Fall 2009
Math 1A  Section 1  Calculus Instructor: Michael Christ Lectures: MWF 10:0011:00am, Room 2050 Valley LSB Course Control Number: 53903 Office: 809 Evans Office Hours: Prerequisites: Reasonable mastery of high school trigonometry and analytic geometry, plus sufficient intellectual maturity for a college Mathematics course. An online placement exam is available at: http://math.berkeley.edu/courses_placement.html for diagnostic use; it is not required. Please see professional advisors Thomas Brown or Jennifer Sixt of the Mathematics department ASAP if unsure which of Math 1A, 1B, 16A, 16B, 32 is most appropriate for you. Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 9781424055005 or 1424055008. Recommended Reading: Syllabus: Limits, derivatives and applications, inverse functions, integrals and applications. Chapters 1 through 6 of the text. Course Webpage: http://math.berkeley.edu/~mchrist/Math1A/homepage.html Grading: HW 10%, quizzes 15%, first midterm exam 15%, second midterm 20%, final exam 40%. Students will be rank ordered according to total course points. Distribution of letter grades will be consistent with Mathematics department averages for calculus courses. Homework: Weekly problem sets, due on Wednesdays. Assignments posted weekly on course web page. Comments: Math 1A  Section 2  Calculus Instructor: Jenny Harrison Lectures: MWF 2:003:00pm, Room 2050 Valley LSB Course Control Number: 53948 Office: 829 Evans Office Hours: Prerequisites: Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 9781424055005 or 1424055008. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1A  Section 3  Calculus Instructor: Richard Borcherds Lectures: TT 12:302:00pm, Room 2050 Valley LSB Course Control Number: 53993 Office: 927 Evans Office Hours: TT 2:003:30 927 Evans Hall. (For quick questions ask me before or after class.) Prerequisites: Three and onehalf years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A. Required Text: Stewart, Single variable calculus: Early Transcendentals for University of California, (special Berkeley edition), ISBN 9781424055005 or 1424055008, Cengage Learning. Recommended Reading: Syllabus: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. Course Webpage: http://math.berkeley.edu/~reb/1A Grading: The homework, quizzes, midterms, and final will each account for about a quarter of the total marks. Homework: Homework will be assigned on the web every class, and due once a week. Comments: Math 1B  Section 1  Calculus Instructor: Paul Vojta Lectures: TT 8:009:30am, Room 155 Dwinelle Course Control Number: 54041 Office: 883 Evans Office Hours: TBA Prerequisites: Math 1A. Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 978 1424055005 or 1424055008. Recommended Reading: Syllabus: A paper copy will be distributed on the first day of class. It will also be available on the course web page shortly before classes begin. Course Webpage: http://math.berkeley.edu/~vojta/1b.html Grading: Grading will be based on a first midterm (10%), a second midterm (20%), the final exam (45%), and a component stemming from the discussion sections (25%). This latter component is left to the discretion of the section leader, but it is likely to be determined primarily by homework assignments and biweekly quizzes. Homework: Homework will consist of weekly assignments, given on the syllabus. Information on solutions will be announced later. Comments: This is the second semester of the yearlong calculus sequence; this particular course is intended primarily for majors in engineering and the physical sciences. This semester's topics will include:
Math 1B  Section 2  Calculus Instructor: PerfOlof Persson Lectures: MWF 9:0010:00am, Room 105 Stanley Course Control Number: 54083 Office: 1089 Evans Office Hours: TBA Prerequisites: Math 1A Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 978 1424055005 or 1424055008. Recommended Reading: Syllabus: Chapters 717: Techniques and Applications of Integration, First and SecondOrder Differential Equations, Infinite Sequences and Series. Course Webpage: http://persson.berkeley.edu/1B Grading: Homework assignments and weekly quizzes (20%), Midterm Exam 1 (15%), Midterm Exam 2 (20%), Final Exam (45%). Homework: Weekly homework assignments will be posted on the course web page. Comments: Second part of the introduction to differential and integral calculus of functions of one variable, with applications. This course is intended for majors in engineering and the physical sciences. Math 16A  Section 1  Analytic Geometry & Calculus Instructor: Thomas Scanlon Lectures: TT 12:302:00pm, Room 100 Lewis Course Control Number: 54119 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & It's Applications Vol. I (Custom Edition), ISBN# 0558372694 Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A  Section 2  Analytic Geometry & Calculus Instructor: Ming Gu Lectures: MWF 10:0011:00am, Room 1 Pimental Course Control Number: 54158 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & It's Applications Vol. I (Custom Edition), ISBN# 0558372694 Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B  Section 1  Analytic Geometry & Calculus Instructor: Jack Silver Lectures: TT 9:3011:00am, Room 105 Stanley Course Control Number: 54203 Office: 753 Evans Office Hours: TBA Prerequisites: Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & It's Applications Vol. II (Custom Edition), ISBN# 0558372740 Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24  Section 1  Freshman Seminar Instructor: Alberto Grunbaum Lectures: Tu 11:0012:30pm, Room 939 Evans Course Control Number: 54242 Office: 903 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24  Section 2  Freshman Seminar Instructor: Jenny Harrison Lectures: F 3:004:00pm, Room 891 Evans Course Control Number: 54245 Office: 829 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24  Section 3  Freshman Seminar Instructor: Robion Kirby Lectures: Tu 8:009:00am, Room 939 Evans Course Control Number: 54247 Office: 919 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32  Section 1  Precalculus Instructor: Staff Lectures: TT 8:009:30am, Room 4 LeConte Course Control Number: 54248 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 53  Section 1  Multivariable Calculus Instructor: Edward Frenkel Lectures: TT 3:305:00pm, Room 155 Dwinelle Course Control Number: 54296 Office: 819 Evans Office Hours: TBA Prerequisites: Math 1A, 1B. Required Text: Stewart, Multivariable Calculus, (custom edition). Recommended Reading: Syllabus: Course Webpage: To be linked from http://math.berkeley.edu/~frenkel/Math53 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: John Neu Lectures: MWF 12:001:00pm, Room 155 Dwinelle Course Control Number: 54347 Office: 1051 Evans Office Hours: TBA Prerequisites: Required Text: Stewart, Multivariable Calculus, (custom edition). Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~neu/Math53.html Grading: Homework: Comments: Math 54  Section 1  Linear Algebra & Differential Equations Instructor: Constantin Teleman Lectures: TT 12:302:00pm, Room 104 Stanley Course Control Number: 54383 Office: 905 Evans Office Hours: TBA Prerequisites: Required Text: Lay, Linear Algebra, Custom Berkeley Edition, AddisonWesley. Nagel, Saff & Snider, Fundamentals of Differential Equations, Custom Berkeley Edition, AddisonWesley. Recommended Reading: Syllabus: The topics for the course will be:
Course Webpage: Will be ready at the start of the semester. Grading: 20% Section (quizzes+homework), 20% each midterm, 40% Final. Homework: Assigned on the web, due in section weekly. Comments: Math 54  Section 2  Linear Algebra & Differential Equations Instructor: DanVirgil Voiculescu Lectures: MWF 3:004:00pm, Room 155 Dwinelle Course Control Number: 54428 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H54  Section 1  Linear Algebra & Differential Equations Instructor: Calder Daenzer Lectures: TT 2:003:30pm, Room 70 Evans Course Control Number: 54455 Office: 1083 Evans Office Hours: TBA Prerequisites: Math 1B. Required Text: See course webpage. Recommended Reading: Syllabus: See course webpage. Course Webpage: To be linked from http://math.berkeley.edu/~cdaenzer/MathH54Fall2009.html Grading: See course webpage. Homework: See course webpage. Comments: Math 55  Section 1  Discrete Mathematics Instructor: John Strain Lectures: TT 2:003:30pm, Room 10 Evans Course Control Number: 54461 Office: 1099 Evans Office Hours: TBA Prerequisites: Math 1A and 1B recommended. Required Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th edition, McGrawHill, 2007. Recommended Reading: Syllabus: Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory. Course Webpage: To be linked from http://math.berkeley.edu/~strain/55.F09/ Grading: 10% quizzes, 10% homework, 40% midterms, 40% final Homework: Comments: Math 104  Section 1  Introduction to Analysis Instructor: Ian Agol Lectures: TT 2:003:30pm, Room 10 Evans Course Control Number: 54533 Office: 921 Evans Office Hours: TBA Prerequisites: Math 53 and 54. Required Text: C. Pugh, Real Mathematical Analysis, Springer, 2002. Recommended Reading: Walter Rudin, Principles of Mathematical Analysis. Syllabus: Course Webpage: http://math.berkeley.edu/~ianagol/104.F09/ Grading: Homework: Comments: Math 104  Section 2  Introduction to Analysis Instructor: Lectures: CLOSED 0:000:00am, Room Course Control Number: 54536 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104  Section 3  Introduction to Analysis Instructor: Michael Klass Lectures: MWF 1:002:00pm, Room 332 Evans Course Control Number: 54539 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Rudin, Principles of Mathematical Analysis, McGrawHill; & Ross, Elementary Analysis: The Theory of Calculus, Springer. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104  Section 4  Introduction to Analysis Instructor: Joshua Sussan Lectures: MWF 8:009:00am, Room 4 Evans Course Control Number: 54542 Office: 795 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104  Section 5  Introduction to Analysis Instructor: Atilla Yilmaz Lectures: TT 3:305:00pm, Room 85 Evans Course Control Number: 54545 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104  Section 6  Introduction to Analysis Instructor: Marco Aldi Lectures: TT 8:009:30am, Room 2 Evans Course Control Number: 54548 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H104  Section 1  Introduction to Analysis/Honors Instructor: Mariusz Wodzicki Lectures: MWF 10:0011:00am, Room 5 Evans Course Control Number: 54551 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110  Section 1  Linear Algebra Instructor: Mark Haiman Lectures: MWF 1:002:00pm, Room 100 Lewis Course Control Number: 54554 Office: 855 Evans Office Hours: M 10:3011:30, W 2:303:30 Prerequisites: 54 or equivalent preparation in linear algebra at the lower division level. Required Text: Friedberg, Insel, and Spence, Linear Algebra, 4th Ed. Recommended Reading: Syllabus: See course web page. Course Webpage: http://math.berkeley.edu/~mhaiman/math110fall09/ Grading: Homework 15%, 3 Midterms 15% each, Final 40% Homework: Weekly problem sets. Comments: Math H110  Section 1  Linear Algebra/Honors Instructor: Marc Rieffel Lectures: MWF 9:0010:00am, Room 71 Evans Course Control Number: 54581 Office: 811 Evans Office Hours: TBA Prerequisites: Math 54 or equivalent preparation in linear algebra at the lower division level. Required Text: Friedberg, Insel, and Spence: Linear Algebra, 4th ed. Recommended Reading: Syllabus: Linear algebra is a beautiful subject that is very widely used in the technology that our society uses. The main topics that we will cover are: Vector spaces, linear transformations, matrices, determinants, diagonalization, inner product spaces, canonical forms. These are the topics for the regular course. As an honors course, we will try to develop a deeper understanding of these topic than is developed in the regular course. So at some points the lectures may go slightly beyond what is in the textbook. In my lectures I will try to give wellmotivated careful presentations of the material. Course Webpage: http://www.math.berkeley.edu/~rieffel/110Hann.html Grading: The final examination will count for 50% of the course grade. There will be no early or makeup final examination. There will be two midterm examinations, which will each count for 20% of the course grade. Makeup 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 accomodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance what specific accomodation they need, so that I will have enough time to arrange it. Math 113  Section 1  Introduction to Abstract Algebra Instructor: David Hill Lectures: MWF 12:001:00pm, Room 2 Evans Course Control Number: 54584 Office: 785 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113  Section 2  Introduction to Abstract Algebra Instructor: Alvaro Pelayo Lectures: TT 8:009:30am, Room 4 Evans Course Control Number: 54587 Office: 791 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113  Section 3  Introduction to Abstract Algebra Instructor: Alexander Paulin Lectures: TT 12:302:00pm, Room 2 Evans Course Control Number: 54590 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: I will not be using a single textbook. I'll give out a complete set of course notes at the beginning. Recommended Reading: Classic Algebra  P.M. Cohn. It's at a higher standard than what we'll do but is the gold standard. I'll also suggest other books to look at at the beginning of the course. Syllabus: Basics of group, ring and field theory. I'll be more precise closer to the time. Course Webpage: Grading: Final: 50%. Two midterms: 15% each. Homework: 20% Homework: Eight or so problems each week. Comments: I'll give out hand written notes at the start of each lecture so you can concentrate on following the material rather than writing the whole time. Math 113  Section 4  Introduction to Abstract Algebra Instructor: Michael Rose Lectures: MWF 8:009:00am, Room 2 Evans Course Control Number: 54593 Office: 849 Evans Office Hours: TBA Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: Beachy and Blair, Abstract Algebra, 3rd edition. Recommended Reading: Syllabus: TBA Course Webpage: TBA Grading: Homework (25%), two midterm exams (20% each), and a final exam (35%). Homework: Homework will be collected at every class period. Comments: Math 113  Section 5  Introduction to Abstract Algebra Instructor: Michael Hutchings Lectures: MWF 2:003:00pm, Room 4 Evans Course Control Number: 54596 Office: 923 Evans Office Hours: TBA Prerequisites: Required Text: John Fraleigh, A First Course in Abstract Algebra, 7th edition, AddisonWesley. Recommended Equipment: Rubik's cube Syllabus: Groups, rings, fields Course Webpage: To be linked from http://math.berkeley.edu/~hutching Grading: homework, two midterms, final Homework: weekly Comments: Math 115  Section 1  Number Theory Instructor: Chung Pang Mok Lectures: MW 4:005:30pm, Room 4 Evans Course Control Number: 54599 Office: 889 Evans Office Hours: TBA Prerequisites: Required Text: Niven, Zuckerman and Montgomery, An Introduction to the Theory of Numbers, Wiley, 5th edition. Recommended Reading: Syllabus: Divisibility, congruences, quadratic reciprocity and quadratic forms, simple continued fractions. Course Webpage: http://math.berkeley.edu/~mok/math115.html Grading: 20% homeworks, 30% for two midterms, 50% for final. Homework: Assigned on a weekly basis. Comments: Math 121A  Section 1  Math Tools For the Physical Sciences Instructor: DanVirgil Voiculescu Lectures: MWF 1:002:00pm, Room 85 Evans Course Control Number: 54602 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 121A  Section 2  Math Tools For the Physical Sciences Instructor: Chung Pang Mok Lectures: MWF 10:0011:00am, Room 3 Evans Course Control Number: 54605 Office: 889 Evans Office Hours: TBA Prerequisites: Required Text: Brown and Churchill, Fourier Series and Boundary Value Problems, McGrawHill, 7th edition. Recommended Reading: Fourier Series, Mathematical Association of America. Syllabus: Fourier series, eigenfunctions expansions, boundary value problems. Course Webpage: http://math.berkeley.edu/~mok/math121.html Grading: 20% homeworks, 30% for two midterms, 50% for final. Homework: Assigned on a weekly basis. Comments: Math 123  Section 1  Ordinary Differential Equations Instructor: Ming Gu Lectures: MWF 2:003:00pm, Room 3 Evans Course Control Number: 54608 Office: 861 Evans Office Hours: TBA Prerequisites: Required Text: Brauer and Nohel, The Qualitative Theory of Ordinary Differential Equations: An Introduction, Dover. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A  Section 1  Mathematical Logic Instructor: Jan Reimann Lectures: MWF 12:001:00pm, Room 3 Evans Course Control Number: 54611 Office: 705 Evans Office Hours: TBA Prerequisites: One upper division math course or consent of instructor, ideally some acquaintance with algebraic structures (Math 113). Required Text: Lectures Notes by Slaman and Woodin, will be provided free of charge to registered students via bSpace. Recommended Reading: Enderton, A Mathematical Introduction to Logic; Ebbinghaus, Flum, Thomas, Mathematical logic. Syllabus: Propositional logic, first order logic  syntax and semantics, first order structures, the Gödel completeness theorem, compactness, basic model theory, undecidability and incompleteness. 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 128A  Section 1  Numerical Analysis Instructor: John Strain Lectures: TT 3:305:00pm, Room 3 LeConte Course Control Number: 54617 Office: 1099 Evans Office Hours: TBA Prerequisites: Math 53 and 54 Required Text: A Quarteroni, R Sacco and F Saleri, Numerical Mathematics. (Texts in Applied Mathematics, vol. 37.) SpringerVerlag, New York, 2000. ISBN 9780387989594 (Print) 9780387227504 (Online). Available online from SpringerLink. Recommended Reading: The following texts present Matlab programming in more detail. 1. S R Otto and J P Denier, An Introduction to Programming and Numerical Methods in MATLAB. SpringerVerlag, New York, 2005. ISBN 9781852339197 (Print) 9781846281334 (Online). 2. A Quarteroni and F Saleri, Scientific Computing with MATLAB and Octave. (Texts in Computational Science and Engineering, vol. 2.) SpringerVerlag, New York, 2005. ISBN 9783540326120 (Print) 9783540326137 (Online). Both are available online from SpringerLink. Syllabus: Programming for numerical calculations, roundoff error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer. Course Webpage: To be linked from http://math.berkeley.edu/~strain/128a.F09/ Grading: 30% weekly homework, 40% midterm, 30% final Homework: Comments: Math 130  Section 1  The Classical Geometries Instructor: Mariusz Wodzicki Lectures: MWF 2:003:00pm, Room 85 Evans Course Control Number: 54632 Office: 995 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 135  Section 1  Introduction To the Theory of Sets Instructor: Thomas Scanlon Lectures: TT 9:3011:00am, Room 85 Course Control Number: 54635 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: TT 12:302:00pm, Room 3 Evans Course Control Number: 54638 Office: 805 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 143  Section 1  Elementary Algebraic Geometry Instructor: Mauricio Velasco Lectures: TT 3:305:00pm, Room 87 Evans Course Control Number: 54641 Office: 1063 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 152  Section 1  Math Of the Secondary School Curriculum Instructor: HungHsi Wu Lectures: MWF 1:002:00pm, Room 81 Evans Course Control Number: 54644 Office: 733 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185  Section 1  Complex Analysis Instructor: LekHeng Lim Lectures: MWF 1:002:00pm, Room 9 Evans Course Control Number: 54653 Office: 873 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185  Section 2  Complex Analysis Instructor: Atilla Yilmaz Lectures: TT 11:0012:30pm, Room 3 Evans Course Control Number: 54656 Office: Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185  Section 3  Complex Analysis Instructor: Michael Christ Lectures: MWF 12:001:00pm, Room 70 Evans Course Control Number: 54659 Office: 809 Evans Office Hours: M 1:302:30 and TBA. Prerequisites: Math 104. Required Text: Basic Complex Analysis by Jerrold E. Marsden and Michael J. Hoffman, 3rd edition, W. H. Freeman. Recommended Reading: Syllabus: Complex numbers and the complex plane; complex power series; holomorphic functions and the CauchyRiemann equations; path integrals; exponential and log functions; arguments and winding numbers; Cauchy's theorem, antidifferentiation, and the Cauchy integral formula; residues; Laurent series; maximal modulus theorem; Discussion of analytic continuation and conformal mapping if time permits. Course Webpage: http://math.berkeley.edu/~mchrist/Math185/complex.html Grading: HW 20%, first midterm exam 15%, second midterm 20%, final exam 45%. Distribution of letter grades will be consistent with Mathematics department averages for core upper division courses. Homework: Weekly problem sets, due on Fridays. Assignments posted weekly on course web page. Comments: Math 185  Section 4  Complex Analysis Instructor: Richard Borcherds Lectures: TT 3:305:00pm, Room 123 Wheeler Course Control Number: 54661 Office: 927 Evans Office Hours: TBA Prerequisites: Math 104 Required Text: Brown & Churchill, Complex Variables & It's Applications, McGrawHill Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~reb/courses/185/index.html Grading: Homework: Comments: Math 191  Section 1  Experimental Courses in Mathematics Instructor: Alexander Givental Lectures: TT 3:305:00pm, Room 81 Evans Course Control Number: 54662 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: This class will function as the Putnam workshop, i.e., a problemsolving seminar intended, in the first place, for those who plan to take the Putnam Exam, the US and Canada math Olympiad for college students, in December 2009. Our objectives will be to build participant's confidence in solving challenging math problems and, more importantly, to learn interesting mathematics, using materials of past Putnam exams for motivation. Expect 2009 hours of work per week. Math 191  Section 2  Experimental Courses in Mathematics Instructor: LekHeng Lim Lectures: MWF 3:004:00pm, Room 2 Evans Course Control Number: 54665 Office: 873 Evans Office Hours: M 4:005:30pm, W 11:30am1:00pm Prerequisites: Math 110: Linear Algebra. Knowledge of basic probability theory and multivariate calculus would be helpful. Programming knowledge is useful though not necessary. Required Text: See course webpage. Recommended Reading: See course webpage. Syllabus: Here's a list of mathematical topics that we shall examine (some only at a very basic level). Of course everything will be motivated by and made relevant to some cool applications: Markov chains, spectral graph theory, diffusion geometry, singular value decomposition Ky Fan norms, compact operators, reproducing kernel Hilbert spaces, Bregman divergence, compressive sensing, submodular functions. Course Webpage: http://math.berkeley.edu/~lekheng/courses/191 Grading: To be determined. Course grade is likely to be based more on projects/term papers and less on homeworks/exams. Homework: To be determined. You should expect to write one or more term papers on at least one topic that interests you. Comments: This class is targeted at anyone who's curious about how mathematics is used by companies like Google, FaceBook, Netflix, etc, for web search, product recommendations, computational advertising, sponsored search auctions, multimedia search, text mining, social network analysis, etc. An alternative course title that would describe 90% of the materials could well have been "The Mathematics of Data Mining, Machine Learning, and Pattern Recognition". The remaining 10% would be on miscellaneous topics like ad auctions. Math 191  Section 3  Experimental Courses in Mathematics Instructor: David Penneys Lectures: TBA, Room 740 Evans Course Control Number: TBA Office: 1049 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 202A  Section 1  Intro. To Topology & Analysis Instructor: Marc Rieffel Lectures: MWF 11:0012:00pm, Room 60 EVANS Course Control Number: 54758 Office: 811 Evans Office Hours: TBA GSI: Michael Hartglass Prerequisites: Math 104 or equivalent preparation in analysis. Further experience with upperdivision mathematics courses, including writing proofs, is strongly recommended. Required Text: Basic Real Analysis by Anthony Knapp. Recommended Reading:For Math 202B next Spring I will probably require Advanced Real Analysis by Anthony Knapp. It is my impression that, at least online, one can purchase the two Knapp books together as a package at a more attractive price than if they are purchased singly. Syllabus: We will cover basic mathematical concepts that are of importance in virtually all areas of mathematics. These include: Metric spaces and general topological spaces. Compactness and connectedness. Characterization of compact metric spaces. Theorems of Tychonoff, Urysohn, Tietze. Complete spaces and the Baire category theorem. Function spaces; ArzelaAscoli and StoneWeierstrass theorems. Partitions of unity. Locally compact spaces; onepoint compactification. Introduction to measure and integration. Sigma algebras of sets. Measures and outer measures. Lebesgue measure on the line. Construction of the integral. In my lectures I will try to give wellmotivated careful presentations of the material. Course Webpage: Grading: I plan to assign roughlyweekly problem sets. Collectively they will count for 50% of the course grade. Students are strongly encouraged to discuss the problem sets and the course content with each other, but each student should write up their own solutions, reflecting their own understanding, to turn in. I will give one midterm examination and a final examination, which will count for 15% and 35% of the course grade respectively. There will be no early or makeup final examination. Nor will a makeup midterm exam be given; instead, if you tell me ahead of time that you must miss the midterm exam, then the final exam will count for 50% of your course grade. 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 count for 50% of your course grade. Homework: Comments: Students who need special accomodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance what specific accomodation they need, so that I will have enough time to arrange it. Math 204  Section 1  Ordinary & Partial Differential Equations Instructor: Jon Wilkening Lectures: TT 11:0012:30pm, Room 7 Evans Course Control Number: 54761 Office: 1091 Evans Office Hours: Tues 1011, 34 Prerequisites: Undergraduate Analysis and Linear Algebra. Required Text: Coddington and Levinson, Theory of Ordinary Differential Equations. Recommended Reading: Hurewicz, Lectures on Ordinary Differential Equations Courant; and Hilbert, Methods of Mathematical Physics, vol 1. Syllabus: Rigorous theory of ordinary differential equations. The first third of the course deals with fundamental existence, uniqueness and continuity theorems for initial value problems. We'll also discuss variational equations, linearization, periodic coefficients and Floquet Theory. Then we move on to boundary value problems, studying Green's functions, SturmLiouville theory, and eigenvalue problems (linear and nonlinear). If time permits, I'll also talk about ODE in abstract spaces, semigroup theory and the HilleYosida theorem. We end with phase plane analysis, the PoincareBendixson Theorem, bifurcation theory, the LiapunovSchmidt reduction, Hamiltonian systems, generalized coordinates, and HamiltonJacobi equations. Course Webpage: http://math.berkeley.edu/~wilken/204.F09 Grading: 100% Homework Homework: 10 assignments Comments: Math 206  Section 1  Banach Algebras & Spectral Theory Instructor: Donald Sarason Lectures: MWF 9:0010:00am, Room 3 Evans Course Control Number: 54764 Office: 779 Evans Office Hours: TBA Prerequisites: Math 202AB, or the equivalent. Required Text: Recommended Reading: Syllabus: The course covers three main topics. The first is operator theory in Banach spaces and includes the study of compact operators, Fredholm operators, and idempotents. The second is Banach algebras, a basic introduction, including the Gelfand theory of commutative Banach algebras. The third is Hilbert space operators, including various versions of the spectral theorem. Course Webpage: Grading: The course grade will be based on homework. There will be no exams. Homework: Homework will be assigned regularly. Comments: The lectures will be selfcontained except for routine details. No textbook will be followed in detail. Suggested references are William Arveson, A SHORT COURSE ON SPECTRAL THEORY, SPRINGE, 2002 Walter Rudin, FUNCTIONAL ANALYSIS, 2nd edition, McGrawHill, 1991. Math 209  Section 1  Von Neumann Algebras Instructor: Vaughan Jones Lectures: TT 12:302:00pm, Room 55 Evans Course Control Number: 54767 Office: 929 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 214  Section 1  Differential Manifolds Instructor: Alvaro Pelayo Lectures: TT 9:3011:00am, Room 87 Evans Course Control Number: 54770 Office: 791 Evans Office Hours: TBA Prerequisites: Required Text: John M. Lee, Introduction to Smooth Manifolds, Springer, ISBN# 0387954481 Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 215A  Section 1  Algebraic Topology Instructor: Christian Zickert Lectures: MWF 3:004:00pm, Room 3 Evans Course Control Number: 54773 Office: 1053 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C218A  Section 1  Probability Theory Instructor: Steve Evans Lectures: TT 12:302:00pm, Room 334 Evans Course Control Number: 54776 Office: 329 Evans Office Hours: TBA Prerequisites: A fair degree of mathematical sophistication and at least some acquaintance with topology, functional analysis, complex analysis, and real analysis  particularly Lebesgue integration theory. Required Text: Foundations of Modern Probability, (2nd edition), by Olav Kallenberg, (Springer). Recommended Reading: Real Analysis and Probability, by R.M. Dudley, (Cambridge University Press). Syllabus: Review of basic measure theory o measurable sets and functions o measures and integration o monotone and dominated convergence o transformation of integrals o product measures and Fubini's theorem o Lpspaces and projection o measure spaces and kernels o outer measure and extension o Lebesgue and LebesgueStieltjes measures o JordanHahn and Lebesgue decompositions o RadonNikodym theorem o Lebesgue's differentiation theorem o functions of finite variation o Riesz representation theorem o Haar and invariant measures Random sequences and processes o random elements and processes o distributions and expectation o independence o zeroone laws o BorelCantelli lemma o Bernoulli sequences o moments and continuity of paths Convergence concepts o convergence in probability and in Lp o uniform integrability and tightness o convergence in distribution o convergence of random series o strong laws of large numbers o portmanteau theorem o continuous mapping o coupling Weak convergence o uniqueness and continuity theorem o Poisson convergence o Lindeberg's condition o general Gaussian convergence o weak laws of large numbers o domain of Gaussian attraction o vague and weak compactness Conditioning and disintegration o conditional expectations and probabilities o regular conditional distributions o disintegration o conditional independence o transfer and coupling o existence of sequences and processes o extension through conditioning Martingales o filtrations and optional times o random timechange o martingale property o optional stopping and sampling o maximum and upcrossing inequalities o martingale convergence, regularity, and closure o limits of conditional expectations o regularization of submartingales Course Webpage: Course webpage available on bSpace. Grading: See course webpage. Homework: See course webpage. Comments: The laptop slides projected in class are available on the course webpage. Math 221  Section 1  Advanced Matrix Computations Instructor: James Demmel Lectures: TT 12:302:00pm, Room 81 Evans Course Control Number: 54779 Office: 831 Evans Office Hours: TBA Prerequisites: Required Text: Demmel, Applied Numerical Linear Algebra. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 222A  Section 1  Partial Differential Equations Instructor: Maciej Zworski Lectures: TT 12:302:00pm, Room 87 Evans Course Control Number: 54782 Office: 801 Evans Office Hours: Tu 2:154 PM Prerequisites: 202A or equivalent Required Text: L.C. Evans, Partial Differential Equations; L. Hörmander, The Analysis of Linear Partial Differential Operators, vol.I. Recommended Reading: Syllabus: The course, and its sequel Math 222B, will provide a comprehensive introduction to the theory of partial differential equations. Math 222A: transport, Laplace's, wave, and heat equations; nonlinear first order scalar equations, HamiltonJacobi equations, viscosity solutions (Evans); theory of distributions, Fourier transform, linear equations with constant coefficients (Hörmander). Math 222B: Sobolev spaces, 2nd order elliptic equations, spectral theory, calculus of variations (Evans) + additional topics (e.g. Moser's paper on the NashDeGiorgi theorem; Calderón's paper on the linearized inverse conductivity problem). Course Webpage: http://math.berkeley.edu/~zworski/222.html Grading: The grade will be based on weekly homework. Homework:Homework will be assigned every week and due the following week. Comments: Math 224A  Section 1  Mathematical Methods For the Physical Sciences Instructor: Alexandre Chorin Lectures: MWF 12:001:00pm, Room 81 Evans Course Control Number: 54788 Office: 911 Evans Office Hours: TBA Prerequisites: Some exposure to the partial differential equations of physics. Required Text: R. Showalter, Hilbert Space Methods for Partial Differential Equations, (available electronically). Recommended Reading: Syllabus: I expect to cover Chapter 1,2,3,7 of the textbook: distributions, Hilbert space, selfadjoint operators, eigenvalue problem, boundary value problems, variational inequalities, control of differential equations, evolution equations. To the extent that time allows, I will also discuss some nonlinear problems involving diffusion, dispersion, and discontinuities. Course Webpage: To be linked from http://math.berkeley.edu/~chorin/math224 Grading: Based on homework. Homework: Homework will be assigned every week. Comments: My lecturing style is informal and I enjoy class discussion. Math 225A  Section 1  Metamathematics Instructor: Jack Silver Lectures: TT 12:302:00pm, Room 35 Course Control Number: 54791 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: Jan Reimann Lectures: MWF 3:004:00pm, Room 71 Evans Course Control Number: 54794 Office: 705 Evans Office Hours: TBA Prerequisites: Math 225A & 225B Required Text: None. We will use several texts and lecture notes. They will be available for download. Recommended Reading: Syllabus: Review of computability, recursively enumerable sets, Turing degrees; priority constructions; forcing and reducibilities; constructive ordinals, the hyperarithmetical and analytical hierarchies; algorithmic randomness. Course Webpage: Will be set up on bSpace. Grading: Based on homework. Homework: Homework will be assigned every week. Comments: Math 228A  Section 1  Numerical Solutions of Differential Equations Instructor: PerOlof Persson Lectures: MWF 1:002:00pm, Room 70 Evans Course Control Number: 54797 Office: 1089 Evans Office Hours: TBA Prerequisites: Math 128A or equivalent knowledge of basic numerical analysis, some MATLAB programming experience. Required Text: A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Second Edition, Cambridge University Press, 2008. ISBN 9780521734905. Recommended Reading: E. Hairer, S. P. Norsett and G. Wanner, Solving ordinary differential equations, Second Edition (2 vols.), Springer, 2008. ISBN 9783540566700, 9783540604525. R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, SIAM, 2007. ISBN 9780898716290. Syllabus: Theory and practical methods for numerical solution of differential equations. RungeKutta and multistep methods, stability theory, stiff equations, boundary value problems. Finite element methods for boundary value problems in higher dimensions. Direct and iterative linear solvers. Discontinuous Galerkin methods for conservation laws. Course Webpage: http://persson.berkeley.edu/228A Grading: Grades will be based entirely on the problem sets. Homework: About 8 program sets. Comments: Math 250A  Section 1  Groups, Rings & Fields Instructor: Martin Olsson Lectures: MWF 10:0011:00am, Room 6 Evans Course Control Number: 54800 Office: 879 Evans Office Hours: TBA Prerequisites: Math 114 (or equivalent undergraduate abstract algebra) or consent of instructor. Required Text: Lang, Algebra (revised third edition from Springer). Recommended Reading: Syllabus: My goal is to cover most of Chapters IVI in Lang's text, with some possible detours for background material, more advanced topics etc. There is a lot of material, so students will be expected to read the text for definitions and theorems not covered in class. Class time will serve to emphasize important points, to clarify difficult topics, and to supplement the text as needed. Course Webpage: Will be maintained in bSpace. Grading: Grades will be based on homework, two midterms, and a final exam. Homework: Homework will be assigned weekly. Comments: Math 254A  Section 1  Number Theory Instructor: Alexander Paulin Lectures: TT 3:305:00pm, Room 85 Evans Course Control Number: 54806 Office: 887 Evans Office Hours: TBA Prerequisites: Required Text: None. Recommended Reading: Brush up on your basic field theory stuff  finite and infinite Galois groups. Make sure you know what a profinite group is. Find out what the padic numbers/ local fields are. Syllabus: I want to give you a broad understanding of the guiding philosophy behind modern algebraic number theory  Langlands duality. We'll start off by reviewing the basic properties of number fields and hopefully get to a reasonable understanding what it means for a Galois Representation to be automorphic. Course Webpage: Grading: I think I'll get you to writing a short review article on some aspect of the course you want to know more about. Homework: Given the volume of material we'll try and cover I'll leave lots of the detailed proofs you you guys. I'll tell you as we go along. Comments: I want you to understand the big picture. Math 256A  Section 1  Algebraic Geometry Instructor: Paul Vojta Lectures: TT 11:0012:30pm, Room 5 Evans Course Control Number: 54809 Office: 883 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 261A  Section 1  Lie Groups Instructor: Ian Agol Lectures: TT 9:3011:00am, Room 31 Evans Course Control Number: 54812 Office: 921 Evans Office Hours: TBA Prerequisites: 113, 214. Required Text: Brian C. Hall, Lie Groups, Lie Algebras, and Representations, Springer, 2003. Recommended Reading: Fulton and Harris, Representation Theory: A First Course, Springer, 2008. Syllabus: Course Webpage: http://math.berkeley.edu/~ianagol/261A.F09/ Grading: Homework: Comments: Math 274  Section 1  Topics in Algebra Instructor: Vera Serganova Lectures: MWF 2:003:00pm, Room 81 Evans Course Control Number: 54815 Office: 709 Evans Office Hours: MW 12:001:00pm. Prerequisites: Algebraic geometry. Required Text: Recommended Reading: Mukai, An introduction to invariants and moduli; Mumford, Fogarty, Kirwan, Geometric invariant theory. Syllabus: The purpose of this course is introduction to geometric invariant theory and moduli spaces. I will start with basic facts about representations of reductive algebraic groups and classical invariant theory, then define the notion of universal geometric quotient, discuss stability and numerical criterion. The moduli space of curves will be considered in detail as well as some other examples. Course Webpage: Grading: To get a grade one should give a short talk on a subject related to the course during the last two weeks of classes. Homework: Homework will be assigned on the webpage every two weeks. Comments: Math 277  Section 1  Topics In Differential Geometry Instructor: John Lott Lectures: MWF 3:004:00pm, Room 81 Evans Course Control Number: 54818 Office: 897 Evans Office Hours: MWF 4:005:00pm Prerequisites: Math 240 or equivalent Required Text: None Recommended Reading: Lectures on the Ricci Flow by Peter Topping, Cambridge University Press Syllabus: The Ricci flow, devised by Richard Hamilton, is a way to evolve a Riemannian metric. It was used by Grisha Perelman to prove the Poincare Conjecture and the Geometrization Conjecture. This course will be an introduction to Ricci flow. Among other things, we will prove Hamilton's theorem that a compact 3manifold with positive Ricci curvature is diffeomorphic to a spherical space form. We will also discuss some of the monotonic quantities for Ricci flow that were introduced by Perelman. A text for the course is Peter Topping's "Lectures on Ricci Flow". This book can be downloaded at http://www.warwick.ac.uk/~maseq/RFnotes.html but is worth buying. Course Webpage: http://math.berkeley.edu/~lott/teaching.html Grading: The grade will be based on homework Homework: Homework will be assigned periodically. Comments: Math 277  Section 2  Topics In Differential Geometry Instructor: Robert Bryant Lectures: TT 5:006:30pm, Room 41 Evans Course Control Number: 54821 Office: 907 Evans Office Hours: TBA Prerequisites: Basic differential topology (smooth manifolds, inverse and implicit function theorems, and tensors, especially vector fields and differential forms), basic Riemannian geometry (metrics, connections and curvature, submanifolds), basic Lie groups (definitions and classical examples, left invariant vector fields and forms, homogeneous spaces; no classification theorems will be needed). The material in Math 214 and Math 240 will be more than adequate. Required Text: None. Class notes will be provided. Recommended Reading:
Course Webpage: http://math.berkeley.edu/~bryant/math277/
(To be activated after the semester starts)
