# Fall 2006

Math 1A - Section 1 - CalculusInstructor: Richard BorcherdsLectures: TuTh 2:00-3:30pm, Room 2050 Valley Life ScienceCourse Control Number: 54103Office: 927 EvansOffice 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.Required Text: Stewart, Calculus: Early Transcendentals, Brooks/ColeRecommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~reb/courses/1A/Grading: 40% homework and quizzes, 15% each midterm, 30% finalHomework: Homework is assigned on the course web page and is due once a week.Comments: Math 1A - Section 2 - Calculus Instructor: Mark HaimanLectures: MWF 10:00-11:00am, Room 1 PimentelCourse Control Number: 54154Office: 771 EvansOffice Hours: MWF 12:30-1:30pm Prerequisites: 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.Recommended Reading: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/math1A-fall06 Grading:Homework:Comments:Math 1A - Section 3 - Calculus Instructor: John SteelLectures: MWF 1:00-2:00pm, Room 1 LeConteCourse Control Number: 54205Office: 717 EvansOffice Hours: TuTh 10:30am-12:00pm Prerequisites: 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.Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole, 5th edition. We will cover Chapters 1-6.Recommended Reading: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: http://math.berkeley.edu/~steel/courses/Courses.htmlGrading: 20% homework, quizzes, and section participation. 20% each midterm, 40% finalHomework: Homework is assigned on the course web page and is due once a week.Comments:Math 1B - Section 1 - Calculus Instructor: Daniel TataruLectures: TuTh 8:00-9:30am, Room 2040 Valley Life ScienceCourse Control Number: 54250Office: 841 EvansOffice Hours: TBA Prerequisites: 1ARequired Text: Stewart, Calculus: Early Transcendentals, Brooks/ColeRecommended Reading:Syllabus: Techniques of integration; applications of integration.
Infinite sequences and series. First-order ordinary differential
equations. Second-order ordinary differential equations; oscillation and
damping; series solutions of ordinary differential equations.Course Webpage: http://math.berkeley.edu/~tataru/1B.html (after the middle of August)Grading: 1/3 quizzes+homework, 1/6 each midterm, 1/3 finalHomework: Homework will be assigned on the web every class, and due once a week.Comments:Math 1B - Section 2 - Calculus Instructor: Martin OlssonLectures: MWF 9:00-10:00am, Room 155 DwinelleCourse Control Number: 54298Office: 887 EvansOffice Hours: TBAPrerequisites: Math 1A or equivalentRequired Text: Stewart, Calculus: Early Transcendentals, 5th edition or Custom 1A/1BRecommended Reading:Syllabus: Course Webpage: http://math.berkeley.edu/~molsson/math1b.htmlGrading: Comments: Math 16A - Section 1 - Analytical Geometry and CalculusInstructor: Hugh WoodinLectures: MWF 9:00-10:00am, Room 10 EvansCourse Control Number: 54349Office: 721 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytical Geometry and CalculusInstructor: Bjorn PoonenLectures: MWF 10:00-11:00am, Room 155 DwinelleCourse Control Number: 54382Office: 879 EvansOffice Hours: TBAPrerequisites: Math 32 or three years of high school mathematics including trigonometry.Required Text: Goldstein, Lay, Schneider, Asmar, Calculus and its applications,
11th edition, Pearson Prentice Hall, 2007. We may be using some of the
computer materials associated with this text that are becoming available
this summer. Because of the possibility of purchasing these materials
with the text as a package, I recommend holding off on purchasing the
text until later this summer when the materials are ready, and I have a
chance to try them myself. (I'm not going to make them part of the
course unless they are helpful and easy to use.)Recommended Reading:Syllabus: The derivative and its applications (e.g., to
optimization), techniques for differentiation, exponential and
logarithmic functions, the definite integral. We will cover Chapters 0
through 6 of the text.Course Webpage: http://math.berkeley.edu/~poonen/math16A.htmlExams: There will be two in-class midterms, and a 3-hour final exam Tuesday, December 12, 8-11am.Grading: 20% section grade (homeworks and quizzes), 20% midterm
1, 20% midterm 2, 40% final exam. If your section grade or one of your
midterm grades is below your final exam grade, it will be boosted up to
the final exam grade. The course grade will be curved.Homework: There will be weekly assignments.Comments: Math 16A and 16B are intended for students who do not
intend to take further mathematics courses. If your intended major lies
in the sciences, you might consider taking 1A and 1B instead, even if
