# Fall 2006

 Math 1A - Section 1 - Calculus Instructor: Richard Borcherds Lectures: TuTh 2:00-3:30pm, Room 2050 Valley Life Science Course Control Number: 54103 Office: 927 Evans Office Hours: TuTh 3:30-5:00pm Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~reb/courses/1A/ Grading: 40% homework and quizzes, 15% each midterm, 30% final Homework: Homework is assigned on the course web page and is due once a week. Comments: Math 1A - Section 2 - Calculus Instructor: Mark Haiman Lectures: MWF 10:00-11:00am, Room 1 Pimentel Course Control Number: 54154 Office: 771 Evans Office Hours: MWF 12:30-1:30pm Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: James Stewart, Calculus: Early Transcendentals, 5th edition (Brooks/Cole, 2003). We will cover chapters 1-6. Recommended Reading: Syllabus: An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. Intended for majors in engineering and the physical sciences. Course Webpage: math.berkeley.edu/~mhaiman/math1A-fall06 Grading: Homework: Comments: Math 1A - Section 3 - Calculus Instructor: John Steel Lectures: MWF 1:00-2:00pm, Room 1 LeConte Course Control Number: 54205 Office: 717 Evans Office Hours: TuTh 10:30am-12:00pm Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole, 5th edition. We will cover Chapters 1-6. Recommended Reading: Syllabus: An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. Intended for majors in engineering and the physical sciences. Course Webpage: http://math.berkeley.edu/~steel/courses/Courses.html Grading: 20% homework, quizzes, and section participation. 20% each midterm, 40% final Homework: Homework is assigned on the course web page and is due once a week. Comments: Math 1B - Section 1 - Calculus Instructor: Daniel Tataru Lectures: TuTh 8:00-9:30am, Room 2040 Valley Life Science Course Control Number: 54250 Office: 841 Evans Office Hours: TBA Prerequisites: 1A Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole Recommended Reading: Syllabus: Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations. Course Webpage: http://math.berkeley.edu/~tataru/1B.html (after the middle of August) Grading: 1/3 quizzes+homework, 1/6 each midterm, 1/3 final Homework: Homework will be assigned on the web every class, and due once a week. Comments: Math 1B - Section 2 - Calculus Instructor: Martin Olsson Lectures: MWF 9:00-10:00am, Room 155 Dwinelle Course Control Number: 54298 Office: 887 Evans Office Hours: TBA Prerequisites: Math 1A or equivalent Required Text: Stewart, Calculus: Early Transcendentals, 5th edition or Custom 1A/1B Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~molsson/math1b.html Grading: Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Hugh Woodin Lectures: MWF 9:00-10:00am, Room 10 Evans Course Control Number: 54349 Office: 721 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and Calculus Instructor: Bjorn Poonen Lectures: MWF 10:00-11:00am, Room 155 Dwinelle Course Control Number: 54382 Office: 879 Evans Office Hours: TBA Prerequisites: Math 32 or three years of high school mathematics including trigonometry. Required Text: Goldstein, Lay, Schneider, Asmar, Calculus and its applications, 11th edition, Pearson Prentice Hall, 2007. We may be using some of the computer materials associated with this text that are becoming available this summer. Because of the possibility of purchasing these materials with the text as a package, I recommend holding off on purchasing the text until later this summer when the materials are ready, and I have a chance to try them myself. (I'm not going to make them part of the course unless they are helpful and easy to use.) Recommended Reading: Syllabus: The derivative and its applications (e.g., to optimization), techniques for differentiation, exponential and logarithmic functions, the definite integral. We will cover Chapters 0 through 6 of the text. Course Webpage: http://math.berkeley.edu/~poonen/math16A.html Exams: There will be two in-class midterms, and a 3-hour final exam Tuesday, December 12, 8-11am. Grading: 20% section grade (homeworks and quizzes), 20% midterm 1, 20% midterm 2, 40% final exam. If your section grade or one of your midterm grades is below your final exam grade, it will be boosted up to the final exam grade. The course grade will be curved. Homework: There will be weekly assignments. Comments: Math 16A and 16B are intended for students who do not intend to take further mathematics courses. If your intended major lies in the sciences, you might consider taking 1A and 1B instead, even if your department does not require it. Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Leo Harrington Lectures: TuTh 3:30-5:00pm, Room 100 Lewis Course Control Number: 54439 Office: 711 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: 54484 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: Martin Vito Cruz Lectures: MWF 8:00-9:00am, Room 277 Cory Course Control Number: 54487 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Alexander Givental Lectures: MWF 12:00-1:00pm, Room 155 Dwinelle Course Control Number: 54535 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: Fraydoun Rezakhanlou Lectures: TuTh 3:30-5:00pm, Room 1 Pimentel Course Control Number: 54586 Office: 815 Evans Office Hours: TuTh 2:30-3:30pm, W 2:00-3:00pm Prerequisites: Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole, 5th ed. or Custom 53 Recommended Reading: Syllabus: Course Webpage: Grading: homework and quizzes, 50 points 3 midterms, the best two counting, worth 75 points each, totalling 150 points Final Exam, 200 points Total: 400 points possible. The first midterm will be in class on Thurs., Sep. 28. The second midterm will be on Tues., Oct. 31. The third midterm will be on Tues., Nov. 28. The Final Exam will be on