# Fall 2008

Math 1A - Section 1 - CalculusInstructor: Ian AgolLectures: TuTh 8:00-9:30am, Room 155 DwinelleCourse Control Number: 54103Office: 921 EvansOffice Hours: TBAPrerequisites: 3.5 years of high school math, including
trigonometry and analytic geometry, plus a satisfactory grade in one of
the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic
test, or Math 32. There is an on-line exam you can take to help you
decide if you are ready for this course.Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~ianagol/1A.F08/Grading: Homework: Comments: Math 1A - Section 2 - Calculus Instructor: Ole HaldLectures: MWF 1:00-2:00pm, Room 2050 Valley LSBCourse Control Number: 54142Office: 995 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework:Comments:Math 1A - Section 3 - Calculus Instructor: Martin OlssonLectures: MWF 12:00-1:00pm, Room 155 DwinelleCourse Control Number: 54184Office: 887 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 1B - Section 1 - Calculus Instructor: Jon WilkeningLectures: TuTh 11:00am-12:30pm, Room 2050 Valley LSBCourse Control Number: 54223Office: 1091 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 2 - Second Semester Calculus Instructor: George BergmanLectures: MWF 3:00-4:00pm, Room 155 DwinelleCourse Control Number: 54262Office: 865 EvansOffice Hours: Tu 10:30-11:30, W 4:15-5:15, F 10:30-11:30Prerequisites: Math 1A or equivalent background. (If you have
taken the Math AP exams, there is advice on which math course you are
ready for at http://math.berkeley.edu/courses_AP.html.)Required Text: Stewart, Single Variable Essential Calculus, Thomson LearningSyllabus: Chapters 6, 7, 8 and 17 of the text.Grading: Grades will be based on two midterms (15% + 20%), a final (35%), and weekly quizzes in section (30%).Homework: Homework will be assigned every week and discussed in
section. It will not be graded, but section quizzes will be modeled on
the homework problems, so you should do it.Comments: This course continues where Math 1A leaves off,
developing techniques of integration, and further applications and
techniques of calculus, including 4 weeks of differential equations. I
hope to show you some of the beauty of these topics, along with the
facts and techniques.I will give out a schedule of readings. My lecture each day will assume that you have studied the reading for the day, but that you may need to see things clarified or explained from another point of view, more examples worked, etc.. In lower-division math courses, proofs are not the main topic, but I will assign a certain number, typically one on each exam and one or two per homework assignment, and discuss some of the proofs from the text in lecture, to help get you ready for upper division math, and introduce you to mathematical thinking. Despite my best intentions, I am not a well-organized lecturer. I will do my best, as always; but if you want something more polished, you might take the other lecture. Math 16A - Section 1 - Analytical Geometry and CalculusInstructor: James DemmelLectures: TuTh 12:30-2:00pm, Room 105 StanleyCourse Control Number: 54298Office: 737 SodaOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and CalculusInstructor: Tsit-Yuen LamLectures: MWF 10:00-11:00am, Room 1 PimentalCourse Control Number: 54337Office: 871 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and CalculusInstructor: Jenny HarrisonLectures: MWF 9:00-10:00am, Room 105 StanleyCourse Control Number: 54379Office: Office Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman SeminarsInstructor: Alberto GrünbaumLectures: Tu 11:00am-12:30pm, Room 939 EvansCourse Control Number: 54418Office: 903 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 24 - Section 2 - Freshman SeminarsInstructor: Jenny HarrisonLectures: F 3:00-4:00pm, Room 891 EvansCourse Control Number: 54421Office: 851 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 32 - Section 1 - PrecalculusInstructor: The StaffLectures: MWF 8:00-9:00am, Room 2060 Valley LSBCourse Control Number: 54424Office:Office Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 53 - Section 1 - Multivariable CalculusInstructor: Michael HutchingsLectures: MWF 11:00am-12:00pm, Room 2050 Valley LSBCourse Control Number: 54472Office: 923 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus:Course Webpage: Grading: Homework: Comments:Math 53 - Section 2 - Multivariable CalculusInstructor: Constantin TelemanLectures: TuTh 3:30-5:00pm, Room 100 LewisCourse Control Number: 54514Office: 905 EvansOffice Hours: W 12:00-1:30pm, Th 5:00-6:30pmPrerequisites: Required Text: Stewart, Multivariable Essential Calculus, ThomsonRecommended Reading:Syllabus: Standard Multivarible calculusCourse Webpage: http://math.berkeley.edu/~teleman/53f08Grading: 20% Homework + quizzes, 20% each of two midterms, 40% finalHomework: Assigned for every lecture (see the web schedule), collected in Section.Comments:Math 54 - Section 1 - Linear Algebra and Differential EquationsInstructor: Alberto GrünbaumLectures: TuTh 8:00-9:30am, Room 150 WheelerCourse Control Number: 54550Office: 903 EvansOffice Hours: TBAPrerequisites: Math 1BRequired Text: David Lay, Linear Algebra and Its Applications, 3rd editionNagle, Saff & Snider, Fundamentals of Differential Equations and Boundary Value ProblemsFor both you can get the paperback Berkeley editions. Recommended Reading:Syllabus: Basic linear algebra; matrix arithmetic and
determinants. Vector spaces; inner product as spaces. Eigenvalues and
eigenvectors; linear transformations. Homogeneous ordinary differential
equations; second-order differential equations with constant
coefficients. Fourier series and partial differential equations.Course Webpage: http://math.berkeley.edu/~grunbaum/54.htmlGrading: Homework 20%, midterms 20% each, and final exam 40%.Homework: Homework will be assigned weekly.Comments: Math H54 - Section 1 - Honors Linear Algebra and Differential EquationsInstructor: Alexander PaulinLectures: TuTh 3:30-5:00pm, Room 85 EvansCourse Control Number: 54616Office: 1053 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 55 - Section 1 - Discrete MathematicsInstructor: Mark HaimanLectures: MWF 12:00-1:00pm, Room 2060 Valley LSBCourse Control Number: 54622Office: 855 EvansOffice Hours: WF 1:30-3:00pmPrerequisites: Mathematical maturity appropriate to a sophomore
math class. 1A-1B recommended. Freshmen with strong high school math
background and a possible interest in majoring in mathematics may also
wish to consider taking this course.Required Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th EditionRecommended Reading:Syllabus: Logic and proof techniques, basics of set theory,
algorithms, elementary number theory, combinatorial enumeration,
discrete probability, graphs and trees, with applications to coding
theory.Course Webpage: http://math.berkeley.edu/~mhaiman/math55-fall08Grading: Based on weekly homework, two midterm exams, and final exam.Homework: Comments:Math 74 - Section 1 - Transition to Upper Division MathematicsInstructor: The StaffLectures: MWF 3:00-4:00pm, Room 71 EvansCourse Control Number: 54637Office:Office Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math 74 - Section 2 - Transition to Upper Division MathematicsInstructor: The StaffLectures: TuTh 3:30-5:00pm, Room 75 EvansCourse Control Number: 54640Office:Office Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math 104 - Section 1 - Introduction to AnalysisInstructor: Jan ReimannLectures: TuTh 2:00-3:30pm, Room 241 CoryCourse Control Number: 54706Office: 705 EvansOffice Hours: TBAPrerequisites: Math 53 and 54Required Text: C. Pugh, Real Mathematical Analysis, Springer, 2002Recommended Reading:Syllabus: Roughly Chapters 1 to 4: The real number system,
cardinalities, metric spaces, convergence, compactness and
connectedness, continuous functions on metric spaces, uniform
convergence, power series, differentiation and integration. (We will
leave out some rather advanced material in Chapters 2 and 4.)Course Webpage: Will be set up on bSpace.Grading: 20% homework, 20% each midterm, 40% finalHomework:Comments: Math 104 - Section 2 - Introduction to AnalysisInstructor: Ole HaldLectures: MWF 11:00am-12:00pm, Room 71 EvansCourse Control Number: 54709Office: 875 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math 104 - Section 3 - Introduction to AnalysisInstructor: Michael KlassLectures: MWF 1:00-2:00pm, Room 71 EvansCourse Control Number: 54712Office: 319 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 104 - Section 4 - Introduction to AnalysisInstructor: Joshua SussanLectures: MWF 3:00-4:00pm, Room 75 EvansCourse Control Number: 54715Office: 761 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 104 - Section 5 - Introduction to AnalysisInstructor: Brett ParkerLectures: TuTh 3:30-5:00pm, Room 87 EvansCourse Control Number: 54718Office: Office Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 6 - Introduction to AnalysisInstructor: Robert ColemanLectures: MWF 2:00-3:00pm, Room 4 EvansCourse Control Number: 54721Office: 901 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: In this course we will construct the real numbers,
define differentiation and integration, prove the fundamental theorem of
calculus and Taylor's theorem and make the gamma function.Course Webpage: Grading: Homework: Comments:Math H104 - Section 1 - Honors Introduction to AnalysisInstructor: Alexander GiventalLectures: TuTh 3:30-5:00pm, Room 81 EvansCourse Control Number: 54724Office: 701 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 110 - Section 1 - Linear AlgebraInstructor: Shamgar GurevichLectures: MWF 3:00-4:00pm, Room 4 EvansCourse Control Number: 54727Office: 867 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 110 - Section 2 - Linear AlgebraInstructor: Marco AldiLectures: TuTh 8:00-9:30am, Room 71 EvansCourse Control Number: 54730Office: 805 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 110 - Section 3 - Linear AlgebraInstructor: Arthur OgusLectures: MWF 11:00am-12:00pm, Room 3113 EtcheverryCourse Control Number: 54733Office: 877 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 110 - Section 4 - Linear AlgebraInstructor: Sebastian HerrLectures: TuTh 12:30-2:00pm, Room 70 EvansCourse Control Number: 54736Office: 837 EvansOffice Hours: TBAPrerequisites: 54 or a course with equivalent linear algebra content.Required Text: S. Friedberg, A. Insel, and L. Spence, Linear Algebra, Prentice Hall, 2002.Recommended Reading: You may find the following textbook helpful as supplementary reading (optional):S. Axler, Linear Algebra Done Right, Springer, 2004.Syllabus: Vector spaces, linear independence, bases, dimension.
Linear transformations, matrices, change of bases, linear functionals.
Systems of linear equations. Determinants, eigenvalues and eigenvectors,
diagonalization. Inner products, orthonormalization and QR
factorization, quadratic forms, spectral theorem, Rayleigh's principle.
Jordan canonical form and applications.Course Webpage: http://math.berkeley.edu/~herr/110S4Fall08.htmlGrading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam.Homework: Homework will be assigned once a week, and will be due the following week.Comments: For more information, please take a look at the course webpage.Math 110 - Section 5 - Linear AlgebraInstructor: Kenneth RibetLectures: TuTh 3:50-5:00pm, Room 3 EvansCourse Control Number: 54739Office: 885 EvansOffice Hours: TBAPrerequisites: 54 or a course with equivalent linear algebra contentRequired Text: TBARecommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~ribet/110/Grading: Determined by a numerical composite grade that weights the three exams and the homework scores in some logical manner.Homework: Assigned weeklyComments: This course has the latest possible final exam slot:
Saturday, December 20, 2008 at 12:30PM. Sign up for another section if
you need to start your vacation before then.Math 110 - Section 6 - Linear AlgebraInstructor: Christian ZickertLectures: TuTh 2:00-3:30pm, Room 70 EvansCourse Control Number: 54741Office: 1053 EvansOffice Hours: TBAPrerequisites: Required Text: Friedberg, Insel & Spence, Linear Algebra, Prentice-Hall, 2002Recommended Reading: Syllabus: Vector spaces and linear maps, eigenvalues and eigenvectors, diagonalization, inner products, Jordan form, polar decomposition.Course Webpage: http://math.berkeley.edu/~zickert/Grading: Homework: Comments:Math H110 - Section 1 - Honors Linear AlgebraInstructor: George BergmanLectures: MWF 1:00-2:00pm, Room 4 EvansCourse Control Number: 54742Office: 865 EvansOffice Hours: Tu 10:30-11:30, W 4:15-5:15, F 10:30-11:30Prerequisites: Math 54 or a course with equivalent linear algebra
content, and a GPA of at least 3.3 in math courses taken over past
year; or consent of the instructor. The course is aimed at mathematics
majors and other students with a strong interest in mathematics.Required Text: S. H. Friedberg, A. J. Insel and L. E. Spence, Linear Algebra, 4th Edition, Prentice-Hall. Recommended Reading: None.Syllabus: We will cover most of the text, and possibly some additional topics.Course Webpage: None.Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam, 35%; regular submission of the daily question (see below), 5%.Homework: Comments: In Math 54 you saw elementary linear algebra, with an
emphasis on solving linear equations, and with the abstract concept of a
vector space briefly treated. Math 110 focuses on further development
of the properties of abstract vector spaces and linear maps among them.After several days looking through texts that might give a more advanced approach to the material, and not finding one that I liked, I have ended up falling back on the text most commonly used in regular 110. This is well written, and has the advantage that students should be able to move between H110 and the majority of the regular 110 sections without too much difficulty. In H110, however, we will look into the ideas more deeply than in regular 110, we will include one or two topics that are not usually covered, and the exercises assigned will be more challenging. I am not a fan of the conventional lecture system, where students spend the hour copying the contents of the course from the blackboard into their notebooks. Hence I assign readings in the text, and conduct the class on the assumption that you have done the assigned reading and thought about what you've read. In lecture I may go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, discuss points to watch out for in the next reading, etc.. If you are unbreakably attached to learning first from the lecture, and only then turning to the book, then my course is not for you. On each day for which there is an assigned reading, each student is required to submit, preferably by e-mail, a question
on the reading. (If there is nothing in the reading that you don't
understand, you can submit a question marked "pro forma", together with
its answer.) I try to incorporate answers to students' questions into my
lectures; when I can't do this, I usually answer by e-mail. More
details on this and other matters will be given on the course handout,
distributed in class the first day, and available on the door to my
office thereafter.Math 113 - Section 1 - Introduction to Abstract AlgebraInstructor: David HillLectures: MWF 10:00-11:00am, Room 70 EvansCourse Control Number: 54745Office: 757 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 113 - Section 2 - Introduction to Abstract AlgebraInstructor: Alvaro PelayoLectures: TuTh 8:00-9:30am, Room 2 EvansCourse Control Number: 54748Office: Office Hours: TBAPrerequisites: Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th ed.Recommended Reading: Syllabus: Course Webpage: Grading: 2 midterm exams, a final exam and weekly homework.Homework: Weekly.Comments:Math 113 - Section 3 - Introduction to Abstract AlgebraInstructor: Mauricio VelascoLectures: MWF 8:00-9:00am, Room 71 EvansCourse Control Number: 54751Office: 1063 EvansOffice Hours: TBAPrerequisites: Math 54Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th editionRecommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 113 - Section 4 - Introduction to Abstract AlgebraInstructor: Alvaro PelayoLectures: TuTh 3:30-5:00pm, Room 71 EvansCourse Control Number: 54754Office: Office Hours: TBAPrerequisites: Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th ed.Recommended Reading: Syllabus: Course Webpage: Grading: 2 midterm exams, a final exam and weekly homework.Homework: Weekly.Comments:Math 113 - Section 5 - Introduction to Abstract AlgebraInstructor: Irwin KraLectures: TuTh 2:00-3:30pm, Room 4 EvansCourse Control Number: 54756Office: Office Hours: TuW 4:00-5:00Prerequisites: Math 54 or a course with equivalent linear algebra contentRequired Text: John Stilwell, Elements of Algebra, Springer-Verlag, 2001Recommended Reading: (1) John B. Fraleigh and Victor J. Katz, A First Course in Abstract Algebra, Addison-Wesley, 2003 (2) J.F. Humphreys and M.Y. Prest, Numbers, Groups and Codes, Cambridge University Press, 2004Syllabus: This is an introductory algebra course designed
specifically for students interested in secondary school mathematics
teaching. It covers "the usual topics:" groups, rings, fields that all
math majors must know. The emphasis will be on connecting abstract
concepts to practical problems such as public key cryptograhy and error
correcting codes and to topics appearing in the high school math
curriculum such as solutions of equations. More details will be found on
the Course Webpage.Course Webpage: Grading: quizzes 20% (there will be 4 quizzes), midterm examinations 40% (there will be two midterm tests), final examination 40%Homework: About 7 homework sets will be posted on theCourse Webpage. Each will be due approximately two weeks after it is posted. Comments:Math 115 - Section 1 - Introduction to Number TheoryInstructor: Chung Pang MokLectures: MWF 12:00-1:00pm, Room 241 CoryCourse Control Number: 54757Office: 889 EvansOffice Hours: TBAPrerequisites: Required Text: Niven, Zuckerman and Montgomery, An Introduction to the Theory of Numbers, Wiley, 5th editionRecommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~mok/115.htmlGrading: 20% homework, 30% for two mid-terms, 50% finalHomework: Assigned and due weekly.Comments:Math 121A - Section 1 - Mathematics for the Physical SciencesInstructor: John NeuLectures: TuTh 9:30-11:00am, Room 85 EvansCourse Control Number: 54760Office: 1051 EvansOffice Hours: TBAPrerequisites: Required Text: Boa, Mathematical Methods for Physical SciencesRecommended Reading: Syllabus: This course begins with subjects from math 1b, 53 and
54 that many do not get the first time around. That is, Taylor series
and applications (from 1b), differential calculus in several variables
(from math 53) and complex exponential and its applications to ODE and
PDE (math 54) What's different is the maturity level, and that you are
strongly encouraged to get it this time.Next, is Fourier series (a math 54 topic too) but now using the full power of complex numbers and the complex exponential. Fourier transform is introduced as the limit of Fourier series as the period interval goes to infinity. Applications of Fourier series and transforms to solutions of ODE and PDE lead naturally to delta functions and Green's functions. That's where the course finishes. In summary, this course is a basic survival kit for students getting slammed by their first serious upper division courses in physics, chemistry, ME, EE, etc. Course Webpage: Grading: Course has 2 midterms, 5th and 10th week (no delay) and a
final. Problem set scores make a small contribution to grade. But
bottom line is you gotta get it done on the exams.Homework: Comments: Math 121A - Section 2 - Mathematical Tools for the Physical SciencesInstructor: Vera SerganovaLectures: MWF 10:00-11:00am, Room 85 EvansCourse Control Number: 54763Office: 709 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 123 - Section 1 - Ordinary Differential EquationsInstructor: Alexander GiventalLectures: TuTh 11:00am-12:30pm, Room 87 EvansCourse Control Number: 54766Office: 701 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 125A - Section 1 - Mathematical LogicInstructor: Jan ReimannLectures: TuTh 12:30-2:00pm, Room 3 EvansCourse Control Number: 54769Office: 705 EvansOffice Hours: TBAPrerequisites: One upper division math course or consent of instructor.Required Text: Lectures Notes by Slaman and Woodin, free of charge will be provided to registered students.Recommended Reading: Syllabus: Propositional logic, first order logic - syntax and
semantics, first order structures, the Gödel completeness theorem,
compacntess, basic model theory, undecidability and incompleteness.Course Webpage: Will be set up on bSpace.Grading: TBAHomework: Homework will be assigned once a week, due the following week.Comments:Math 127 - Section 1 - Mathematical and Computational Methods in Molecular BiologyInstructor: Lior PachterLectures: TuTh 9:30-11:00am, Room 75 EvansCourse Control Number: 54772Office: 1081 EvansOffice Hours: TuTh 11:00am-12:30pmPrerequisites: Math 55 or permission of instructorRequired Text: Durbin, Eddy, Krogh and Mitchison, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic AcidsRecommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~lpachter/127/Grading: homework 50%, midterm 20%, final presentation/project 30%Homework: WeeklyComments: This course provides an introduction to the
mathematical aspects of computational genomics with an emphasis on
evolutionary biology.Math 128A - Section 1 - Numerical AnalysisInstructor: Ming GuLectures: MWF 2:00-3:00pm, Room 60 EvansCourse Control Number: 54775Office: 877 EvansOffice Hours: TBAPrerequisites: Required Text: R. L. Burden and J. D. Faires, Numerical Analysis, 8th editionRecommended Reading:Syllabus: In this course, we will learn some of the most basic concepts and methods in scientific computing. Many physical phenomena are governed by differential equations. Newton's second law of motion is in general a set of second order time-dependent differential equations. In this course our main goal is to develop a number of tools for solving these and other equations numerically. Our main focus is in developing numerical methods for such purposes. Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to the Theory of SetsInstructor: John KruegerLectures: MWF 3:00-4:00pm, Room 85 EvansCourse Control Number: 54790Office: 751 EvansOffice Hours: TBAPrerequisites: 113 and 104Required Text: Yiannis Moschovakis, Notes on Set TheoryRecommended Reading:Syllabus: Cardinality of sets, axioms of set theory, well-orderings, axiom of choice and its consequences, ordinal and cardinal numbers.Course Webpage: http://math.berkeley.edu/~jkrueger/math135.htmlGrading:Homework:Comments: The course, while primarily aimed at students
interested in mathematical logic, will also benefit students in any area
of pure mathematics, including abstract algebra and analysis. The
course will help improve skills in abstract thinking and reading and
writing of proofs, and also assist in developing a general perspective
of mathematics from the foundational point of view.Math 142 - Section 1 - Elementary Algebraic TopologyInstructor: Mauricio VelascoLectures: MWF 9:00-10:00am, Room 71 EvansCourse Control Number: 54793Office: 1063 EvansOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 143 - Section 1 - Elementary Algebraic GeometryInstructor: David EisenbudLectures: TuTh 11:00am-12:30pm, Room 3102 EtcheverryCourse Control Number: 54795Office: 909 EvansOffice Hours: Tu-Th 2:00-3:00pm (tentative)Prerequisites: Math 113 or the equivalentRequired Text: Hassett, Introduction to Algebraic Geometry, (softcover), Cambridge U. PressRecommended Reading:Syllabus: Topics to be covered include affine and projective
varieties, elimination theory, Groebner bases, Bezout's theorem,
Grassmann varieties and the theory of algebraic curves, especially plane
curves.Course Webpage: https://bspace.berkeley.eduGrading: Homework, two in-class tests, and a take-home final or project.Homework: Homework will be assigned every week.Comments: The course is suitable both for those interested in
pure mathematics and for those interested in applications, as
constructive and computational aspects of the subject will also be
treated.Math 152 - Section 1 - School CurriculumInstructor: Emiliano GomezLectures: MWF 11:00am-12:00pm, Room 5 EvansCourse Control Number: 54796Office: 985 EvansOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 160 - Section 1 - History of MathematicsInstructor: Hung-Hsi WuLectures: TuTh 12:30-2:00pm, Room 85 EvansCourse Control Number: 54802Office: 733 EvansOffice Hours: TBAPrerequisites: Math 53, 54, 113Required Text: C.B. Boyer and U.C. Merzbach, A History of Mathematics, 2nd edition, Wiley, 1991Recommended Reading: To be given throughout the course.Syllabus: After a very short chronological overview (two or three
lectures) of the main events in the development of mathematics, we will
trace the evolution of geometry, algebra, analysis, and number theory
from the time of the Babylonians to the nineteenth century. The
discussion of geometry and algebra will be intentionally brief, so that
we can concentrate more on analysis and number theory. The
Boyer-Merzbach text will be a main reference, but will not be followed
chapter by chapter.Course Webpage: See b-space.Grading: Homework 30%, Midterm 20%, Final 50%Homework: Homework will be assigned every week, and due once a week. Students are expected to consult the web.Comments: The assignments and the exams will both involve writing short essays about historical or biographical information.Math 185 - Section 1 - Introduction to Complex AnalysisInstructor: Lek-Heng LimLectures: MWF 2:00-3:00pm, Room 70 EvansCourse Control Number: 54805Office: 873 EvansOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 185 - Section 2 - Introduction to Complex AnalysisInstructor: Marco AldiLectures: TuTh 11:00am-12:30pm, Room 75 EvansCourse Control Number: 54808Office: 805 EvansOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 185 - Section 3 - Introduction to Complex AnalysisInstructor: Michael RoseLectures: MWF 8:00-9:00am, Room 75 EvansCourse Control Number: 54811Office: 849 EvansOffice Hours: TBAPrerequisites: Math 104Required Text: J. Brown and R. Churchill, Complex Variables and Applications, 8th editionRecommended Reading:Syllabus: See course webpage.Course Webpage: http://math.berkeley.edu/~rose/math185Grading: 20% homework, 20% first midterm, 20% second midterm, 40% final exam.Homework: Homework will be assigned once a week, and will be due on Wednesdays.Comments:Math 191 - Section 1 - Advanced Problem SolvingInstructor: Olga HoltzLectures: TuTh 3:30-5:00pm, Room 5 EvansCourse Control Number: 54814Office: 821 EvansOffice Hours: TuTh 10:00-11:00am & by appt.Prerequisites: Math 16A-B, 53, 54, 55, or equivalent backgroundRequired Text: None: some reading material will be posted on the web.Recommended Reading: Gleason, A. M.; Greenwood, R. E.; and Kelly, L. M.; The William Lowell Putnam Mathematical Competition. Problems and solutions: 1938--1964. Mathematical Association of America, Washington, D.C., 1980. ISBN 0-88385-428-7The William Lowell Putnam mathematical competition. Problems and solutions: 1965--1984.
Edited by Gerald L. Alexanderson, Leonard F. Klosinski and Loren C.
Larson. Mathematical Association of America, Washington, DC, 1985. ISBN
0-88385-441-4Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi; The William Lowell Putnam Mathematical Competition, 1985--2000. Problems, solutions, and commentary. MAA Problem Books Series. ISBN 0-88385-807-X Syllabus: Mathematical induction. Integer and prime numbers.
Congruence. Rational and irrational numbers. Complex numbers.
Progressions and sums. Diophantine equations. Quadratic reciprocity.
Basic theorems and techniques from algebra. Polynomials. Inequalities.
Extremal problems. Limits. Integrals. Series. Differential equations.
Combinatorial counting. Recurrence relations. Generating functions. The
inclusion-exclusion principle. The pigeonhole principle. Combinatorial
averaging.Course Webpage: http://www.cs.berkeley.edu/~oholtz/191/Grading: Based on homework and class participation.Homework: Homework will be assigned on the web every week, due next week.Comments: This is an advanced class intended to improve students'
problem solving skills. A sub-goal of this class is to prepare
UC-Berkeley competitors for the Putnam competition. The class will be
taught in an informal, problem-oriented way. Homework problems will
require hard work, ingenuity, and good mathematical writing. Math 191 - Section 2 - CryptographyInstructor: Robert ColemanLectures: MWF 11:00am-12:00pm, Room 4 EvansCourse Control Number: 54817Office: 901 EvansOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus: In 1757, Cassanova could say:Five or six weeks later, she [Madame d'Urfé] asked me if I had deciphered the manuscript which had the transmutation procedure. I told her that I had. In this course we'll see why he couldn't get away with it today. Course Webpage:Grading:Homework:Comments:Math 202A - Section 1 - Introduction to Topology and AnalysisInstructor: Donald SarasonLectures: MWF 8:00-9:00am, Room 60 EvansCourse Control Number: 54910Office: 779 EvansOffice Hours: TBAPrerequisites: Math 104 or the equivalent, plus familiarity with
basic set theory. There will be a handout on the axiom of choice and
Zorn's lemma for those who want it.Required Text: None. See below for suggested references.Syllabus: POINT-SET TOPOLOGY. Fundamentals (such as open and
closed sets, convergence, continuity, connectedness, boundary, closure,
interior, etc.), metric spaces, product spaces, compactness,
separationaxioms, theorems of Urysohn and Tietze, locally compact
spaces, quotientspaces, spaces of continuous functions,
Stone-Weierstrass theorem, Arzela-Ascoli theorem, metrization. MEASURE
AND INTEGRATION. Sigma-rings and sigma-algebras, measures and outer
measures, extensions of measures, Lebesgue measure in Euclidean spaces,
integration, convergence theorems.Course Webpage:Grading: The course grade will be based on homework. There will be no exams.Homework: Homework will be assigned weekly and will be carefully
graded. On average there will be 3-4 HW problems per week, many of them
challenging.Comments: The lectures will be self-contained except for routine
details. The basic approach will be abstract, but moderated by frequent
examples. No textbook will be followed in detail. The following
references are suggested.G. B. Folland, Real Analysis, Second Edition, Wiley Interscience, 1999 H. L. Royden, Real Analysis, Third Edition, Prentice Hall, 1988 J. L. Kelley, General Topology, Springer-Verlag, 1975 The books of Folland and Royden cover most of the material in Math 202AB, in some cases more thoroughly, in some cases less thoroughly, than in the courses. The classic of Kelley contains the material on topology in Math 202A, i.e., the first half of the course. Math 204 - Section 1 - Ordinary Differential EquationsInstructor: Richard BorcherdsLectures: TuTh 9:30-11:00am, Room 81 EvansCourse Control Number: 54913Office: 927 EvansOffice Hours: TuTh 11:00am-12:00pmPrerequisites: Math 104Required Text: E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, ISBN-13:978-0898747553 (This is not the same as "Introduction to Ordinary Differential Equations" by Coddington.)Recommended Reading:Syllabus: Rigorous theory of ordinary differential equations.
Fundamental existence theorems for initial and boundary value problems,
variational equilibria, periodic coefficients and Floquet Theory,
Green's functions, eigenvalue problems, Sturm-Liouville theory, phase
plane analysis, Poincare-Bendixon Theorem, bifurcation, chaos.Course Webpage: http://math.berkeley.edu/~reb/204Grading: Based on homework and possibly a final exam.Homework: To be assigned each week.Comments:Math 214 - Section 1 - Differentiable ManifoldsInstructor: Mariusz WodzickiLectures: MWF 11:00am-12:00pm, Room 47 EvansCourse Control Number: 54916Office: 995 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 215A - Section 1 - Algebraic Topology Instructor: Christian ZickertLectures: TuTh 11:00am-12:30pm, Room 3 EvansCourse Control Number: 54919Office: 1053 EvansOffice Hours: TBAPrerequisites:Required Text: Glen E. Bredon, Topology and Geometry, GTM 139, SpringerRecommended Reading: Allen Hatcher, Algebraic Topology, available at http://www.math.cornell.edu/~hatcher/AT/ATpage.htmlSyllabus: Fundamental group, covering spaces, homology and cohomology, homotopy groups.Course Webpage: http://math.berkeley.edu/~zickert/Grading:Homework:Comments:Math C218A - Section 1 - Probability TheoryInstructor: James PitmanLectures: TuTh 12:30-2:00pm, Room 334 EvansCourse Control Number: 54922Office: 303 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 221 - Section 1 - Advanced Matrix Computation Instructor: Ming GuLectures: MWF 10:00-11:00am, Room 5 EvansCourse Control Number: 54925Office: 861 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Matrix computations are among the most basic of all
scientific computations. A surprising number of scientific and
engineering problems can be formulated and solved effectively using
matrix tools and algorithms. In this course we will introduce numerical
methods for solving the three basic problems in matrix computations:
linear systems of equations, linear least squares problems, and
eigenvalue problems. Along the way, we will also discuss the two most
important issues concerning a numerical method, namely speed (or
computational efficiency) and accuracy.Course Webpage: Grading:Homework: Comments: Math 222A - Section 1 - Partial Differential EquationsInstructor: Lawrence C. EvansLectures: MWF 12:00-1:00pm, Room 3 EvansCourse Control Number: 54928Office: 1033 EvansOffice Hours: TBAPrerequisites: Math 105 or Math 202ARequired Text: Lawrence C. Evans, Partial Differential Equations, American Math Society.Recommended Reading:Syllabus: The theory of boundary value and initial value problems
for partial differential equations, with emphasis on nonlinear
equations. Laplace's equation, heat equation, wave equation, nonlinear
first-order equations, conservation laws, Hamilton-Jacobi equations,
Fourier transform, Sobolev spaces.Course Webpage: Grading: 25% homework, 25% midterm, 50% finalHomework: I will assign a homework problem, due in one week, at the start of each class.Comments: Math C223A - Section 1 - Stochastic ProcessesInstructor: Sourav ChatterjeeLectures: TuTh 2:00-3:30pm, Room 330 EvansCourse Control Number: 54931Office: 333 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Percolation is one of the deepest and most
well-researched branches of probability theory, and yet a repository of a
large number of important open questions. Advances in percolation were
responsible, in part, for Wendelin Werner's Fields Medal in 2006. The
purpose of this course is to serve as an introduction to this
fascinating and beautiful area of mathematics to advanced graduate
students.Course Webpage: http://www.stat.berkeley.edu/~sourav/stat206Afall08.htmlGrading:Homework: Comments: Math 224A - Section 1 - Mathematical Methods for the Physical SciencesInstructor: F. Alberto GrünbaumLectures: TuTh 9:30-11:00am, Room 5 EvansCourse Control Number: 54934Office: 903 EvansOffice Hours: TuWTh 11:00am-12:00pmPrerequisites:Required Text: Stakgold, Green's functions and boundary value problemsRecommended Reading:Syllabus: This is the first semester of a two semester sequence.
The main topic here is basic functional analysis, i.e. infinite
dimensional linear algebra. I would like to think of this class as "Functional Analysis in action" In this class we will see how this subject arises naturally form the study of concrete problems in ordinary and partial differential equations, Fourier and other transforms, Green functions, perturbation theory, etc. and how this has always been a natural tool to study many linear problems in several areas of physics, chemistry and related sciences. We will see that in many cases these tools are well suited to study non-linear problems too. In the first semester I will try to cover most of the material in Stakgold's book "Green's functions and boundary value problems". This will give us the tools needed to go into many "applications". I will supplement the material in the book with a number of concrete physical models such as Brownian motion. Course Webpage: Grading:Homework: There will be weekly assignments, mainly from the book.Comments: The grade will be based on the homework.Math 225A - Section 1 - MetamathematicsInstructor: Leo HarringtonLectures: MWF 12:00-1:00pm, Room 35 EvansCourse Control Number: 54937Office: 711 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage: Grading:Homework:Comments:Math 228A - Section 1 - Numerical Solution of Differential EquationsInstructor: John StrainLectures: TuTh 11:00am-12:30pm, Room 70 EvansCourse Control Number: 54940Office: 1099 EvansOffice Hours: TBAPrerequisites: Math 128A or equivalent knowledge of basic
numerical analysis. Sufficient computer skills and gumption to download,
compile, modify and run numerical packages written in Fortran and C.Required Text:Recommended Reading: E. Hairer, S. P. Norsett and G. Wanner, Solving ordinary differential equations, Second Edition (2 vols.), SpringerU. M. Ascher, R. M. M. Mattheij, and R. D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, SIAM, 1995P. Deuflhard and F. Bornemann, Scientific Computing with Ordinary Differential Equations, Springer, 2002Syllabus: The course will cover theory and practical methods for solving systems of one-dimensional differential and integral equations.Methods for solving initial value problems for systems of ordinary differential equations: construction, convergence and implementation: Classical multistep (Adams and BDF) and Runge-Kutta methods. Stable high-order deferred correction methods. Solution of initial value problems for systems of ordinary differential-algebraic equations. Solution of boundary value problems for systems of ordinary differential equations: Classical shooting and finite difference techniques. Divide and conquer algorithms for integral equations. Solution of boundary value problems for elliptic systems of linear partial differential equations: Second-order finite difference methods. Derivation and fast solution of boundary integral equations. Course Webpage: http://math.berkeley.edu/~strain/228a.F08/Grading: Grades will be based on weekly problem sets, some individualized.Homework:Comments: Class Notes available from the course webpage.Math 229 - Section 1 - Theory of ModelsInstructor: Thomas ScanlonLectures: TuTh 12:30-2:00pm, Room 5 EvansCourse Control Number: 54943Office: 723 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage: Grading:Homework:Comments:Math 239 - Section 1 - Algebraic StatisticsInstructor: Bernd SturmfelsLectures: TuTh 8:00-9:30am, Room 81 EvansCourse Control Number: 54946Office: 925 EvansOffice Hours: W 9:00-11:00 and by appointmentPrerequisites: Fluency in discrete probability and a serious interest in statistics. Knowledge of undergraduate abstract algebra(at the level of Math 113) and computational algebra (at the level of the [Cox-Little-O'Shea]). Experience with mathematical software (Matlab, R, Maple, Magma, M2, etc.) will be helpful. Required Text: There is no required text book for this course. Lecture notes will be posted at this website.Recommended Reading:Syllabus:Course Webpage: http://math.berkeley.edu/~bernd/stat260.htmlGrading: The course grade will be based on both the homework and the course projects.Homework: There will be weekly homework during the first eight weeks of the course.Comments:Math 240 - Section 1 - Riemannian GeometryInstructor: Ian AgolLectures: TuTh 9:30-11:00am, Room 47 EvansCourse Control Number: 54949Office: 907 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage: Grading:Homework:Comments:Math 250A - Section 1 - Groups, Rings, and FieldsInstructor: David EisenbudLectures: TuTh 8:00-9:30am, Room 70 EvansCourse Control Number: 54952Office: 909 EvansOffice Hours: Tu-Th 2:00-3:00pm (tentative)Prerequisites: Math 114 or consent of instructor.Required Text: Lorenz, Algebra, Vols. 1,2, Springer-VerlagRecommended Reading: Freyd, Abelian Categories (on course website).Lang, AlgebraSyllabus: This course will focus on the basic problems of solving
polynomial equations as a unifying theme in the study of groups, rings
and fields, following the new text "Algebra", by Falko Lorenz (Vols. 1
and 2, Springer Verlag "Universitext".) Basic ideas of Category Theory
will be introduced as well.From the Catalogue Description: Group theory, including the Jordan-Hoolder theorem and the Sylow theorems. Basic theory of rings and their ideals. Unique factorization domains and principal ideal domains. Modules. Chain conditions. Fields, including fundamental theorem of Galois theory, theory of finite fields, and transcendence degree. Course Webpage: https://bspace.berkeley.eduGrading: 50% homework, 20% midterm, 30% finalHomework: Homework will be assigned in class, and due once a week.Comments: This course treats many of the same topics as in Math
113-114, but much faster and at a higher level of abstraction. Students
will be expected to read the text independently, with only some of the
topics covered in class. There will be a lot of independent reading and
homework.Math 254A - Section 1 - Number TheoryInstructor: Martin OlssonLectures: MWF 2:00-3:00pm, Room 85 EvansCourse Control Number: 54958Office: 887 EvansOffice Hours: TBAPrerequisites:Required Text: S. Lang, Algebraic Number Theory.Recommended Reading:Syllabus: This will be an introduction to algebraic number
theory. I intend to cover Part I of Lang's book (Chapters I-VIII), and
time permitting some selected topics from Parts two and three. This
includes the basic theory of algebraic integers, completions,
ramification, cyclotomic fields, Minkowski bound, and some basic
properties of zeta and L-functions.Course Webpage: Grading: Based on weekly (substantial) homeworks.Homework: Weekly.Comments:Math 256A - Section 1 - Algebraic GeometryInstructor: Arthur OgusLectures: MWF 9:00-10:00am, Room 81 EvansCourse Control Number: 54961Office: 877 EvansOffice Hours: TBAPrerequisites:Required Text: R. Hartshorne, Algebraic GeometryRecommended Reading: Qing Liu, Algebraic Geometry and Algebraic CurvesA. Grothendieck and J. Dieudonne, Elements de Geometrie AlgebriqueSyllabus: Grothendieck's theory of schemes has proved to be a
spectacularly successful foundation for algebraic geometry, providing
the framework for the understanding and solution of many classical
problems. It has also established a unification between geometry and
number theory--``arithmetic geometry''--that has been equally, if not
more, spectacular, leading to solutions of the Weil conjectures, the
Mordell conjecture, and the proof of Fermat's Last Theorem. My goal in
this course will be to provide an introduction to scheme theory,
preparing both for work both in ``classical'' algebraic geometry over
the complex numbers and in the ``arithmetic'' theory of schemes over
rings of integers in numberfields. Hartshorne's classic text will be our
main guide, but I plan to supplement it with other more arithmetic
treatments, including Grothendieck's EGA. I will skip chapter I of
Hartshorne's book, beginning instead by discussing affine algebraic sets
and spaces; then I will go straight to chapter II. Students should have
a good foundation in commutative algebra, as well as some experience
with global techniques in geometry (e.g. differential or algebraic
topology).Course Webpage: http://math.berkeley.edu/~ogus/Math%20_256A--08/index.htmlGrading: Yes.Homework: Lots and lots.Comments:Math 261A - Section 1 - Lie GroupsInstructor: Mark HaimanLectures: MWF 10:00-11:00am, Room 145 McConeCourse Control Number: 54967Office: 855 EvansOffice Hours: WF 1:30-3:00pmPrerequisites: Background in algebra and topology equivalent to
202A and 250A. Although 214 (Differential Manifolds) is the official
prerequisite, I will review in the lectures those bits of differential
geometry that we will needed.Required Text: Anthony W. Knapp, Lie Groups Beyond an Introduction, 2nd EditionRecommended Reading: Armand Borel, Linear Algebraic Groups, 2nd Enlarged EditionSyllabus: General theory of real and complex Lie groups and their
Lie algebras; classification of compact Lie groups and complex
semisimple Lie groups and their representations. I will also give an
introduction to algebraic groups and Hopf algebras, to serve as
preparation for Reshetikhin covering quantum groups in 261B.Course Webpage: http://math.berkeley.edu/~mhaiman/math261A-fall08Grading: Based on homework assignments.Homework:Comments:Math 265 - Section 1 - Differential TopologyInstructor: Peter TeichnerLectures: TuTh 11:00am-12:30pm, Room 85 EvansCourse Control Number: 54970Office: 703 EvansOffice Hours: TBAPrerequisites: 214, 215ARequired Text:Recommended Reading: Davis-Kirk, Milnor-Stasheff, Stong, Switzer are good text books.Syllabus: The course will start with a short survey on Morse
theory and the s-cobordism theorem. Then the Thom-Pontrjagin
construction will be discussed in detail. It translates smooth manifolds
(with additional structure) up to bordism into the homotopy groups of
certain Thom spaces. This will lead to the notion of Thom spectra and
the associated homology theories. In some cases, these can be computed
using characteristic classes which form the next topic of the class. We
will then use characteristic numbers to write down certain genera (e.g.
Todd-genus, L-genus, A-genus, Witten-genus) that have an interpretation
as the index of elliptic operators. If time permits, the heat equation
proof of the index theorem will be sketched with an emphasis on its
relation to super symmetry.Course Webpage: Will appear at http://math.berkeley.edu/~teichnerGrading:Homework: Regular homework will be offered.Comments:Math 270 - Section 1 - Hot Topics Course in MathematicsInstructor: Peter TeichnerLectures: Tu 3:30-5:00pm, Room 51 EvansCourse Control Number: 54973Office: 703 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 273I - Section 1 - Numerical Functional AnalysisInstructor: Olga HoltzLectures: TuTh 12:30-2:00pm, Room 81 EvansCourse Control Number: 54978Office: 821Office Hours: TuTh 10:00-11:00am & by appt.Prerequisites: Math 104 & Math 110 & Math 128A or equivalent background Required Text: Online lecture notes by Carl de Boor (see http://pages.cs.wisc.edu/~deboor/717/)Recommended Reading:Syllabus: Fundamentals of normed linear spaces and their duals.
Linear and nonlinear operators acting on normed linear spaces.
Applications to approximate solutions of operator equations by
discretization and iteration. Perturbation and error. Variational
problems. Basics of approximation theory.Chapter headings: 1. Linear algebra. 2. Advanced calculus. 3. Normed linear spaces. 4. The (continuous) dual. 5. Baire category and consequences. 6. Convexity. 7. Inner product spaces. 8. Compact perturbation of the identity. 9. The spectrum of a linear map. 10. Linearization and Newton's method. Course Webpage: http://www.cs.berkeley.edu/~oholtz/273I/Grading: Based on homework and final presentation.Homework: Homework will be assigned on the web every week, due next week.Comments:Math 276 - Section 1 - Topics in TopologyInstructor: Constantin TelemanLectures: TuTh 12:30-2:00pm, Room 9 EvansCourse Control Number: 54979Office: 905 EvansOffice Hours: W 1:00-2:00pm, Th 5:00-6:30pmPrerequisites: Algebraic Topology 215A,BRequired Text: A list of papers (downloadable)Recommended Reading: Félix, Halperin and Thomas, Rational Homotopy Theory, Springer GTM, 2001.Griffiths and Morgan, Rational Homotopy Theory and Differential Forms, Birkhäuser, 1983.Syllabus: The first 2/3 of the course will cover the description
of rational homotopy types by differential graded algebras (Sullivan)
and differential graded Lie algebras (Quillen). Some highlights include
Haefliger's computation of the rational homotopy of spaces of maps and
the formality theorem for compact Kähler manifolds. We will start with
concrete constructions for single spaces and move on to the categorical
set-up, and the main theorems on equivalences of homotopy categories.
The final third of the course will discuss the non-commutative theory:
A-infinity algebras and topological conformal field theories (after
Kontsevich, Costello etc).Course Webpage: http://math.berkeley.edu/~teleman/RatGrading: There will be a thoroughly thought-out system.Homework: Assigned periodically.Comments:Math 276 - Section 2 - Topics in Analysis - Smooth Algebras of Operators and K-TheoryInstructor: Richard MelroseLectures: MWF 1:00-2:00pm, Room 45 EvansCourse Control Number: 54981Office: 895 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: In this course I plan to describe aspects of smooth K-theory.I will start with a discussion of the algebra of smoothing operators in its various forms and properties including finite-dimensional approximation, the Fredholm determinant, group of invertible perturbations of the identity and hence to definitions of odd and even K-theory. Subsequently I will discuss: 1. The loop group and delooping sequence and the Chern character. 2. Semiclassical quantization and Bott periodicity. Thom isomorphism and Atiyah-Singer theorem. 3. The quantization (looping) sequence and Quillen's line bundle. 4. Segal's representation of the loop group and the K-theory gerbe. As time (and the enthusiasm of the audience) permits I will discuss K-homology, twisting of K-theory and bordism (for which I will need some pseudodifferential machinery which I will acquire by fiat). Course Webpage: Grading: Homework: Comments:Math 279 - Section 1 - Topics in Partial Differential EquationsInstructor: Maciej ZworskiLectures: TuTh 2:00-3:30pm, Room 2 EvansCourse Control Number: 54982Office: 897 EvansOffice Hours: M 2:00-3:00pm or by appt.Prerequisites: Math 222A or equivalentRequired Text: Recommended Reading: S.H. Tang and M. Zworski, Potential scattering on the real line, http://math.berkeley.edu/~zworski/tz1.pdfJ. Sjöstrand, Lectures on resonances, http://www.math.polytechnique.fr/~sjoestrand/CoursgbgWeb.pdfSyllabus: The course will provide an introduction to mathematical
scattering theory from the PDE point of view. A basic graduate course
in real and functional analysis is the only prerequisite. Needed facts,
such as analytic Fredholm theory, or properties of solutions to
hyperbolic equations will be developed as we move along. The ﬁrst
quarter of the course will be based on the notes by S.H. Tang and M.
Zworski (available on line, see above). That will introduce basic
concepts of scattering theory in the simplest setting. There will be no
formal requirements. 1. Scattering theory in one dimension: scattering matrix, resolvent spectral decomposition. 2. Trace formulae in one dimension; the Maaß-Selberg relation, the Eisenbud-Wigner formula. 3. Resonances: asymptotic distribution, complex scaling in one dimension, the Breit-Wigner formula. 4. Scattering theory of the free Laplacian: the resolvent, spectral decomposition, generalized eigenfuctions, absolute scattering matrix. 5. Compactly supported potentials: distorted Fourier transform, scattering matrix, wave operators. 6. Resonances in higher dimensions: upper bounds on the number of resonances, the method of complex scaling, Poisson formula for resonances, lower bounds on the density of resonances. 7. Possible additional topics: obstacle scattering, “black box” formalism, long range perturbations, scattering on manifolds. Course Webpage:Grading:Homework:Comments:Math 300 - Section 1 - Teaching WorkshopInstructor: The StaffLectures: W 4:00-6:00pm, Room 70 EvansCourse Control Number: 55663Office: Office Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: |