic Functions to Complex Manifolds by K. Fritzsche and H. Grauert. This book is recommended for additional reading on topics related to complex manifolds, and for a treatment with less emphasis on PDE, but is not in any sense required. It is not available through the bookstore. Krantz, Steven G. Function theory of several complex variables Range, R. Michael. Holomorphic functions and integral representations in several complex variables. Syllabus: The course will be a general introduction to multivariable complex analysis, emphasizing scalar-valued holomorphic functions, pseudoconvexity and domains of holomorphy, plurisubharmonic functions and their applications, solution of the inhomogeneous Cauchy-Riemann equations by the method of weighted L2 estimates, and Cousin problems. Coherent analytic sheaves will be introduced but not discussed in detail. The core of the course will be Chapters 2,4,5,6 of Hörmander’s text, plus an overview of Chapter 7. Partial differential equations methods will be a fundamental tool in the course, but merely a tool; the focus will be on their applications to function theory and complex geometry. All the background needed concerning PDE will be developed in the course. Hörmander’s text concisely treats the basics but cannot begin to survey all aspects of a large subject, so other sources will be placed on reserve in the math library for consultation. Required Work: Problem sets will be distributed approximately every two weeks. There will be no examinations. Math 214 - Section 1 - Differentiable Manifolds Instructor: Alexander Givental Lectures: TuTh 3:30-5:00pm, Room 47 Evans Course Control Number: 55000 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 215A - Section 1 - Algebraic Topology Instructor: Michael Hutchings Lectures: MWF 1:00-2:00pm, Room 3 Evans Course Control Number: 55003 Office: 923 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C218A - Section 1 - Probability Theory Instructor: James Pitman Lectures: TuTh 2:00-3:30pm, Room 332 Evans Course Control Number: 55006 Office: 303 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 221 - Section 1 - Advanced Matrix Computation Instructor: Ming Gu Lectures: TuTh 11:00am-12:30pm, Room 55 Evans Course Control Number: 55009 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 222A - Section 1 - Partial Differential Equations Instructor: Ole Hald Lectures: MWF 2:00-3:00pm, Room 45 Evans Course Control Number: 55012 Office: 875 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C223A - Section 1 - Stochastic Processes Instructor: Sourav Chatterjee Lectures: MWF 2:00-3:00pm, Room 31 Evans Course Control Number: 55014 Office: 333 Evans Office Hours: TBA Prerequisites: A graduate course in probability such as STAT 205A. Required Text: Recommended Reading: Syllabus: The following is a possible list of topics for this course. Ideally we would like to cover all of them in the order in which they are listed, but adjustments may have to be made because of time constraints. Stein operators, inversions, and basic lemmas. Classical techniques and applications: The method of dependency graphs. Size bias and zero bias couplings. Exchangeable pairs. The diffusion approach to Stein's method. Concentration inequalities using Stein's method, including: Basics of concentration inequalities: Ledoux, Talagrand, etc. The semigroup method and connection with exchangeable pairs. Applications to Gibbs measures and combinatorial problems. Applications to random matrices, including: Derivation of Wigner's theorem using Stein's method. Central limit theorems for random matrix spectra. Applications to spin glasses, including: An introduction to Talagrand's work. Derivation of the TAP equations for the SK model of spin glasses using Stein's method. Analysis of the critical temperature regimes of the Curie-Weiss and SK models using Stein's method. Dynamic interaction graphs and recent applications. Applications to strong embedding problems. If time permits, discussion of the Chen-Stein method of Poisson approximation. Discussion of open problems. Course Webpage: Grading: Will be based on solutions to a certain number of homework problems and producing scribe notes. Homework: Comments: Math 224A - Section 1 - Mathematical Methods for the Physical Sciences Instructor: Alexandre Chorin Lectures: MWF 9:00-10:00am, Room 81 Evans Course Control Number: 55015 Office: 911 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 225A - Section 1 - Metamathematics Instructor: John Krueger Lectures: MWF 12:00-1:00pm, Room 39 Evans Course Control Number: 55018 Office: 