TUESDAY, DECEMBER 19, 12:30-3:30 pm. Make sure you can make the final exam — check the schedule now to see that it is acceptable to you. It is not possible to have make-up exams. Incompletes. Official University policy states that an Incomplete can be given only for valid medical excuses with a doctor’s certificate, and only if at the point the grade is given the student has a passing grade (C or better). If you are behind in the course, Incomplete is not an option! Homework: Homework will be assigned weekly. This semester we do not have readers, so your homework should be self-corrected, based on the solutions provided weekly by your TA. Nevertheless, homework must be handed in every Monday in your TA section for recording. There will be three quizzes (given in section) that count; with homework and quizzes totalling 50 points; quizzes will vary with the TA section. The first assignment is due in your TA section on Wednesday, Sep. 6. Homework Set #1. From the textbook: 10.1, #5, 8, 12, 13, 15, 41 10.2, #2,4,19,26,32,42,60,65 10.3, #15,18,22,32,35,55,58,63 Comments: Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Ming Gu Lectures: MWF 3:00-4:00pm, Room 155 Dwinelle Course Control Number: 54631 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Dan Voiculescu Lectures: TuTh 12:30-2:00pm, Room 100 Lewis Course Control Number: 54682 Office: 783 Evans Office Hours: M 1:15-2:50, Th 3:00-3:50 Prerequisites: Math 1B Required Text: R. Hill, Elementary Linear Algebra with Applications (for the linear algebra part) W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 8th ed. (for the differential equations part) Recommended Reading: A. Givental, Linear Algebra and Differential Equations Berkeley Mathematics Lecture Notes, Vol. 11, American Mathematical Society and Berkeley Center for Pure and Applied Mathematics Syllabus: First part of course Linear Algebra and second part Differential Equations Course Webpage: Grading: All grades will be computed using a scale of 0-20 points The correspondence with letter grades is: A+ [19,20) , A [17,19), A- [16,17) B+ [15,16) , B [13,15), B- [12,13) C+ [11,12) , C [9,11) , C- [8,9) etc. Discussion Section Grade = 1/3 Hwrk + 2/3 Quizzes Grade in Course = 15% DiscSect + 20% Mdtrm1 + 20% Mdtrm2 + 45% Final No Make-ups for Midertms No Midterm 1 and No Midterm 2 then Failed No Midterm 1 then Grade in Course = 15% DiscSect + 40% Midterm 2 + 45% Final No Midterm 2 then there is a 10% Penalty (i.e., 10% is 0) Grade in Course = 10% Penalty + 15% DiscSect + 20% Midterm 1 + 55% Final (= zero) Midterm 1 Thursday September 28 Midterm 2 Thursday November 2 Final Monday December 18 12:30-3:30 Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: Olga Holtz Lectures: TuTh 8:00-9:30am, Room 2060 Valley Life Science Course Control Number: 54733 Office: 821 Evans Office Hours: TuTh 11:00am-12:00pm and by appt. Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B recommended. Required Text: Kenneth H. Rosen Discrete Mathematics & It's Applications 6th ed., McGraw-Hill Recommended Reading: Ronald L. Graham, Donald E. Knuth and Oren Patashnik Concrete Mathematics, 2nd ed., Addison-Wesley Syllabus: Logic, set theory, functions. Relations and graphs. basic number theory. Integer algorithms. Mathematical proofs, induction. Combinatorics and probability theory. Grading: 20% homework, 20% each midterm, 40% final. Homework: Assigned weekly, due next week. Comments: This goal of this class is to achieve fluency with discrete operations (such as finite sums, recurrences, discrete probability and so on) just like the goal of a calculus course is to achieve fluency with continuous operations. Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: Scott Armstrong Lectures: MWF 3:00-4:00pm, Room 70 Evans Course Control Number: 54748 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: Patrick Barrow Lectures: TuTh 3:30-5:00pm, Room 70 Evans Course Control Number: 54751 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H90 - Section 1 - Undergraduate Seminar in Mathematical Problem Solving (Honors) Instructor: William Kahan Lectures: M 4:00-6:00pm, Room 71 Evans Course Control Number: 54754 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: Dapeng Zhan Lectures: MWF 12:00-1:00pm, Room 75 Evans Course Control Number: 54817 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Jan Reimann Lectures: TuTh 9:30-11:00am, Room 70 Evans Course Control Number: 54820 Office: 705 Evans Office Hours: Tu 11:00am-1:00pm, W 1:00-2:00pm Prerequisites: Math 53, Math 54 Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus Recommended Reading: Rudin, Principles of Mathematical Analysis Pugh, Real Mathematical Analysis Syllabus: The real number system. Sequences, limits, and continuous functions in R and R. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Differentiation. Mean value theorem and applications. The Riemann integral. Course Webpage: http://math.berkeley.edu/~reimann/Fall_06/104.html Grading: 20% homework, 20% each midterm, 40% final Homework: Weekly Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Dapeng Zhan Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54823 Office: 873 Evans Office Hours: TBA Prerequisites: Math 53 and Math 54 Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus Recommended Reading: Syllabus: In this course we will study basic notations of real analysis, limits and convergence, series, continuous functions, power series, differentiation and integration, and metric spaces. Course Webpage: http://math.berkeley.edu/~dapeng/ma104-S3.html Grading: 20% homework, 20% each midterm (2), 40% final Homework: Homework will be assigned in every class, and due once a week. Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Vaughan Jones Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54826 Office: 929 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Alexandre Chorin Lectures: MWF 8:00-9:00am, Room 71 Evans Course Control Number: 54829 Office: 911 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H104 - Section 1 - Introduction to Analysis (Honors) Instructor: George Bergman Lectures: MWF 10:00-11:00am, Room 5 Evans Course Control Number: 54832 Office: 865 Evans Office Hours: Tu 1:30-2:30pm, Th 10:30-11:30am, F 3:00-4:00pm Prerequisites: Math 1AB, and a GPA of at least 3.3 in math courses taken over past year; or consent of the instructor. Math 53 is also recommended. The course is aimed at mathematics majors and other students with a strong interest in mathematics. Required Text: W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill. Recommended Reading: None. Syllabus: We will cover Chapters 1-7 of the text. Course Webpage: None. Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam, 35%; regular submission of the daily question (see below), 5%. Homework: Weekly. Comments: This is the course in which the material you saw in calculus is put on a solid mathematical basis. It begins with the properties of the real numbers that underlie these results. I will cover the same material as when I teach regular 104, but the exercises will be more challenging, and we will be able to discuss the ideas more deeply. I don't like the conventional lecture system, where students spend the hour copying the contents of the course from the blackboard into their notebooks. Hence I assign readings in the text, and conduct the class on the assumption that you have done the assigned reading and thought about what you've read. In lecture I may go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, discuss points to watch out for in the next reading, etc. If you are unbreakably attached to learning first from the lecture, and only afterward turning to the book, my course is not for you. On each day for which there is an assigned reading, each student is required to submit, in writing or (preferably) by e-mail, a question on the reading. (If there is nothing in the reading that you don't understand, you can submit a question marked "pro forma", together with its answer.) I try to incorporate answers to students' questions into my lectures; when I can't do this, I usually answer by e-mail. More details on this and other matters will be given on the course handout distributed in class the first day, and available on the door to my office thereafter. Math 110 - Section 1 - Linear Algebra Instructor: Olga Holtz Lectures: TuTh 2:00-3:30pm, Room 100 Lewis Course Control Number: 54835 Office: 821 Evans Office Hours: TuTh 11:00am-12:00pm and by appt. Prerequisites: Math 53, Math 54 Required Text: S.H. Friedberg, A.J. Insel, L.E. Spence, Linear Algebra, 4th Edition, Pearson Education Recommended Reading: Online lecture notes by C. de Boor (will be posted). Syllabus: Vector spaces. Linear maps and matrices. Linear systems of equations. Eigenvalues and eigenvectors. Determinants and other functions of matrices. Inner product spaces. Self-adjoint, normal and unitary maps. Canonical forms. Course Webpage: http://www.cs.berkeley.edu/~oholtz/110/index.html Grading: 30% homework, 30% midterm, 40% final. Homework: Homework will be assigned on the web every week, due the week after. Comments: The instructor intends to stress practical applications of matrix theory and its numerical aspects. To this ends, MATLAB experiments, demos and animation will be presented in class. However, there will be no computer homework assignments. Math H110 - Section 1 - Linear Algebra (Honors) Instructor: Jenny Harrison Lectures: MWF 11:00am-12:00pm, Room 70 Evans Course Control Number: 54862 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Giulio Caviglia Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54865 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Sarah Mason Lectures: TuTh 12:30-2:00pm, Room 2 Evans Course Control Number: 54868 Office: 765 Evans Office Hours: Tu 2:00-3:00pm, W 1:00-2:00pm, Th 10:30-11:30am Prerequisites: Linear Algebra Required Text: Fraleigh, A First Course in Abstract Algebra, 7th ed. Recommended Reading: Syllabus: The main objects studied in this course are groups, rings, and fields. We will cover several related topics and include plenty of examples. Course Webpage: http://math.berkeley.edu/~sarahm/m113.html Grading: 40% homework and groupwork, 15% each midterm, 30% final exam Homework: Weekly individual homework plus some group work. Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Alexander Givental Lectures: MWF 2:00-3:00pm, Room 71 Evans Course Control Number: 54871 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: John Krueger Lectures: TuTh 8:00-9:30am, Room 75 Evans Course Control Number: 54874 Office: 751 Evans Office Hours: TBA Prerequisites: Required Text: Dummit and Foote, Abstract Algebra, 3rd ed. Recommended Reading: Syllabus: http://math.berkeley.edu/~jkrueger/syllabus.html Course Webpage: http://math.berkeley.edu/~jkrueger/math113.html Grading: Homework: Comments: Math 115 - Section 1 - Introduction to Number Theory Instructor: Kenneth A. Ribet Lectures: MWF 2:10-3:00pm, Room 60 Evans Course Control Number: 54877 Office: 885 Evans Office Hours: TBA Prerequisites: Math 53 and Math 54 Required Text: To be announced later. Here are some candidates; please give me feedback if you have the time and inclination to explore these books: Topics in the theory of numbers by Erdös and Suranyi An introduction to the theory of numbers by Niven, Zuckerman and Montgomery A computational introduction to number theory and algebra by Victor Shoup Elementary number theory by William Stein Recommended Reading: Syllabus: The catalog suggests a study of "Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems." One highlight of the course is the theorem of quadratic reciprocity. Course Webpage: http://math.berkeley.edu/~ribet/115/ (the current version is for an old course; this web page will get fixed up in August) Grading: Based on two midterms,the final exam, and homework, with the exact mix to be announced later. Homework: Substantial problem sets will be assigned weekly. Comments: Math 118 - Section 1 - Mathematical Signal Processing Instructor: L. Craig Evans Lectures: TuTh 9:30-11:00am, Room 81 Evans Course Control Number: 54880 Office: 907 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: Fourier analysis (Fourier series and Fourier transform), wavelets, theory and applications 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 121A - Section 1 - Mathematics for the Physical Sciences Instructor: Shamgar Gurevich Lectures: TuTh 11:00am-12:30pm, Room 289 Cory Course Control Number: 54883 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 123 - Section 1 - Ordinary Differential Equations Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54892 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Theodore Slaman Lectures: TuTh 2:00-3:30pm, Room 289 Cory Course Control Number: 54895 Office: 719 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Xuemin Tu Lectures: TuTh 9:30-11:00am, Room 60 Evans Course Control Number: 54898 Office: 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 9:30-11:00am, Room 39 Evans Course Control Number: 54919 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 241 Cory Course Control Number: 54922 Office: 907 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 141 - Section 1 - Elementary Differential Topology Instructor: Dagan Karp Lectures: MWF 10:00-11:00am, Room 247 Cory Course Control Number: 54925 Office: 1053 Evans Office Hours: TBA and by appointment Prerequisites: 104 Required Text: Guillemin/Pollack, Differential Topology, Prentice-Hall Recommended Reading: Milnor, Top. From Diff. View.; Bott/Tu, Diff. Forms in Alg. Top. Syllabus: The official course description includes: "Manifolds in n-dimensional Euclidean space and smooth maps, Sard's Theorem, classification of compact one-manifolds, transversality and intersection modulo 2." What we actually cover will depend upon the interests and background of the class as a whole. Differential topology contains some of the most beautiful and basic ideas in all of mathematics and we will let our curiosity drive us as much as possible. Course Webpage: http://math.berkeley.edu/~dkarp/courses/141/ Grading: Homework will be a very significant part of the total grade. There will also be one midterm and one final exam (perhaps they will both be take home). Homework: Will be assigned and collected regularly. Comments: Math 151 - Section 1 - Mathematics of the Secondary School Curriculum I Instructor: Hung-Hsi Wu Lectures: TuTh 2:00-3:30pm, Room 7 Evans; Discussion: M 4:00-5:00pm, Room 81 Evans Course Control Number: Lectures: 54927; Discussion: 55822 Office: 733 Evans Office Hours: M 1:00-3:00pm, Tu 10:00-11:00am, Th 11:00am-12:00pm Prerequisites: Math 1A, 1B, 53, or equivalent. Required Text: None. Lecture notes will be made available as the course progresses. Recommended Reading: Syllabus: This course is 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, and in fact, to middle school as well. To put this in context, the development of of rational numbers in Math 113 (Introduction to Abstract Algebra), for example, would *not* be usable in the school classroom, no matter which grade is considered. For Math 151, the topics are: theory of rational numbers based on the number line, the Euclidean algorithm and fractions in lowest terms, the concepts of congruence and similarity, equation of a line, linear functions and quadratic functions. 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 you witness in most school classrooms. Course Webpage: TBA Grading: Homework 30%, First midterm 10%, Second midterm 20%, Final 40%. Homework: Weekly assignments, due every Monday. Comments: Students are required to form study groups to work on the homework problems but not to copy from each other. There will be a Yahoo "groups" chat room for communications to form study groups. The purpose of the problem session, every monday 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: Constantin Teleman Lectures: TuTh 9:30-11:00am, Room 7 Evans Course Control Number: 54928 Office: 905 Evans Office Hours: TuTh 11:00am-12:00pm Prerequisites: Math 104, some linear algebra Required Text: Tristan Needham, Visual Complex Analysis, see http://www.usfca.edu/vca/ Recommended Reading: Donald Sarason, Notes on Complex Function Theory Syllabus: Complex numbers, power series, Moebius transformations, analytic functions, winding numbers, complex integration, residues and poles Course Webpage: Under construction, please check my homepage http://math.berkeley.edu/~teleman/ where a link will be posted. Grading: 15% homework, 25% each for two midterms, 35% final Homework: Will be assigned on the webpage every week. Comments: We will cover the standard topics in complex analysis through the eyes of planar geometry. Most of the fundamental results of complex analysis were obtained by the 1850's and the theory has been polished into a perfect formalism since then. Many textbooks explain mostly this finished product, whereas we shall ask 'why' the theory works and try to find visual answers, usually in the (complex) plane. Once a geometric idea is understood, it becomes much easier, and less mysterious, to work with the corresponding formalism. Math 185 - Section 2 - Introduction to Complex Analysis Instructor: William Kahan Lectures: MWF 1:00-2:00pm, Room 289 Cory Course Control Number: 54931 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Jason Metcalfe Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54934 Office: 837 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Churchill & Brown: Complex Variables and Applications, 7th edition (McGraw-Hill) Recommended Reading: Syllabus: Main topics: Complex numbers, analytic functions, integrals, series, residues and poles, and conformal mappings. Please see the webpage for a detailed syllabus. Course Webpage: http://math.berkeley.edu/~metcalfe/teaching/math185/ 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 202A - Section 1 - Introduction to Topology and Analysis Instructor: Justin Holmer Lectures: TuTh 8:00-9:30am, Room 150 GSPP Course Control Number: 55024 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. Required Text: None (but subject to change) Recommended Reading: Stein & Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces Royden, Real Analysis Munkres, Topology Syllabus: During the first half of the course, we will cover general point-set topology. 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 and then launch into functional analysis. Course Webpage: http://math.berkeley.edu/~holmer/teaching/f202a/. Contains an expanded version of this course announcement. Grading: 50% homework, 25% midterm, 25% final. There will be one two-day midterm covering point set topology (first half of course). The final will cover measure theory only (second half of the course). Both exams will be in-class. 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: Jon Wilkening Lectures: TuTh 12:30-2:00pm, Room 5 Evans Course Control Number: 55027 Office: 1091 Evans Office Hours: TBA Prerequisites: Undergraduate Analysis and Linear Algebra Required Text: Coddington and Levinson, Theory of Ordinary Differential Equations Recommended Reading: Hurewicz, Lectures on Ordinary Differential Equations Courant and Hilbert, Methods of Mathematical Physics, Vol 1 Syllabus: In the first part of the course, we will study fundamental questions of existence, uniqueness and dependence of solutions of ODE's on initial conditions and parameters. We will then study linear systems (e.g. with constant or periodic coefficients), boundary value problems, adjoint equations, expansion and completeness theorems, Sturm-Liouville theory, perturbation theory, and the Poincare-Bendixson Theorem. We fill finish the course with ODE methods in PDE and the Cauchy-Kowalewski theorem. Course Webpage: http://math.berkeley.edu/~wilken/204A.F06 Grading: 75% Homework, 25% Final Exam Homework: 10 assignments Comments: Math 205 - Section 1 - Theory of Functions of a Complex Variable Instructor: Donald Sarason Lectures: MWF 8:00-9:00am, Room 5 Evans Course Control Number: 55030 Office: 779 Evans Office Hours: TBA Prerequisites: Math 185 or the equivalent 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. Comments: The lectures will be self-contained except for routine details. Math 206 - Section 1 - Banach Algebras and Spectral Theory Instructor: Donald Sarason Lectures: MWF 10:00-11:00am, Room 41 Evans Course Control Number: 55033 Office: 779 Evans Office Hours: TBA Prerequisites: Math 185 and Math 202AB, or the equivalents Required Text: No textbook will be followed closely. W. Rudin's book Functional Analysis contains much of the course materaial. Other possible references will be mentioned in the first lecture. Recommended Reading: Syllabus: Review of some basic operator theory; operators with closes ranges; idempotents; compact operators; Fredholm operators; Banach algebras (basics, spectrum, holomorphic functional calculus, Gelfand theory of commutative Banach algebras, C*-algebras); basics of operators theory in Hilbert spaces; various versions of the spectral theorem (commutative C*-algebras, normal operators, one-parameter unitary groups); possible additional topics, time permitting. Course Webpage: Grading: The course grade will be based on homework. There will be no exams. Homework: There will be regular homework assignments. Comments: The lectures will be self-contained except for routine details. Math 215A - Section 1 - Algebraic Topology Instructor: Peter Teichner Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 55036 Office: 703 Evans Office Hours: TuTh 11:00am-12:00pm Prerequisites: Linear algebra and point-set topology Required Text: Hatcher, Algebraic Topology see http://www.math.cornell.edu/~hatcher/AT/ATpage.html Recommended Reading: Bredon, Topology and Geometry Syllabus: Algebraic topology seeks to capture the essence of a topological space in terms of various algebraic and combinatorial objects. We will construct and apply three such gadgets: the fundamental group, homology groups, and the cohomology ring. Much but by no means all of the course content is in the book by Hatcher. Like in Bredon's book, the topology of manifolds will play a prominent role in this course. Course Webpage: Will be linked from http://math.berkeley.edu/~teichner Grading: The grade will be based on homework. Homework: Yes. Comments: Math 221 - Section 1 - Advanced Matrix Computation Instructor: John Strain Lectures: TuTh 9:30-11:00am, Room 61 Evans Course Control Number: 55042 Office: 1099 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 222A - Section 1 - Partial Differential Equations Instructor: Daniel Tataru Lectures: TuTh 12:30-2:00pm, Room 7 Evans Course Control Number: 55045 Office: 841 Evans Office Hours: TBA Prerequisites: 105 or 202B 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. (with 222B) Course Webpage: Grading: Homework + take home final exam. Homework: Homework will be assigned every week. Comments: Math 224A - Section 1 - Mathematical Methods for the Physical Sciences Instructor: Fraydoun Rezakhanlou Lectures: TuTh 11:00am-12:30pm, Room 5 Evans Course Control Number: 55048 Office: 815 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: None Recommended Reading: Syllabus: The majority of the fundamental processes of our natural world are described by differential equations. Some examples are the vibration of solids, the flow of fluids, the formation of crystals, the spread of infections, the diffusion of chemicals, the structure of molecules, etc. These examples are responsible for our interest in partial differential equations such as Hamilton-Jacobi equation, Euler equation, Navier-Stokes equation, Diffusion equation, Wave equation and Korteweg-deVries equation. As the primary goal of the course, I discuss some of the above equations and explain some mathematicals tools that are needed to solve them. I also use these equation as an excuse to introduce students to some basic questions in fluid mechanics and statistical physics. Some of the topics are: 1. Advection, diffusion, Brownian motion, sources, Green's function. 2. Fluid mechanics, Euler equation, incompressible limit, shallow water equation. 3. Shock waves, Rarefaction waves, Riemann invariants. 4. Similarity methods. 5. Scattering theory, Korteweg-deVries equation. There is no required text and I will distribute handwritten notes in the class. Course Webpage: Grading: There will be weekly homework assignments (due Tuesdays) and one take-home exam. Homework: Comments: Math 225A - Section 1 - Metamathematics Instructor: Leo Harrington Lectures: TuTh 12:30-2:00pm, Room 72 Evans Course Control Number: 55051 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228A - Section 1 - Numerical Solution of Differential Equations Instructor: Jon Wilkening Lectures: TuTh 11:00am-12:30pm, Room 87 Evans Course Control Number: 55054 Office: 1091 Evans Office Hours: TBA 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 Morton and Mayers, Numerical Solution of Partial Differential Equations Recommended Reading: Hairer/Norsett/Wanner, Solving Ordinary Differential Equations (2 Vols) Syllabus: The first half 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. We will then move on to study finite difference solutions of hyperbolic and parabolic partial differential equations, where we will develop tools (e.g. Von Neumann stability theory, CFL conditions, consistency and convergence) to analyze popular schemes (e.g. Lax-Wendroff, leapfrog, Cranck-Nicholson, ADI, etc.) Course Webpage: http://math.berkeley.edu/~wilken/228A.F06 Grading: Grades will be based entirely on homework. Homework: 10 assignments Comments: Math 229 - Section 1 - Theory of Models Instructor: Thomas Scanlon Lectures: MWF 9:00-10:00am, Room 5 Evans Course Control Number: 55057 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 242 - Section 1 - Symplectic Geometry Instructor: Christian Blohmann Lectures: TuTh 11:00am-12:30pm, Room 61 Evans Course Control Number: 55062 Office: 898 Evans Office Hours: TBA Prerequisites: Math 214 or equivalent familiarity with basic material on differentiable manifolds. Required Text: Cannas da Silva, Lectures on Symplectic Geometry, Springer Lecture Notes in Mathematics Recommended Reading: Syllabus: As per the catalog, I will discuss symplectic linear algebra, symplectic manifolds, Darboux's theorem, cotangent bundles, variational problems and Legendre transform, hamiltonian systems, lagrangian submanifolds, Poisson brackets, symmetry groups and momentum mappings, coadjoint orbits and Kähler manifolds. If time remains at the end, I will go into advanced topics. Course Webpage: See http://math.berkeley.edu/~blohmann/ Grading: The grade will be based class participation, homework, and an expository paper on some aspect of symplectic geometry or its applications. Homework: There will be reading assignments from the main text and homework problems which will be discussed in class. Selected homework problems will be graded. Comments: This course is meant to equip the student with a knowledge of the essential definitions, methods, and results in symplectic geometry, either for the further study of symplectic geometry itself, or for applications to other fields of mathematics and mathematical physics (e.g. topology, representation theory, algebraic geometry, partial differential equations, classical and quantum mechanics and field theory). Math 249 - Section 1 - Algebraic Combinatorics Instructor: Vera Serganova Lectures: TuTh 12:30-2:00pm, Room 41 Evans Course Control Number: 55063 Office: 709 Evans Office Hours: TuTh 11:00am-12:00pm Prerequisites: Math 250A, can be taken at the same time. Required Text: Richard Stanley, Enumerative Combinatorics, Cambridge University Press, v.1,2 Recommended Reading: I. Macdonald, Symmetric functions and Hall polynomials, W. Fulton, Young tableaux Syllabus: I plan to cover the following topics: posets, lattices, generating functions, partitions, symmetric functions, Schur polynomials, representations of symmetric groups, q-binomial coefficients, geometric lattices, hyperplane arrangements Course Webpage: http://math.berkeley.edu/~serganov Grading: Homework: Homework will be assigned on the web every week, and due once a week. Comments: Math 250A - Section 1 - Groups, Rings, and Fields Instructor: George Bergman Lectures: MWF 1:00-2:00pm, Room 70 Evans Course Control Number: 55066 Office: 865 Evans Office Hours: Tu 1:30-2:30pm, Th 10:30-11:30am, F 3:00-4:00pm Prerequisites: Reasonable mathematical maturity, and/or the equivalent of Math 113. 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 edition (Springer-Verlag, 2002, or Addison-Wesley, 1993). Recommended Reading: TBA Syllabus: Main topics: groups, rings, modules, Galois theory. Other topics: Sets, categories, transcendental field extensions. This is the basic what every mathematician needs to know about algebra'' course. Course Webpage: Grading: Homework: 50%, Midterm 17%, Final Exam 33% Homework: There is a lot of material to cover; expect a heavy course. I try to assign interesting and challenging exercises; however, I have all students hand in anonymous weekly estimates of the time spent on study and on homework, and I use this feedback to keep the total time from running too high. Comments: As in my other courses, I will not waste your time and mine by putting material from the book on the blackboard for you to copy. Rather, we will use assigned readings from Lang as the primary teacher'', and devote the classroom time to motivation of material in the forthcoming reading, clarification of points that students ask about or that I feel needs it, supplementary material, alternative approaches, discussion of homework exercises, etc. To make this work, I require each student to submit, on each day for which there is an assigned reading, a question on that reading. Details (including what to submit if you understood everything perfectly) will be given on the first-day handout. Math 254A - Section 1 - Number Theory Instructor: Paul Vojta Lectures: MWF 11:00am-12:00pm, Room 72 Evans Course Control Number: 55069 Office: 883 Evans Office Hours: MWF 12:30-1:30pm Prerequisites: Math 250A or equivalent Required Text: Neukirch, Algebraic Number Theory, Springer Recommended Reading: Syllabus: This is the standard first-year graduate course on number theory. In the fall semester the course will cover the basics of number theory over a Dedekind domain: completions, fractional ideals, ideles and adeles, etc., as in the catalog description or the first three chapters of the textbook. Basically, the idea is to study finite algebraic extensions of Z or Q and determine which properties still hold in this more general setting, because often the structure of a system of diophantine equations over Z or Q is more apparent after extending the field of definition. The course will also include some introductory material on analytic number theory and class field theory. The second half of this course, Math 254B, will be taught by Ken Ribet. Course Webpage: http://math.berkeley.edu/~vojta/254a.html Grading: Grading will be based on homework assignments, including a take-home final. Homework: Weekly or biweekly; assigned in class. Comments: This is my first time using this textbook, but I plan to emphasize its material on the analogy with the function field case. Math 256A - Section 1 - Algebraic Geometry Instructor: Brian Osserman Lectures: TuTh 2:00-3:30pm, Room 103 Moffitt Course Control Number: 55072 Office: 767 Evans Office Hours: TBA Prerequisites: 250A; 250B strongly encouraged Required Text: Hartshorne, Algebraic Geometry Recommended Reading: Eisenbud and Harris, The Geometry of Schemes Syllabus: This is the first semester of an integrated, year-long course in algebraic geometry. Although the primary source text will be Hartshorne's Algebraic Geometry, we will start from the beginning with schemes to emphasize their close connection with classical varieties and geometry, and we will supplement the text heavily with additional topics from both modern and classical algebraic geometry. Course Webpage: http://math.berkeley.edu/~osserman/classes/256A/ Grading: Primarily homework-based, with the possibility of a takehome final exam or final paper. Homework: Homework will be assigned roughly weekly. Comments: Math 258 - Section 1 - Classic Harmonic Analysis Instructor: Michael Christ Lectures: MWF 12:00-1:00pm, Room 3 Evans Course Control Number: 55075 Office: 809 Evans Office Hours: TBA Prerequisites: Math 202AB (graduate real/functional analysis) or equivalent. Required Text: M. Christ, Lecture notes Euclidean Harmonic Analysis. (These typewritten notes will be distributed in installments throughout the term at no charge.) Recommended Reading: Y. Katznelson, An Introduction to Harmonic Analysis. This award-winning classic costs only $12.95. E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Syllabus: This introductory course will treat harmonic analysis in Euclidean spaces and allied topics in real and, to a lesser extent, complex analysis. Topics: Most but not all of: Fourier transform and series. Functorial properties, inversion, Poisson summation, localization, symmetry, identities. Fourier transform on finite cyclic groups. Schwartz space, tempered distributions, approximations to the identity. Convergence and divergence. Uniform, Lp, almost everywhere convergence. Pointwise divergence. Maximal operators. Decay of Fourier coefficients. Convolution. The algebras of L1 functions and finite measures. Inequalities, Wiener's theorem. Connections with complex analysis and harmonic functions. Boundary values, Dirichlet problem, conjugate function. F. and M. Riesz theorem. Hardy-Littlewood maximal function, stopping time constructions, L1,∞, John-Nirenberg inequality, Carleson's inequality, sharp function, good-λ inequality. Singular integral operators. Principal-value distributions. Multilinear singular integrals. Interpolation of operators. The real and complex methods. Lorentz spaces. Analytic families of operators. Almost orthogonality. A phase plane Bessel inequality. Littlewood-Paley theory. Connection with Carleson measures. Fourier multiplier operators. Comparison of the Fourier basis with other orthonormal bases and frames: Haar, wavelet, Hermite, Gabor. Paley-Wiener theorem and uncertainty principle. Oscillatory integrals. Stationary phase, van der Corput's lemma, connections with curvature. Sobolev and Hölder classes. Fractional integrals, potentials, embedding, compactness. Convergence of multiple Fourier series: Introduction to the Kakeya and Bochner-Riesz problems. Restriction and Strichartz inequalities. Connections with dispersive and hyperbolic PDE. Required work: Either solve and hand in a reasonable number of exercises from the text, or write a short report on a topic relevant to the course. Typically this will involve reading one or several research or expository articles, and writing a summary (5-10 pages). A list of suggested topics and references will be distributed by October. Students are welcome to find their own topics, subject to instructor's approval. Course Webpage: http://math.berkeley.edu/~mchrist/ Grading: Homework: Comments: Math 270 - Section 1 - Hot Topics Course in Mathematics Instructor: Peter Teichner Lectures: Th 2:00-3:30pm, Room 71 Evans Course Control Number: 55077 Office: 703 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~teichner/Courses/270-Derived.html Grading: Homework: Comments: Math 271 - Section 1 - Topics in Foundations Instructor: John Addison Lectures: MWF 2:00-3:00pm, Room 39 Evans Course Control Number: 55828 Office: 763 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra Instructor: Tsit-Yuen Lam Lectures: MWF 10:00-11:00am, Room 31 Evans Course Control Number: 55078 Office: 871 Evans Office Hours: TBA Prerequisites: Math 250AB Required Text: Kaplansky, Commutative Rings, Polygonal Publishing House, Washington, New Jersey Recommended Reading: Atiyah-MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Massachusetts Hutchins, Examples of Commutative Rings, Polygonal Publishing House, Washington, New Jersey Lam, First Course in Noncommutative Rings, Springer, New York Syllabus: I will teach a course in commutative algebra, in memory of Professor Irving Kaplansky who passed away in July, 2006. The main text will be Kaplansky's book "Commutative Rings". The course will be taught in the main spirit of this text, namely, more from the viewpoint of algebra than from the viewpoint of algebraic geometry. In particular, students need not have taken Math 256A prior to taking this course. I will, however, assume that students have a very thorough grounding in abstract algebra, as is typically taught in Math 250AB. To save time in re-developing the basic material from scratch, I'll assume my audience is familiar with exact sequences, tensor products and "Hom", basic localization theory, behavior of primes under localization, existence lemmas on prime and maximal ideals, integrality notions, Hilbert Basis Theorem, and a few facts about modules and rings with chain conditions (such as the Jordan-Hölder Theorem and the (composition) length of modules). Assuming these prerequisites will enable us to start off on a slightly higher ground. The course will start with Chapter I, covering some theorems of McCoy, nilradical and Jacobson radical, associated primes of modules and rings, noetherian rings and artinian rings, primary decompositions, etc. This will be followed by chapters on integral extensions and dimension theory, and other standard material in commutative algebra. We may not get to the more advanced topics in the field, but it is hoped that whatever the course covers will be well covered. The textbook will not be followed closely, although students are expected to have a copy of it, as well as some of the other reference books listed. Occasionally, class notes will be provided. Many homework problems will be assigned. It will be best if students can start a course webpage, to which they can write up and post their homework problem solutions. Grades will be based on class attendance, HW performance, and possible seminar talks and class projects. I will not intimidate people with exams! The textbook is available only through Polygonal Publishing House, and costs a modest$18, with a possible discount if we order multiple copies. We are planning to place a class order, hopefully BEFORE classes start. Thus, if you want to add your name to the class order, please stop by my office (871 Evans) ASAP to sign up and pay for a copy. Course Webpage: Grading: Grades will be based on class attendance, HW performance, and possible seminar talks and class projects. Homework: Many homework problems will be assigned. Comments: Math 279 - Section 1 - Semiclassical Analysis Instructor: Maciej Zworski Lectures: MWF 11:00am-12:00pm, Room 39 Evans Course Control Number: 55081 Office: 897 Evans Office Hours: TBA Prerequisites: Math 222A or equivalent. Required Text: L.C. Evans and M. Zworski Lectures on Semiclassical Analysis http://math.berkeley.edu/~zworski/semiclassical.pdf Recommended Reading: Syllabus: The course will provide a broad introduction to many aspects of semiclassical/microlocal analysis. A basic graduate course in real and functional analysis is the only prerequisite. The material will follow notes by L.C. Evans and M. Zworski (available on line, see above): 1. Symplectic geometry 2. Fourier transform and the method of stationary phase 3. Quantization of classical observables 4. Semiclassical defect measures and their applications 5. Eigenvalues and eigenfunctions: Weyl laws 6. Exponential estimates for eigenfunctions: Agmon and Carleman 7. Quantum ergodicity 8. Quantization of symplectic transformation: normal forms, Strichartz estimates etc. 9. Semiclassical/microlocal generalizations of the Selberg trace formula Course Webpage: Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor:Jameel Al-Aidroos Lectures: W 5:00-7:00pm, Room 3109 Etcheverry Course Control Number: 55756Office:Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework:Comments: