# Spring 2007

Math 1A - Section 1 - CalculusInstructor: Mina AganagicLectures: TuTh 11:00am-12:30pm, Room 155 DwinelleCourse Control Number: 54103Office: 715 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1B - Section 1 - Calculus Instructor: Ole HaldLectures: MWF 10:00-11:00am, Room 155 DwinelleCourse Control Number: 54145Office: 875 EvansOffice Hours: TBA Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 1B - Section 2 - Calculus Instructor: Marina RatnerLectures: MWF 12:00-1:00pm, Room 2050 Valley Life ScienceCourse Control Number: 54184Office: 827 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 1B - Section 3 - Calculus Instructor: James SethianLectures: TuTh 11:00am-12:30pm, Room 10 EvansCourse Control Number: 54235Office: 725 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 16A - Section 1 - Analytical Geometry and CalculusInstructor: Tsit-Yuen LamLectures: MWF 9:00-10:00am, Room 100 LewisCourse Control Number: 54277Office: 871 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 16A - Section 2 - Analytical Geometry and CalculusInstructor: Zachary JudsonLectures: MWF 9:00-10:00am, Room 60 EvansCourse Control Number: 54324Office: 814 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 1 - Analytical Geometry and CalculusInstructor: Jack WagonerLectures: MWF 10:00-11:00am, Room 100 LewisCourse Control Number: 54325Office: 899 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 16B - Section 2 - Analytical Geometry and CalculusInstructor: Jack SilverLectures: TuTh 11:00am-12:30pm, Room 2050 Valley Life ScienceCourse Control Number: 54373Office: 753 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman SeminarsInstructor: Jenny HarrisonLectures: F 3:00-4:00pm, Room 891 EvansCourse Control Number: 54409Office: 851 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 2 - Freshman SeminarsInstructor: Theodore Slaman & Jan ReimannLectures: W 11:00am-12:00pm, Room 39 EvansCourse Control Number: 54411Office: 719 Evans & 705 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 3 - The Geometry of RelativityInstructor: Alan WeinsteinLectures: Tu 2:00-3:30pm, Room 891 EvansCourse Control Number: 55672Office: 825 EvansOffice Hours: TBAPrerequisites: Math 1A or equivalentRequired Text: TBARecommended Reading: TBASyllabus: This seminar will meet in the first week of classes and nine more Tuesdays, with precise dates to be arranged. This seminar is meant to fill in some of the mathematical background behind Hawking's "A Briefer History of Time." We will study some of the geometry underlying Einstein's special and general theories of relativity. Topics will include the geometry of Lorentz transformations in flat space time (for special relativity) and an introduction to riemannian geometry (for general relativity). The seminar activities will be a mix of reading, discussion, and presentations by students and the instructor. The math which will be taught in the seminar will give students a head start (or a review) for more advanced courses. Students should have had Math 1A or the equivalent. This seminar is part of the On the Same Page initiative: http://onthesamepage.berkeley.edu. Course Webpage: http://math.berkeley.edu/~alanwGrading: P/NP based on class participation and some written work.Homework: Comments: Math 32 - Section 1 - PrecalculusInstructor: Martin Vito-CruzLectures: MWF 8:00-9:00am, Room 9 LewisCourse Control Number: 54412Office: 835 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 4:00-6:00pm, Room 71 EvansCourse Control Number: 54423Office: 985 EvansOffice Hours: TBAPrerequisites: Math 1ARequired Text: NoneRecommended Reading: To be handed out in class.Syllabus: We will discuss mathematics topics that are difficult
for students in K-12, interesting mathematics problems from K-12, and
issues pertaining to the practice of teaching.Course Webpage:Grading: P/NP based on homework, journal and final project.Homework: There will be weekly homework assigned during class.Comments:Math 53 - Section 1 - Multivariable CalculusInstructor: Vaughan JonesLectures: MWF 2:00-3:00pm, Room 1 PimentalCourse Control Number: 54445Office: 929 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 53 - Section 2 - Multivariable CalculusInstructor: Michael HutchingsLectures: TuTh 3:30-5:00pm, Room F0295 HaasCourse Control Number: 54484Office: 923 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 54 - Section 1 - Linear Algebra and Differential EquationsInstructor: Robion KirbyLectures: MWF 8:10-9:00am, Room 155 DwinelleCourse Control Number: 54532Office: 919 EvansOffice Hours: Tu 10:00am-12:00pm, Th 10:30-11:30amPrerequisites: Math 1BRequired Text: Richard Hill, Elementary Linear AlgebraBoyce and DiPrima, Elementary Differential Equations and Boundary Value ProblemsBoth in special editions for Math 54 at Berkeley. Recommended Reading:Syllabus: Linear equations and matrices, vector spaces, linear
transformations, determinants, second order differential equations,
systems of ordinary differential equations, Fourier series and partial
differential equations.Course Webpage: http://math.berkeley.edu/~kirby/math54.htmlGrading: There will be 3 midterms worth 100 points each, a final worth 200 points, and these will constitute most of the final grade.Homework: Homework will be assigned on the web and due once a week.Comments: Math 54 - Section 2 - Linear Algebra and Differential EquationsInstructor: Kenneth RibetLectures: TuTh 3:30-5:00pm, Room 1 PimentalCourse Control Number: 54580Office: 885 EvansOffice Hours: TBA in JanuaryPrerequisites: Math 1BRequired Text: Hill, Elementary Linear Algebra; Boyce and DiPrima, Elementary Differential Equations and Boundary Value ProblemsRecommended Reading:Syllabus: Basic linear algebra; matrix arithmetic and
determinants. Vector spaces; inner product as spaces. Eigenvalues and
eigenvectors; linear transformations. Homogeneous ordinary differential
equations; first-order differential equations with constant
coefficients. Fourier series and partial differential equations.Course Webpage: http://math.berkeley.edu/~ribet/54/; the current version of this page is left over from the Math 54 that I taught in Fall, 2005.Grading: Based on two midterms, the final, homework, and quizzes.
The exact weights will be similar to the weights used in other
lower-division math courses. In 2005, I declared that the midterms
would be worth 15% each and that homework and quizzes would count 25%
all together. That left 45% for the final exam.Homework: Homework will be due in discussion section twice each week.Comments: When you sign up for the course, please join the google discussion group Math 54.
As you can see, the group proved to be a useful forum for students to
ask questions and make comments. Questions received replies from me,
the GSIs and other students.In 2005, I set up Math 54 lunches. I hope to be able to do the same thing again. Math 55 - Section 1 - Discrete MathematicsInstructor: Paul VojtaLectures: MWF 2:00-3:00pm, Room 277 CoryCourse Control Number: 54631Office: 883 EvansOffice Hours: TBAPrerequisites: Math 1A-1B, or consent of instructor.Required Text: Kenneth H. Rosen, Discrete Mathematics and its Applications, 6th edition, McGraw-HillRecommended Reading: NoneSyllabus: A paper copy will be distributed on the first day of classes; see also the course web page.Course Webpage: http://math.berkeley.edu/~vojta/55.htmlGrading: Grading will be based on a first midterm (10%), a second
midterm (20%), the final exam (45%), and a component stemming from the
discussion sections (25%). This latter component is left to the
discretion of the section leader, but it is likely to be determined
primarily by homework assignments and biweekly quizzes.Homework: Homework will consist of weekly assignments, to be given on the syllabus.Comments: Math 1A-1B and (if you've had them) 53 and 54 are about
smooth functions of one or more real variables; this course is about
some very different topics. The main reason 1A-1B are prerequisites is
to be sure students have enough familiarity with mathematical thinking;
it also means that I will be free to occasionally make connections with
topics from that sequence. Section 6.4 is related to a topic in Math 1B
(power series), so students who have had 1B may find that section easier
than those who have not. Nevertheless, the author's aim was to write
the book so as not to assume calculus. If you haven't had calculus and
want to take this course, come see me and we will discuss whether you
are ready.Math 74 - Section 1 - Transition to Upper Division MathematicsInstructor: Patrick BarrowLectures: MWF 3:00-4:00pm, Room 70 EvansCourse Control Number: 54649Office: 937 EvansOffice Hours: Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 74 - Section 2 - Transition to Upper Division MathematicsInstructor: Dennis CourtneyLectures: MWF 3:00-4:00pm, Room 87 EvansCourse Control Number: 54651Office: 1008 EvansOffice Hours: Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 104 - Section 1 - Introduction to AnalysisInstructor: Giulio CavigliaLectures: TuTh 2:00-3:30pm, Room 71 EvansCourse Control Number: 54709Office: 805 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 104 - Section 2 - 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 3 - Introduction to AnalysisInstructor: Marina RatnerLectures: MWF 10:00-11:00am, Room 75 EvansCourse Control Number: 54715Office: 827 EvansOffice Hours: TBAPrerequisites: Required Text: Rudin, Principles of Mathematical AnalysisRecommended Reading:Syllabus: Completeness of real numbers, metric spaces,
convergence, compactness, connectedness. Continuous functions, uniform
convergence, series. Differentiation. Riemann integral.Course Webpage: Grading: The grade will be based 40% on the final examination, 25% on a midterm, 20% on quizzes, and 15% on weekly homework.Homework: Comments: Math 104 - Section 4 - Introduction to AnalysisInstructor: John KruegerLectures: TuTh 9:30-11:00am, Room 71 EvansCourse Control Number: 54718Office: 751 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: http://math.berkeley.edu/~jkrueger/math104.htmlGrading: Homework: Comments: Math 105 - Section 1 - Analysis IIInstructor: John KruegerLectures: MWF 12:00-1:00pm, Room 85 EvansCourse Control Number: 54721Office: 751 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: http://math.berkeley.edu/~jkrueger/math105.htmlGrading: Homework: Comments: Math 110 - Section 1 - Linear AlgebraInstructor: Arthur OgusLectures: TuTh 3:30-5:00pm, Room 100 LewisCourse Control Number: 54724Office: 877 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract AlgebraInstructor: Paul VojtaLectures: MWF 3:00-4:00pm, Room 75 EvansCourse Control Number: 54748Office: 883 EvansOffice Hours: TBAPrerequisites: 53 and 54Required Text: John A. Beachy and William D. Blair, Abstract Algebra, Third Edition, Waveland Press, Long Grove, Ill.Recommended Reading:Syllabus: This course will cover the basics of groups, rings, and
fields, as given in Chapters 1-7 and 9 of the textbook, omitting some
sections of the higher-numbered chapters.Details will be announced at the beginning of the course. Course Webpage: http://math.berkeley.edu/~vojta/113.htmlGrading: Homeworks, 30%; midterms, 15% and 20%; final exam, 35%.Homework: Assigned weekly.Comments: I tend to follow the book rather closely, but will try to give more examples this time.Math 113 - Section 2 - Introduction to Abstract AlgebraInstructor: Shamgar GurevitchLectures: TuTh 8:00-9:30am, Room 70 EvansCourse Control Number: 54751Office: 867 EvansOffice Hours: TuW 1:00-2:00pmPrerequisites: Required Text: M. Artin, AlgebraRecommended Reading:Syllabus: Topics from Linear Algebra, Groups, Symmetry, Linear Groups, Rings, Modules, Fields.Course Webpage: http://math.berkeley.edu/~shamgar/113S07.htmlGrading: There will be weekly assignments which will be due in
one week, a midterm exam and a final. They will count toward the grade
as follows: Assignments 30% Midterm 30% Final 40% Homework: Comments: Attitude: In our course we will study basic
algebraic structures. The attitude will be to help you to develop your
way on how to think about some mathematical objects that appears in the
formulations and solutions of various problems. Moreover, I expect you
to be an integral part of the course, i.e., to attend lectures, to
submit homework, and to visit me during my office hours.Math 113 - Section 3 - Introduction to Abstract AlgebraInstructor: Jack WagonerLectures: MWF 1:00-2:00pm, Room 3105 EtcheverryCourse Control Number: 54754Office: 899 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 113 - Section 4 - Introduction to Abstract AlgebraInstructor: George BergmanLectures: TuTh 2:00-3:30pm, Room 75 EvansCourse Control Number: 54757Office: 865 EvansOffice Hours: M 1:30-2:30pm, WTh 10:30-11:30amPrerequisites: Math 54 or a course with similar linear algebra content, and mathematical maturity appropriate to upper-division status.Required Text: John A. Beachy and William D. Blair, Abstract Algebra, third edition, Waveland Press, Long Grove, Illinois, 60047.Recommended Reading:Syllabus: 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
familiar 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. The parts of the book we will cover will be: Chapters 1, 2, 3 (Integers, Functions, Groups) followed by parts of 7 (Structures of Groups), 4 and 5 (Polynomials and Commutative Rings) and parts of 6 (Fields) and of 9 (Unique Factorization). Course Webpage: 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 Thursdays.Comments: 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..On each day, each student will be required to submit, in writing or 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 often incorporate answers to students' questions into my
lectures; other times I will answer your question by e-mail. More
details on this and other matters will be given on the course handout
(to be distributed in class the first day, and available on the door to
my office thereafter).Math H113 - Section 1 - Honors Introduction to Abstract AlgebraInstructor: Dagan KarpLectures: TuTh 8:00-9:30am, Room 85 EvansCourse Control Number: 54760Office: 1053 EvansOffice Hours: Tu 9:30-10:30am, W 3:00-4:00pmPrerequisites: 54 or a course with equivalent linear algebra contentRequired Text: I. N. Herstein, Topics in Algebra, Wiley & SonsRecommended Reading:Syllabus: Honors section corresponding to 113, which covers: Sets
and relations. The integers, congruences and the Fundamental Theorem of
Arithmetic. Groups and their factor groups. Commutative rings, ideals
and quotient fields. The theory of polynomials: Euclidean algorithm and
unique factorizations. The Fundamental Theorem of Algebra. Fields and
field extensions.Course Webpage: http://math.berkeley.edu/~dkarp/courses/113/Grading: 40% homework, 15% each midterm, 30% finalHomework: Homework will be assigned and collected roughly once a week.Comments: Math 114 - Section 1 - Abstract Algebra IIInstructor: Robert ColemanLectures: MWF 12:00-1:00pm, Room 4 EvansCourse Control Number: 54763Office: 901 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 121A - Section 1 - Mathematical Tools for the Physical SciencesInstructor: Shamgar GurevitchLectures: TuTh 11:00am-12:30pm, Room 71 EvansCourse Control Number: 54766Office: 867 EvansOffice Hours: TuW 1:00-2:00pmPrerequisites: Required Text: Mary L. Boas, Mathematical Methods in the Physical SciencesRecommended Reading:Syllabus: Linear algebra, complex numbers, complex functions,
Harmonic Analysis, Discrete Harmonic Analysis, other topics and
applications.Let me elaborate on some of the topics that will be covered 1. Linear Algebra. Probably the most important notions of mathematics are the notions of abstract vector spaces and Linear operators between them. 2. Complex numbers. We will extend our linear algebra notions to the language of vector spaces over the field of complex numbers. 3. Theory of complex functions. The notion of analytic function will be presented. A central theorem in complex analysis, known as Cauchy's theorem,
will be formulated and proved. Using the language of complex functions
you will be able to understand the calculations of difficult integrals
of real functions. 4. Harmonic Analysis. Here the main question is how to think on a function defined on the circle T or on the real line R? Is it really defined by its values? This will lead us to the definition of the L^{2} spaces and in particular we will introduce one of the most important transforms in mathematics called the Fourier transform.
We will learn about a nice application of Harmonic analysis to applied
mathematics called Shannoni's Sampling Theorem. This is a theorem which
is formulated in terms of the Fourier transform and is one of the corner stones of modern information theory and its applications. 5. Discrete Harmonic Analysis. Here you will see that one can define all the notions of Harmonic analysis in the case of the "discrete line" Z_{N}
= {0,1,...,N-1}. In particular we will introduce the discrete Fourier
transform (DFT). This will help us to solve a model problem in the
application of mathematics to the digital world. Namely, we will learn
how to multiply two polynomials in a fast way. The solution will use the
Cooley-Tukey Fast Fourier Transform algorithm (FFT).Course Webpage: http://math.berkeley.edu/~shamgar/121aS07.htmlGrading: There will be weekly assignments (handout by the TA)
which will be due in one week, a midterm exam and a final. They will
count toward the grade as follows: Assignments 30% Midterm 30% Final 40% Homework: Comments: Attitude: In our course we will study some
fundamental tools of mathematics. The attitude will be to help you to
develop your way on how to think on some mathematical objects that you
will encounter during your undergraduate studies. Moreover, I expect
from you to be an integral part of the course, i.e., I expect from you
to attend lectures, to participate in the discussion, to submit home
works, and to visit me during my office hours. Math 121B - Section 1 - Mathematical Tools for the Physical SciencesInstructor: Jason MetcalfeLectures: TuTh 12:30-2:00pm, Room 241 CoryCourse Control Number: 54769Office: 837 EvansOffice Hours: TBAPrerequisites: Math 53 and Math 54Required Text: M. Boas, Mathematical Methods in the Physical Sciences, 3rd edition (Wiley)Recommended Reading:Syllabus: Mains topics: Special functions (Ch. 11); Series
solutions of ODE and more special functions (Ch. 12); Partial
differential equations (Ch. 13); Probability and Statistics (Ch. 16).
Please see the webpage for a detailed syllabus.Course Webpage: http://math.berkeley.edu/~metcalfe/teaching/math121b/Grading: 15% homework, 25% each for two midterm exams, 35% finalHomework: There will be an assignment corresponding to each lecture which is due one week later.Comments: Math 125A - Section 1 - Mathematical LogicInstructor: Jack SilverLectures: TuTh 2:00-3:30pm, Room 289 CoryCourse Control Number: 54772Office: 753 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 126 - Section 1 - Introduction to Partial Differential EquationsInstructor: Ole HaldLectures: MWF 1:00-2:00pm, Room 70 EvansCourse Control Number: 54775Office: 875 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 127 - Section 1 - Mathematics for Computational BiologyInstructor: Bernd SturmfelsLectures: TuTh 12:30-2:00pm, Room 70 EvansCourse Control Number: 54777Office: 925 EvansOffice Hours: W 9:00-11:00am or by appt.Prerequisites: Some basics of Discrete Mathematics, Statistics and Abstract Algebra. An interest in Molecular Biology.Required Text: Lior Pachter & Bernd Sturmfels, Algebraic Statistics for Computational Biology, Cambridge University Press, 2005Recommended Reading: Will be announced in class.Syllabus: This course offers an introduction to mathematical
foundations which are relevant for computational biology, in particular,
for biological sequence analysis. The emphasis lies on algebraic
statistics (e.g. hidden Markov models) and discrete algorithms (e.g.
neighbor-joining for tree construction). Occasional guest speakers will
discuss biological problems and applications.Course Webpage: http://math.berkeley.edu/~bernd/math127.htmlGrading: Will be based on homework and a course project.Homework: Comments: The expected participants will be a mix of
undergraduate students and graduate students, both from mathematics and
from other departments (MCB, IB, Stat, EECS, etc....). This is a truly
interdisciplinary opportunity. All of us will greatly benefit from
working with each other.Math 128A - Section 1 - Numerical AnalysisInstructor: Marc RieffelLectures: MWF 8:10-9:00am, Room 4 LeConteCourse Control Number: 54778Office: 811 EvansOffice Hours: To be arranged in January.Prerequisites: Math 53 and 54 or equivalent. No prior knowledge of computer programming is expected.Required Text: K. Atkinson and W. Han, Elementary Numerical Analysis, 3rd ed., John Wiley Pub. 2004Recommended Reading: The MATLAB Student Version, if you have your own computer.Syllabus: Solution of nonlinear equations, interpolation and
polynomial approximation, numerical differentiation, numerical
integration, numerical solution of ordinary differential equations.Course Webpage: There will eventually be a Course Webpage, reachable from my personal home page at http://math.berkeley.edu/~rieffel/Grading: There will be homework, which will count for 10% of the
course grade, and there will be programming exercises which will count
for 20% of the course grade.. There will be 2 midterm exams, which will
each count for 15% of the course grade. There will be a final
examination, which will count for 40% of the course grade.Homework: Homework will be assigned at almost every lecture, due the next section meeting.Comments: This is a mathematics course, and so the emphasis will
be on how to obtain effective methods for computation, and on analysing
when methods will, and will not, work well (in contrast to just learning
methods and applying them). You will have an easier time with the
course if you review Taylor's theorem and ordinary differential
equations before the course begins. The programming exercises are to be
done in MATLAB, but no prior knowledge of MATLAB will be assumed, and
help will be provided for learning the relatively small amount of MATLAB
which will be needed for the course. (But if you can learn a bit of
MATLAB before the course begins, that will make the course easier. See
Appendix D of the text.)Math 128B - Section 1 - Numerical AnalysisInstructor: William KahanLectures: TuTh 8:00-9:30am, Room 81 EvansCourse Control Number: 54799Office: 863 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory SetsInstructor: Leo HarringtonLectures: TuTh 12:30-2:00pm, Room 75 EvansCourse Control Number: 54805Office: 711 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 142 - Section 1 - Elementary Algebraic TopologyInstructor: Robion KirbyLectures: MWF 2:00-3:00pm, Room 70 EvansCourse Control Number: 54808Office: 919 EvansOffice Hours: Tu 10:00am-12:00pm, Th 10:30-11:30amPrerequisites: Math 104 and 113Required Text: M. A. Armstrong, Basic TopologyRecommended Reading:Syllabus: Continuity, compactness, connectedness for topological
spaces, surfaces, homotopy type, fundamental group, covering spaces,
knots and links.Course Webpage: http://math.berkeley.edu/~kirby/math142.htmlGrading: There will be 2 or 3 midterms worth 100 points each, a
final worth 200 points, and these will constitute most of the final
grade.Homework: Homework will be assigned on the web and due once a week.Comments:Math 151 - Section 1 - School Curriculum IInstructor: Emiliano GomezLectures: TuTh 3:30-5:00pm, Room 41 EvansCourse Control Number: 54810Office: 985 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 152 - Section 1 - School Curriculum IIInstructor: Hung-Hsi WuLectures: TuTh 2:00-3:30pm, Room 85 EvansCourse Control Number: 54811Office: 733 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 160 - Section 1 - History of MathematicsInstructor: Mariusz WodzickiLectures: TuTh 11:00am-12:30pm, Room 9 EvansCourse Control Number: 54814Office: 995 EvansOffice Hours: TBAPrerequisites: Math 104, 110 and 113 (or my consent)Required Text: We will begin from the following texts:Richard Gillings, Mathematics in the Time of the Pharaohs, Dover PublicationsOtto Neugebauer, The Exact Sciences in Antiquity, Dover PublicationsIvor Thomas (editor), Greek Mathematical Works I/II, Loeb Classical Library, Nos. 335 & 362, Harvard University PressRecommended Reading: Carl B. Boyer, A History of Mathematics, John Wiley & SonsSyllabus: In an introductory course on History of Mathematics
nothing can replace a first hand experience of working with original
texts. We will focus on a number of such texts from various historical
epochs. This will be supplemented by my lectures in which I will be
presenting a panoramic overview of the development of Mathematics in its
cultural perspective.Course Webpage: http://math.berkeley.edu/~wodzicki/160Grading: Midterm 20%, Final 30%, a term paper (25% each), quizzes, homework & class participation 25%Homework: Homework assignemens will take various forms; reading assignments will be given after every class.Comments: Students are expected to attend the class regularly.Math 170 - Section 1 - Mathematical Method OptimizationInstructor: Ming GuLectures: MWF 12:00-1:00pm, Room 3 EvansCourse Control Number: 54817Office: 861 EvansOffice Hours: MF 11:00am-12:00pm, W 1:00-2:00pmPrerequisites: Math 53, Math 54Required Text: Joel Franklin, Methods of Mathematical Economics, SIAMRecommended Reading:Syllabus: Introduction to linear programs and their duals; the
simplex method; Separating planes for convex sets; the Farkas
Alternative; the revised simplex algorithm; multiobjective linear
programming; zero-sum, two-person games; integer programming; Wolfe's
method for Quadratic Programming; Kuhn-Tucker Theory.Course Webpage: http://math.berkeley.edu/~mgu/MA170Grading: 25% homework, 25% midterm, 20% project, 30% finalHomework: Homework will be assigned on the web every week, and due once a week.Comments: Math 172 - Section 1 - CombinatoricsInstructor: Joel KamnitzerLectures: TuTh 3:30-5:00pm, Room 85 EvansCourse Control Number: 54820Office: 1067 EvansOffice Hours: TBAPrerequisites: Math 1B, 54 or consent of instructorRequired Text: Miklos Bona, Enumerative CombinatoricsRecommended Reading:Syllabus: Combinatorics is the study of discrete objects, such as
graphs, permutations, and partially ordered sets. It has applications
both to pure mathematics and computer science.In this course, we will focus mainly on enumerative combinatorics, that is, the art of counting. We will go from simple questions, like how many words can be made by rearranging ABRACADABRA? to more complicated ones such as, how many rooted unlabeled trees are there on n vertices? We will first study generating functions, both ordinary and exponential, as these are the basic tools of enumerative combinatorics. We will then apply our techniques to counting permutations and graphs. Along the way, other concepts such as partially ordered sets will be introduced and explored. Students will also explore a topic of their own choosing through a project. Course Webpage: http://math.berkeley.edu/~jkamnitz/math172Grading: 40% homework, 30% project, 30% finalHomework: There will be homework assignments every two weeks.
These will be difficult problems and you will not be expected to solve
all of them. You are encouraged to work in groups, but must write up
your solutions individually.Comments:Math 185 - Section 1 - Introduction to Complex AnalysisInstructor: Dapeng ZhanLectures: TuTh 8:00-9:30am, Room 75 EvansCourse Control Number: 54823Office: 873 EvansOffice Hours: TBAPrerequisites: Required Text: James Ward Brown and Ruel V. Churchill, Complex Variables and Applications Recommended Reading:Syllabus: This course will cover the content of the textbook from
Chapter 1 to Chapter 9. They include complex numbers, analytic
functions, elementary functions, integerals, Cauchy integral formula,
series, residues and poles, application of residues, etc.Course Webpage: http://math.berkeley.edu/~dapeng/ma185.htmlGrading: 20% homework, 20% each midterm, 40% finalHomework: Homework will be assigned on the web every class, and due once a week.Comments: Math 185 - Section 2 - Introduction to Complex AnalysisInstructor: David CimasoniLectures: TuTh 3:30-5:00pm, Room 141 GianniniCourse Control Number: 54826Office: 749 EvansOffice Hours: W 10:00am-12:00pm, Th 11:00am-12:00pmPrerequisites: Math 104Required Text: Freitag and Busam, Complex Analysis, SpringerRecommended Reading:Syllabus: We shall cover the first three chapters of the
textbook, without following it too closely. They include: complex
numbers, complex derivation, the Cauchy-Riemann equations, analytic
functions, complex line integrals, the Cauchy integral theorem, the
Cauchy integral formula, the fundamental theorem of algebra, the maximum
principal, power series, singularities, Laurent decomposition, the
residue theorem and its applications.Course Webpage: http://math.berkeley.edu/~cimasoni/Math185.htmlGrading: 20% homework, 20% each midterm, 40% finalHomework: Homework will be posted on the web every Tuesday, and due one week later.Comments: Math 185 - Section 3 - Introduction to Complex AnalysisInstructor: Jan ReimannLectures: MWF 3:00-4:00pm, Room 71 EvansCourse Control Number: 54829Office: 705 EvansOffice Hours: TBAPrerequisites: Math 104Required Text: Freitag and Busam, Complex Analysis, SpringerRecommended Reading:Syllabus: 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. If time permits some additional topics such as the Riemann
mapping theorem.Course Webpage: http://math.berkeley.edu/~reimann/Spring_07/185.htmlGrading: 20% Homework, 20% each Midterm, 40% FinalHomework: Comments: Math H185 - Section 1 - Honors Introduction to Complex AnalysisInstructor: Xuemin TuLectures: TuTh 3:30-5:00pm, Room 87 EvansCourse Control Number: 54832Office: 1055 Evans HallOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 189 - Section 1 - Math/Met Class/QuanInstructor: Dan VoiculescuLectures: TuTh 12:30-2:00pm, Room 3102 EtcheverryCourse Control Number: 54835Office: 783 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 202B - Section 1 - Introduction to Topology and AnalysisInstructor: Justin HolmerLectures: TuTh 8:00-9:30am, Room 71 EvansCourse Control Number: 54940Office: 849 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 209 - Section 1 - Von Neumann AlgebraInstructor: Richard BorcherdsLectures: TuTh 3:30-5:00am, Room 75 EvansCourse Control Number: 54946Office: 927 EvansOffice Hours: TuTh 11:00am-12:00pmPrerequisites: Math 206 Banach algebras and spectral theory (this will be reviewed in the course)Required Text: Notes by Vaughan Jones, available on the course home page. Recommended Reading: See course home page.Syllabus: Basic theory of von Neumann algebras. Density theorems,
topologies and normal maps, traces, comparison of projections, type
classification, examples of factors. Additional topics, for example,
Tomita Takasaki theory, subfactors, group actions, and noncommutative
probability.Course Webpage: http://math.berkeley.edu/~reb/209/Grading: Homework: Homework will be assigned on the web every week.Comments: Math 214 - Section 1 - Differential ManifoldsInstructor: Alexander GiventalLectures: MWF 10:00-11:00AM, Room 81 EvansCourse Control Number: 54949Office: 701 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 215B - Section 1 - Algebraic Topology Instructor: Robion KirbyLectures: MWF 11:00am-12:00pm, Room 6 EvansCourse Control Number: 54951Office: 919 EvansOffice Hours: Tu 10:00am-12:00pm, Th 10:30-11:30amPrerequisites: Math 215A or the equivalent.Required Text: Allen Hatcher, Algebraic TopologyMilnor and Stasheff, Characteristic ClassesRecommended Reading:Syllabus: More topics in homotopy and homology theory not covered
in 215A, followed by characteristic classes, with many examples from
low dimensional topology.Course Webpage: http://math.berkeley.edu/~kirby/math215B.htmlGrading: Hard and interesting homework problems will provide the basis for the grade.Homework: Homework will be assigned on the web and due periodically.Comments: Math C218B - Section 1 - Probability TheoryInstructor: Jim PitmanLectures: TuTh 9:30-11:00am, Room 330 EvansCourse Control Number: 54952Office: 303 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 219 - Section 1 - O.D.E. and FlowsInstructor: Fraydoun RezakhanlouLectures: TuTh 11:00am-12:30pm, Room 39 EvansCourse Control Number: 54955Office: 815 EvansOffice Hours: TuTh 1:30-3:00pmPrerequisites: Some analysis and measure theoryRequired Text: No required text. Handwritten notes will be distributed in class.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.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. Thermodynamic formalism. Perron-Frobenius operator. Bowen-Ruelle-Sinai measures. 4. Pesin’s theorem. Ruelle’s inequality. 5. Small perturbations of integrable Hamiltonian systems. Invariant tori. Kolmogorov-Arnold-Moser Theory. Course Webpage: Grading: There will be some homework assignments.Homework: Comments: Math 220 - Section 1 - Methods of Applied Mathematics Instructor: Alexandre ChorinLectures: MWF 11:00am-12:00pm, Room 85 EvansCourse Control Number: 54958Office: 911 EvansOffice Hours: MWF 12:00-1:00pmPrerequisites: Required Text: NoneRecommended Reading: Lecture notes from a previous time I taught
this class will be made available, as well as reading material for
topics not covered in the previous class.Syllabus: Introductory probability, solution of differential
equations by Brownian motion, introduction to stochastic processes,
Markov chains and Markov chain Monte Carlo, renormalization, scaling,
the Langevin and Fokker-Planck equations, the Barenblatt equation, many
coupled oscillators, irreversible processes, applications.Course Webpage: http://math.berkeley.edu/~chorin/math220Grading: Based on homework sets.Homework: Weekly assignments, some may involve computation and due once a week)Comments: I'll try to make the course self-contained and there
are no formal prerequisites; previous experience with the applications
of mathematics to a science would make things easier.Math 222B - Section 1 - Partial Differential EquationsInstructor: Daniel TataruLectures: TuTh 12:30-2:00pm, Room 39 EvansCourse Control Number: 54961Office: 841 EvansOffice Hours: By appt.Prerequisites: 222A or equivalentRequired Text: Recommended Reading: L. C. Evans, Partial Differential EquationsM. E. Taylor, Partial Differential Equations IL. Hormander, Partial Differential Equations ISyllabus: The theory of initial value and boundary value problems
for hyperbolic, parabolic, and elliptic partial differential equations,
with emphasis on nonlinear equations. (Continues 222A)Course Webpage: Grading: Homework + final project.Homework: Homework will be assigned periodically.Comments: Math 225B - Section 1 - MetamathematicsInstructor: Theodore SlamanLectures: TuTh 9:30-11:00am, Room 72 EvansCourse Control Number: 54964Office: 719 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 228B - Section 1 - Numerical Solution of Differential EquationsInstructor: Jon WilkeningLectures: TuTh 11:00am-12:30pm, Room 7 EvansCourse Control Number: 54967Office: 1091 EvansOffice Hours: M 11:00am-1:00pmPrerequisites: Math 128A or equivalent knowledge of basic numerical analysis. Some programming experience (e.g., Matlab, Fortran, C, or C++)Required Text: Morton & Mayers, Numerical Solution of Partial Differential EquationsDietrich Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid MechanicsRecommended Reading:Syllabus: In the first half of the course, we will study finite
difference methods for solving hyperbolic and parabolic partial
differential equations. I will describe von Neumann stability analysis,
CFL conditions, the Lax-Richtmeyer equivalence theorem (consistency +
stability = convergence), dissipation and dispersion. We will use these
tools to analyze several popular schemes (Lax-Wendroff, Lax-Friedrichs,
leapfrog, Crank-Nicolson, ADI, etc.) The second half of the course will
be devoted to finite element methods for elliptic equations (Poisson,
Lamé, Stokes). We will discuss Sobolev spaces, functional analysis, the
Lax-Milgram theorem, Cea's lemma, the Bramble-Hilbert lemma,
variational calculus, mixed methods for saddle point problems, and the
Babuska-Brezzi inf-sup condition. If time permits, I'll also talk about
hyperbolic conservation laws in the first part of the course and least
squares finite elements in the second part.Course Webpage: http://math.berkeley.edu/~wilken/228B.F06Grading: Grades will be based entirely on homework.Homework: 8 assignmentsComments: Homework problems will be graded Right/Wrong, but you
may resubmit the problems you get Wrong within two weeks of getting them
back to convert them to Right. (If you turn in a homework late, you
forfeit this possibility).Math 235A - Section 1 - Theory of SetsInstructor: John SteelLectures: TuTh 3:30-5:00pm, Room 71 EvansCourse Control Number: 54970Office: 717 EvansOffice Hours: TBAPrerequisites: This course will be an introduction to forcing. We
shall assume familiarity with basic set theory (the axions of ZFC,
cardinal arithmetic, definitions and proofs by transfinite recursion).
It would also be good, though not essential, to be familiar with the
basic theory of Gödel’s universe L of constructible sets.Required Text: Recommended Reading: Syllabus: Cohen’s method of forcing is a powerful tool for
producing models of Zeumelo–Fraenkel Set Theory (ZFC), and thereby
showing that many natural mathematical statements are neither provable
nor refutable in ZFC. Besides its metamathematical use, forcing is also
useful in obtaining consequences of ZFC, and more broadly, descriptive
set theory, recursion theory, and model theory as well. Every logician
should know the basics of forcing.Here is a rough course outline: 1. Transitive models, the Levy hierarchy of formulae, truth in transitive models. A short discussion of Gödel’s L. 2. The basic forcing theorem: the generic extension M[G] satisfies ZFC. 3. The independence of CH. Chain conditions and closure. Possible behavior of the function κ → Z ^{κ} in models of ZFC (Easton’s Theorem). 4. Models of ZF where the Axiom of Choice fails. 5. Forcing theory: complete Boolean algebras. Subalgebras versus submodels of M[G]. Characterization of the Levy collapse algebra. Vopenka’s theorem. 6. Solovay’s model of ZF + “All sets of reals are Lebesgue measurable”. 7. Iterated forcing and Martin’s Axiom. 8. Forcing and large cardinals. Prikry forcing. Forcing the failure of the Singular Cardinals Hypothesis. Course Webpage: Grading: Homework: Comments: Math 240 - Section 1 - Riemannian GeometryInstructor: John LottLectures: TuTh 2:00-3:30pm, Room 7 EvansCourse Control Number: 54973Office: 895 EvansOffice Hours: TBAPrerequisites: 214 or equivalentRequired Text: John Lee, Riemannian ManifoldsRecommended Reading:Syllabus: The first 2/3 of the semester will be devoted to basic
topics of Riemannian geometry, such as Riemannian metrics, connections,
geodesics, Riemannian curvature and relations to topology. The last few
weeks will be an introduction to Ricci flow. In particular, we will
prove Perelman's no local collapsing theorem.Course Webpage: Grading: Based on homework.Homework: Weekly homework assignments will be given.Comments: Math 250B - Section 1 - Multilinear AlgebraInstructor: Giulio CavigliaLectures: TuTh 9:30-11:00am, Room 5 EvansCourse Control Number: 54976Office: 805 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 254B - Section 1 - Number TheoryInstructor: Kenneth RibetLectures: TuTh 11:00am-12:30pm, Room 5 EvansCourse Control Number: 54979Office: 885 EvansOffice Hours: TBA and by appointmentPrerequisites: Math 254A or some basic knowledge of algebraic number fields and their completions.Required Text: Number Theory, edited by Cassels and
FröhlichRecommended Reading: Notes of an analogous course this year at Harvard.Syllabus: We will study local classfield theory and then global
classfield theory, following the lectures by Serre and Tate
(respectively) in Cassels-Fröhlich. We will pause frequently for
background lectures on cohomolgy and other relevant topics.Course Webpage: Grading: Generous.Homework: Homework will be assigned occasionally.Comments: Most of us know the bare statements of classfield
theory but have never bothered to learn the proofs and techniques that
were developed 50 odd years ago to bring order into the subject. Now is
our chance to fill in the gaps in our understanding!Math 256B - Section 1 - Algebraic GeometryInstructor: Brian OssermanLectures: TuTh 2:00-3:30pm, Room 41 EvansCourse Control Number: 54982Office: 767 EvansOffice Hours: Tu 1:00-2:00, W 2:00-3:00Prerequisites: 256ARequired Text: Hartshorne, Algebraic GeometryRecommended Reading: Eisenbud and Harris, the Geometry of SchemesSyllabus: This is the second semester of an integrated, year-long
course in algebraic geometry. The primary source text will be
Hartshorne's Algebraic Geometry. We will have already covered
most of Chapter II in the fall. We will begin with the basic properties
of sheaf cohomology and the statement of the Riemann-Roch theorem, and
classical applications to the study of curves. This will focus as
motivation for the development of cohomology in Chapter III. Finally, we
will conclude with some discussion of special topics, most likely
involving moduli spaces.Course Webpage: http://math.berkeley.edu/~osserman/classes/256B/Grading: 75% homework, 25% final paperHomework: Homework will be assigned roughly weekly.Comments: Math 257 - Section 1 - Group TheoryInstructor: Mariusz WodzickiLectures: TuTh 3:30-5:00pm, Room 7 EvansCourse Control Number: 54985Office: 995 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 274 - Section 1 - Topics in Algebra - StacksInstructor: Martin OlssonLectures: MWF 10:00-11:00am, Room 385 LeConteCourse Control Number: 54987Office: 887 EvansOffice Hours: TBAPrerequisites: Math 256A or equivalent course on schemesRequired Text: NoneRecommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Algebraic stacks were originally introduced by
Grothendieck, Artin, Deligne, and Mumford as the natural setting for the
study of moduli spaces. In recent years stacks have found much broader
applications and are now a standard tool of the modern algebraic
geometer. Stacks are generalizations of schemes, which enable one to
handle geometric objects with symmetries which cannot be studied
adequately using schemes. For example, many moduli spaces are stacks
(for example moduli spaces for curves), and quotients of varieties by
