# Fall 2004

Math 1A - Section 1 - CalculusInstructor: Richard BorcherdsLectures: TuTh 2:00-3:30pm, Room 2050 Valley Life ScienceCourse Control Number: 54303Office: 927 Evans, e-mail: reb [at] math [dot] berkeley [dot] eduOffice Hours: TuTh 3:30-5:00pmPrerequisites: 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, 5th edition, Brooks/Cole.Syllabus: An introduction to differential and integral calculus
of functions of one variable, with applications and an introduction to
transcendental functions.Course Webpage: math.berkeley.edu/~reb/1AGrading: 20% quizzes and homework, 20% each midterm, 40% final.Homework: Homework for each week is given in the course handout (available at math.berkeley.edu/~reb/1A) and is due in the discussion section on Monday the next week. Comments: See the course page math.berkeley.edu/~reb/1A for the course handout.Math 1A - Section 2 - CalculusInstructor: Mark HaimanLectures: MWF 11:00am-12:00pm, Room 155 DwinelleCourse Control Number: 54348Office: 771 Evans, e-mail: Office Hours: TBAPrerequisites: 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: James Stewart, Calculus: Early Transcendentals, 5th edition (Brooks/Cole, 2003). We will cover chapters 1-6.Syllabus: An introduction to differential and integral calculus
of functions of one variable, with applications and an introduction to
transcendental functions. Intended for majors in engineering and the
physical sciences.Course Webpage: math.berkeley.edu/~mhaiman/math1AMath 1A - Section 3 - CalculusInstructor: Daniel TataruLectures: TuTh 3:30-5:00pm, Room 155 DwinelleCourse Control Number: 54393Office: 841 Evans, e-mail: tataru [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: 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, 5th edition, Brooks/Cole.Recommended Reading:Syllabus: This course provides an
introduction to differential and integral calculus of functions of one
variable, with applications and an introduction to transcendental
functions. It is intended for majors in
engineering and the physical sciences. Course Webpage: http://math.berkeley.edu/~tataru/1A/ (to come)Grading: 20% quizzes and homework, 20% each midterm, 40% finalHomework: Homework will be assigned on the web every class, and due once a week.Math 1B - Section 1 - Calculus Instructor: Ole HaldLectures: MWF 10:00-11:00am, Room 1 PimentelCourse Control Number: 54432Office: 875 Evans, e-mail: hald [at] math [dot] berkeley [dot] eduOffice Hours: TBA Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 1B - Section 2 - Calculus Instructor: Zvezdelina StankovaLectures: TuTh 12:30-2:00pm, Room 2050 Valley Life ScienceCourse Control Number: 54477Office: 719 Evans, e-mail: stankova [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 16A - Section 1 - Analytical Geometry and CalculusInstructor: Vaughan JonesLectures: TuTh 3:30-5:00pm, Room 1 PimentelCourse Control Number: 54516Office: 929 Evans, e-mail: vfr [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 16A - Section 2 - Analytical Geometry and CalculusInstructor: Tsit-Yuen LamLectures: MWF 12:00-1:00pm, Room 155 DwinelleCourse Control Number: 54555Office: 871 Evans, e-mail: lam [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 16B - Section 1 - Analytical Geometry and CalculusInstructor: Donald SarasonLectures: MWF 8:00-9:00am, Room 10 EvansCourse Control Number: 54594Office: 779 Evans, e-mail: sarason [at] math [dot] berkeley [dot] eduOffice Hours: MW 9:30-11:30amPrerequisites: Math 16ARequired Text: Goldstein, Lay and Schneider, Calculus and its Applications, 10th edition, Prentice-HallSyllabus: Functions of several variables, trigonometric
functions, techniques of integration, differential equations, Taylor
polynomials and infinite series, probability and calculus (Chapters 7-12
of the textbook)Course Webpage: http://math.berkeley.edu/~sarason/Class_Webpages/Fall_2004/Math16B_S1.htmlGrading: The course grade will be based on two midterm exams, the
final exam, and section performance. Details will be provided at the
first lecture.Homework: There will be weekly homework assignments.Comments: At the first lecture, a lecture schedule, exam dates,
and a schedule of homework assignments will be provided. My lectures
tend to be slow moving. They cannot possible cover all of the course
material; that would be true even if I spoke much more quickly than I
do. So expect to pick up a lot by reading the textbook. Needless to
say, if you attend lecture, it would be best to look beforehand at the
relevant parts of the textbook to get at least a rough idea of the
topics that will be discussed.Before enrolling in the course, check the final exam date to make sure you do not have a conflict. There will be no make-up exams, neither final nor midterms. Math 24 - Section 1 - Freshman SeminarsInstructor: Jenny HarrisonLectures: F 3:00-4:00pm, Room 891 EvansCourse Control Number: 54633Office: 851 Evans, e-mail: harrison [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 32 - Section 1 - PrecalculusInstructor: The StaffLectures: MWF 8:00-9:00am, Room 4 LeConteCourse Control Number: 54636Office:Office Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 53 - Section 1 - Multivariable CalculusInstructor: Rob KirbyLectures: MWF 9:00-10:00am, Room 2050 Valley Life ScienceCourse Control Number: 54684Office: 919 Evans, e-mail: kirby [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 53M - Section 1 - Multivariable Calculus With ComputersInstructor: Alexander GiventalLectures: MWF 2:00-3:00pm, Room 100 LewisCourse Control Number: 54735Office: 701 Evans, e-mail: givental [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 54 - Section 1 - Linear Algebra and Differential EquationsInstructor: Marc RieffelLectures: MWF 12:00-1:00pm, Room 1 PimentelCourse Control Number: 54756Office: 811 Evans, e-mail: rieffel [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: Math 1B or equivalentRequired Text: Richard Hill, Elementary Linear Algebra with ApplicationsW. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value ProblemsRecommended Reading:Syllabus: Basic linear algebra; matrix arithmetic and
