# Spring 2009

Math 1A - Section 1 - CalculusInstructor: Zvezdelina StankovaLectures: TuTh 3:30-5:00pm, Room 105 StanleyCourse Control Number: 53903Office: 713 EvansOffice Hours: TuTh 2:00-3:30pmPrerequisites: Three and one-half years of high school math,
including trigonometry and analytic geometry, plus a satisfactory grade
in one of the following: CEEB MAT test, an AP test, the UC/CSU math
diagnostic test, or 32. Consult the mathematics department for details.
Students with AP credit should consider choosing a course more advanced
than 1A.Required Text: Stewart, Calculus: Early Transcendentals, Brooks/ColeRecommended 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: The following course webpage will be updated in the beginning of the spring'09 term: http://math.berkeley.edu/~stankova/Grading: 15% quizzes, 25% each midterm, 35% finalHomework: Homework will be assigned on the web every class, and due once a week.Comments: Math 1B - Section 1 - CalculusInstructor: Marina RatnerLectures: MWF 12:00-1:00pm, Room 2050 Valley LSBCourse Control Number: 53942Office: 827 EvansOffice Hours: TBA Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 1B - Section 2 - CalculusInstructor: Marina RatnerLectures: MWF 2:00-3:00pm, Room 155 DwinelleCourse Control Number: 53981Office: 827 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 1B - Section 3 - CalculusInstructor: Richard BorcherdsLectures: TuTh 12:30-2:00pm, Room 2050 Valley LSBCourse Control Number: 54026Office: 927 EvansOffice Hours: TuTh 2:00-3:30pmPrerequisites: Math 1ARequired Text: Stewart, Calculus: Early Transcendentals, Brooks/ColeRecommended Reading:Syllabus: Techniques of integration; applications of integration.
Infinite sequences and series. First-order ordinary differential
equations. Second-order ordinary differential equations; oscillation and
damping; series solutions of ordinary differential equations.Course Webpage: http://math.berkeley.edu/~reb/1B/index.htmlGrading: 20% homework, 20% quizzes, 15% each midterm, 30% finalHomework: Homework will be assigned on the web every week, and is due once a week.Comments:Math 16A - Section 1 - Analytical Geometry and CalculusInstructor: Hugh WoodinLectures: TuTh 2:00-3:30pm, Room 155 DwinelleCourse Control Number: 54062Office: 721 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 16B - Section 1 - Analytical Geometry and CalculusInstructor: Leo HarringtonLectures: MWF 11:00am-12:00pm, Room 1 PimentalCourse Control Number: 54107Office: 711 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 2 - Analytical Geometry and CalculusInstructor: Thomas ScanlonLectures: TuTh 11:00am-12:30pm, Room 105 StanleyCourse Control Number: 54152Office: 723 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - The Mathematics of GamblingInstructor: Alberto GrünbaumLectures: Tu 11:00am-12:30pm, Room 939 EvansCourse Control Number: 54182Office: 903 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - What is Happening in Math and Science?Instructor: Jenny HarrisonLectures: F 3:00-4:00pm, Room 891 EvansCourse Control Number: 54185Office: 851 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 3 - Flipping Coins and Other Fun Problems in Probability TheoryInstructor: Nicolai ReshetikhinLectures: Tu 1:00-3:00pm, Room 740 EvansCourse Control Number: 54187Office: 915 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: The goal of this course is an introduction to
probability and its applications. Flipping a coin and estimating how
many times it will land on one side and how many times it will land on
the other side is a good illustration to how determinism enters into
randomness. We will start with this example (after a short recollection
of basic principles of probability).We will compute the probability of a coin landing n times on one side after N flipping. Then we will discuss random processes and an important class known as Markov processes. We will also discuss the question known in probability theory as large deviations and will see that some times there is an element of determinism in randomness. We will consider some simple combinatorial examples such as pile of squares to illustrate this phenomenon. The seminar will start with a series of introductory lectures, and then, towards the end of the seminar, students will give presentations. Knowledge of elements of probability theory is desirable but not required. The list of suggested reading will be given on the first seminar and will be posted at the seminar's web site before the beginning of the semester. Course Webpage: Grading: Homework: Comments: The class is P/NP. The class will meet for the first 10 weeks of the semester.Math 32 - Section 1 - PrecalculusInstructor: Michael RoseLectures: MWF 8:00-9:00am, Room 101 Valley LSACourse Control Number: 54188Office: 849 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 39A - Section 1 - Seminar for Teaching Math in SchoolsInstructor: Emiliano GomezLectures: M 2:00-4:00pm, Room 45 EvansCourse Control Number: 54202Office: 985 EvansOffice Hours: TBAPrerequisites: Math 1ARequired Text: NoneRecommended Reading: To be handed out in class.Syllabus: We will discuss important mathematics topics for
students in K-12, interesting mathematics problems for collaborative
group work, and issues pertaining to the practice of teaching. The
course includes a field placement in a local school.Course Webpage: Grading: Based on homework, journal of field placement observations, and a final project.Homework: There will be weekly homework assigned during class.Comments: Math 53 - Section 1 - Multivariable CalculusInstructor: James SethianLectures: TuTh 8:00-9:30am, Room Wheeler AuditoriumCourse Control Number: 54224Office: 725 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 54 - Section 1 - Linear Algebra and Differential EquationsInstructor: Paul VojtaLectures: TuTh 9:30-11:00am, Room 2050 Valley LSBCourse Control Number: 54281Office: 883 EvansOffice Hours: MTuTh 2:00-3:00pm (subject to change)Prerequisites: 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: The topics for the course will be:
- Basic linear algebra
- Matrix arithmetic and determinants
- Vectors in
**R**^{2}and**R**^{3} - Vector spaces and inner product spaces
- Eigenvalues and eigenvectors
- Linear transformations
- Homogeneous ordinary differential equations
- First-order differential equations with constant coefficients
- Fourier series and partial differential equations
Course Webpage: http://math.berkeley.edu/~vojta/54.htmlGrading: Grading will be based on:
The component of the grade coming from discussion sections is left to the discretion of the section leader, but it is likely to be determined primarily by weekly quizzes and homework assignments. Homework: Weekly homework will be assigned; the exact problems will be made available closer to the start of the semester.Comments:Math 54 - Section 2 - Linear Algebra and Differential EquationsInstructor: Jack WagonerLectures: MWF 10:00-11:00am, Room 1 PimentelCourse Control Number: 54320Office: 899 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete MathematicsInstructor: Bernd SturmfelsLectures: TuTh 8:00-9:30am, Room 145 DwinelleCourse Control Number: 54359Office: 925 EvansOffice Hours: W 8:00-11:00amPrerequisites: Mathematical maturity appropriate to a sophomore
math class. 1A-1B is recommended but not required. Freshmen with strong
high school math background and a possible interest in majoring in
mathematics are encouraged to take this course.Required Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th EditionRecommended Reading:Syllabus: This course provides an introduction to logic and proof
techniques, basics of set theory, algorithms, elementary number theory,
combinatorial enumeration, discrete probability, graphs and trees, with
a view towards applications in engineering and the life sciences. It is
designed for majors in mathematics, computer science, statistics, and
other related science and engineering disciplines.Course Webpage: http://math.berkeley.edu/~bernd/math55.htmlGrading: 5% quizzes, 15% homework, 20% each of two midterm exams, 40% final examHomework: Weekly homework will be due on Mondays and returned in discussion sections on Wednesdays.Comments:Math 74 - Section 1 - Transition to Upper Division MathematicsInstructor: Daniel Berwick-EvansLectures: MWF 3:00-4:00pm, Room 87 EvansCourse Control Number: 54374Office: Office Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math C103 - Section 1 - Introduction to Mathematical EconomicsInstructor: David AhnLectures: TuTh 2:00-3:30pm, Room 101 WursterCourse Control Number: 54434Office: 549 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 104 - Section 1 - Introduction to AnalysisInstructor: Shamgar GurevitchLectures: MWF 3:00-4:00pm, Room 75 EvansCourse Control Number: 54437Office: 867 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to AnalysisInstructor: Brett ParkerLectures: TuTh 3:30-5:00pm, Room 4 EvansCourse Control Number: 54440Office: 796 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to AnalysisInstructor: Sebastian HerrLectures: TuTh 9:30-11:00am, Room 71 EvansCourse Control Number: 54443Office: 837 EvansOffice Hours: TBAPrerequisites: Math 53 and Math 54Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer (latest edition).Recommended Reading: You may find the following book helpful (optional): Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill.Syllabus: This course provides an introduction to Mathematical
Analysis with a focus on rigorous theory and mathematical reasoning. The
main topics are the following: The real numbers, countable and
uncountable sets. Sequences and limits, Cauchy sequences, subsequences,
infinite series. Metric spaces, compactness. Limits of functions,
continuous functions, uniform continuity. Power series, exponential and
trigonometric functions, uniform convergence of sequences of functions,
interchange of limit operations. Differentiation, the mean value theorem
and applications. The Riemann integral, the fundamental theorem of
calculus, Taylor's theorem. Course Webpage: http://math.berkeley.edu/~herr/104S3Spring09.htmlGrading: 20% homework, 20% first midterm, 20% second midterm, 40% final examHomework: Homework will be assigned every Tuesday and will be due on the following Tuesday, 9:30am in class.Comments: For more information, please take a look at the course webpage.Math 104 - Section 4 - Introduction to AnalysisInstructor: Michael KlassLectures: MWF 1:00-2:00pm, Room 332 EvansCourse Control Number: 54446Office: 319 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to AnalysisInstructor: Lek-Heng LimLectures: MWF 3:00-4:00pm, Room 71 EvansCourse Control Number: 54449Office: 873 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 105 - Section 1 - Second Course in AnalysisInstructor: John KruegerLectures: MWF 4:00-5:00pm, Room 85 EvansCourse Control Number: 54452Office: 751 EvansOffice Hours: TBAPrerequisites: Math 104Required Text: James R. Munkres, Analysis on Manifolds and Howard Wilcox and David Meyers, An Introduction to Lebesgue Integration and Fourier SeriesRecommended Reading: Syllabus: Differential calculus in Rn: the derivative as a linear
map; the chain rule; inverse and implicit function theorems. Lebesgue
integration on the line; comparison of Lebesgue and Riemann integrals.
Convergence theorems. Fourier series, L2 theory. Fubini's theorem,
change of variable.Course Webpage: http://math.berkeley.edu/~jkrueger/math105.htmlGrading: Homework: Comments: Math 110 - Section 1 - Linear AlgebraInstructor: Ole HaldLectures: MWF 2:00-3:00pm, Room 71 EvansCourse Control Number: 54455Office: 875 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 2 - Linear AlgebraInstructor: Joshua SussanLectures: MWF 11:00am-12:00pm, Room 2 EvansCourse Control Number: 54458Office: 761 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 3 - Linear AlgebraInstructor: Mariusz WodzickiLectures: TuTh 9:30-11:00am, Room 200 WheelerCourse Control Number: 54461Office: 995 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 4 - Linear AlgebraInstructor: Chung Pang MokLectures: TuTh 11:00am-12:30pm, Room B51 HildebrandCourse Control Number: 54464Office: 889 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: http://math.berkeley.edu/~mok/110.htmlGrading: Homework: Comments: Math 110 - Section 5 - Linear AlgebraInstructor: Alexander GiventalLectures: MWF 9:00-10:00am, Room 110 BarkerCourse Control Number: 54467Office: 701 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract AlgebraInstructor: Alexander PaulinLectures: MWF 12:00-1:00pm, Room 71 EvansCourse Control Number: 54470Office: 887 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract AlgebraInstructor: Chung Pang MokLectures: TuTh 2:00-3:30pm, Room 3107 EtcheverryCourse Control Number: 54473Office: 889 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: http://math.berkeley.edu/~mok/113.htmlGrading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract AlgebraInstructor: Alexander PaulinLectures: MWF 3:00-4:00pm, Room 2 EvansCourse Control Number: 54476Office: 887 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:< Math 113 - Section 4 - Introduction to Abstract AlgebraInstructor: Brett ParkerLectures: TuTh 12:30-2:00pm, Room 71 EvansCourse Control Number: 54479Office: 796 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math H113 - Section 1 - Honors Introduction to Abstract AlgebraInstructor: George BergmanLectures: MWF 3:00-4:00pm, Room 85 EvansCourse Control Number: 54482Office: 865 EvansOffice Hours: Tu 10:30-11:30am, W 4:15-5:15pm, F 10:30-11:30amPrerequisites: 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: David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd edition, Wiley (2004)Recommended Reading: None.Syllabus: I expect to cover most of Chapters 1-9 and sections 13.1-13.2, and possibly a few other topics.Course Webpage: None.Grading: Homework (25%), two Midterms (15% and 20%), a Final (35%), and regular submission of the daily question (see below) (5%).Homework: An important part of the learning process! Will generally be due on Wednesdays.Comments: Abstract algebra is the study of sets of elements on
which one or more operations are defined, which satisfy specified laws.
The most familiar examples are various systems of numbers, under the
usual operations of addition, multiplication, etc.. But you have already
had a taste of the exotic: In Math 54 you saw matrices, and the fact
that their multiplication operation does not satisfy the commutative law
xy = yx.This course will mainly study two sorts of algebraic structures: groups, and commutative rings (including fields). I am not happy with 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 this reading and have thought about the what you've read. In lecture I go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, motivate ideas in the next reading, discuss points to watch out for in that 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 114 - Section 1 - Second Course in Abstract AlgebraInstructor: Lek-Heng LimLectures: MWF 12:00-1:00pm, Room 6 EvansCourse Control Number: 54485Office: 873 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 116 - Section 1 - CryptographyInstructor: Kenneth A. RibetLectures: TuTh 11:00am-12:30pm, Room 3 EvansCourse Control Number: 54488Office: 885 EvansOffice Hours: TBAPrerequisites: Math 55 is the official prerequisite. In addition,
it would be helpful to have had one or more of Math 110, Math 113, Math
115. If you have had a couple of these upper-division courses but have
never taken Math 55, that should be fine.Required Text: An introduction to mathematical cryptography (Springer link) by Hoffstein, Pipher and SilvermanRecommended Reading: There are lots of interesting books that
have been written about cryptography. During the winter break, you
might want to borrow one or more from your public library. Perhaps Simon Singh's The Code Book is a good place to start.Syllabus: The catalog description is very terse: "Construction
and analysis of simple cryptosystems, public key cryptography, RSA,
signature schemes, key distribution, hash functions, elliptic curves,
and applications". The book covers these topics and more. We'll start
on page 1 and see how far we can get.Course Webpage: http://math.berkeley.edu/~ribet/116/, but it doesn't exist yet. Look for it in December.Grading: Something like 20% homework, 15% each midterm, 50% final. That's my standard mix.Homework: A fair amount, assigned weekly.Comments: The book claims to be self-contained, but it includes
compact summaries of material from and abstract and linear algebra and
from number theory. If you haven't had courses in these subjects, be
prepared for moments when you will need to digest a lot of material in a
short amount of time. I would recommend purchasing the book well ahead
of time and looking over the contents to see whether there are passages
that will be problematic for you. If there are such passages, devote
some time to mastering them before the start of the semester.Math 118 - Section 1 - Fourier Analysis, Wavelets, and Signal ProcessingInstructor: Jon WilkeningLectures: TuTh 11:00am-12:30pm, Room 71 EvansCourse Control Number: 54491Office: 1091 EvansOffice Hours: TBAPrerequisites: Math 53 and 54 or equivalentRequired Text: Boggess & Narcowich, A First Course in Wavelets with Fourier AnalysisRecommended Reading: Yves Nievergelt, Wavelets Made EasyStephane Mallat, A Wavelet Tour of Signal ProcessingSyllabus: This course will cover the basic mathematical theory
and practical applications of Fourier analysis and wavelets, including
one-dimensional signal processing and multi-dimensional image
processing:
- Fourier series, orthogonal systems, sampling and aliasing, FFT
- Fourier integrals and transforms, linear filters, sampling theorem, uncertainty principle, two-dimensional Fourier analysis
- Haar wavelets, Daubechies wavelets, scaling functions, multiresolution analysis, filter banks
- approximation with wavelets, linear and nonlinear techniques, image approximation and adaptive basis selection, edge detection
- transform coding, signal compression, quantization, high bit-rate compression, image and video compression
Course Webpage: http://math.berkeley.edu/~wilken/118.S09Grading: 30% homework, 30% midterm, 40% finalHomework: 8-10 assignments, some involving programming in MatlabComments: Math 121A - Section 1 - Mathematical Tools for the Physical SciencesInstructor: Shamgar GurevitchLectures: MWF 12:00-1:00pm, Room 75 EvansCourse Control Number: 54494Office: 867 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 121B - Section 1 - Mathematical Tools for the Physical SciencesInstructor: Vera SerganovaLectures: MWF 1:00-2:00pm, Room 75 EvansCourse Control Number: 54497Office: 709 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 126 - Section 1 - Introduction to Partial Differential EquationsInstructor: John NeuLectures: TuTh 9:30-11:00am, Room 75 EvansCourse Control Number: 54500Office: 1051 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical AnalysisInstructor: Per-Olof PerssonLectures: MWF 10:00-11:00am, Room 160 KroeberCourse Control Number: 54503Office: 1089 EvansOffice Hours: TBAPrerequisites: Math 53 and 54, basic programming skillsRequired Text: R. L. Burden and J. D. Faires, Numerical Analysis, 8th edition, Brooks-Cole, 2005.Recommended Reading: J. Dorfman, Introduction to MATLAB Programming, Decagon Press, Inc.Syllabus: Basic concepts and methods in numerical analysis:
Solution of equations in one variable; Polynomial interpolation and
approximation; Numerical differentiation and integration; Initial-value
problems for ordinary differential equations; Direct methods for solving
linear system; Least square approximation.Course Webpage: http://math.berkeley.edu/~persson/128AGrading: Homework (30%), midterm exams (20% + 20%), final exam (30%).Homework: Assigned weekly.Comments: Math 128B - Section 1 - Numerical AnalysisInstructor: Ming GuLectures: MWF 2:00-3:00pm, Room 9 EvansCourse Control Number: 54521Office: 861 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 130 - Section 1 - The Classical GeometriesInstructor: Vera SerganovaLectures: MWF 10:00-11:00am, Room 85 EvansCourse Control Number: 54527Office: 709 EvansOffice Hours: TBAPrerequisites: Required Text:Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory SetsInstructor: Thomas ScanlonLectures: TuTh 12:30-2:00pm, Room 75 EvansCourse Control Number: 54530Office: 723 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 136 - Section 1 - Incompleteness and UndecidabilityInstructor: John SteelLectures: TuTh 11:00am-12:30pm, Room 5 EvansCourse Control Number: 54533Office: 717 EvansOffice Hours: TBAPrerequisites: Math 55 would help. Math 125A might help a
little. Math 113, or some equivalent experience with abstract
mathematics (definitions, theorems, and proofs), might help.
Nevertheless, the course will be self-contained.Required Text: Nigel Cutland, Compatibility: An Introduction to Recursive Function Theory, Cambridge University PressRecommended Reading:Syllabus: The course title sounds a bit negative, doesn't it?
Actually, we'll cover some of the most beautiful theorems in Logic,
results of Church, Turing, Kleene, and Godel from the 1930's. These
theorems established basic limitations on what can be computed by
algorithm, and what is provable in axiomatic systems. Among these
results are Kurt Godel's famous incompleteness theorems, which we will
cover toward the end of the semester.Course Webpage: http://math.berkeley.edu/~steel/courses/Courses.htmlGrading: Homework: Homework will be assigned weekly. The assignments will be announced at lecture and posted on the web at http://math.berkeley.edu/~steel/courses/Courses.htmlComments: There will be two midterms, the first in late February
or early March, after we have covered Chapter 5, and the second in late
April. I will announce the exact date for each midterm at least 2 weeks
in advance of it. There will be a written final exam as well.Math 140 - Section 1 - Metric Differential GeometryInstructor: Fraydoun RezakhanlouLectures: MWF 3:00-4:00pm, Room 6 EvansCourse Control Number: 54536Office: 815 EvansOffice Hours: MWF 2:00-3:00pmPrerequisites: Math 140Required Text: Richard S. Millman and George D. Parker, Elements of Differential Geometry, Prentice-Hall Inc.Recommended Reading:Syllabus: This class will be an introduction to the mathematical theory of curves and surfaces. The main topics are:1. Frenet-Serret formula, isoperimetric inequality. 2. Local theory of surfaces in Euclidean space, first and second fundamental forms, Gaussian and mean curvature. 3. Gauss's Theorema Egregium, geodesics, parallelism, the Gauss-Bonnet Theorem. 3. Manifolds and linear connections. Course Webpage: Grading: Homework 30 points, Midterm 30 points, Final exam 40 points.Homework: Comments: Math 141 - Section 1 - Elementary Differential TopologyInstructor: Rob KirbyLectures: MWF 9:00-10:00am, Room 81 EvansCourse Control Number: 54539Office: 919 EvansOffice Hours: MW 10:00-11:00am, Th 11:00am-12:00pmPrerequisites: Math 104 and Linear algebra.Required Text: J. Munkres, Analysis on ManifoldsRecommended Reading: Michael Spivak, Calculus on ManifoldsSyllabus: Inverse and implicit function theorems, Sard's Theorem,
transversality, manifolds, differential forms, integration on
manifolds, de Rham cohomology.Course Webpage: http://math.berkeley.edu/~kirby/math141.htmlGrading: 10% homework, 20% each of two midterms, 50% final.Homework: Homework will be assigned and due once a week.Comments: Math 151 - Section 1 - Mathematics of the Secondary School Curriculum IInstructor: Hung-Hsi WuLectures: MWF 2:00-3:00pm, Room 3 EvansCourse Control Number: 54542Office: 733 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 153 - Section 1 - Mathematics of the Secondary School Curriculum IIIInstructor: Hung-Hsi WuLectures: MWF 11:00am-12:00pm, Room 75 EvansCourse Control Number: 54548Office: 733 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 170 - Section 1 - Mathematical Methods for OptimizationInstructor: John StrainLectures: TuTh 3:30-5:00pm, Room 85 EvansCourse Control Number: 54554Office: 1099 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 172 - Section 1 - CombinatoricsInstructor: Mauricio VelascoLectures: TuTh 2:00-3:30pm, Room 75 EvansCourse Control Number: 54557Office: 1063 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 185 - Section 1 - Introduction to Complex AnalysisInstructor: John LottLectures: MWF 10:00-11:00am, Room 71 EvansCourse Control Number: 54560Office: Office Hours: MWF 11:00am-12:00pmPrerequisites: Math 104Required Text: Brown and Churchill, Complex Variables and Applications, McGraw-Hill, 8th EditionRecommended Reading:Syllabus: See course webpage.Course Webpage: http://math.berkeley.edu/~lott/185.htmlGrading: Final 30%, Midterms 30%, Homework 40%Homework: WeeklyComments:Math 185 - Section 2 - Introduction to Complex AnalysisInstructor: Sebastian HerrLectures: TuTh 2:00-3:30pm, Room 71 EvansCourse Control Number: 54563Office: 837 EvansOffice Hours: TBAPrerequisites: Math 104Required Text: Donald Sarason, Complex Function Theory, American Mathematical Society (latest edition). Recommended Reading: You may find the following textbook helpful (optional): J.W. Brown and R.V. Churchill, Complex Variables and Applications, McGraw Hill.Syllabus: The main topics are the following: Analytic functions
of a complex variable. Cauchy's integral theorem, power series, Laurent
series, singularities of analytic functions, the residue theorem with
application to definite integrals, conformal maps. We will discuss
futher topics if time permits. Course Webpage: http://math.berkeley.edu/~herr/185S2Spring09.htmlGrading: 20% homework, 20% first midterm, 20% second midterm, 40% final examHomework: Homework will be assigned every Tuesday and will be due on the following Tuesday, 2:00pm in class.Comments: For more information, please take a look at the course webpage.Math 185 - Section 3 - Introduction to Complex AnalysisInstructor: Marco AldiLectures: TuTh 8:00-9:30am, Room 71 EvansCourse Control Number: 54566Office: 805 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math H185 - Section 1 - Honors Introduction to Complex AnalysisInstructor: Marina RatnerLectures: MWF 10:00-11:00am, Room 81 EvansCourse Control Number: 54569Office: 827 EvansOffice Hours: TBAPrerequisites: Required Text: John Conway, Functions of one complex variable, Springer, 2nd ed.Recommended Reading:Syllabus: Analytic functions, Cauchy's Integral Theorem, Power
Series, Laurent Series, singularities of analytic functions, the Residue
Theorem with applications to definite integrals. Identity Theorem,
Maximum Modulus Theorem, Open Mapping Theorem. Harmonic Functions.Course Webpage: Grading: The grade will be based: 15% on a weekly homework, 20% on quizzes, 25% on a mid-term, 40% on a final exam.Homework: Weekly.Comments: Math 191 - Section 1 - Experimental Courses in MathematicsInstructor: Alberto GrünbaumLectures: MWF 4:00-5:30pm, Room 3107 EtcheverryCourse Control Number: 54572Office: 903 EvansOffice Hours: TBAPrerequisites: The official prerequisites are Math 53 and Math 54. Having taken Math 55 or an upper division class or two will be useful.Required Text: None.Recommended Reading: All books in the Math/Stat library.Syllabus: Students will work in teams on three open-ended
projects over the course of the semester, using any means they choose.
They will write reports and give presentations for the other teams. The
objective is to gain research experience by working on interesting,
tractable problems.Course Webpage: TBAGrading: Approximately 50% written reports and 50% presentations.Homework: The three projects.Comments: Math 202B - Section 1 - Introduction to Topology and AnalysisInstructor: Don SarasonLectures: MWF 8:00-9:00am, Room 70 EvansCourse Control Number: 54683Office: 779 EvansOffice Hours: TBAPrerequisites: Math 202A or the equivalentRequired Text: No text will be followed in detail.Recommended Reading: Folland's Real Analysis and Rudin'sFunctional Analysis could be helpful references.Syllabus: CONTINUATION OF MEASURE THEORY. Product measures,
Fubini's theorem, Tonelli's theorem, the distribution function,
convolution. Signed measures, Hahn decomposition. Absolute continuity,
Radon-Nikodym theorem, Lebesgue decomposition, differentiation of
measures in N-space. Measure theory in locally compact spaces.FUNCTIONAL ANALYSIS. Banach spaces and their duals, Hahn-Banach theorem, biduals, quotient spaces. Bounded linear transformations, principle of uniform boundedness, open mapping theorem,. Topological vector spaces, dual pairs, separation theorem, locally convex spaces, polar sets, bipolar theorem. Weak and weak-* topologies, Banach-Alaoglu theorem, Banach-Krein-Smulyan theorem. Extreme points, Krein-Milman theorem. Possible additional topics. Applications of most of the main theorems will be given. Course Webpage: Grading: The course grade will be based on weekly homework assignments, which will be carefully graded. No exam.Homework: See above.Comments: Except for routine details and an occasional handout, the lectures will be self-contained.Math 203 - Section 1 - Singular Perturbation Methods in Applied ODE and PDEInstructor: John NeuLectures: TuTh 12:30-2:00pm, Room 7 EvansCourse Control Number: 54686Office: 1051 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus:
- Prototype singular perturbations - examples of matched inner and outer approximations and multiple scales. Theme of examples - distinguished limits by scaling.
- Minicourse on asymptotic expansion (as opposed to convergent series). Asymptotic evaluation of integrals from Laplace method to steepest descents in complex plane.
- Matched asymptotic expansions - beyond leading order, boundary layers, internal layers, and derivative layers in nonlinear problems. Singularly perturbed eigenfunctions of the Laplacian. Phase fronts and motion by mean curvature. Classic boundary layer theory for Navier-Stokes equations.
- Multiple scales - portfolio of definitive elementary examples. Modulation theory of nonlinear resonance, and of limit cycles. "Extended" Poincare method of "asymptotic expansion of solution interbraided with the modulation equations".
- Scary special topic - JBK smoothing method of waves in random media in real space and time.
Course mechanics - fat, hard problem sets. 1 take home midterm and 1 final (Glorified problem sets with honor bound rules of engagement).Course Webpage: Grading: 50% problem sets, 20% midterm, 30% finalHomework: Lots.Comments: May the force be with you.Math 206 - Section 1 - Banach Algebras and Spectral TheoryInstructor: Marc RieffelLectures: MWF 8:00-9:00am, Room 31 EvansCourse Control Number: 54692Office: 811 EvansOffice Hours: TBAPrerequisites: Math 202AB or equivalent. Students who have
studied only part of the material of Math 202AB and wish to enroll in
Math 206 should discuss this with me.Required Text: John B. Conway, A Course in Functional Analysis, 2nd ed., Springer-Verlag.Recommended Reading:Syllabus: I will also be teaching Math 208, C*-algebras, this
Spring semester, and in Math 206 I will try to discuss first the
material that is most important for Math 208, so that it will be
feasible to take both of these courses concurrently. This will probably
also make it feasible to take Math 206 and Math 209 (von Neumann
algebras) concurrently, but students who would like to do that should
consult Professor Voiculescu.The theory of Banach algebras is a very elegant blend of algebra and topology which provides unifying principles for a number of different parts of mathematics, notably operator theory, commutative and non-commutative harmonic analysis and the theory of group representations, and the theory of functions of one and several complex variables. But at the present time probably its most extensive use is as a foundation for non-commutative topology and geometry (C*-algebras, Math 208) and non-commutative measure theory (von Neumann algebras, Math 209). These in turn provide a foundation for quantum physics, but they also have myriad applications in many other directions, including group representations and harmonic analysis, ordinary topology and geometry, and even number theory. (For a vast panorama of the applications see Connes' book "Noncommutative Geometry", available on the web for free download.) In Math 206 I will cover the standard topics as listed in the catalog. Beyond the basic general theory of Banach algebras this will include several forms of the spectral theorem for self-adjoint operators on Hilbert space, Hilbert-Schmidt and Fredholm operators, and group algebras and the Fourier transform. Course Webpage: Grading: Most weeks I will give out a problem set, and the course
grade will be based on the work done on these. There will be no final
examination.Homework: Comments: Math 208 - Section 1 - C^{*}-AlgebrasInstructor: Marc RieffelLectures: MWF 9:00-10:00am, Room 9 EvansCourse Control Number: 54695Office: 811 EvansOffice Hours: TBAPrerequisites: The basic theory of bounded operators on Hilbert
space and of Banach algebras, especially commutative ones. Math 206 is
more than sufficient. I will be teaching Math 206 this semester, and I
will try to discuss first the material that is most important for Math
208, so that it will be feasible to take both of these courses
concurrently. As another alternative, self-study of sections 3.1-2,
4.1-4 of "Analysis Now" by G. K. Pedersen would be sufficient.Required Text: Recommended Reading: None of the available textbooks follows closely the path that I will take through the material. The closest is probably: K. R. Davidson, C, Fields Institute Monographs, A.M.S.^{*}-algebras by ExampleI strongly recommend this text for its wealth of examples (and attractive exposition). Syllabus: The theory of operator algebras grew out of the needs
of quantum mechanics, but by now it also has strong interactions with
many other areas of mathematics. Operator algebras are very profitably
viewed as "non-commutative (algebras "of functions" on) spaces", thus
"quantum spaces". As a rough outline, we will first develop the basic
facts about C^{*}-algebras ("non-commutative locally compact
spaces") We will then briefly look at "non-commutative vector bundles"
and K-theory ("noncommutative algebraic topology"). Finally we will
glance at "non-commutative differential geometry" (e.g. cyclic homology
as "noncomutative deRham cohomology"). But I will not assume prior
knowledge of algebraic topology or differential geometry, and we are
unlikely to have time to go into these last topics in any depth.I will discuss a variety of examples, drawn from dynamical systems, group representations and mathematical physics. But I will somewhat emphasize examples which go in the directions of my current research interests, which involve certain mathematical issues that arise in string theory and related parts of high-energy physics. Thus one thread that will run through the course will be to see what the various concepts look like for quantum tori, which are the most accessible non-commutative differential manifolds. In spite of what is written above, the style of my lectures will be to give motivational discussion and complete proofs for the central topics, rather than just a rapid survey of a large amount of material. Course Webpage: Grading: I plan to assign several problem sets. Grades for the
course will be based on the work done on these. But students who would
like a different arrangement are very welcome to discuss this with me.Homework: Comments: Math 209 - Section 1 - Von Neumann AlgebrasInstructor: Dan VoiculescuLectures: MWF 11:00am-12:00pm, Room 5 EvansCourse Control Number: 54698Office: 783 EvansOffice Hours: F 2:30-4:00pmPrerequisites: From Math 206: commutative C*-algebras and spectral theory for normal operators.Required Text: Recommended Reading: For the general theory part:Vaughan Jones Notes for Math 209 Kadison and Ringrose, Fundamentals of the theory of operator algebrasStratila and Zsido, Lectures on von Neumann algebrasTakesaki, Theory of operator algebrasFor the free probability part: Voiculescu, Dykema and Nica, Free random variablesSyllabus: The course will be an introduction to von Neumann algebras emphasizing II_{1} factors. The last part of the course will deal with free probability and the random matrix model it provides for the II_{1} factors of free groups (depending on how much time will be left).Course Webpage: Grading: Homework: Homework assigned during classes will be collected once a week.Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Ian AgolLectures: TuTh 8:00-9:30am, Room 81 EvansCourse Control Number: 54701Office: 921 EvansOffice Hours: TBAPrerequisites: Math 215ARequired Text: Hatcher, Algebraic TopologyMilnor & Stasheff, Characteristic ClassesRecommended Reading: Greenberg & HarperSyllabus: Homotopy Theory (Chapter 4 of Hatcher), Characteristic ClassesCourse Webpage: Grading: Based on homework.Homework: Weekly homework.Comments: Math C218B - Section 1 - Probability TheoryInstructor: David AldousLectures: TuTh 9:30-11:00am, Room 330 EvansCourse Control Number: 54704Office: 351 EvansOffice Hours: TBAPrerequisites: Math C218A or similarRequired Text: Durrett, Probability, DuxburyRecommended Reading:Syllabus: For more information see course webpage.Course Webpage: http://www.stat.berkeley.edu/~aldous/205B/index.htmlGrading: Homework: Comments: Math 219 - Section 1 - Dynamical SystemsInstructor: Fraydoun RezakhanlouLectures: MWF 1:00-2:00pm, Room 81 EvansCourse Control Number: 54707Office: 815 EvansOffice Hours: MTuTh 2:00-3:00pmPrerequisites: Some measure theoryRequired Text: Recommended Reading:Syllabus: The main goal of the theory of dynamical system is the
study of the global orbit structure of maps and flows. This course
reviews some fundamental concepts and results in the theory of dynamical
systems with an emphasis on differentiable dynamics.Several important notions in the theory of dynamical systems have their roots in the work of Maxwell, Boltzmann and Gibbs who tried to explain the macroscopic behavior of fluids and gases on the basic of the classical dynamics of many particle systems. The notion of ergodicity
was introduced by Boltzmann as a property satisfied by a Hamiltonian
flow on its constant energy surfaces. Boltzmann also initiated a
mathematical expression for the entropy and the entropy production to derive Maxwell's description for the equilibrium states. Gibbs introduced the notion of mixing systems to explain how reversible mechanical systems could
approach equilibrium states. The ergodicity and mixing are only two
possible properties in the hierarchy of stochastic behavior of a
dynamical system. Hopf invented a versatile method for proving the
ergodicity of geodesic flows. The key role in Hopf's approach is played
by the hyperbolicity. Lyapunov exponents and Kolmogorov-Sinai entropy
are used to measure the hyperbolicity of a system.There is no required text and I will distribute typed notes in the class. Here is an outline of the course: 1. Examples: Linear systems. Translations on Tori. Arnold can map. Baker's transformation. Geodesic flows. Sinai's billiard. Lorentz gas. 2. Invariant measures. Ergodic theory. Kolmogorov-Sinai Entropy. Lyapunov exponents. Hyperbolic systems. Smale horseshoe. 3. Perron-Frobenius operator. Bowen-Ruelle-Sinai measures. 4. Pesin's theorem. Ruelle's inequality. 5. Billiards. 6. Aubry-Mather theory. Course Webpage: Grading: There will be some homework assignments.Homework: Comments: Math 220 - Section 1 - Stochastic Methods of Applied MathematicsInstructor: Alexandre ChorinLectures: MWF 9:00-10:00am, Room 85 EvansCourse Control Number: 54710Office: 911 EvansOffice Hours: TBAPrerequisites: Some familiarity with the applications of mathematics or with PDEsRequired Text: Chorin/Hald, Stochastic tools in mathematics and science, copies will be distributed without charge Recommended Reading:Syllabus: Some probability, conditional averaging, Brownian
motion, Langevin and Fokker-Planck equations, path integrals, Feynman
diagrams, time series, Monte Carlo methods, renormalization and scaling,
an introduction to statistical mechanics, optimal prediction,
filtering. Course Webpage: http://math.berkeley.edu/~chorin/math220Grading: Based on homework assignments.Homework: Homework will be assigned on the web every week.Comments: Math 222B - Section 1 - Partial Differential EquationsInstructor: L. Craig EvansLectures: MWF 12:00-1:00pm, Room 31 EvansCourse Control Number: 54713Office: 1033 EvansOffice Hours: TBAPrerequisites: Math 222ARequired Text: Lawrence C. Evans, Partial Differential Equations, American Math SocietyRecommended Reading:Syllabus: The theory of boundary value and initial value problems
for partial differential equations, with emphasis on nonlinear
equations. Second-order elliptic equations, parabolic and hyperbolic
equations, calculus of variations methods, additional topics selected by
instructor.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 C223B - Section 1 - Statistical Mechanics and the (Ferromagnetic) Ising ModelInstructor: Nick CrawfordLectures: TuTh 11:00am-12:30pm, Room 340 EvansCourse Control Number: 54716Office: Office Hours: TBAPrerequisites: References: Will give complete list during the first class, o/w email me at crawford [at] stat [dot] berkeley [dot] eduSyllabus: The Ising model was originally introduced (in the
1920’s) as a caricature of the physical phenomenon of ferromagnetism. It
has become a paradigm for the study of emergent macroscopic behavior
from microscopic interactions and appears in various forms in an array
of different fields from computer science and phylogenetics to
statistical mechanics. In this course, we will provide an introduction
to this model, with a particular emphasis on the issues which arise in
its formulation on Z^{d}.Topics to be Covered (not nesc. in this order): Classical Theory: (1) Finite Volume Gibbs States (2) Correlation inequalities I; FKG, GKS. (3) Thermodynamics: the free energy. (4) Rigorous definition of phase transition. (5) Infinite volume Gibbs states and the DLR conditions. (6) Gibbs variational principle. (7) Occurrence of phase transition in d ≥ 2: the High and Low Temperature Expansions. (8) Lee Yang Circle theorem. (9) Uniqueness of ∞ volume Gibbs States with non-zero external field. (10) Relationship to Potts models and the random cluster representation/domination of measures/percolation signature of the phase transition. Advanced Topics: (Some selection of these, depending on interest): (1) The random field Ising model: absence of phase transition in dimension d = 2. (2) The random field Ising model: existence of phase transition in dimension d ≥ 3. (3) Critical Behavior of the Ising model: d ≥ 5 (1980’s, follows Aizenman and coauthors). (4) Conformal Invariance in the Ising model: d = 2 (2006-2008, follows Smirnov). (5) An introduction to the roughening transition in d = 3. Finally, we hope that this class will be interactive in the sense that students will give presentations for credit. These presentations can take on a number of forms, from original research related to this subject to the presentation of a paper relevant to the field (perhaps on one of the topics not covered in the second set). Math 224B - Section 1 - Mathematical Methods for the Physical SciencesInstructor: Alberto GrünbaumLectures: TuTh 9:30-11:00am, Room 5 EvansCourse Control Number: 54719Office: 903 EvansOffice Hours: TuWTh 11:00am-12:00pmPrerequisites: Required Text: Stakgold, Green's functions and boundary value problemsRecommended Reading:Syllabus: This is the second 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. This second semester will cover mostly the spectral theory of operators in infinite dimensional space, with particular emphasis on selfadjoint and unitary operators. I will make a fresh beginning for those students that are not too familiar with the infinite dimensional setup. The issue of the importance of Boundary conditions will be discussed in detail in terms of H. Weyl's classification in limit point-limit circle cases. We will illustrate all this material with applications taken from the physical sciences. Course Webpage: Grading: Homework: There will be weekly assignments, mainly from the book.Comments: The grade will be based on the homework.Math 225B - Section 1 - MetamathematicsInstructor: Jan ReimannLectures: TuTh 2:00-3:30pm, Room 81 EvansCourse Control Number: 54722Office: 705 EvansOffice Hours: TBAPrerequisites: 225ARequired Text: I will provide my own notes.Recommended Reading: Rautenberg, A Concise Introduction to Mathematical Logic; Shoenfield, Mathematical Logic; Soare, Recursively Enumerable Sets and Degrees; Kaye, Models of Peano ArithmeticSyllabus: Metamathematics of number theory, models of Peano
Arithmetic, recursive functions, computability, Turing machines,
undecidable problems, the arithmetical hierarchy, coding and
arithmetization, the Goedel incompleteness theorems, Theorems of Tarski
and Church, the Paris-Harrington theorem, examples of undecidable
theories.Course Webpage: Will be set up on bSpaceGrading:Homework: Homework will be assigned every week.Comments:Math 228B - Section 1 - Numerical Solution of Differential EquationsInstructor: John StrainLectures: TuTh 11:00am-12:30pm, Room 30 WheelerCourse Control Number: 54725Office: 1099 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 236 - Section 1 - Metamathematics of Set TheoryInstructor: John KruegerLectures: MWF 12:00-1:00pm, Room 81 EvansCourse Control Number: 54728Office: 751 EvansOffice Hours: TBAPrerequisites: 225B, 235A, or permission of instructorRequired Text: NoneRecommended Reading:Syllabus: Basics of forcing. Chain conditions and closure. Consistency results. Iterated forcing.Course Webpage: http://math.berkeley.edu/~jkrueger/math236.htmlGrading:Homework:Comments:Math 242 - Section 1 - Symplectic GeometryInstructor: Michael HutchingsLectures: TuTh 12:30-2:00pm, Room 81 EvansCourse Control Number: 54731Office: 923 EvansOffice Hours: TBAPrerequisites: 214 and 215a or equivalent required; 215b helpfulRequired Text: McDuff and Salamon, Introduction to Symplectic Topology, 2nd edition, Oxford Univ PressRecommended Reading: Geiges, An Introduction to Contact Topology, Cambridge Univ PressSyllabus: We will introduce some of the fundamental ideas that
underlie current research in symplectic geometry (and also contact
geometry, its odd-dimensional sibling). Although holomorphic curves
play a major role in this area, we will emphasize more basic concepts
which are less technically demanding but still essential.Course Webpage: Will be linked from math.berkeley.edu/~hutchingGrading: Each student will be expected to investigate a
particular topic of interest and either write a 5-10 page expository
article about it or give a 40 minute presentation to the class. The
books by McDuff-Salamon and Geiges suggest a number of good starting
points for this.Homework:Comments:Math 249 - Section 1 - Algebraic CombinatoricsInstructor: Lior PachterLectures: TuTh 9:30-11:00am, Room 101 WheelerCourse Control Number: 54734Office: 1081 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 250B - Section 1 - Multilinear Algebra and Further TopicsInstructor: Paul VojtaLectures: TuTh 12:30-2:00pm, Room 3105 EtcheverryCourse Control Number: 54737Office: 883 EvansOffice Hours: MTuTh 2:00-3:00pm (subject to change)Prerequisites: Math 250ARequired Text: Eisenbud, Commutative algebra with a view toward algebraic geometry, SpringerRecommended Reading:Syllabus: The course will cover the following chapters or parts of the text:
Course Webpage: http://math.berkeley.edu/~vojta/250b.htmlGrading: Grades will be based on homework assignments, including a final problem set in place of a final exam.Homework: Homework will be assigned approximately every two weeks.Comments:
- The course title does not accurately reflect recent practice in teaching this course. There really isn't much (if any) multilinear algebra taught in 250b anymore. Currently, Math 250B covers commutative algebra, with an emphasis on what will be useful for algebraic geometry.
- Current information on the course is available on the course web page.
Math 252 - Section 1 - Representation TheoryInstructor: Brendon RhoadesLectures: MWF 3:00-4:00pm, Room 81 EvansCourse Control Number: 54740Office: 851 EvansOffice Hours: MWF 2:00-3:00pmPrerequisites: Linear algebra, abstract algebraRequired Text: NoneRecommended Reading:Syllabus: This will be an introductory course inrepresentation
theory. Topics will include representations of finite-dimensional
algebras and, in particular, representations of finite groups in
characteristic zero with special emphasis on the case of symmetric
groups. I hope to conclude with an introduction to Hecke algebras and
Kazhdan-Lusztig theory. Course Webpage:Grading:Homework: Several homeworks.Comments: Math 254B - Section 1 - Number TheoryInstructor: Robert ColemanLectures: MWF 12:00-1:00pm, Room 4 EvansCourse Control Number: 54743Office: 901 EvansOffice Hours: TBAPrerequisites:Required Text: Serre, Local FieldsRecommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: When doing arithmetic or geometry it is usually
helpful, if not essential, to look closely at what is happening near a
point (or prime ideal). Fortunately points are simpler than global
spaces and easier to study, but the closer one looks the more
interesting things get and in the end one can learn deep information
about the global space by really understanding its points. We will
begin to investigate this local perspective in this course.Math 255 - Section 1 - Algebraic CurvesInstructor: Konrad WaldorfLectures: TuTh 3:30-5:00pm, Room 81 EvansCourse Control Number: 54746Office: 833 Evans (could possibly change)Office Hours: TuTh 5:00-6:30pmPrerequisites: Point-set topology (202A), groups, rings and fields (the basics of 250A, or 114), complex analysis (185).Required Text:Recommended Reading: Available on the course webpage.Syllabus: Riemann surfaces, projective curves, curves with nodes,
meromorphic functions and holomorphic maps, divisors, Bezout's theorem,
algebraic curves, the Riemann-Roch theorem, Jacobians, Abel's Theorem,
elliptic curves, possibly further topics.Course Webpage: http://math.berkeley.edu/~waldorf/algebraiccurvesGrading: Based on homework.Homework: TBAComments: Math 256B - Section 1 - Algebraic GeometryInstructor: Arthur OgusLectures: MWF 11:00am-12:00pm, Room 31 EvansCourse Control Number: 54749Office: 877 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 257 - Section 1 - Group TheoryInstructor: David HillLectures: MWF 2:00-3:00pm, Room 81 EvansCourse Control Number: 54752Office: 785 EvansOffice Hours: TBAPrerequisites: Math 250ARequired Text: Recommended Reading: Kleshchev, Linear and Projective Representations of Symmetric GroupsSyllabus: In this course, we will study the representation theory
of the affine Hecke algebra of type A. This algebra has a family of
remarkable finite dimensional quotients, including the group algebra of
the symmetric group. We will approach this subject from various points
of view. We will review classical Schur-Weyl duality and its
affinization. Next, we will go on to investigate how this representation
theory can be understood by studying highest weight representations of
affine Kac-Moody algebras of type A. Time permitting, we will also
explore connections to a new diagram calculus introduced by Khovanov and
Lauda.Course Webpage: http://math.berkeley.edu/~dhill1/Grading: Homework: Comments: Math 261B - Section 1 - Quantum GroupsInstructor: Nicolai ReshetikhinLectures: MWF 10:00-11:00am, Room 5 EvansCourse Control Number: 54755Office: 915 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: The goal of this part of the Lie groups and Lie
algebras course is an introduction to quantum groups. The subject was
developed over the last 20 years. Many ideas and techniques are natural
extensions of those in Lie groups, Lie algebras, and their
representation theory. The main hero of this course (at least in the
first part of it) will be quantum sl_{2}. Elements of symplectic
geometry will be used in parts of this course. A symplectic geometry
course as a pre-requisite is desirable, but not necessary.Here is a tentative outline of the course: 1. Lie bialgebras and Poisson Lie groups. Standard Poisson Lie structure for SL _{2} in details. Standard Poisson Lie structures on simple Lie groups.2. Deformation quantization of Poisson-Lie groups and of universal enveloping algebras of Lie bialgebras. Hopf algebras and basic constructions with Hopf algebras. Monoidal categories. Category of vector spaces. Category of modules over a Hopf algebra. Duality in a monoidal category (dual vector spaces for the category of vector spaces) 3. Braiding in monoidal categories. The Drinfeld double construction. Braiding for quantized universal enveloping algebras of simple Lie algebras. 4. Integral forms of quantized universal enveloping algebras. 5. Elements of the representation theory of quantized universal enveloping algebras. Finite dimensional irreducible representations. The category of finite dimensional modules as a braided monoidal category. 6. Elements of harmonic analysis on quantum groups. 7. Specializations at roots of unity and corresponding representation theories. There are several books on the subject. They all can be used as a supplementary reading material. The list of reading material will be posted at the web-site of the course before the beginning of the semester. Course Webpage: Grading: Homework: Comments: Math 270 - Section 1 - Hot Topics Course in MathematicsInstructor: Peter TeichnerLectures: Tu 11:00am-12:30pm, Room 736 EvansCourse Control Number: 54758Office: 703 EvansOffice Hours: TBAPrerequisites: Required Text: Lurie, On the Classification of Topological Field TheoriesRecommended Reading: Other papers by Lurie at http://www-math.mit.edu/~lurie/Syllabus: Course Webpage: Check at http://web.me.com/teichner/Math/Hot_Topics.htmlGrading: Homework: Comments: Math 270 - Section 2 - Hot Topics Course in MathematicsInstructor: Leo HarringtonLectures: M 4:00-5:30pm, Room 35 EvansCourse Control Number: 54761Office: 711 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in Algebra - Tropical GeometryInstructor: Bernd SturmfelsLectures: TuTh 11:00am-12:30pm, Room 3107 EtcheverryCourse Control Number: 54764Office: 925 EvansOffice Hours: W 8:00-11:00amPrerequisites: Commutative algebra (250B), an interest in
geometric combinatorics and algebraic geometry, and willingness to work
hard in a team.Required Text: I will post some lecture notes and pointers to research articles on the course webpage.Recommended Reading:Syllabus: Tropical geometry is the algebraic geometry over the
min-plus algebra. It is a young subject that in recent years has both
established itself as an area of its own right and unveiled its deep
connections to numerous branches of pure and applied mathematics. From
an algebraic geometric point of view, algebraic varieties over a field
with non-archimedean valuation are replaced by polyhedral complexes,
thereby retaining much of the information about the original varieties.
This course offers an introduction to tropical geometry, with emphasis
on algebraic, computational and combinatorial aspects. One concrete goal
is to prepare the students for possible participation in activities of
the Fall 2009 research program on Tropical Geometry at MSRI.Course Webpage: http://math.berkeley.edu/~bernd/math274.htmlGrading: The course grade will be based on both the homework and the course projects.Homework: There will be regular assignments during the first eight weeks of the course.Comments: After spring break students will work on a term project in tropical geometry.Math 274 - Section 2 - Infinitesimal Geometry (Topics in Algebra)Instructor: Mariusz WodzickiLectures: TuTh 5:00-6:30pm, Room 72 EvansCourse Control Number: 54767Office: 995 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: This course will describe the current state of our knowledge in what I like to call “Infinitesimal Geometry”. One of the great achievements of 20th Century Mathematics was the realization that de Rham theory provided an adequate, "analytic" means of understanding geometry of smooth C ^{∞} manifolds, smooth complex manifolds, and smooth algebraic varieties over fields of characteristic zero. When singularities appear, or the ring of coefficients is not a field of characteristic zero, it has been known since 1950-ies that de Rham theory is not adequate at all. Yet, the concepts of Infinitesimal Geometry, infinitesimal invariants, infinitesimal cohomology groups, make perfect sense in all situations. The following is the tentative list of topics: - the algebras of differential operators on various spaces (including “arithmetic” and singular ones, as well as exotic spaces with “divided” points)
- noncommutative p-residue – an interesting recent discovery how familiar noncommutative residue manifests itself in characteristic p > 0
- Fock p-spaces
- Cartier operations; Illusie-de Rham cohomology groups
- Spencer complexes and Hamiltonian duality
- homology of various algebras of differential operators in characteristic zero, positive characteristic, and in “arithmetic” contexts
- results of Smith and Stafford on the Morita equivalence of algebras of differential operators on curves
- some recently discovered unexpected links with the theory of
Hopf-algebras, modules/comodules, semi-simple Lie algebras (including
{fraktur e}
_{6}, {fraktur e}_{7}), and certain special irreducible representations – all coming from the study of differential operators in various contexts.
The scheduled time appears to be causing conflict for a number of
people. Please contact me by email ASAP if you would be interested in
attending the lectures but you have time conflict with MWF 3-4. I would
be happy to change the time to accommodate those with the time conflict.Course Webpage: Grading: Homework: Math 275 - Section 1 - Topics in Applied Mathematics - Flow, Deformation, Fracture and TurbulenceInstructor: Grigory BarenblattLectures: TuTh 9:30-11:00am, Room 61 EvansCourse Control Number: 54770Office: 735 EvansOffice Hours: TuTh 11:15am-12:50pmPrerequisites: No special knowledge of advanced mathematics and
continuum mechanics will be assumed - all needed concepts and methods
will be explained on the spot, however the knowledge of the elements of
vector analysis and ordinary differential equations will be useful.Required Texts: Landau, L. D. and Lifshits, E. M., Fluid Mechanics (Pergamon Press, London, New York 1987)Landau, L. D. and Lifshits, E. M., Theory of Elasticity (Pergamon Press, London, New York, 1986)Chorin, A. J. and Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (Springer, 1990)Barenblatt, G. I., Scaling (Cambridge University Press, 2003)Batchelor, G. K., An Introduction to Fluid Dynamics (Cambridge University Press, 1998)Recommended Reading: Syllabus: Fluid Mechanics, including Turbulence and Mechanics of
Deformable Solids, including Fracture Mechanics are fundamental
disciplines, playing an important and ever-growing role in applied
mathematics, including computing, and also physics, and engineering
science. The models of fluid flow, deformation and fracture of solids
under various conditions appear in all branches of applied mathematics,
engineering science and many branches of physical science. Among the
problems of these sciences which are under current active study there
are great scientific challenges of our time such as turbulence, fracture
and fatigue of metals, damage accumulation and nanotechnology.The proposed course will present the basic ideas and methods of fluid mechanics, including turbulence, mechanics of deformable solids, including fracture as a unified mathematical, physical and engineering discipline. The possibility of such a unified presentation is based on the specific `intermediate-asymptotic approach’ which allows the explanation of the main ideas simultaneously for the problems of fluid mechanics and deformable solids. The basic distinction of this year course will have special emphasis on turbulence. The instructor expects to present the basic ideas and to evaluate the current state of the turbulence studies. In particular, scaling laws for the shear flows and local structure of the developed turbulent flows will be presented and discussed. Course Webpage: Grading: Homework: There will be no systematic homework. Some problems
will be presented shortly at the lectures, their solutions will be
outlined, and interested students will be offered the opportunity to
finish the solutions. This will not be related to the final exams.Comments: In the end of the course the instructor will give a
list of 10 topics. Students are expected to come to the exam having an
essay (5-6 pages) concerning one of these topics which they have chosen.
They should be able to answer questions concerning the details of these
topics. After that general questions (without details) will be asked
concerning the other parts of the course.Math 278 - Section 1 - Topics in Analysis - Free AnalysisInstructor: Dan VoiculescuLectures: MWF 1:00-2:00pm, Room 31 EvansCourse Control Number: 54776Office: 783 EvansOffice Hours: F 2:30-4:00pmPrerequisites: Basic notions from Math 206Required Text: Recommended Reading:Syllabus: The course will be about analysis with variables having
the highest degree of noncommutativity. The free difference quotient, a
noncommutative extension of the difference quotient, replaces then the
usual derivative. The analogue of the Fourier transform, in this
context, is a noncommutative generalization of the Cauchy-Stieltjes
transform. There are more entries in this dictionary which will be
discussed.I plan also to cover some of the motivation for this development originating in free probability (random matrix and operator algebra questions, the free analogue of entropy). Course Webpage: Grading: Homework: There will be a few homeworks.Comments: Math 300 - Section 1 - Teaching WorkshopInstructor: Anthony VarillyLectures: TBACourse Control Number: 55388Office: Office Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments: |