group actions are stacks.In this course I will discuss the foundations of algebraic stacks, and time permitting some more recent applications towards the end of the class. I aim to make the course accessible to students familiar with schemes as taught for example in 256A though of course more background will be helpful (in particular a course in algebraic topology would be helpful). In light of these limited prerequisites, I will spend some time at the beginning of the course to develop the foundations necessary for the basic definitions in the theory of stacks (Grothendieck topologies, descent, groupoids, ...). I will then discuss the basic theory of quasi-coherent and coherent sheaves on stacks, separated and proper morphisms, Chow's lemma, and other generalizations of standard scheme theory to stacks. Throughout I will discuss in detail examples to illustrate the theory. At the end of the course I hope to discuss Artin's method for proving representability by an algebraic stack, as well as other more advanced topics (to be chosen based on the interests of the participants). Math 275 - Section 1 - Topics in Applied Mathematics: Flow, Deformation and FractureInstructor: Grigory BarenblattLectures: TuTh 9:30-11:00am, Room 41 EvansCourse Control Number: 54988Office: 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.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 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, and damage accumulation.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. 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 - Chainlet Theory - New Geometric Methods in AnalysisInstructor: Jenny HarrisonLectures: MWF 1:00-2:00pm, Room 39 EvansCourse Control Number: 54991Office: 851 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: In the first half of this course we present a class of
objects called ‘chainlets’, a particularly well-behaved subspace of de
Rham currents. Chainlets are a generalization of k-surfaces in n-space,
but with algebraic information encoded both locally and globally.
Equipped with a new, ‘natural’ norm, we discard many cumbersome methods
used in geometric measure theory, instead building an elegant calculus
from the ground up on domains that include, but are not limited to,
discrete and continuous domains, soap films, fractals, and particle
fields. The second half of the course will cover a wide array of
applications, from analysis to differential and algebraic topology,
calculus of variations, PDEs, and physics, as time permits.Course Webpage:Grading:Homework:Comments:Math 278 - Section 2 - Topics in Random MatricesInstructor: Alice GuionnetLectures: MWF 12:00-1:00pm, Room 55 EvansCourse Control Number: 54993Office: 757 EvansOffice Hours: W 2:00-3:00pm, F 2:00-4:00pmPrerequisites: Basic probability theoryRequired Text: No textbook will be required but lecture notes (from a course I gave in Saint Flour) will be posted on my web page http://www.umpa.ens-lyon.fr/~aguionne/ .Recommended Reading:Syllabus: Random matrices appeared first in statistics in the
work of Wishart in the thirties and then in quantum mechanics when
Wigner introduced them as a model to the Hamiltonian of highly excited
nuclei. Since then, random matrices appeared in many different branches
of physics (e.g. theoretical physics, string theory, quantum field
theory) and mathematics (e.g. number theory, combinatorics, free
probability and operator algebras, hydrodynamics via the totally
asymmetric simple exclusion process). The goal of the course is to give
an introduction to the rapidly developing theory of random matrices. In
the first part of the course I will focus on properties of random
matrices which are 'universal' in the sense that they do not depend much
on the distribution of the entries. In the second part, I will focus on
properties more closely related with Gaussian entries. Most results and
proofs will be given for the so-called Wigner's matrices which are
self-adjoint matrices with independent entries modulo the symmetry
constraints, but generalizations to other classical ensembles will be
pointed out. The following is a possible list of topics forthis course. Ideally, we would like to cover all of them, but adjustments may have to be made because of time constraints. - Wigner's theorem; convergence of the spectral measure of Wigner matrices.
- Convergence of the spectral radius of Wigner's matrices.
- Concentration of measure for random matrices.
- Central limit theorem for the spectral measure of random matrices.
- Gaussian Wigner Matrices. We shall describe the joint law of their eigenvalues.
- Large deviations for the empirical measure and the maximal eigenvalue of Gaussian Wigner Matrices.
- Matrix Models. Relation with the combinatorics of maps.
- Free Probability. We shall give an introduction to Free Probability and show how it can be used to find out the asymptotic spectral distribution of sums or products of random matrices.
- Eigenvalues spacing and determinantal processes. This topic is quite different from the others but will be developed sufficiently to show the convergence to Tracy-Widom distribution.
- If students know the basis of stochastic differential calculus, or are interested in this topic, we may consider its applications to Gaussian random matrices, in particular to estimate the so-called Itzykson-Zuber-Harich-Chandra integral.
Course Webpage:Grading:Homework:Comments:Math 300 - Section 1 - Teaching WorkshopInstructor: Jenny HarrisonLectures: W 5:00-7:00pm, Room 47 EvansCourse Control Number: 55603Office: 851 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments: |