751 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~jkrueger/math225.html Grading: Homework: Comments: Math 228A - Section 1 - Numerical Solution of Differential Equations Instructor: Jon Wilkening Lectures: TuTh 12:30-2:00pm, Room 289 Cory Course Control Number: 55021 Office: 1091 Evans Office Hours: Tu 3:00-5:00pm Prerequisites: Math 128A or equivalent knowledge of basic numerical analysis. Some programming experience (e.g. Matlab, Fortran, C, or C++) Required Text: Iserles, A First Course in the Numerical Analysis of Differential Equations Recommended Reading: Hairer/Norsett/Wanner, Solving Ordinary Differential Equations (2 vols) Syllabus: The first 10 weeks of the course will cover thoery and practical methods for solving systems of ordinary differential equations. We will discuss Runge-Kutta and multistep methods, stability theory, Richardson extrapolation, stiff equations and boundary value problems (e.g. the shooting method). We will then study boundary value problems in higher dimensions using boundary integral methods and potential theory. If time permits, we will conclude the course with fast solvers for elliptic equations (multigrid, FFT methods, conjugate gradients, GMRES). Course Webpage: http://math.berkeley.edu/~wilken/228A.F07 Grading: Grades will be based entirely on homework. Homework: At least 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 250A - Section 1 - Groups, Rings, and Fields Instructor: David Eisenbud Lectures: TuTh 9:30-11:00am, Room 285 Cory Course Control Number: 55024 Office: 909 Evans Office Hours: TuTh 1:30-2:30pm Prerequisites: Reasonable mathematical maturity, and the equivalent of Math 114 or consent of the instructor. Undergraduates taking this course should have an upper division math GPA of at least 3.0, or consent of the instructor. Required Text: Serge Lang, Algebra, 3rd ed., Springer-Verlag, 2002, or Addison-Wesley, 1993. Recommended Reading: Notes on Lang's book, by George Bergman, will be available in class. Syllabus: Groups, rings, modules, Galois theory. Categories and homological algebra as time permits. Course Webpage: Grading: Homework 50%, Midterm 17%, Final, 33% Homework: There is a lot of material to cover; expect a heavy course. Homework will generally be assigned once a week. Comments: Math 252 - Section 1 - Representation Theory Instructor: Tsit-Yuen Lam Lectures: MWF 10:00-11:00am, Room 87 Evans Course Control Number: 55026 Office: 871 Evans Office Hours: TBA Prerequisites: The prerequisite for the course is a strong background in graduate algebra, through 250B and hopefully a little beyond. Students are assumed to be familiar with groups and group actions, tensor products over noncommutative rings, and basic module theory including semisimple modules and the Jordon-Hölder theorem, etc. Required Text: T. Y. Lam, First Course in Noncommutative Rings, 2nd ed., Springer-Verlag James and Liebeck, Representations and Characters of Groups, 2nd ed., Cambridge University Press Recommended Reading: Syllabus: I will teach a course in the basic theory of the representations of groups. The main focus of the course will be on the case of finite groups. We'll take a largely ring-theoretic approach - presenting the main theory of group representations as a case study of finitely generated modules over group rings. The course will begin with semisimple rings and the Artin-Wedderburn theorem, which the students should review ahead of time (from my ring theory textbook "First Course in Noncommutative Rings") if possible. Course Webpage: I am looking for a student volunteer who could run a webpage for the course. This webpage will serve as a repository for homework problems, their solutions, and other communications. If you are interested in helping run this course webpage, please let me know ASAP. Grading: Homework: Comments: Math 254A - Section 1 - Number Theory Instructor: Arthur Ogus Lectures: MWF 12:00-1:00pm, Room 51 Evans (Effective 9/5/07) Course Control Number: 55027 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: This will be a basic course in number theory, from a modern'' geometric point of view. I hope to cover most of the following topics, although not necessarily in this order: algebraic integer rings, the geometry of numbers, units and the class number, extensions of Dedekind domains, valuations and ramification, different and discriminant, and if possible, zeta and L-functions and the distributions of primes. Our main examples will be quadratic fields and cyclotomic fields. I will assume some knowledge of graduate algebra as background. In particular, students should be comfortable with Galois theory, localization, tensor products, and polynomial rings. Course Webpage: http://math.berkeley.edu/~ogus/Math_254-07/index.html Grading: Homework: Comments: Math 256A - Section 1 - Algebraic Geometry Instructor: Martin Olsson Lectures: MWF 2:00-3:00pm, Room 81 Evans Course Control Number: 55030 Office: 887 Evans Office Hours: TBA Prerequisites: A graduate-level course in abstract algebra. Required Text: Hartshorne, Algebraic Geometry, Springer Graduate Texts in Mathematics 52. Recommended Reading: Syllabus: This course together with its sequel Math 256B in the spring is an introduction to scheme theory and algebraic geometry in its modern formulation. The one-year course will loosely follow Chapter II-V of Harshorne's Algebraic Geometry book, with some supplemental material from other sources. The first semester I hope to cover the basic language of scheme theory and some curve theory. The second semester will be focused on cohomology and surface theory. Course Webpage: Grading: Grades will be based on weekly homeworks. Homework: There will be weekly homework. Comments: Math 270 - Section 1 - Hot Topics Course in Mathematics Instructor: Peter Teichner Lectures: Tu 2:00-3:30pm, Room 72 Evans Course Control Number: 55033 Office: 703 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 2 - Locally Finite Lie Algebras and Their Representations with a View Toward Open Problems Instructor: Ivan Penkov Lectures: MWF 2:00-3:00pm, Room 72 Evans Course Control Number: 55038 Office: TBA Office Hours: TBA Prerequisites: Required Text: No textbooks required. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: The first class will meet on Friday, August 31, 2007. Math 276 - Section 1 - Topics in Topology Instructor: Peter Teichner Lectures: TuTh 11:00am-12:30pm, Room 70 Evans (effective 9/13/07) Course Control Number: 55039 Office: 703 Evans Office Hours: Th 2:00-3:00pm Prerequisites: Smooth manifolds and differential forms Required Text: Relevant paper will be distributed in class. Recommended Reading: Papers by Segal and Stolz-Teichner Syllabus: We'll explain how to extend Graeme Segal's definition of a QFT over a manifold X in various directions, most significantly to super symmetric QFT's. We then show how these behave for d-dimensional space-time when d=0,1,2. It turns out that d=0 leads to closed differential forms on X, d=1 to interesting representatives for elements in K(X) and that 2-dimensional susy QFT's give integral modular forms. If time permits, we'll show how open-closed theories are related to locality for these (generalized) cohomology theories. Course Webpage: Under construction. Grading: Homework: Comments: Math 276 - Section 2 - Conformal and Topological Quantum Field Theories Instructor: Nicolai Reshetikhin Lectures: MWF 1:00-2:00pm, Room 61 Evans Course Control Number: 55041 Office: 917 Evans Office Hours: TBA Prerequisites: Required Text: No textbook required. Reading material will be given at the beginning of the course. Recommended Reading: Syllabus: See http://math.berkeley.edu/~reshetik/topics/CFT-TQFT.pdf for a complete syllabus of the course. Course Webpage: Grading: Homework: Comments: This is a brief outline of the course. It is likely that the course will go slower and that only part of this material will be covered. Classical and quantum mechanics in few lectures. The definition of classical and quantum field theories. Local classical field theories. Space-time categories. Lagrangian and Hamiltonian approaches. Examples of classical field theories. Linear and non-linear field theories. Wess-Zumino-Witten (conformal) and Chern-Simons (topological) as main examples. Quantum field theories, the idea of a path integral. Topological quantum field theories, conformal QFT. Semiclassical limit and perturbation theory and finite type invariants of 3-manifolds. Axiomatic construction of topological quantum field theories from modular categories using surgery. Axiomatic construction of TQT based on a triangulation of 3-manifolds. Quantum conformal field theories in 2D and how they are related to modular categories. The relation between conformal and topological field theories. If time permits: more involved discussion of conformal field theory and gauge theories and how they are related to the representation theory of infinite-dimensional Lie algebras. Math 300 - Section 1 - Teaching Workshop Instructor: Jameel Al-Aidroos Lectures: W 5:00-7:00pm, Room 3108 Etcheverry Course Control Number: 55723 Office: 741 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: