Spring 2011
Math 1A - Section 1 - Calculus Instructor: John Steel Lectures: MWF 12:00-1:00pm, Room 10 Evans Course Control Number: 53603 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Mina Aganagic Lectures: TuTh 9:30-11:00am, Room 2050 Valley LSB Course Control Number: 53642 Office: Office Hours: Prerequisites: Math 1A, or its equivalent. Required Text: Stewart, Single Variable Essential Calculus, Cengage, (Custom Berkeley edition 1A/1B). Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Calculus Instructor: Marina Ratner Lectures: MWF 9:00-10:00am, Room 100 Lewis Course Control Number: 53696 Office: Office Hours: Prerequisites: Math 1A Required Text: James Stewart, Single variable calculus: Early Transcendentals for University of California, (special Berkeley edition), ISBN 978-1-4240-5500-5 or 1-4240-5500-8, Cengage Learning. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 3 - Calculus Instructor: Richard Borcherds Lectures: TuTh 2:00-3:00pm, Room 100 Lewis Course Control Number: 53744 Office: 927 Evans Office Hours: TuTh 12:30-2:00 Prerequisites: Math 1A Required Text: James Stewart, Single variable calculus: Early Transcendentals for University of California, (special Berkeley edition), ISBN 978-1-4240-5500-5 or 1-4240-5500-8, Cengage Learning. Recommended Reading: Syllabus: We will cover the material in the text that is not in 1A, in other words chapters 7, 8, 9, 11, 17. 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/~ref/1B Grading: Roughly 25% quizzes, 25% midterms, 25% homework, 25% final. Homework: Homework is assigned on the course home page for every class, and due once a week. Comments: Math 16A - Section 1 - Analytical Geometry and Calculus Instructor: Keith Conrad Lectures: TuTh 11:00-12:30pm, Room 2050 Valley LSB Course Control Number: 53783 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and Calculus Instructor: Donald Sarason Lectures: MWF 11:00am-12:00pm, Room 2050 Valley LSB Course Control Number: 53837 Office: 779 Evans Hall, email: sarason [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 16A or the equivalent Required Text: Goldstein, Lay, Schneider, Asmar, Calculus & Its Applications, Custom Edition for Math 16B, Volume 2, University of California, Berkeley. Recommended Reading: Syllabus: Functions of several variables, trigonometric func- tions, techniques of integration, differential equations, Taylor polynomials and infinite series, probability and calculus (Chapters 7-12 of the text- book). Course Webpage: TBA Grading: The course grade will be based on two midterm exams, the final exam, and section performance. Details will be provided at the beginning of the semester. The midterm exams will be held during the lecture period and are tentatively scheduled for Wednesday, March 2 and Wednesday, April 13. The final exam is scheduled for Monday, May 10, starting at 7 p.m. (Exam Group 8). Do not enroll in the course if you have a conflict. There will be no make-up exams. Homework: Homework will be assigned weekly, except for week 1 and the weeks of midterm exams. Comments: The lectures will be fairly slow paced and will strive to get across the main ideas, often by means of examples. Students should expect to learn a lot on their own by studying the textbook and working homework exercises, and to solidify their understanding by attending discussion sections. The discussion sections meet on Thursdays. Special arrangements for exams will be made only for students entitled to them as authorized by the Disabled Students Program. Such students should obtain authorization as soon as possible. Math 16B - Section 2 - Analytical Geometry and Calculus Instructor: Zachary Judson Lectures: TuTh 3:30pm-5:00pm, Room 1 Pimental Course Control Number: 53888 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman Seminar Instructor: Jenny Harrison Lectures: F 3:00pm-4:00pm, Room 939 Evans Course Control Number: 53936 Office: Office Hours: 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 60 Evans Course Control Number: 53942 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Edward Frenkel Lectures: MWF 10:00am-11:00am, Room 2050 Valley LSB Course Control Number: 53981 Office: 819 Evans Office Hours: MWF 11-12 Prerequisites: Math 1A, 1B Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole. Recommended Reading: Syllabus: Course Webpage: Grading: 25% quizzes and HW, 20% each midterm, 35% final. Homework: Homework for the entire course will be assigned at the beginning of the semester, and weekly homework will be due at the beginning of each week. Comments: Students have to make sure that they have no scheduling conflicts with the final exam. Missing final exam means automatic Fail grade for the entire course. Math 53 - Section 2 - Multivariable Calculus Instructor: Zvezdelina Stankova Lectures: TuTh 3:30pm-5:00pm, Room 100 Lewis Course Control Number: 54020 Office: 713 Evans Office Hours: TuTh 2:10-3:30pm Prerequisites: Math 1B, Calculus II Required Text: Stewart, Multivariable Calculus (Custom Edition for UCB) ISBN: 978-1-424-05499-2. Recommended Reading: Syllabus: 1. Vectors, dot-product, cross-product 2. Geometry of linear and quadratic functions 3. Quadratic curves and surfaces 4. Polar, cylindrical and spherical coordinates 5. Vector-functions and parametric curves 6. Kepler's laws 7. Functions of several variables 8. Differentiability 9. Clairaut's Theorem 10. The chain rule 11. Gradient 12. Extrema, classification of critical points 13. Constraint extrema 14. Finding maximum and minimum values 15. Double integrals 16. Fubini's Theorem 17. Triple integrals 18. Change of variables 19. Applications of integration 20. Vector fields 21. Newton-Leibnitz's Theorem 22. Green's Theorem 23. Curl and divergence 24. Parametric surfaces and surface integrals 25. Stokes' and Gauss' Theorems and their applications Course Webpage: http://math.berkeley.edu/~stankova Grading: 15% quizzes, 25% each midterm, 35% final Homework: Homework will be assigned on the web every class, and due once a week. Comments: Final Exam is on Friday, May 13, 2011, 7-10pm. There will be two in-class midterms, dates TBA. Math H53 - Section 1 - Multivariable Calculus Instructor: Benjamin Stamm Lectures: MWF 10:00am-11:00am, Room 151 Barrows Course Control Number: 54059 Office: Office Hours: Prerequisites: Math 1B Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 1 - Linear Algebra and Differential Equations Instructor: Constantin Teleman Lectures: TuTh 12:30-2:00pm, Room 2050 Valley LSB Course Control Number: 54065 Office: Office Hours: Prerequisites: Math 1B Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 2 - Linear Algebra and Differential Equations Instructor: Ming Gu Lectures: MWF 3:00-4:00pm, Room 155 Dwinel Course Control Number: 54104 Office: Office Hours: Prerequisites: Math 1B Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: Paul Vojta Lectures: MWF 2:00-3:00pm, Room 10 Evans Course Control Number: 54143 Office: 883 Evans Office Hours:TBD Prerequisites: Math 1A-1B, or consent of instructor. Required Text: Kenneth H. Rosen, Discrete Mathematics and its Applications, 6th edition, McGraw-Hill. Recommended Reading: None Syllabus: A paper copy will be distributed on the first day of classes; see also the course web page. Course Webpage: http://math.berkeley.edu/~vojta/55.html Grading: Grading will be based on a first midterm (10%), a second midterm (20%), the final exam (45%), and a component coming from the discussion sections (25%). This last component is left to the discretion of the section leader, but it is likely to be determined primarily by homework assignments and biweekly quizzes. Homework: Homework will consist of weekly assignments, to be given on the syllabus. Comments: Math 1A-1B and (if you've had them) 53 and 54 are about smooth functions of one or more real variables; this course is about some very different topics. The main reason 1A-1B are prerequisites is to be sure students have enough familiarity with mathematical thinking; it also means that I will be free to occasionally make connections with topics from that sequence. Section 6.4 is related to a topic in Math 1B (power series), so students who have had 1B may find that section easier than those who have not. Nevertheless, the author's aim was to write the book so as not to assume calculus. If you haven't had calculus and want to take this course, come see me and we will discuss whether you are ready. Math C103 - Section 1 - Introduction to Mathematical Economics Instructor: Lectures: TuTh 9:30-11:00pm, Room 9 Evans Course Control Number: 54230 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Atilla Yilmaz Lectures: TuTh 8:00-9:30pm, Room 2 Evans Course Control Number: 54233 Office: 796 EVANS Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross. Recommended Reading: Syllabus: Real numbers; sequences; continuity; series; differentiation; integration (if time permits). Course Webpage: http://math.berkeley.edu/~atilla/ Grading: Homework 1/8, first midterm 1/8, second midterm 1/4, final 1/2. Homework: Weekly problem sets. Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Vaughan Jones Lectures: TuTh 12:30-2:00pm, Room 2 Evans Course Control Number: 54236 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Jonathan Dahl Lectures: MWF 8:00-9:00am, Room 2 Evans Course Control Number: 54239 Office: Office Hours: Prerequisites: Math 53 and 54. Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Alexander Givental Lectures: TuTh 3:30-5:00pm, Room 85 Evans Course Control Number: 54242 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Christopher Rycroft Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54245 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 105 - Section 1 - Second Course in Analysis Instructor: Michael Klass Lectures: MWF 1:00-2:00pm, Room 332 Evans Course Control Number: 54248 Office: Office Hours: Prerequisites: Math 104 Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Alberto Grunbaum Lectures: TuTh 8:00-9:30am, Room 145 Dwinel Course Control Number: 54251 Office: 903 Evans Office Hours: Tu-Th 9:30-11:00am Prerequisites: Math 54, or a course with equivalent linear algebra content. (Math 74 also recommended for students not familiar with proofs.) Required Text: S. H. Friedberg, A. J. Insel & L. E. Spence, Linear Algebra, 4th edition. Recommended Reading: Syllabus: In this class we take a second look at linear algebra, something you have seen in Math 54. The basic issues are the same: solving linear equations, doing least square problems, finding eigenvalues and eigenvectors of a matrix, thinking of a matrix as a linear map between vector spaces, writing matrices in a more revealing form by choosing a basis appropriately, etc. We will revisit all these items form a more general viewpoint than that of Math 54, and proofs will play an important part in this class. There are TWO reasons for looking anew at these basic tasks: with the advent of the computer age there has been a revival in the search for ways of performing these basic tasks with faster and more accurate algorithms. Think of applications like signal processing, medical imaging, Pixar animation, etc. The second reason is equally important: the ability to do abstract reasoning gives a beautiful and powerful tool not only to organize the material you already know but also to make new discoveries. If you are going to be more than just a user of "black boxes" of software (which I also love to use) you have to develop your own mental tools to judge the merit and quality of these packages. Course Webpage: Grading: The grade will be based on your homework ( 25% ), two midterms (20% and 20%) and a final ( 35%). Homework: There will be a weekly homework assignment, with problems from the book. Comments: Practical advice -- start doing the homework as soon as possible. Learn to walk around with these problems in your head, sometimes you will wake up with some new idea on how to solve them. Try to put together a group of two or three of you that meets regularly to discuss the material in the class; try to explain the material to each other: there is a chance that you will discover that you do not really understand it yourself. This is the first step in learning and you should repeat this till you all understand what is going on. Ask questions, propose counterexamples, challenge each other... Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: Mariusz Wodzicki Lectures: MWF 12:00-1:00pm, Room 2 Evans Course Control Number: 54272 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Alexander Paulin Lectures: MWF 3:00-4:00pm, Room 2 Evans Course Control Number: 54275 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Alice Medvedev Lectures: TuTh 9:30-11:00am, Room 4 Evans Course Control Number: 54278 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: The Staff Lectures: TuTh 3:30-5:00pm, Room 2 Evans Course Control Number: 54281 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H113 - Section 1 - Honors Introduction to Abstract Algebra Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54284 Office: 901 Evans Office Hours: M 3-4pm F 2:00-3:00pm Prerequisites: Required Text:Fraleigh, Abstract Algebra. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Homework will be assigned very class, and due once a week. Comments: One fundamental aspect of the universe which enables humans to try to understand it is symmetry. The set of symmetries of an object like a crystal or a rubic's cube is one of its most important features. The theory of groups is an abstract mathematical approach to analyzing such a set. This is one of the topics we will begin to investigate in this course. Math 114 - Section 1 - Second Course in Abstract Algebra Instructor: Christian Zickert Lectures: MWF 10:00-11:00am, Room 2 Evans Course Control Number: 54287 Office: Office Hours: Prerequisites: Math 113 Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 118 - Section 1 - Fourier Analysis, Wavelets, and Signal Processing Instructor: John Wilkening Lectures: TuTh 2:00-3:30pm, Room 2 Evans Course Control Number: 54290 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121A - Section 1 - Mathematical Tools for the Physical Sciences Instructor: Constantin Teleman Lectures: TuTh 9:30-11:00am, Room 6 Evans Course Control Number: 54293 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121B - Section 1 - Mathematical Tools for the Physical Sciences Instructor: John Neu Lectures: TuTh 3:30-5:00pm, Room 6 Evans Course Control Number: 54296 Office: Office Hours: Prerequisites: Required Text: M. Boas, Mathematical Methods in the Physical Sciences Recommended Reading: Syllabus: 1) Basic PDE (starting with chapter 10 in Boas, incorporating some special functions from chapter 12. Further handouts and problem sets for the spirited and brave.) 2) Calculus of variations (starting with chapter 9 in Boas, handouts by professor on variational principles and conservation laws for PDE.) 3) Basic probability (chapter 15: counting, basic distributions, binomial, poisson. Sum of random variables and diffusion. Einstein and Avagadro's number.) Course Webpage: Grading: Homework = 20% of total Midterm I (5th week) = 20% of total Midterm II (10th week) = 20% of total Final = 40% of total Homework: Weekly problem sets Comments: Learn to use the Dark Side of the Math. Math 127 - Section 1 - Mathematical/Computational Methods in Molecular Bio. Instructor: CLOSED Lectures: MWF 11:00am-12:00pm, Room 2 Evans Course Control Number: 54299 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: John Strain Lectures: MWF 10:00-11:00am, Room 101 Barker Course Control Number: 54302 Office: 1099 Evans Office Hours: TBA Prerequisites: Math 53 and 54 or equivalent knowledge of calculus and linear algebra. Required Text: J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd edition, Springer-Verlag New York, 2002. ISBN-10 038795452X, ISBN-13 978-0387954523. Recommended Reading: Syllabus: The course will cover basic theory and practical methods for solving the fundamental problems of computational science.
Grading: 40% weekly homework, 30% midterm, 30% final. Exams:
Math 128B - Section 1 - Numerical Analysis Instructor: John Strain Lectures: MWF 1:00-2:00pm, Room 9 Evans Course Control Number: 54317 Office: 1099 Evans Office Hours: TBA Prerequisites: Math 110 and 128a or equivalent knowledge of numerical analysis and linear algebra. Required Text: J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd edition, Springer-Verlag New York, 2002. ISBN-10 038795452X, ISBN-13 978-0387954523. Recommended Reading: Syllabus: Math 128B is a second course in numerical analysis, the art of constructing and analyzing practical computational methods for approximately solving the vast majority of scientific problems which cannot be solved exactly. The course will introduce some standard numerical methods for three major problem areas and tell when, how and why they can be expected to work. Analytically, we'll focus on the stability and accuracy properties of famous algorithms. Computationally, we will study and apply well-known packages such as Matlab, LAPACK and so forth rather than writing our own codes. The first half of the course will be devoted to the numerical solution of linear and nonlinear systems of equations.
Course Webpage: http://math.berkeley.edu/~strain/128b.S11/index.html Grading: 40% weekly homework, 30% midterm, 30% final. Exams:
Math 130 - Section 1 - The Classical Geometries Instructor: Vera Serganova Lectures: TuTh 3:30-5:00pm, Room 87 Evans Course Control Number: 54323 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory Sets Instructor: Marina Ratner Lectures: MWF 11:00-12:00pm, Room 4 Evans Course Control Number: 54326 Office: 827 Evans Office Hours: TBA Prerequisites: None, but an ability to understand proofs. Required Text: Enderton, Elements of Set Theory Recommended Reading: Syllabus: Zermelo-Frankel axiom system, relations and functions, the theory of natural numbers, cardinal numbers and the Axiom of Choice, well orderings and ordinals, transfinite induction, alephs. Course Webpage: Grading: The grade will be based 10% on the homework, 20% on quizzes, 40% on a midterm, and 40% on the final. Homework: Comments: Math 136 - Section 1 - Incompleteness and Undecidability Instructor: John Steel Lectures: TuTh 12:30-2:00pm, Room 6 Evans Course Control Number: 54329 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 140 - Section 1 - Metric Differential Geometry Instructor: Marc Rieffel Lectures: MWF 12:00-1:00pm, Room 6 Evans Course Control Number: 54332 Office: 811 Evans Office Hours: TBA Prerequisites: Math 104 or equivalent. Required Text: T. Banchoff and S. Lovett: Differential Geometry of Curves and Surfaces, AK Peters Ltd, 2010. The authors have provided many fine computer graphics applets on-line, that are freely available to the public even without having the text. I encourage prospective students (and others) to try these out even before the course starts. They can be found at graphics applets Recommended Reading: Syllabus: This course studies the metric aspects of curves and surfaces in space. Although we will not have time to study the applications, there are many of them, ranging for example from use in realistic computer-generated animation, to designing airplane wings and many other things, through much of classical mechanics, all the way to the theory of general relativity. In preparation for the course students are strongly urged to review the process of diagonalizing 2x2 matrices and quadratic forms in two variables, as well as the inverse and implicit function theorems. In my lectures I will try to give well-motivated careful presentations of the material. I encourage class discussion. Course Webpage: Grading: The final examination will take place on Wednesday May 11, 2011, 3-6 PM. It will count for 50% of the course grade. There will be no early or make-up final examination. There will be two midterm examinations, which will each count for 20% of the course grade. Make-up midterm exams will not be given; instead, if you tell me ahead of time that you must miss a midterm exam, then the final exam and the other midterm exam will count more to make up for it. If you miss a midterm exam but do not tell me ahead of time, then you will need to bring me a doctor's note or equivalent in order to have the final exam and the other midterm exam count more to make up for it. If you miss both midterm exams the circumstances will need to be truly extraordinary to avoid a score of 0 on at least one of them. Homework: Homework will be assigned at nearly every class meeting, and be due the following class meeting. Students are strongly encouraged to discuss the homework and the course content with each other, but each student should write up their own solutions, reflecting their own understanding, to turn in. Comments: Students who need special accommodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance of each examination what specific accommodation they need, so that I will have enough time to arrange it. The above procedures are subject to change. This page was last updated on 11/23/2010 Math 141 - Section 1 - Elementary Differential Topology Instructor: Christian Zickert Lectures: MWF 1:00-2:00pm, Room 81 Evans Course Control Number: 54335 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 151 - Section 1 - Mathematics of the Secondary School Curriculum I Instructor: Ole Hald Lectures: MWF 4:00-5:00pm, Room 71 Evans Course Control Number: 54338 Office: 875 Evans Hall Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 153 - Section 1 - Mathematics of the Secondary School Curriculum III Instructor: Emiliano Gomez Lectures: MWF 3:00am-4:00pm, Room 6 Evans Course Control Number: 54344 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 160 - Section 1 - History of Mathematics Instructor: Ole Hald Lectures: MWF 1:00-2:00pm, Room 2 Evans Course Control Number: 54350 Office: 875 Evans Hall Office Hours: Prerequisites: Math 104 Required Text: C.H. Edwards, Jr. The Historical Development of the Calculus, Springer Verlag. Recommended Reading: Syllabus: A serious study of the history of calculus would require knowledge of Greek, Latin, Arabic, Italian, French, English, German and Russian. The book chosen for this course drags the reader through the original arguments, but uses English and modern notation. The work will consist of filling in the gaps and solving the exercises. The grade will be based on homework, essays, and bi-weekly oral presentations. Course Webpage: Grading: Homework: Comments: Math 172 - Section 1 - Combinatorics Instructor: Christopher Manon Lectures: MWF 3:00-4:00pm, Room 4 Evans Course Control Number: 54353 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 1 - Introduction to Complex Analysis Instructor: Alexander Givental Lectures: TuTh 12:30-2:00pm, Room 4 Evans Course Control Number: 54356 Office: Office Hours: Prerequisites: Math 104 Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 2 - Introduction to Complex Analysis Instructor: Michael VanValkenburg Lectures: MWF 4:00-5:00pm, Room 6 Evans Course Control Number: 54359 Office: Office Hours: Prerequisites: Math 104 Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 3 - Introduction to Complex Analysis Instructor: Atilla Yilmaz Lectures: TuTh 9:30-11:00am, Room 2 Evans Course Control Number: 54362 Office: 796 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Complex Variables and Applications, by James W. Brown and Ruel V. Churchill, eighth edition. Recommended Reading: Syllabus: Complex numbers; analytic functions; elementary functions; integrals; series; residues and poles; applications of residues. Course Webpage: http://math.berkeley.edu/~atilla/ Grading: Homework 1/8, first midterm 1/8, second midterm 1/4, final 1/2. Homework: Weekly problem sets. Comments: Math H185 - Section 1 - Honors Introduction to Complex Analysis Instructor: Mariusz Wodzicki Lectures: MWF 4:00-5:00pm, Room 81 Evans Course Control Number: 54365 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 195 - Section 1 - Advanced Linear Algebra Instructor: Jenny Harrison Lectures: MWF 4:00-5:00pm, Room 4 Evans Course Control Number: 54367 Office: 829 Evans Office Hours: MWF 4-5 Prerequisites: Math H110 or Math 110 (with permission from instructor). Required Text: Advanced Linear Algebra, by Steven Roman Recommended Reading: Structures of Linear Algebra, by Jenny Harrison Syllabus: This is an exciting new course on Advanced Linear Algebra for those who enjoy learning about algebraic structures of mathematics which arise in analysis, geometry, topology, and mathematical physics. We shall work through Steven Roman's "Advanced Linear Algebra", assuming the material taught in Math H110 during the fall semester. Those who have only studied Math 110 can catch up using my class notes, available now in pdf, and former students from H110 can certainly help you out. We will also duplicate necessary material taught in H110 last semester in lectures. We will not leave you in the dust. This is a great new book with excellent reviews. Roman's writing is concise, clear and friendly. The material is not usually available to undergraduates, yet it is vital to understanding what is going on in math and science from the viewpoint of mathematics. If you know this material, you will find droves of wikipedia articles now at your disposal, including applications to physics, engineering, computer science, and chemistry. The table of contents can easily be found on amazon.com. We surely can't cover the entire book, but will select what interests us the most. I am of a mind to start with Part II or Roman since much of Part I is available in other undergraduate courses and is not required for Part II. Topics from Part II of Roman: 1) Metric vector spaces, the theory of bilinear forms, quadratic forms, hyperbolic spaces, nonsingular completions of a subspace, Witt's Theorems, symplectic geometry, orthogonal geometries, the orthogonal group, 2) Metric spaces and topology: Open and closed sets, convergence in a metric space, dense subsets, continuity, completeness 3) Hilbert spaces: Hilbert bases, Fourier expansions, Hilbert dimension, Riesz Representation Theorem 4) Free spaces, tensor product, exterior algebra, symmetric algebra, determinant 5) Convexity and separation: convex and compact sets, convex hulls, hyperplanes, separation 6) Operator factorization: The QR decomposition, singular values, the Moore-Penrose generalized inverse, leas squares approximation. Topics from Part I of Roman (in case we have time): 1) Modules: Torsion, annihilators, free modules, quotient modules, Noetherian modules, Hilbert Basis Theorem, primary cyclic decomposition of a primary module 2) Structure of a linear operator: brief review of basics, orders and minimal polynomial, cyclic submodules and subspaces, The Rational Canonical Form, 3) Eigenvalues and eigenvectors: Jordan Canonical form (review), Schur's Lemma, the algebra of projections, resolutions of the identity, spectral resolutions 4) Inner product spaces: normal operators, spectral theorem, positive operators, polar decomposition of an operator (we covered this in H110, though.) Course Webpage: Grading: Grades will be based on homework, class participation, student lectures. Homework: Moderate amount of basic exercises to help learn the material. Comments: Math 202B - Section 1 - Introduction to Topology and Analysis Instructor: Donald Sarason Lectures: MWF 9:00-10:00am, Room 70 Evans Course Control Number: 54485 Office: 779 Evans, e-mail: sarason [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Math 202A or the equivalent. Required Text: Recommended Reading: Syllabus: About half the course will be on measure and integration, about half on basic functional analysis. Those two topics will be interwoven to an extent. 201A in F 2010 is covering Chapters 1-3 in Folland. Students who want to take 202B but are not taking 202A should study those chapters. Course Webpage: Grading: The course grade will be based on weekly homework assignments, which will be carefully graded. No exams. Homework: See above. Comments: Except for routine details and an occasional handout, the lectures will be self-contained. No textbook will be followed in detail. Helpful references include Folland, "Real Analysis," Royden, "Real Analysis," and Rudin, "Functional Analysis." Math 203 - Section 1 - Singular Perturbation Methods in Applied ODE and PDE Instructor: L. Craig Evans Lectures: TuTh 3:30-5:00pm, Room 54 Barrows Course Control Number: 54488 Office: 1033 Evans, e-mail: evans [at] math [dot] berkeley [dot] edu Office Hours: TBA Prerequisites: Good knowledge of undergraduate analysis and differential equations. Required Text: None, although I may be able to provide some notes from a new book written by John Neu. Recommended Reading: Syllabus:This will be an applied differential equations course, covering various sort-of rigorous and actually rigorous methods for nonlinear ODE and PDE in interesting asymptotic limits. Main topics: 1. Introduction 2. Multiple scales 3. Averaging 4. Other methods: matched expansions, WKB approximations, Laplace's method 5. Hamiltonian methods, KAM Theorem 6. Moser-Nash Implicit Function Theorem (if there is time) Course Webpage: TBA Grading: TBA Homework: TBA Comments: Math 208 - Section 1 - C*-Algebras Instructor: Marc Rieffel Lectures: MWF 2:00-3:00pm, Room 31 Evans Course Control Number: 54491 Office: 811 Evans, e-mail: rieffel [at] math [dot] berkeley [dot] edu 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: "C*-algebras by Example", K. R. Davidson, 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: Michael Hutchings Lectures: TuTh 9:30-11:00am, Room 35 Evans Course Control Number: 54494 Office: 923 Evans Office Hours: W 2:00-4:00pm Prerequisites: Math 215A or equivalent, (some of this material will be briefly reviewed as needed). Required Text: Milnor and Stasheff, Characteristic Classes Recommended Reading: Additional references and notes to be provided. Syllabus: Homotopy theory, characteristic classes, and spectral sequences. If time permits, additional topics such as Morse theory. Course Webpage: To be linked from math.berkeley.edu/~hutching Grading: Each student will be expected to write a short expository term paper on a topic in algebraic topology that they are interested in (I can help you select a topic), to "referee" another student's paper, and to revise their own paper based on the referee's comments. Homework: Comments: Math C218B - Section 1 - Probability Theory Instructor: Jim Pitman Lectures: TuTh 9:30-11:00am, Room 330 Evans Course Control Number: 54497 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 220 - Section 1 - Stochastic Methods of Applied Mathematics Instructor: Alexandre Chorin Lectures: MWF 11:00-12:00pm, Room 85 Evans Course Control Number: 54500 Office: 911 Evans Office Hours: MWF 12:00-1:00pm Prerequisites: Some familiarity with differential equations and their application, or permission of the instructor. Required Text: Chorin and Hald, Stochastic tools in mathematics and science (will be made available to the class without charge). Recommended Reading: Will be distributed to the class. Syllabus: Introduction to probability and stochastic processes, Brownian motion, the Fokker-Planck and Langevin equations, Feynman diagrams, equilibrium and non-equilibrium statistical mechanics, Monte Carlo methods, selected applications. Course Webpage: math.berkeley.edu/~chorin/math220.html Grading: Based on homework and projects Homework: Homework will be assigned on the web every week. Comments: My lecturing style is informal and I enjoy class discussion. Math 222B - Section 1 - Partial Differential Equations Instructor: The Staff Lectures: MWF 1:00-2:00pm, Room 35 Evans Course Control Number: 54503 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C223B - Section 1 - Stochastic Processes Instructor: Nathan Ross Lectures: TuTh 11:00-12:30pm, Room 332 Evans Course Control Number: 54506 Office: Office Hours: Prerequisites: Required Reading: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 225B - Section 1 - Metamathematics Instructor: Leo Harrington Lectures: MWF 10:00-11:00am, Room 81 Evans Course Control Number: 54509 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228B - Section 1 - Numerical Solution of Differential Equations Instructor: Jon Wilkening Lectures: TuTh 9:30-11:00am, Room 3111 Etcheverry Course Control Number: 54512 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 229 - Section 1 - Theory of Models Instructor: Leo Harrington Lectures: MWF 12:00-1:00pm, Room 3 Evans Course Control Number: 54515 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 240 - Section 1 - Riemannian Geometry Instructor: John Lott Lectures: MWF 3:00pm-4:00pm, Room 81 Evans Course Control Number: 54521 Office: 897 Evans Office Hours: TBA Prerequisites: 214 or equivalent. Required Text: John Lee, Riemannian Manifolds, Springer Graduate Texts in Mathematics. Recommended Reading: Burago-Burago-Ivanov, A Course in Metric Geometry, AMS. Syllabus: The first 2/3 of the semester will be devoted to basic topics of Riemannian geometry, such as Riemannian metrics, connections, geodesics, Riemannian curvature and relations to topology. The last few weeks will be an introduction to metric geometry. Course Webpage: http://math.berkeley.edu/~lott/teaching.html Grading: Based on homemwork. Homework: Weekly homework assignments will be given. Comments: Math 241 - Section 1 - Complex Manifolds Instructor: Denis Auroux Lectures: TuTh 11:00am-12:30pm, Room 81 Evans Course Control Number: 54524 Office: 817 Evans Office Hours: Prerequisites: Math 214 (Differentiable Manifolds) and 215A (Algebraic Topology) Required Text: Huybrechts, Complex geometry: an introduction, Springer Forster, Lectures on Riemann surfaces, Springer Recommended Reading: Syllabus: The course will begin with Riemann surfaces, then proceed with higher-dimensional complex manifolds. The topics include: differential forms, Cech and Dolbeault cohomology, divisors and line bundles, Riemann-Roch, vector bundles, connections and curvature, Kahler-Hodge theory, Lefschetz theorems, Kodaira theorems. Course Webpage: http://math.berkeley.edu/~auroux/241s11 Grading: Homework: Will be assigned periodically. Comments: Math 249 - Section 1 - Algebraic Combinatorics Instructor: Mark Haiman Lectures: MWF 3:00-4:00pm, Room 5 Evans Course Control Number: 54527 Office: 855 Evans Office Hours: Prerequisites: Algebra background equivalent to 250A. Required Text: Richard P. Stanley, Enumerative Combinatorics, Vols. I & II. Cambridge Univ. Press 1999, 2000. Recommended Reading: See course web page. Syllabus: See course web page. Course Webpage: math.berkeley.edu/~mhaiman/math249-spring11 Grading: Based on homework. Homework: Problems assigned for each lecture. Comments: Math 250B - Section 1 - Multilinear Algebra and Further Topics Instructor: David Eisenbud Lectures: TuTh 9:30-11:00am, Room 5 Evans Course Control Number: 54530 Office: Evans 909 Office Hours: Wednesday, 11-12 or by arrangement Prerequisites: 250A or Consent of Instructor Required Text: Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Springer Verlag 1995. Recommended Reading: A list of classic research papers will be distributed. Syllabus: Topics in (mostly commutative) ring theory and homological algebra. Primary decomposition, flatness, dimension theory, Groebner bases. Course Webpage: Grading: Homework assignments 70%, Presentation of a paper near the end of the term 30%. Homework: Due once a week. Comments: Commutative Algebra is a beautiful and active field that forms the basis of much of modern algebraic geometry and enters into many applications. Math 252 - Section 1 - Representation Theory Instructor: Vera Serganova Lectures: TuTh 12:30-2:00pm, Room 35 Evans Course Control Number: 54533 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 253 - Section 1 - Homological Algebra Instructor: Martin Olsson Lectures: MWF 1:00-2:00pm, Room 51 Evans Course Control Number: 54536 Office: 879 Evans Office Hours: TBA Prerequisites: Math 250 A and B or equivalent. Required Text: none Recommended Reading: Gelfand-Manin, Methods of Homological Algebra. MacLane, Homological Algebra. Weibel, Introduction to Homological Algebra. Syllabus: I intend to start the class by developing the basic theory of derived categories and derived functors. Then I will spend some time developing several basic examples in detail. This will necessarily involve some discussion of spectral sequences which will be used for computations. After that I intend to discuss more deeply the notion of t-structure, and more advanced topics decided upon in consultation with the students. Course Webpage: Grading: Students registered for the class should complete the homework and a final project to be determined in consultation with the instructor. Homework: Periodic homework will be assigned. Comments: Math 254B - Section 1 - Number Theory Instructor: Alexander Paulin Lectures: MWF 10:00-11:00am, Room 75 Evans Course Control Number: 54539 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 256B - Section 1 - Algebraic Geometry Instructor: Paul Vojta Lectures: MWF 11:00am-12:00pm, Room 31 Evans Course Control Number: 54542 Office: 883 Evans Office Hours: TBA Prerequisites: 256A Required Text: Hartshorne, Algebraic Geometry, Springer. Recommended Reading: Syllabus: The course will pick up where 256A left off and finish Chapter II. After that, we will proceed on to do much of Chapter III (Cohomology), plus possibly a few sections of Chapter IV (Curves). Course Webpage: http://math.berkeley.edu/~vojta/256b.html Grading: Grades will be based on homework assignments. There will be no final exam, but the last problem set will be due about a week after the last day of classes. Homework: Weekly or biweekly, assigned in class. Comments: I tend to follow the book fairly closely, but try to give interesting examples. Math 261B - Section 1 - Lie Groups and Lie Algebras Instructor: Robert Bryant Lectures: TuTh 5:00-6:30pm, Room 101 Wheeler Course Control Number: 54545 Office: 907 Evans Office Hours: TuTh 3:00-4:30 PM and by appointment Prerequisites: Math 261 A or equivalent Required Text: Recommended Reading:
Course Webpage: http://math.berkeley.edu/~bryant/ Grading: Based on participation and homework. Homework: Homework will be assigned in class and posted on the course web site. Comments: I will try to make the course relatively self-contained (assuming the material from 261A), but for the compact theory, integration over compact groups is important, as is some basic topology and calculus on manifolds. It's a curious fact that topology and geometry are so useful for proving what are essentially algebraic results. Math 265 - Section 1 - Differential Topology Instructor: Ian Agol Lectures: TuTh 12:30-2:00pm, Room 285 Cory (Note: first class 1/18/11 meets 2-3:30 pm in 891 Evans.) Course Control Number: 54547 Office: 921 Evans Office Hours: TBA Prerequisites: Math 214, Math 251A Required Text: Morse Theory, Milnor; Lectures on the h-cobordism theorem, Milnor Recommended Reading: Syllabus: We'll discuss Morse theory, and its applications to Bott periodicity and to the Poincare conjecture via the h-cobordism theorem. We may discuss other related topics depending on interest, such as exotic 7-spheres, Cerf theory, Morse theory for 3-manifolds, and Kirby calculus. Course Webpage: http://math.berkeley.edu/~ianagol/265.S11/ Grading: Homework: Comments: Math 270 - Section 1 - Hot Topics Course on the Blob Complex Instructor: Peter Teichner Lectures: Tu 3:30-5:00pm, Room 72 Evans Course Control Number: 54548 Office: 703 Evans Office Hours: Mon 2:30-3:30 Prerequisites: 214, 215A Required Text: The Blob Complex, by Scott Morrison and Kevin Walker, please download the latest version from the archive Recommended Reading: Syllabus: Course Webpage: http://web.me.com/teichner/Math/Blob-Complex.html Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra Instructor: Lauren Williams Lectures: TuTh 11:00am-12:30pm, Room 9 Evans Course Control Number: 54551 Office: 913 Evans Office Hours: TBA Prerequisites: graduate algebra Required Text: none Recommended Reading: Syllabus: We will be studying cluster algebras and their connections to a variety of topics, including polyhedral combinatorics, Teichmuller theory, and total positivity. Course Webpage: http://www.math.berkeley.edu/~williams/274.html Grading: based on in-class presentation and a paper Homework: Comments: Math 274 - Section 2 - Topics in Algebra Instructor: Thomas Scanlon Lectures: TuTh 2:00-3:30pm, Room 31 Evans Course Control Number: 54554 Office: 723 Evans Office Hours: TBA Prerequisites: Math 250A or consent of instructor. Required Text: The Arithmetic of Dynamical Systems by J. Silverman. Recommended Reading: Dynamics in One Complex Variable by J. Milnor. Syllabus: We will be studying the arithmetic and algebraic geometric properties of discrete dynamical systems, especially those given by the action of a rational function. For the most part, we will follow the presentation in Silverman's book The Arithmetic of Dynamical Systems which develops the theory in analogy with the theory of the arithmetic of elliptic curves. Highlights include the construction of canonical heights for dynamical systems, a theory of $p$-adic dynamical systems, connections to actions of algebraic groups, local uniformization theorems and a theory of moduli spaces for dynamical systems. Course Webpage: Grading: I will assign homework and evaluate your solutions. Moreover, all students will be responsible for producing an exposition of a topic or paper in the subject. Homework: Comments: While my own research interests in algebraic dynamics involve connections to logic, my approach to this class will be firmly algebraic/algebro-geometric. Math 276 - Section 1 - Lectures on the Index Theorem Instructor: Peter Teichner Lectures: TuTh 12:30-2:00pm, Room 51 Evans Course Control Number: 54557 Office: 703 Evans Office Hours: Mon 2:30-4:30 Prerequisites: 214, 215A Required Text: Recommended Reading: Atiyah, Singer, Segal: The index of elliptic operators I-V, Annals of Math. 1968-1971 Hirzebruch: Topological methods in algebraic geometry Roe: Elliptic operators, topology, and asymptotic methods Berline, Getzler, Vergne: Heat kernels and Dirac operators Lawson, Michelsohn: Spin geometry Course Webpage: http://web.me.com/teichner/Math/Index-Theorem.html Grading: Homework: Will be given and graded weekly, with discussion sessions lead by Dmitri Pavlov Comments: Math 300 - Section 1 - Teaching Workshop Instructor: Ken Ribet Lectures: TBA Course Control Number: 55187 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: |