determinants. Vector spaces; inner product on 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/~rieffel/54web.htmlGrading:Homework:Comments:Math H54 - Section 1 - Honors Linear Algebra and Differential EquationsInstructor: Robert ColemanLectures: MWF 1:00-2:00pm, Room 9 EvansCourse Control Number: 54806Office: 901 Evans, e-mail: coleman [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: First year calculus and motivation.Required Text: Richard Hill, Elementary Linear Algebra with ApplicationsW. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value ProblemsRecommended Reading:Syllabus: Linear Algebra, the theory of linear equations, is the
simplest of higher mathematics. The theory of Differential Equations
involves some of the deepest ideas in mathematics. In this course, I
will teach enough linear algebra so that some important properties of
differential equation can be revealed.Course Webpage:Grading:Homework:Comments:Math 54M - Section 1 - Linear Algebra and Differential EquationsInstructor: Fraydoun RezakhanlouLectures: MWF 9:00-10:00am, Room 1 LeConteCourse Control Number: 54807Office: 815 Evans, e-mail: rezakhan [at] math [dot] berkeley [dot] eduOffice Hours: MWF 10:00-11:00amPrerequisites:Required Text: Hill, Elemetary Linear AlgebraBoyce-DiPrima, Elemetary DE and Boundary Value Problems, Wiley, 8th editionRecommended Reading:Syllabus: The M version of Math 54 schedules students to
meet with their teaching assistants twice a week in the computer lab 38B
located in the basement of Evans hall. Students will have
computer-based homework exercises. No prior computer experience is
required. Course Webpage:Grading:homework and quizzes, 150 points 3 midterms, the best two counting, worth 75 points each, totalling 150 points Final Exam, 200 points Total: 500 points possible. Homework: Due every Tuesday in your TA section. You must give a detailed solution for each problem - the correct answer is not sufficient. Late homework is not accepted
by the TA's under any circumstances. To allow for sickness, we delete
the single worst homework set from your record and add up the rest for a
total possible of 120 points. There will be three quizzes
(given in section) that count, for a total of 30 points. Quizzes will
vary with the TA section. The first assignment is due in your TA section
on Tuesday, September 7.Comments: The first midterm will be in class on Monday, October 4.The second midterm will be on Wednesday, November 3.The third midterm will be on Wednesday, December 1.The Final Exam will be on Monday, December 20. Make sure you can make the final exam - check the schedule now to see that it is acceptable to you. It is not possible to have make-up exams.Incompletes. Official University policy states that an Incomplete
can be given only for valid medical excuses with a doctor's
certificate, and only if at the point the grade is given the student has
a passing grade (C or better). If you are behind in the course,
Incomplete is not an option!Math 55 - Section 1 - Discrete MathematicsInstructor: George M. BergmanLectures: MWF 3:00-4:00pm, Room 10 EvansCourse Control Number: 54828Office: 865 Evans, e-mail: gbergman [at] math [dot] berkeley [dot] eduOffice Hours: Tu 10:30-11:30am, W 4:15-5:15pm, F 10:30-11:30amPrerequisites: Math 1A-1B, or consent of the instructorRequired Text: Kenneth H. Rosen, Discrete Mathematics and its Applications, 5th edition, McGraw-HillSyllabus: We will cover Chapters 1-5 and 7 in Rosen. We'll also
use some notes prepared by a previous instructor (available online both
in pdf and in postscript format) to supplement Chapter 5.Grading: Grades will be based on two Midterms (15% + 20%), a
Final (35%), and weekly Quizzes in Section (30%). The Department cannot
at present afford graders for homework in lower-division courses, but I
will assign problems for you to do, the solutions will be discussed in
section, and section Quizzes will be based largely on them.Homework: WeeklyComments: Math 1A-1B and (if you've had them) 53 and 54 have all
been about smooth functions of one or more real variables. This course
is about some very different topics. The main reason 1A-1B is a
prerequisite 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. But if you haven't
had it 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: The StaffLectures: MWF 12:00-1:00pm, Room 70 EvansCourse Control Number: 54849Office:Office Hours:Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math 74 - Section 2 - Transition to Upper Division MathematicsInstructor: The StaffLectures: TuTh 3:30-5:00pm, Room 241 CoryCourse Control Number: 54852Office:Office Hours:Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math H90 - Section 1 - Honors Problem SolvingInstructor: Olga HoltzLectures: MF 4:00-6:00pm, Room 71 EvansCourse Control Number: 54855Office: 821 Evans, e-mail: holtz [at] math [dot] berkeley [dot] eduOffice Hours: MF 11:00am-12:00pmPrerequisites: Very good grasp of pre-calculus math is a must; basic calculus and linear algebra background is desirable.Required Text: No required text, will use several problem books.Recommended Reading: Gleason, A. M.; Greenwood, R. E.; Kelly, L.
M.; The William Lowell Putnam Mathematical Competition. Problems and
solutions: 1938--1964. Mathematical Association of America, Washington,
D.C., 1980. ISBN 0-88385-428-7MR0837662 The William Lowell Putnam mathematical competition. Problems and solutions: 1965--1984. Edited by Gerald L. Alexanderson, Leonard F. Klosinski and Loren C. Larson. Mathematical Association of America, Washington, DC, 1985. ISBN 0-88385-441-4 MR1933844 (2003k:00002) Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi; The William Lowell Putnam Mathematical Competition, 1985--2000. Problems, solutions, and commentary. MAA Problem Books Series. ISBN 0-88385-807-X Contests in higher mathematics. Miklos Schweitzer Competitions 1962--1991. Edited by Gbor J. Szkely. Problem Books in Mathematics. Springer-Verlag, New York, 1996. ISBN 0-387-94588-1 Syllabus: NoneCourse Webpage: http://math.berkeley.edu/~holtz/H90.htmlGrading: Based entirely on homework.Homework: 10-12 problems weekly.Comments: This course is for hard working students who enjoy
solving challenging math problems, especially for those who want to
participate and do well on the Putnam competition in December.Math C103 - Section 1 - Introduction to Mathematical EconomicsInstructor: D. AhnLectures: TuTh 3:30-5:00pm, Room 130 WheelerCourse Control Number: 54915Office:Office Hours:Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading: Homework:Comments: Math 104 - Section 1 - Introduction to AnalysisInstructor: Donald SarasonLectures: MWF 1:00-2:00pm, Room 71 EvansCourse Control Number: 54918Office: 779 Evans, e-mail: sarason [at] math [dot] berkeley [dot] eduOffice Hours: MW 9:30-11:30amPrerequisites: Math 53 and 54Required Text: Charles Pugh, Real Mathematical Analysis, Springer-Verlag, 2002Recommended Reading:Syllabus: Review of elementary set
theory, countable and uncountable sets, the system of real numbers and
its basic properties, convergence, continuity, differentiation,
integration, Euclidean spaces, metric spaces, compactness,
connectedness.Course Webpage: http://www.math.berkeley.edu/~sarason/Class_Webpages/Fall_2004/Math104_S1.htmlGrading: The course grade will be based on two midterm exams, the
final exam, and homework. Details will be provided at the first class
meeting. All exams will be open book.Homework: Homework will be assigned weekly and will be carefully graded.Comments: The course has two basic goals. One is to present a
rigorous development of the fundamental ideas underlying calculus (and
much of the rest of mathematics). The other is to foster students in
acquiring (or coerce them into acquiring) skill in mathematical
reasoning and in constructing coherent, rigorous mathematical proofs.The lectures will discuss the basic ideas, but students can expect to have to pick up much on their own from the textbook. Many students find Math 104 difficult. Unless you aced lower-division mathematics, and perhaps even if you did, Math 104 is probably not a wise choice as a first upper-division math course. Lower-division math involves a heavy dose of symbol manipulation. Math 104 is concerned with the ideas that justify the symbolism. Math 104 - Section 2 - Introduction to AnalysisInstructor: Alexander YongLectures: TuTh 3:30-5:00pm, Room 71 EvansCourse Control Number: 54921Office: 1035 Evans, e-mail: ayong [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: Math 53, Math 54.Required Text: Charles Pugh, Real Mathematical AnalysisRecommended Reading: Walter Rudin, Principles of Mathematical AnalysisKenneth Ross, Elementary Analysis: the theory of calculusSyllabus: Review of elementary set theory, countable and
uncountable sets, the system of real numbers and its basic properties,
convergence, continuity, differentiation, integration, Euclidean spaces,
metric spaces, compactness, connectedness.Course Webpage: http://math.berkeley.edu/~ayong/Fall2004_Math104.htmlGrading: TBAHomework: TBAExams: TBAComments: Send ayong [at] math [dot] berkeley [dot] edu (me) an email about you and your (mathematical) background so I can get to better know you. Math 104 - Section 3 - Introduction to AnalysisInstructor: Paul ChernoffLectures: MWF 3:00-4:00pm, Room 71 EvansCourse Control Number: 54924Office: 933 Evans, e-mail: chernoff [at] math [dot] berkeley [dot] eduOffice Hours: M 1:30-2:30pm; W 11:00am-12:00pm; F 1:30-2:30pmPrerequisites: Math 53 and 54Required Text: K. Ross, Elementary Analysis: The Theory of Calculus, first edition (13th or later printing advised), published by Springer.Recommended Reading: M. Protter, Basic Elements of Real Analysis, paperback, published by Springer.Syllabus: Primarily Chapters 1-4 of Ross: The real number system;
convergence of sequences and series. Convergence and uniform
convergence of sequences of functions; power series. Main facts about
differentiation and integration. Some discussion of metric spaces.Grading: 15% homework, 45% midterms and quizzes, 40% final.Homework: Weekly assignments.Comments: This is a very challenging course. Its content is very
important. It is also important to master the art of writing
mathematics clearly and concisely.
- COURSE OUTLINE:
Introduction 1. Linear programming 2. Nonlinear programming, convex analysis 3. Game theory 4. Calculus of variations 5. Introduction to control theory
Grading: 25% homework, 25% midterm, 50% finalHomework: At the start of each class, I will assign a homework problem, due in one week.Math 172 - Section 1 - CombinatoricsInstructor: Alexander YongLectures: TuTh 12:30-2:00pm, Room 103 MoffittCourse Control Number: 55026Office: 1035 Evans, e-mail: ayong [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: No specific prerequisites, however exposure to
courses such as abstract algebra (Math 113) will be helpful. This will
be an advanced undergraduate course on combinatorics. Required Text: Peter J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 1994 (reprinted 1996). Recommended Reading: R. P. Stanley, Enumerative Combinatorics IR. P. Stanley, Enumerative Combinatorics IID. Stanton and D. White, Constructive combinatoricsR. Brualdi, Introductory CombinatoricsSyllabus: This is the ultimate fun course on combinatorics.
Combinatorial methods are applied widely throughout mathematics; this
class will be an introduction to various aspects of combinatorial
theory. Some sample topics include: generating series, graph theory,
poset theory, combinatorics of trees (parking functions, Catalan
numbers, matrix-tree theorem), tableaux and the symmetric group
(permutation statistics, the Schensted correspondence, hook-length
formula), partitions, symmetric functions.A different with the same course number was taught in Spring 2004. This course will not depend on the material covered in that course. Although there will be some material overlap, I plan to cover a wider range of topics this term. This course should be of interest to anyone who like algorithms, computation, and problem solving. Course Webpage: http://math.berkeley.edu/~ayong/Fall2004_Math172.htmlGrading: TBAHomework: TBAExams: TBAComments: Send ayong [at] math [dot] berkeley [dot] edu (me) an email about you and your (mathematical) background so I can get to better know you. Math 185 - Section 1 - Introduction to Complex AnalysisInstructor: Daniel GebaLectures: TuTh 2:00-3:30pm, Room 71 EvansCourse Control Number: 55029Office: 837 Evans, e-mail: dangeba [at] math [dot] berkeley [dot] eduOffice Hours: TuTh 3:30-5:00pmPrerequisites: Math 104Required Text: J. W. Brown and R. V. Churchill, Complex Variables and Applications, 6th edition, 1995.Syllabus: Complex numbers. Analytic functions. Elementary
functions. Integrals. Series. Residues and poles. Application of
residues. Mapping by elementary functions.Grading: Homework (25%), Midterm (25%), Final (50%)Homework: Assigned on Wednesday, due next Thursday. Worst 3 homeworks not counted. No late homeworks. Comments: No make-up exams.Math 185 - Section 2 - Introduction to Complex AnalysisInstructor: Leo HarringtonLectures: MWF 12:00-1:00pm, Room 71 EvansCourse Control Number: 55032Office: 711 Evans, e-mail: leo [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 185 - Section 3 - Introduction to Complex AnalysisInstructor: Dapeng ZhanLectures: MWF 3:00-4:00pm, Room 75 EvansCourse Control Number: 55035Office:Office Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 191 - Section 1 - High School Mathematics from an Advanced PerspectiveInstructor: Emiliano GomezLectures: MW 4:00-7:00pm, Room 230-D StephensCourse Control Number: 55038Office: 985 Evans, e-mail: emgomez [at] math [dot] berkeley [dot] eduOffice Hours: To be decided in class. Most likely they will be
on Monday and Wednesday afternoons/evenings (to accomodate teachers),
and also by appointment.Prerequisites: Interest in math education/teaching. Willingness to work in groups. At least one upper-level math class.Required Text: Usiskin, Peressini, Marchisotto and Stanley, Mathematics for High School Teachers (an Advanced Perspective), Prentice Hall, 2003. ISBN: 0-13-044941-5Recommended Reading: Familiarity with the high school curriculum,
as well as with some high school texts, is desired but not necessary.
Another recommendation is to read articles from "Mathematics Teacher", a
journal of the National Council of Teachers of Mathematics.Syllabus: We will cover topics such as number systems (integers,
rationals, reals, complex), equations, functions, congruence and
similarity, area and volume, axioms, trigonometry. Clarity and proof
will be emphasized. Topics will pertain to the high school curriculum,
but we will give them a depth far beyond that which high schools
students see at school.Grading: Based on weekly homework and reading assignments, a midterm take-home exam, and presentation of a semester project.Homework: Reading and exercises will be assigned and collected weekly.Comments: This course is for upper-level students interested in
teaching High School mathematics, for grad students in the School of
Education, and for High School teachers (who can register through UC
Extension). It emphazises problem solving and group work, so that class
participation is important. It MUST be taken for 4 units, unless there
are very good reasons why that cannot be done.Math 198 - Section 1 - Directed Group StudyInstructor: L. Craig EvansLectures: M 4:00-5:00pm, Room 2 EvansCourse Control Number: 55073Office: 907 Evans, e-mail: evans [at] stat [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework: Comments:Math 202A - Section 1 - Introduction to Topology and AnalysisInstructor: Michael KlassLectures: MWF 12:00-1:00pm, Room 332 EvansCourse Control Number: 55104Office: 319 Evans, e-mail: klass [at] stat [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework: Comments:Math 204A - Section 1 - Ordinary and Partial Differential EquationsInstructor: Alexandre ChorinLectures: MWF 10:00-11:00am, Room 85 EvansCourse Control Number: 55107Office: 911 Evans, e-mail: chorin [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: No previous acquaintance with differential equations is assumed; some analysis (e.g., Math 104) is helpful.Required Text: Coddington and Levinson, Ordinary Differential EquationsRecommended Reading: Dorfman, An Introduction to Chaos in Nonequilibrium Statistical MechanicsGrading: Grading mostly on the homework. Homework: Homework will be assigned once a week and due a week later.Comments: My lecturing style is informal and I enjoy class discussion.Math 206 - Section 1 - Banach Algebras and Spectral TheoryInstructor: Dan VoiculescuLectures: TuTh 12:30-2:00pm, Room 6 EvansCourse Control Number: 55110Office: 783 Evans, e-mail: dvv [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 214 - Section 1 - Differential ManifoldsInstructor: Jenny HarrisonLectures: MWF 11:00am-12:00pm, Room 31 EvansCourse Control Number: 55113Office: 851 Evans, e-mail: harrison [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 215A - Section 1 - Algebraic Topology Instructor: Jack WagonerLectures: MWF 9:00-10:00am, Room 39 EvansCourse Control Number: 55116Office: 899 Evans, e-mail: wagoner [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 218A - Section 1 - Probability Theory Instructor: David AldousLectures: MWF 2:00-3:00pm, Room 106 MoffittCourse Control Number: 55118Office: 371 Evans, e-mail: aldous [at] stat [dot] berkeley [dot] eduOffice Hours: W 9:30-11:30pm, 351 EvansPrerequisites: Ideally
- Upper division probability - familiarity with calculations using random variables.
- Upper division analysis, e.g. uniform convergence of functions, basics of complex numbers. Basic properties of metric spaces helpful.
Required Text: R. Durrett, Probability: Theory and Examples
is the required text, and the single most relevant text for the whole
year's course. Quite a few of the homework problems are from there.
The new 3rd edition corrects typos from the 2nd edition; either will be
OK to use. The style is deliberately concise.Recommended Reading: P. Billingsley, Probability and Measure (3rd Edition)Chapters 1-30 contain a more careful and detailed treatment of the topics of this semester, in particular the measure-theory background. Recommended for students who have not done measure theory. K.L. Chung, A Course in Probability Theory covers many of the topics of 205A: more leisurely than Durrett and more focused than Billingsley.There are many other books at roughly the same ``first year graduate" level. Here are my personal comments on some. Y.S. Chow and H. Teicher, Probability Theory. Uninspired exposition, but has useful variations on technical topics such as inequalities for sums and for martingales.R.M. Dudley, Real Analysis and Probability. Best account of the functional analysis and metric space background relevant for research in theoretical probability.B. Fristedt and L. Gray, A Modern Approach to Probability Theory. 700 pages allow coverage of broad range of topics in probability and stochastic processes.L. Breiman, Probability. Classical; concise and broad coverage.There are some lecture notes for Jim Pitman's Fall 2002 STAT 205A which covers more ground than my course will! Syllabus: This is the first half of a year course in mathematical
probability at the measure-theoretic level. It is designed for students
whose ultimate research will involve rigorous proofs in mathematical
probability. It is aimed at Ph.D. students in the Statistics and
Mathematics Depts, but is also taken by Ph.D. students in Computer
Science, Electrical Engineering, Business and Economics who expect their
thesis work to involve probability.NoteThere is a parallel first year graduate course in probability theory, STAT 204 taught by Evans, which does not have a measure theory prerequisite. In brief, the course will cover - Sketch of pure measure theory (not responsible for proofs)
- Measure-theoretic formulation of probability theory
- Classical theory of sums of independent random variables: laws of large numbers
- Technical topics relating to proofs of above: notions of convergence, a.s. convergence techniques
- Conditional distributions, conditional expectation
- Discrete time martingales
- Introduction to Brownian motion
Course Webpage: http://www.stat.berkeley.edu/users/aldous/205A/index.htmlGrading: 60% homework, 40% final.Homework: See week-by-week schedule for more details and for the weekly homework assignments.Comments: There will be a take-home final exam: tentatively December 10 - December 14.Math 221 - Section 1 - Advanced Matrix Computation Instructor: James DemmelLectures: MWF 9:00-10:00am, Room 5 EvansCourse Control Number: 55119Office: 737 Soda, e-mail: demmel [at] cs [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework: Comments:Math 222A - Section 1 - Partial Differential EquationsInstructor: Fraydoun RezakhanlouLectures: MWF 1:00-2:00pm, Room 5 EvansCourse Control Number: 55122Office: 815 Evans, e-mail: rezakhan [at] math [dot] berkeley [dot] eduOffice Hours: MWF 10:00-11:00amPrerequisites: Math 104Required Text: L. C. Evans, Partial Differential Equations, AMS.Recommended Reading:Syllabus: In this course we discuss the issues concerning the
solvability and regularity for some basic partial differential
equations. The main topics are:(1) Laplace, Diffusion and Wave equations (2) Scalar consevation laws (3) Hamilton-Jacobi equations (4) Sobolev spaces Course Webpage:Grading: There will be weekly homework assignments (due Mondays)
and one take-home exam. Homework (70 points), take-home exam (30
points).Homework:Comments:Math 224A - Section 1 - Transport Processes, Conservation Laws and SymmetryInstructor: John NeuLectures: MWF 3:00-4:00pm, Room 5 EvansCourse Control Number: 55125Office: 1051 Evans, e-mail: neu [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Basic Prototypes
- Advection
- Diffusion-Einstein theory of Brownian motion
- Advection-diffusion, Smoluchowski PDE in stat mech
Sources, delta functions and Green's functionsCase studies
- Ideal fluid mechanics and vorticity
- Waves in elastic media
- Motion of melting fronts
Asymptotic reductions by scaling
- Diffusion in thin domain
- Incompressible limit of compressible flow
- Shallow water theory
Scaling symmetries in BVP
- Point source solution of diffusion equation
- Planar melting front
- Nonlinear diffusions with compact support
- Green's function of 2-D wave equation
- Advection-diffusion in a vortex
- Eigenvalue optimization problem-shape of the tallest building
Course Webpage:Grading: Problems given at beginning of each class, 50%2 in class MT (simple and basic), 30% Final (simple and basic), 20% Homework:Comments:Math 225A - Section 1 - MetamathematicsInstructor: Leo HarringtonLectures: MWF 2:00-3:00pm, Room 31 EvansCourse Control Number: 55128Office: 711 Evans, e-mail: leo [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 228A - Section 1 - Numerical Solution of Differential EquationsInstructor: John StrainLectures: TuTh 2:00-3:30pm, Room 75 EvansCourse Control Number: 55131Office: 1099 Evans, e-mail: strain [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: 128A or equivalent.Required Text: 1. J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995.2. J. W. Thomas, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, Springer, 1999.Syllabus: Math 228B will survey the theory and practice of finite
difference methods for parabolic, hyperbolic and elliptic partial
differential equations. Topics will include:Basic linear partial differential equations and schemes. Convergence, stability and consistency. Practical stability analysis. ADI schemes. Numerical boundary conditions. GKSO theory. Dispersion and dissipation. Theory of nonlinear hyperbolic conservation laws. Entropy conditions and TVD schemes. Relaxation and multigrid for linear elliptic equations. Course Webpage: http://math.berkeley.edu/~strain/228b.S04/Grading: Based on weekly homework and one or two projects.Homework: Will be posted on the class web site, and due once a week.Math 229 - Section 1 - Theory of Models Instructor: Thomas ScanlonLectures: TuTh 11:00am-12:30pm, Room 5 EvansCourse Control Number: 55134Office: 723 Evans, e-mail: scanlon [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 240 - Section 1 - Riemannian GeometryInstructor: Ai-Ko LiuLectures: MWF 11:00am-12:00pm, Room 5 EvansCourse Control Number: 55137Office: 905 Evans, e-mail: akliu [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading: Homework:Comments:Math 249 - Section 1 - Combinatorial Commutative AlgebraInstructor: Bernd SturmfelsLectures: TuTh 8:00-9:30am, Room 81 EvansCourse Control Number: 55140Office: 925 Evans, e-mail: bernd [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: Math 250B or equivalent background in commutative
algebra, some exposure to combinatorics and geometry. Students who have
already taken a previous version of Math 249 may register for this
course as Math 274, Section 3, CCN 55160.Required Text: Ezra Miller and Bernd Sturmfels, Combinatorial Commutative Algebra, Springer Graduate Texts in Mathematics, to appear in late 2004.Recommended Reading:Syllabus: The book has the following 18 chapters. A
rough plan to discuss a different chapter each week, so we may cover
about two-thirds of the book. Your input on the selection and order of
topics is welcome.1. Squarefree Monomial Ideals2. Borel-fixed Monomial Ideals 3. Three-dimensional Staircases 4. Cellular Resolutions 5. Alexander Duality 6. Generic Monomial Ideals 7. Semigroup Algebras 8. Multigraded Polynomial Rings 9. Syzygies of Lattice Ideals 10. Toric Varieties 11. Irreducible and Injective Resolutions 12. Ehrhart Polynomials 13. Local Cohomology 14. Plücker Coordinates 15. Matrix Schubert Varieties 16. Antidiagonal Initial Ideals 17. Minors in Matrix Products 18. Hilbert Schemes of Points To read this book click here.
The posted version has now been submitted to Springer Verlag, but we
are still able to make minor corrections until the end of June 2004.
Please do take a look and e-mail me all your comments and corrections
during the month of June.Course Webpge:Grading:Homework:Comments:Math 250A - Section 1 - Groups Rings and FieldsInstructor: Kenneth A. RibetLectures: TuTh 12:30-2:00pm, Room 70 EvansCourse Control Number: 55143Office: 885 Evans, e-mail: ribet [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: A strong background in undergraduate abstract algebra.Required Text: Lang, Algebra, 3rd rev. ed.Syllabus: We will study such fundamental structures as groups,
rings, modules and fields. It is likely that the course will end with a
treatment of Galois theory.Course Webpage: http://math.berkeley.edu/~ribet/250/Grading: Based on exams and homework, with the exact mix to be announced laterHomework: Long problem sets will be assigned weekly.Math 254A - Section 1 - Number Theory Instructor: Martin WeissmanLectures: MWF 3:00-4:00pm, Room 9 EvansCourse Control Number: 55146Office: 1067 Evans, e-mail: marty [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: A strong background in abstract algebra, such as Math 250A-B, including groups, rings, fields, modules, and Galois theory.Required Text: Jurgen Neukirch, Algebraic number TheoryRecommended Reading: TBASyllabus: This will be a rigorous introduction to algebraic
number theory. Topics include algebraic number fields, orders, etale
algebras, valuations and localizations, ramification, units and
class-groups, quadratic forms, function field analogues, quaternion
algebras and central simple algebras. Two lectures per week will cover
"standard" material, and one lecture per week will be a "fun" topic like
"RSA cryptography", and "Why primes are like knots", and "The topograph
of a quadratic form". Students are expected to read 10-15 pages per
week of the textbook as well.Course Webpge: TBAGrading: Grades will be based on bi-weekly problem sets, and a final exam.Homework: Homework assignments will be available on the web.Math 256A - Section 1 - Algebraic GeometryInstructor: Robin HartshorneLectures: TuTh 9:30-11:00am, Room 5 EvansCourse Control Number: 55149Office: 881 Evans, e-mail: robin [at] math [dot] berkeley [dot] eduOffice Hours: TuTh 1:30-3:00Prerequisites:Required Text: Robin Hartshorne, Algebraic Geometry, SpringerRecommended Reading:Syllabus: This is a first course in algebraic geometry. I do not
presuppose any geometry, but I will make use of results from
commutative algebra as needed. The most important topics you need to
know are Hilbert's Nullstellensatz, dimension theory for local rings,
integral closure, and exact sequences of modules. For a more detailed
list see "Results from Algebra" on pp. 470-471 of the text. References
for commutative algebra are Atiyah and Macdonald; Eisenbud; or
Matsumura's "Commutative ring theory".I expect to cover most of Chapters I and II of the text in the Fall semester. This course will be followed in Spring '05 by a Math 274 "topics" course on deformation theory in algebraic geometry. Course Webpage:Grading:Homework:Comments:Math 265 - Section 1 - Differential TopologyInstructor: Peter TeichnerLectures: TuTh 11:00am-12:30pm, Room 31 EvansCourse Control Number: 55154Office:Office Hours: TBAPrerequisites:Required Text: None.Recommended Reading:Syllabus: In this course, we'll first introduce vector bundles
and their characterstic classes, and use them to get cobordism
invariants of manifolds. We'll apply the Thom-Pontrjagin construction to
translate the question of computing the cobordism ring into a problem
in stable homotopy. We'll solve this problem in the nonoriented case and
show how to get various (generalized) homology theories out of
cobordism groups. The relation to ordinary homology and K-theory will be
explained via the signature and other genera.This course will be continued as a topics course in the Spring 2005, where we'll study one particularly important cohomology theory in full detail: elliptic cohomology. Course Webpage:Grading:Homework:Comments:Math 274 - Section 1 - Topics in AlgebraInstructor: Edward FrenkelLectures: MWF 2:00-3:00pm, Room 51 EvansCourse Control Number: 55155Office: 819 Evans, e-mail: frenkel [at] math [dot] berkeley [dot] eduOffice Hours: MW 3:00-4:00pm and by appointmentPrerequisites: Basic knowledge of Lie groups, Lie algebras and algebraic geometry.Required Text: E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, Second Edition, AMS 2004.Recommended Reading:Syllabus: We will discuss the geometric Langlands correspondence over the field of complex numbers.The local correspondence amounts to a "spectral decomposition" of the categories of smooth representations of an affine Kac-Moody algebra with respect to the local systems of the Langlands dual group over the punctured disc. In order to construct it, we will introduce a certain class of representations caled Wakimoto modules and describe the center of the completed enveloping algebra of an affine Kac-Moody algebra at the critical level. Representations of affine Kac-Moody algebras may then be used to construct the global Langlands correspondence, which associates to local systems defined over a smooth projective curve X the so-called Hecke eigensheaves on the moduli space of G-bundles on X. We will consider explicit examples of this correspondence, such as the Gaudin integrable system, which arises in the Langlands correspondence in genus zero. The lectures will be augmented by a seminar that will meet on Fridays after the lectures, in which we will discuss the classical Langlands correspondence (so as to give some motivation to the topics discussed in the course) and other related material. Course Webpage: http://math.berkeley.edu/~frenkel/Math274Grading:Homework:Comments:Math 274 - Section 2 - Topics in AlgebraInstructor: Mark HaimanLectures: MWF 3:00-4:00pm, Room 7 EvansCourse Control Number: 55158Office: 771 Evans, e-mail: Office Hours: TBAPrerequisites: Good general algebra background.Required Text: Probably none.Recommended Reading: See course web page.Syllabus: Quantized Kac-Moody algebras and their representations;
crystal and canonical bases; affine algebras; connections with
combinatorics; conjectures and open problems. See course web page for
more details.Course Webpage: math.berkeley.edu/~mhaiman/math274Math 275 - Section 1 - Topics in Applied MathematicsInstructor: Lior PachterLectures: TuTh 2:00-3:30pm, Room 7 EvansCourse Control Number: 55161Office: 1081 Evans, e-mail: lpachter [at] math [dot] berkeley [dot] eduOffice Hours: TBAPrerequisites: The class is suitable for graduate students who
have a background in discrete applied mathematics, preferrably with
experience in algebra and/or combinatorics. Familiarity with basic
biology will be helpful, but is neither necessary nor sufficient for
taking the course. Required Text:Recommended Reading:Syllabus: A graphical model is a family of joint probability
distributions for a collection of random variables that factors
according to a graph. Graphical models have proved to be extremely
useful for problems in computational biology, because they provide
useful and versatile probabilistic frameworks for a wide range of
problems, and at the same time are suitably structured for efficient
inference. For example, in biological sequence analysis, specialized
directed graphical models with discrete random variables are used for
applications ranging from annotation and alignment to phylogeny
reconstruction.Discrete graphical models are instances of statistical models that can be characterized by polynomials in the joint probabilities. The emerging and active field of algebraic statistics offers algorithms for this polynomial representation, and is a fertile area for the application of ideas from commutative algebra and algebraic geometry. We will focus on the rich interaction between the theory of algebraic statistics, and the motivating application of computational biology. Several recent papers have demonstrated that algebraic statistics can be applied to developing practical algorithms for biological applications, and conversely that computational biology questions motivate interesting research directions in the theory of algebraic statistics. After a brief primer in algebra and biology, we will survey some of this current literature. Students will be encouraged to select topics for study and to participate in class discussions. Course Webpage: http://math.berkeley.edu/~lpachter/275/Grading:Homework:Comments:Math 300 - Section 1 - Teaching Workshop
Instructor: A. DieslLectures:Course Control Number: 55812Office:Office Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: |