Spring 2008
| Math 1A - Section 1 - Calculus Instructor: Jon Wilkening Lectures: MWF 12:00-1:00pm, Room 2050 Valley Life Science Course Control Number: 54103 Office: 1091 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Vaughan Jones Lectures: TuTh 2:00-3:30pm, Room 100 Lewis Course Control Number: 54142 Office: 929 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Calculus Instructor: Vera Serganova Lectures: MWF 9:00-10:00am, Room 155 Dwinelle Course Control Number: 54190 Office: 709 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 3 - Calculus Instructor: Marina Ratner Lectures: MWF 2:00-3:00pm, Room 2050 Valley Life Science Course Control Number: 54238 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Hugh Woodin Lectures: TuTh 12:30-2:00pm, Room 2050 Valley Life Science Course Control Number: 54280 Office: 721 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Leo Harrington Lectures: TuTh 2:00-3:30pm, Room 155 Dwinelle Course Control Number: 54325 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 2 - Analytical Geometry and Calculus Instructor: Thomas Scanlon Lectures: MWF 10:00-11:00am, Room 10 Evans Course Control Number: 54364 Office: 723 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: 54397 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: 54400 Office: 851 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 3 - Freshman Seminars Instructor: Rob Kirby Lectures: Tu 8:30-10:00am, Room 939 Evans Course Control Number: 54403 Office: 919 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 4 - The Geometry of Relativity Instructor: Alan Weinstein Lectures: Tu 2:00-3:30pm, Room 939 Evans Course Control Number: 54405 Office: 825 Evans Office Hours: TBA Prerequisites: Math 1A or equivalent Required Text: Sander Bais, Very Special Relativity, Harvard U. Press Recommended Reading: Syllabus: This seminar will meet the first week of classes and nine more dates to be arranged. We will look at some of the mathematical ideas, particularly the geometric ideas, behind Einstein's special and general theories of relativity. Topics will include the linear algebra and geometry of Lorentz transformations in flat space time (for special relativity) and an introduction to riemannian geometry (for general relativity). The seminar activities will be a mix of reading, discussion, and presentations by students and the instructor. Students should have had Math 1A or the equivalent. Further background in calculus and/or linear algebra is helpful but not essential. The math that will be taught in the seminar will give students a head start (or a review) for more advanced courses. Course Webpage: Grading: Homework: Comments: Math 24 - Section 5 - Freshman Seminars Instructor: Hugh Woodin Lectures: W 1:00-2:00pm, Room 939 Evans Course Control Number: 55660 Office: 721 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: The Staff Lectures: MWF 8:00-9:00am, Room 160 Kroeber Course Control Number: 54406 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 39A - Section 1 - Seminar for Teaching Math in Schools Instructor: Emiliano Gomez Lectures: M 4:00-6:00pm, Room 35 Evans Course Control Number: 54426 Office: 985 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: The purpose of this seminar is to introduce the participants to life in a K-12 mathematics classroom. Several specific mathematical topics that are known to be troublesome in the K-12 curriculum will be discussed. Students will contrast what they learn about these topics in mathematics courses in college with how they will teach them to their students. The course includes a field placement in a local school. Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: John Neu Lectures: MWF 1:00-2:00pm, Room 2050 Valley Life Science Course Control Number: 54448 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: John Steel Lectures: TuTh 3:30-5:00pm, Room 100 Lewis Course Control Number: 54487 Office: 717 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H53 - Section 1 - Honors Multivariable Calculus Instructor: Calder Daenzer Lectures: TuTh 3:30-5:00pm, Room B51 Hildebrand Course Control Number: 54526 Office: 1083 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: Daniel Tataru Lectures: TuTh 11:00am-12:30pm, Room 2050 Valley Life Science Course Control Number: 54532 Office: 841 Evans Office Hours: TBA Prerequisites: Math 1B Required Text: David Lay, Linear Algebra and It's Applications, 3rd edition Nagle, Saff and Snider, Fundamentals of Differential Equations and Boundary Value Problems For both you can get the paperback Berkeley editions. Recommended Reading: Syllabus: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. Course Webpage: http://math.berkeley.edu/~tataru/54.html (to be created) Grading: Homework 20%, midterms 20% each, and final exam 40%. Homework: Homework will be assigned weekly. Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Alexandre Chorin Lectures: MWF 3:10-4:00pm, Room 155 Dwinelle Course Control Number: 54565 Office: 911 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: John Strain Lectures: TuTh 9:30-11:00am, Room 60 Evans Course Control Number: 54610 Office: 1099 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 1 - Transition to Upper Division Mathematics Instructor: Adam Booth Lectures: MWF 3:00-4:00pm, Room 85 Evans Course Control Number: 54628 Office: 845 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 74 - Section 2 - Transition to Upper Division Mathematics Instructor: Anthony Varilly Lectures: MWF 8:00-9:00am, Room 85 Evans Course Control Number: 54631 Office: 941 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 98 - Section 5 - MATLAB Adjunct to Math 128A Instructor: Maxim Trokhimtchouk Lectures: Days & Times TBA, Room B0003A Evans Course Control Number: Office: 1097 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: This course is intended as an introduction to programming and programming concepts using MATLAB. It not only focuses on the use of MATLAB itself, but also introduces students to the fundamentals of programming, with emphasis on techniques and style. We will learn how to use MATLAB to implement and debug a complex program and how to use facilities such as MATLAB Help and other resources. We will also learn how to use MATLAB to produce plots and graphics, which are essential for presenting numerical computations. This course is recommended even for those who had prior programming experience, however, prior knowledge of programming if not necessary. Course Webpage: Grading: Homework: Comments: Math 98 - Section 6 - MATLAB Adjunct to Math 128A Instructor: Maxim Trokhimtchouk Lectures: Days & Times TBA, Room B0003A Evans Course Control Number: Office: 1097 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: This course is intended as an introduction to programming and programming concepts using MATLAB. It not only focuses on the use of MATLAB itself, but also introduces students to the fundamentals of programming, with emphasis on techniques and style. We will learn how to use MATLAB to implement and debug a complex program and how to use facilities such as MATLAB Help and other resources. We will also learn how to use MATLAB to produce plots and graphics, which are essential for presenting numerical computations. This course is recommended even for those who had prior programming experience, however, prior knowledge of programming if not necessary. Course Webpage: Grading: Homework: Comments: Math C103 - Section 1 - Introduction to Mathematical Economics Instructor: David Sraer Lectures: MWF 1:00-2:00pm, Room 241 Cory Course Control Number: 54682 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: David Hill Lectures: MWF 9:00-10:00am, Room 71 Evans Course Control Number: 54685 Office: 757 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 3:30-5:00pm, Room 2 Evans Course Control Number: 54688 Office: 705 Evans Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: C. Pugh, Real Mathematical Analysis, Springer, 2002. Recommended Reading: Syllabus: Roughly Chapters 1 to 4: The real number system, cardinalities, metric spaces, convergence, compactness and connectedness, continuous functions on metric spaces, uniform convergence, power series, differentiation and integration. (We will leave out some rather advanced material in Chapters 2 and 4.) 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 3 - Introduction to Analysis Instructor: Elizabeth Gasparim Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54691 Office: 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 11:00am-12:30pm, Room 141 Giannini Course Control Number: 54694 Office: 1053 Evans Office Hours: TBA Prerequisites: 53 and 54 Required Text: Ross, Elementary Analysis: The Theory of Calculus Recommended Reading: Rudin, Pugh Syllabus: We will cover everything in Ross. This includes: The real number system. Sequences, limits, and continuous functions in R and 'Rn'. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral. Course Webpage: http://math.berkeley.edu/~dkarp/courses/2008Spring/104/ Grading: 50% homework, 20% midterm, 30% final Homework: Homework will be assigned and due once a week. Comments: Math 105 - Section 1 - Second Course in Analysis Instructor: Marina Ratner Lectures: MWF 10:00-11:00am, Room 85 Evans Course Control Number: 54697 Office: 827 Evans Office Hours: TBA Prerequisites: Required Text: Rudin, Principles of Math Analysis Royden, Real Analysis Recommended Reading: Syllabus: The course consists of two different topics. The first topic (approximately first five weeks) uses Rudin's "Principles of Math Analysis", Chapter 9. Differential calculus in Rn: The derivative as a linear map. The Contraction principle. The Inverse and the Implicit Function Theorems. Integral Equations. The second topic (remaining 10 weeks) uses Royden "Real Analysis" Chapters 11 and 12 (1,2) Abstract measure theory. The Lebesgue measure on the line and in Rn. The Cantor Set. Measurable Functions. The Lebesgue Integral. Types of Convergence in Measure Spaces. The Lp spaces. Product measures and the Fubini Theorem. Signed measures. Absolute continuity. Integration and Differentiation. Course Webpage: Grading: The grade of the course will be based 15% on weekly homework, 25% on a Midterm, 20% on Quizzes and 40% on a Final. Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Aaron Greicius Lectures: MWF 12:00-1:00pm, Room 3 Evans Course Control Number: 54700 Office: 796 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 2 - Linear Algebra Instructor: Marco Aldi Lectures: TuTh 9:30-11:00am, Room 87 Evans Course Control Number: 54703 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 3 - Linear Algebra Instructor: Mauricio Velasco Lectures: TuTh 8:00-9:30am, Room 71 Evans Course Control Number: 54706 Office: 1063 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 4 - Linear Algebra Instructor: John Krueger Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54709 Office: 751 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 5 - Linear Algebra Instructor: Lek-Heng Lim Lectures: TuTh 3:30-5:00pm, Room 75 Evans Course Control Number: 54712 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 6 - Linear Algebra Instructor: Aaron Greicius Lectures: MWF 2:00-3:00pm, Room 70 Evans Course Control Number: 54714 Office: 796 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Shamgar Gurevitch Lectures: TuTh 3:30-5:00pm, Room 71 Evans Course Control Number: 54715 Office: 867 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Chung Pang Mok Lectures: MWF 3:00-4:00pm, Room 2 Evans Course Control Number: 54718 Office: 889 Evans Office Hours: Tu 3:00-4:00pm, Th 2:00-3:00pm Prerequisites: Math 54 or equivalent Required Text: John B. Fraleigh, A First Course in Abstract Algebra, Seventh Edition Recommended Reading: R. Allenby, Rings, Fields, and Groups, An Introduction to Abstract Algebra Syllabus: Groups, Rings and Ideals, Fields and their extensions. Course Webpage: http://math.berkeley.edu/~mok/math113.html Grading: 20% homework, 40% for two mid-terms, 40% final Homework: Assigned and due weekly on Friday. Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Arthur Ogus Lectures: MWF 1:00-2:00pm, Room 75 Evans Course Control Number: 54721 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Mariusz Wodzicki Lectures: TuTh 9:30-11:00am, Room 71 Evans Course Control Number: 54724 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H113 - Section 1 - Honors Introduction to Abstract Algebra Instructor: Alexander Givental Lectures: TuTh 9:30-11:00am, Room 85 Evans Course Control Number: 54727 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 114 - Section 1 - Second Course in Abstract Algebra Instructor: Martin Olbermann Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54730 Office: 829 Evans Office Hours: TBA Prerequisites: 110 and 113, or consent of instructor Required Text: Ian Stewart, Galois Theory (You need the 2nd edition, NOT the 3rd edition! I recommend to use the reader made available at Copy Central, 2560 Bancroft Way) Recommended Reading: Syllabus: Galois theory and associated topics in field theory and group theory. Course Webpage: http://math.berkeley.edu/~olber/114/index.html Grading: TBA Homework: Homework will be assigned on the web every week. Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Shamgar Gurevitch Lectures: TuTh 12:30-2:00pm, Room 75 Evans Course Control Number: 54733 Office: 867 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121B - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Vera Serganova Lectures: MWF 12:00-1:00pm, Room 71 Evans Course Control Number: 54736 Office: 709 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Leo Harrington Lectures: TuTh 11:00am-12:30pm, Room 3 Evans Course Control Number: 54739 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 126 - Section 1 - Introduction to Partial Differential Equations Instructor: Xuemin Tu Lectures: MWF 10:00-11:00am, Room 4 Evans Course Control Number: 54742 Office: 1055 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Ming Gu Lectures: MWF 12:00-1:00pm, Room 277 Cory Course Control Number: 54745 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128B - Section 1 - Numerical Analysis Instructor: William Kahan Lectures: MWF 11:00am-12:00pm, Room 5 Evans Course Control Number: 54763 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 130 - Section 1 - The Classical Geometries Instructor: Mariusz Wodzicki Lectures: TuTh 12:30-2:00pm, Room 85 Evans Course Control Number: 54769 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory Sets Instructor: Thomas Scanlon Lectures: MWF 11:00am-12:00pm, Room 103 GPB Course Control Number: 54772 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 142 - Section 1 - Elementary Algebraic Topology Instructor: Marco Aldi Lectures: TuTh 3:30-5:00pm, Room 70 Evans Course Control Number: 54775 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 151 - Section 1 - Mathematics of the Secondary School Curriculum I Instructor: Theodore Slaman Lectures: MWF 2:00-3:00pm, Room 30 Wheeler Course Control Number: 54778 Office: 719 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 152 - Section 1 - Mathematics of the Secondary School Curriculum II Instructor: Hung-Hsi Wu Lectures: TuTh 11:00am-12:30pm, Room 31 Evans; W 4:00-5:00pm, Room 41 Evans Course Control Number: 54784 Office: 733 Evans Office Hours: TBA Prerequisites: Math 53, 54, 113, or equivalent Required Text: Lecture Notes, to be purchased from Copy Central after the first week. Recommended Reading: None. Syllabus: This course is the continuation of Math 151, and 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. The main topics covered are: perpendicularity and parallelism of lines; systems of linear equations; concept of function; linear, quadratic, and polynomial functions; abstract polynomials and the division algorithm; fundamental theorem of algebra; proofs of basic theorems in Euclidean geometry; axiomatic system. Course Webpage: None. Grading: Homework 30%, First midterm 10%, Second midterm 20%, Final 40%. Homework: Homework will be assigned every week, and due once a week. Comments: Study group encouraged. Math 160 - Section 1 - History of Mathematics Instructor: Hung-Hsi Wu Lectures: TuTh 2:00-3:30pm, Room 71 Evans Course Control Number: 54790 Office: 733 Evans Office Hours: TBA Prerequisites: Math 53, 54, 113 Required Text: C.B. Boyer and U.C. Merzbach, A History of Mathematics, 2nd edition, Wiley, 1991 Recommended Reading: To be given later. Syllabus: After a general chronological overview of the main events in the development of mathematics, we will trace the evolution of geometry, algebra, analysis, and number theory from the time of the Babylonians to the nineteenth century. The Boyer-Merzbach text will be a main reference, but will not be followed chapter by chapter. Course Webpage: None. Grading: Homework 30%, First midterm 10%, Second midterm 20%, Final 40%. Homework: Homework will be assigned every week, and due once a week. Comments: The assignments and the exams will both involve writing short essays about historical or biographical information. Math 172 - Section 1 - Combinatorics Instructor: Joshua Sussan Lectures: TuTh 8:00-9:30am, Room 85 Evans Course Control Number: 54793 Office: 761 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Martin Olbermann Lectures: MWF 3:00-4:00pm, Room 4 Evans Course Control Number: 54796 Office: 829 Evans Office Hours: TBA Prerequisites: 104, or consent of instructor Required Text: Sarason, Notes on complex function theory, published by Henry Helson, Berkeley. Recommended Reading: The Sarason text is concise and without many figures or worked examples, so you are encouraged to look also at at least one other text, such as one of the following:
Course Webpage: http://math.berkeley.edu/~olber/185/index.html Grading: TBA Homework: Homework will be assigned on the web every week. Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Paul Vojta Lectures: MWF 10:00-11:00am, Room 241 Cory Course Control Number: 54799 Office: 883 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Mauricio Velasco Lectures: TuTh 12:30-2:00pm, Room 71 Evans Course Control Number: 54802 Office: 1063 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H185 - Section 1 - Honors Introduction to Complex Analysis Instructor: William Kahan Lectures: MWF 9:00-10:00am, Room 5 Evans Course Control Number: 54805 Office: 863 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 189 - Section 1 - Mathematical Methods in Classical and Quantum Mechanics Instructor: Dan Voiculescu Lectures: MWF 3:00-4:00pm, Room 5 Evans Course Control Number: 54808 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 202B - Section 1 - Introduction to Topology and Analysis Instructor: Marc Rieffel Lectures: MWF 8:00-9:00am, Room 70 Evans Course Control Number: 54913 Office: 811 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 208 - Section 1 - C*-Algebras Instructor: Marc Rieffel Lectures: MWF 10:00-11:00am, Room 31 Evans Course Control Number: 54916 Office: 811 Evans Office Hours: TBA Prerequisites: The basic theory of bounded operators on Hilbert space and of Banach algebras, especially commutative ones. (Math 206 is more than sufficient. Self-study of sections 3.1-2, 4.1-4 of "Analysis Now" by G. K. Pedersen would be sufficient.) Required Text: Recommended Reading: None of the available textbooks follows closely the path that I will take through the material. The closest is probably: K. R. Davidson, C*-algebras by Example, Fields Institute Monographs, A.M.S. I strongly recommend this text for its wealth of examples (and attractive exposition). Syllabus: The theory of operator algebras grew out of the needs of quantum mechanics, but by now it also has strong interactions with many other areas of mathematics. Operator algebras are very profitably viewed as "non-commutative (algebras "of functions" on) spaces", thus "quantum spaces". As a rough outline, we will first develop the basic facts about C*-algebras ("non-commutative locally compact spaces") We will then briefly look at "non-commutative vector bundles" and K-theory ("noncommutative algebraic topology"). Finally we will glance at "non-commutative differential geometry" (e.g. cyclic homology as "noncomutative deRham cohomology"). But I will not assume prior knowledge of algebraic topology or differential geometry, and we are unlikely to have time to go into these last topics in any depth. I will discuss a variety of examples, drawn from dynamical systems, group representations and mathematical physics. But I will somewhat emphasize examples which go in the directions of my current research interests, which involve certain mathematical issues which arise in string theory and related parts of high-energy physics. Thus one thread which will run through the course will be to see what the various concepts look like for quantum tori, which are the most accessible non-commutative differential manifolds. In spite of what is written above, the style of my lectures will be to give motivational discussion and complete proofs for the central topics, rather than just a rapid survey of a large amount of material. Course Webpage: Grading: I plan to assign several problem sets. Grades for the course will be based on the work done on these. But students who would like a different arrangement are very welcome to discuss this with me. Homework: Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Robion Kirby Lectures: MWF 9:00-10:00am, Room 81 Evans Course Control Number: 54919 Office: 919 Evans Office Hours: MW 10:00-11:00am Prerequisites: 215A and 214, or equivalent Required Text: None Recommended Reading: Hatcher's Algebraic Topology, Milnor's Characteristic Classes. Syllabus: We will cover homotopy theory and characteristic classes with many examples from low dimensional topology. Course Webpage: Grading: Based on homework. Homework: Homework will be assigned irregularly. Comments: Math C218B - Section 1 - Probability Theory Instructor: Elchanan Mossel Lectures: TuTh 9:30-11:00am, Room 330 Evans Course Control Number: 54922 Office: 423 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 220 - Section 1 - Methods of Applied Mathematics Instructor: Alberto Grünbaum Lectures: TuTh 8:00-9:30am, Room 87 Evans Course Control Number: 54925 Office: 903 Evans Office Hours: TuWTh 11:00am-12:00pm Prerequisites: Required Text: Recommended Reading: Syllabus: The purpose of this class is to present some topics that play in important role in several areas of "applied mathematics". Each of these subjects can be presented in a very detailed and technical fashion, but this is exactly what I will try to avoid. My aim will be to give an ab-initio presentation of several subjects and try to emphasize their connections to each other. These topics include
Course Webpage: Grading: Homework: Comments: Math 222B - Section 1 - Partial Differential Equations Instructor: Justin Holmer Lectures: TuTh 12:30-2:00pm, Room 31 Evans Course Control Number: 54928 Office: 849 Evans Office Hours: TBA Prerequisites: This course is a continuation of Math222a. Math 202a and Math202b, specifically the basics of Lebesgue measure and integration theory and Hilbert space theory, are recommended. Required Text: L.C. Evans, Partial Differential Equations. See also the errata. Recommended Reading: I will provide recommended reading as we go along in the course. Syllabus: We will cover Parts II (linear theory) and III (nonlinear theory) of the text. The topics are: Sobolev spaces and embedding theorems, existence and regularity theory for second-order elliptic, parabolic, and hyperbolic equations, calculus of variations, fixed point methods, Hamilton-Jacobi equations, and systems of conservation laws. Course Webpage: http://math.berkeley.edu/~holmer/teaching/s222b/. Grading: 100% homework Homework: Homework will be assigned each week and due the following week. Each assignment will consist of a few required problems and a few optional problems. Only the required problems will be graded. Comments: The emphasis of this course is on theory, not applications. Math 220, "Methods of Applied Mathematics" and Math 224B, "Mathematical Methods for the Physical Sciences" are PDE courses with emphasis on applications. Math C223B - Section 1 - Stochastic Processes Instructor: David Aldous Lectures: TuTh 11:00am-12:30pm, Room 334 Evans Course Control Number: 54931 Office: 351 Evans Office Hours: TBA Prerequisites: Graduate level mathematical probability. Required Text: Recommended Reading: Dembo-Zeitouni, Large Deviations J. Michael Steele, Probability Theory and Combinatorial Optimization Syllabus: The first half of the course covers technical aspects of large deviation theory in moderate detail. The second half studies mathematical properties of (rather than algorithms for finding) solutions of optimization problem over random points in space or random combinatorial structures. See webpage for more details Course Webpage: http://www.stat.berkeley.edu/~aldous/206/index.html Grading: Homework or talk on a research paper. Homework: One set for the semester. Comments: Math 224B - Section 1 - Mathematical Methods for the Physical Sciences Instructor: Alberto Grünbaum Lectures: TuTh 9:30-11:00am, Room 81 Evans Course Control Number: 54934 Office: 903 Evans Office Hours: TuWTh 11:00am-12:00pm Prerequisites: Required Text: Recommended Reading: Syllabus: The main topic here is basic functional analysis, a rather sophisticated form of infinite dimensional linear algebra. In this class we will see how this subject arises naturally form the study of problems in ordinary and partial differential equations, integral equations, Fourier and other transforms, Green functions, perturbation theory, Riemann-Hilbert problems, etc. and how this became the natural tool to study many linear problems in several areas of physics, chemistry and related sciences. An instance of this is the relation between boundary conditions and extensions of a symmetric operator. We will talk about scattering problems in the case of the wave equation (dim 3) and then study in more detail the one dimensional case. The study of the corresponding "scattering transform" relating the potential to the scattering data will be seen to be a powerful tool to study certain nonlinear partial differential equations. Many of these topics are very classical, and they keep reappearing in more present day developments. I will try to illustrate this by looking at certain concrete examples that appear in "quantum computing" such as quantum random walks. The topics for the last few weeks may be influenced by the interests of the participants in the class. Course Webpage: Grading: Homework: Comments: Math 225B - Section 1 - Metamathematics Instructor: Jack Silver Lectures: TuTh 11:00am-12:30pm, Room 72 Evans Course Control Number: 54937 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 227A - Section 1 - Theory of Recursive Functions Instructor: Theodore Slaman Lectures: MWF 12:00-1:00pm, Room 47 Evans Course Control Number: 54940 Office: 719 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228B - Section 1 - Numerical Solution of Differential Equations Instructor: James Sethian Lectures: TuTh 2:00-3:30pm, Room 9 Evans Course Control Number: 54943 Office: 725 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 235A - Section 1 - Theory of Sets Instructor: John Steel Lectures: TuTh 12:30-2:00pm, Room 81 Evans Course Control Number: 54946 Office: 717 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: We will cover the basic ideas and techniques of set theory, as well as some of the metamathematics of set theory. The plan of the course is: 1. The axioms of ZFC. Wellorders, transfinite recursion. Ordinal and cardinal arithmetic. Boolean algebras, filters and ultrafilters. 2. Infinitary combinatorics: club and stationary sets, trees, partition properties. Suslin's hypothesis, Martin's axiom. Lebesgue measure, Baire category. Cardinal numbers associated to the continuum. 3. The theory of definable sets of real numbers (descriptive set theory). Suslin representations of sets of reals. Determinacy. 4. Some metamathematics of ZFC: Godel's universe L of constructible sets. The set theory of L. 5. Large cardinals. The existence of measurable cardinals implies all Π11 games are determined, hence V is not equal to L. The model L[U]. Course Webpage: Grading: The course grade will be based on homework. Homework: I will assign a lot of homework, at varying levels of difficulty, in hopes of making the course useful to the broadest possible audience. Comments: Math 239 - Section 1 - Discrete Mathematics for the Life Sciences Instructor: Lior Pachter Lectures: TuTh 11:00am-12:30pm, Room 81 Evans Course Control Number: 54949 Office: 1081 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 241 - Section 1 - Complex Manifolds Instructor: Constantin Teleman Lectures: TuTh 2:00-3:30pm, Room 87 Evans Course Control Number: 54952 Office: 905 Evans Office Hours: TuTh 11:30am-1:00pm Prerequisites: Math 214 (Differentiable Manifolds) and 215A (Algebraic Topology) Required Text: Springer, Riemann surfaces Wells, Differential Analysis on Complex Manifolds Recommended Reading: Other books on Riemann surfaces may substitute for some of the topics in Springer (Forster; Miranda; Chapter 2 of Griffiths & Harris) Syllabus: We will cover the basic theory of Riemann surfaces (6 wks), including line bundles, differentials, Riemann-Roch, then proceed with higher-dimensional complex manifolds (9 wks): sheaves, Cech and Dolbeault cohomology, vector bundles, connections and curvature, Sobolev spaces, and the "big theorems": Hodge decomposition, Hard Lefschetz, Kodaira vanishing and perhaps Kodaira embedding. The hard analytic proofs for Riemann surfaces will be rolled into the general theory. Course Webpage: http://math.berkeley.edu/~teleman/241s08 Grading: 50% Homework, 50% Take-home final in the form of a paper on a topic to be agreed with the instructor. Homework: Will be assigned periodically. Comments: None. Math 242 - Section 1 - Symplectic Geometry Instructor: Fraydoun Rezakhanlou Lectures: MWF 11:00am-12:00pm, Room 81 Evans Course Control Number: 54955 Office: 815 Evans Office Hours: MWF 1:00-2:00pm Prerequisites: Some familiarity with differential forms and manifolds. Required Text: Hofer, H. and Zehnder, E., Symplectic invariants and Hamiltonian dynamics, Birkhauser Recommended Reading: McDuff, D. and Salamon, D., Introduction to symplectic topology, 2nd edition, Oxford Syllabus: Hamiltonian systems appear in conservative problems in mechanics as in celestial mechanics but also in the statistical mechanics governing the motion of atoms and molecules in matter. The discoveries of last century have opened up new perspectives for the old field of Hamiltonian systems and let to the formation of the new field of symplectic geometry. In the course, I will give a detailed account of some basic methods and results in symplectic geometry and its application to physics and other fields of mathematics. I will follow Hofer, H. and Zehnder, E., Symplectic invariants and Hamiltonian dynamics, Birkhauser, for most of the course. Another recommended textbook is McDuff, D. and Salamon, D., Introduction to symplectic topology, 2nd edition, Oxford. Hand written notes will be provided in the class. Here is an outline of the course: 1. Sympletic linear algebra. Quadratic Hamiltonians. 2. Symplectic manifolds, cotangent bundles. Darboux’s theorem. Contact manifolds. 3. Variational problems. Generating functions. Lagrange submaifolds. Minimax principle. 4. Sympletic capacities. Gromov’s squeezing theorem. Weinstein’s conjecture, Viterbo’s existence of periodic orbits. Gromov-Eliashberg Theorem, continuous symplectic transformations. 5. Arnold’s conjecture and Conley-Zehnder’s solution. Course Webpage: Grading: There will be some homework assignments. Homework: Comments: Math 245A - Section 1 - General Theory of Algebraic Structures Instructor: George Bergman Lectures: MWF 3:00-4:00pm, Room 81 Evans Course Control Number: 54957 Office: 865 Evans Office Hours: TuF 10:30-11:30am, W 4:15-5:15pm Prerequisites: The equivalent of one of Math H113, 114, or 250A, or consent of the instructor. Math 135 can also be helpful if you have not seen basic set theory in other contexts. Required Text: George M. Bergman, An Invitation to General Algebra and Universal Constructions (but see end of this announcement). Recommended Reading: Syllabus: The theme of Math 245A, as I teach it, is universal constructions. We begin with a well known case, the construction of free groups. We will develop this in three quite different ways, and show why they come to the same thing. We then examine a smorgasbord of other important universal constructions, noting similarities, differences, and general patterns. After that, we settle down to developing the tools needed to study the subject in a unified way: Ordered sets and the axiom of choice, closure operators, category theory, and the general concept of a variety of algebras. (We in fact treat most of these, not merely as means to this goal, but as interesting landscapes worth lingering over.) We find that the free group construction is a particular example of an adjoint functor (it is left adjoint to the underlying set functor on groups), and eventually develop a magnificent result of Peter Freyd, characterizing those functors between varieties of algebras that have left adjoints, and determine, in several cases, all such examples. Course Webpage: Homework & Grading: The text contains more interesting exercises than anyone could do; I will ask you to think briefly about each exercise, and select a few to hand in each week. Grades will be based mainly on this homework. Students wishing a reduced homework-load can enroll S/U. Comments: My philosophy is that it does not make sense to spend the classroom time using the instructor and students as an animated copying machine. Rather, the material that is typically delivered in a lecture should be put in duplicated notes which the students study, and class time should be devoted to the more human activities of discussing and clarifying the material, introducing some topics by the Socratic method, etc.. Such notes for Math 245, begun in Fall 1971 and reworked each time I have taught the course, have developed into the text we will use. There are difficulties with this way of teaching if a textbook leaves out motivation, examples, etc., that might be included in a lecture; but I have made it a point to include these in the notes. Another problem is that doing the reading before class runs counter to the habits many students have acquired. To get around this, I require each student to submit, on each class day, a question about the day's reading, if possible by e-mail at least an hour before class, so that I can prepare to address some of these questions in class. You can view the text online, and see how to purchase it, by clicking on the title above. However, I hope to get a somewhat revised version ready by January, so if you plan to take the course this Spring, don't buy your own copy before then. Math 250B - Section 1 - Multilinear Algebra Instructor: David Eisenbud Lectures: TuTh 9:30-11:00am, Room 5 Evans Course Control Number: 54961 Office: 909 Evans Office Hours: Tu 11:00am-12:00pm Prerequisites: 250A or equivalent Required Text: Eisenbud, Commutative Algebra With a View Toward Algebraic Geometry Recommended Reading: Syllabus: Basic commutative algebra, emphasizing affine and graded rings and the connections to algebraic geometry. An introduction to homological and computational techniques will be included. Special topics as time permits. Course Webpage: Grading: 60% Homework, 40% final exam Homework: Homework will be due once a week, and the grade will be based on homework and a take-home exam. Comments: Math 253 - Section 1 - Homological Algebra Instructor: Peter Teichner Lectures: TuTh 11:00am-12:30pm, Room 3 LeConte Course Control Number: 54964 Office: 703 Evans Office Hours: TBA Prerequisites: 250A and some pointset topology Required Text: Recommended Reading: Brown, Cohomology of groups Gelfan, Manin: Methods of homological algebra Syllabus: The class will start with basic constructions for chain complexes, with an eye towards group cohomology. We'll explain the relation of the first three cohomology groups with extensions of groups and we'll show how group cohomology drastically restricts the class of finite groups that can act freely on spheres. The second part of the class will introduce spectral sequences, a basic tool in all computational aspects of cohomology theory. In the last part of the class we'll study some homotopical algebra, including derived categories and their application. Course Webpage: Under construction, check at http://math.berkeley.edu/~teichner. Grading: Based on homework. Homework: Yes. Comments: Math 254B - Section 1 - Number Theory Instructor: Richard Borcherds Lectures: TuTh 3:30-5:00pm, Room 81 Evans Course Control Number: 54967 Office: 927 Evans Office Hours: TuTh 2:00-3:30pm Prerequisites: 254A Required Text: J. Neukirch, Algebraic number theory (same as for 250A) Recommended Reading: Cassels, Frohlich, Algebraic number theory Syllabus: The exact topics will depend on what gets covered in 254A, but will probably be something like class field theory, zeta-functions and L-series. Course Webpage: http://math.berkeley.edu/~reb/254B/ Grading: Homework: Not yet decided. Comments: Math 256B - Section 1 - Algebraic Geometry Instructor: Martin Olsson Lectures: MWF 2:00-3:00pm, Room 35 Evans Course Control Number: 54970 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 270 - Section 1 - Hot Topics Course in Mathematics Instructor: Peter Teichner Lectures: Tu 3:30-5:00pm, Room 35 Evans Course Control Number: 54972 Office: 703 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Real-p-adic Analysis Instructor: Robert Coleman Lectures: MWF 1:00-2:00pm, Room 4 Evans Course Control Number: 54973 Office: 901 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: In 1959, Tate showed Grothendieck some ad hoc calculations that he had worked out with p-adic theta functions in order to uniformize certain p-adic elliptic curves by a multiplicative group, similarly to the complex-analytic case. Tate wondered if his computations could have deeper meaning within a theory of global p-adic analytic spaces, but Grothendieck was doubtful. In fact, in an August 18, 1959 letter to Serre, Grothendieck expressed serious pessimism that such a global theory could possibly exist: "Tate has written to me about his elliptic curves stuff, and has asked me if I had any ideas for a global definition of analytic varieties over complete valuation fields. I must admit that I have absolutely not understood why his results might suggest the existence of such a definition, and I remain skeptical. Nor do I have the impression of having understood his theorem at all; it does nothing more than exhibit, via brute formulas, a certain isomorphism of analytic groups; one could conceive that other equally explicit formulas might give another one which would be no worse than his (until proof to the contrary!)" In this course, we will begin to see how wrong Grothendieck was. Course Webpage: Grading: Homework: Comments: Math 274 - Section 2 - Topics in Algebra and Representation Theory Instructor: Michel Broue Lectures: TuTh 3:30-5:00pm, Room 72 Evans Course Control Number: 54975 Office: 895 Evans Office Hours: TBA Prerequisites: General algebra, rudiments of group theory Required Text: None Recommended Reading: Serre, Linear representations of finite groups Jacobson, Basic Algebra Syllabus: Complex reflection groups (finite subgroups of GLn(C) generated by pseudo-reflection) play a key role in group theory. A key stone of invariant theory, they are skeletons of algebraic groups over finite field, and they give rise to associated Braid groups and Hecke algebras which are essential in understanding representations.We shall examine all aspects of complex reflection groups, from definition, classification, characterisation, to strong properties of the associated Braid groups. Course Webpage: Grading: Homework: Comments: Math 277 - Section 1 - Topics in Differential Geometry Instructor: Michael Hutchings Lectures: TuTh 8:00-9:30am, Room 179 Stanley Course Control Number: 54979 Office: 923 Evans Office Hours: TBA Prerequisites: Basic algebraic topology and differential topology are required; some differential geometry, symplectic geometry, and functional analysis would be helpful. Required Text: None. Recommended Reading: Readings will be suggested as the course progresses. Syllabus: The topic of this course is Floer theory. The first part of the course will cover Morse homology, which is the prototype for all Floer theories. Morse homology recovers the homology of a smooth manifold from dynamical information, namely the critical points of a smooth function and the gradient flow lines between them. We will also discuss various extensions of Morse homology which have interesting analogues in Floer theory. The second part of the course will introduce pseudoholomorphic curves and Floer homology of symplectomorphisms. The latter is an infinite dimensional generalization of Morse theory which leads to a proof of the Arnold conjecture giving lower bounds on the number of fixed points of generic Hamiltonian symplectomorphisms. The third part of the course will discuss versions of contact homology which give invariants of contact three-manifolds. Some of these are related to the Seiberg-Witten and Ozsvath-Szabo Floer homologies. Course Webpage: Will be linked from http://math.berkeley.edu/~hutching Grading: Homework: Comments: Math 277 - Section 2 - Topics in Differential Geometry Instructor: Elizabeth Gasparim Lectures: MWF 1:00-2:00pm, Room 39 Evans Course Control Number: 54981 Office: TBA Office Hours: MW 4:00-5:00pm Prerequisites: 214, 215 Required Text: Milnor and Stasheff, Characteristic Classes Recommended Reading: Griffiths and Harris, Chapter 0 section 5, Chapter 1 section 1, Chapter 3, section 3. Course notes. Syllabus: The first part of the course will be a topological approach to the basic theory of vector bundles and characteristic classes presented as in Milnor-Stasheff, the second part will be a geometric approach to Chern classes via connections and polynomials on the curvature as in Griffiths-Harris, and the third part will be about local characteristic classes for sheaves on singular varieties (I will distribute notes). Course Webpage: UCB Math 277 Course webpage, University of Edinburgh webpage. Grading: 50% homework and 50% take home final Homework: Homework will be assigned periodically. Comments: Math 279 - Section 1 - Topics in Partial Differential Equations Instructor: Daniel Tataru Lectures: TuTh 12:30-2:00pm, Room 87 Evans Course Control Number: 54982 Office: 841 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 300 - Section 1 - Teaching Workshop Instructor: The Staff Lectures: TBA Course Control Number: 55594 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: |