your department does not require it.Math 16B - Section 1 - Analytical Geometry and CalculusInstructor: Leo HarringtonLectures: TuTh 3:30-5:00pm, Room 100 LewisCourse Control Number: 54439Office: 711 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: 54484Office: 851 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 32 - Section 1 - PrecalculusInstructor: Martin Vito CruzLectures: MWF 8:00-9:00am, Room 277 CoryCourse Control Number: 54487Office:Office Hours: Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 53 - Section 1 - Multivariable CalculusInstructor: Alexander GiventalLectures: MWF 12:00-1:00pm, Room 155 DwinelleCourse Control Number: 54535Office: 701 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus:Course Webpage: Grading: Homework: Comments:Math 53 - Section 2 - Multivariable CalculusInstructor: Fraydoun RezakhanlouLectures: TuTh 3:30-5:00pm, Room 1 PimentelCourse Control Number: 54586Office: 815 EvansOffice Hours: TuTh 2:30-3:30pm, W 2:00-3:00pmPrerequisites: Required Text: Stewart, Calculus: Early Transcendentals, Brooks/Cole, 5th ed. or Custom 53Recommended Reading:Syllabus:Course Webpage:Grading: homework and quizzes, 50 points 3 midterms, the best two counting, worth 75 points each, totalling 150 points Final Exam, 200 points Total: 400 points possible. The first midterm will be in class on Thurs., Sep. 28. The second midterm will be on Tues., Oct. 31. The third midterm will be on Tues., Nov. 28. The Final Exam will be on TUESDAY, DECEMBER 19, 12:30-3:30 pm. 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! Homework: Homework will be assigned weekly. This semester we do
not have readers, so your homework should be self-corrected, based on
the solutions provided weekly by your TA. Nevertheless, homework must be
handed in every Monday in your TA section for recording. There will be
three quizzes (given in section) that count; with homework and quizzes
totalling 50 points; quizzes will vary with the TA section. The first
assignment is due in your TA section on Wednesday, Sep. 6. Homework Set #1. From the textbook: 10.1, #5, 8, 12, 13, 15, 41 10.2, #2,4,19,26,32,42,60,65 10.3, #15,18,22,32,35,55,58,63 Comments: Math 54 - Section 1 - Linear Algebra and Differential EquationsInstructor: Ming GuLectures: MWF 3:00-4:00pm, Room 155 DwinelleCourse Control Number: 54631Office: 861 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 2 - Linear Algebra and Differential EquationsInstructor: Dan VoiculescuLectures: TuTh 12:30-2:00pm, Room 100 LewisCourse Control Number: 54682Office: 783 EvansOffice Hours: M 1:15-2:50, Th 3:00-3:50Prerequisites: Math 1BRequired Text: R. Hill, Elementary Linear Algebra with Applications (for the linear algebra part)W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 8th ed. (for the differential equations part)Recommended Reading: A. Givental, Linear Algebra and Differential EquationsBerkeley Mathematics Lecture Notes, Vol. 11, American Mathematical Society and Berkeley Center for Pure and Applied Mathematics Syllabus: First part of course Linear Algebra and second part Differential EquationsCourse Webpage:Grading: All grades will be computed using a scale of 0-20 pointsThe correspondence with letter grades is: A+ [19,20) , A [17,19), A- [16,17) B+ [15,16) , B [13,15), B- [12,13) C+ [11,12) , C [9,11) , C- [8,9) etc. Discussion Section Grade = 1/3 Hwrk + 2/3 Quizzes Grade in Course = 15% DiscSect + 20% Mdtrm1 + 20% Mdtrm2 + 45% Final No Make-ups for Midertms No Midterm 1 and No Midterm 2 then Failed No Midterm 1 then Grade in Course = 15% DiscSect + 40% Midterm 2 + 45% Final No Midterm 2 then there is a 10% Penalty (i.e., 10% is 0) Grade in Course = 10% Penalty + 15% DiscSect + 20% Midterm 1 + 55% Final (= zero) Midterm 1 Thursday September 28 Midterm 2 Thursday November 2 Final Monday December 18 12:30-3:30 Homework:Comments:Math 55 - Section 1 - Discrete MathematicsInstructor: Olga HoltzLectures: TuTh 8:00-9:30am, Room 2060 Valley Life ScienceCourse Control Number: 54733Office: 821 EvansOffice Hours: TuTh 11:00am-12:00pm and by appt.Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B recommended.Required Text: Kenneth H. Rosen Discrete Mathematics & It's Applications 6th ed., McGraw-HillRecommended Reading: Ronald L. Graham, Donald E. Knuth and Oren Patashnik Concrete Mathematics, 2nd ed., Addison-WesleySyllabus: Logic, set theory, functions. Relations and graphs.
basic number theory. Integer algorithms. Mathematical proofs, induction.
Combinatorics and probability theory.Grading: 20% homework, 20% each midterm, 40% final.Homework: Assigned weekly, due next week.Comments: This goal of this class is to achieve fluency with
discrete operations (such as finite sums, recurrences, discrete
probability and so on) just like the goal of a calculus course is to
achieve fluency with continuous operations.Math 74 - Section 1 - Transition to Upper Division MathematicsInstructor: Scott ArmstrongLectures: MWF 3:00-4:00pm, Room 70 EvansCourse Control Number: 54748Office:Office Hours:Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math 74 - Section 2 - Transition to Upper Division MathematicsInstructor: Patrick BarrowLectures: TuTh 3:30-5:00pm, Room 70 EvansCourse Control Number: 54751Office:Office Hours:Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math H90 - Section 1 - Undergraduate Seminar in Mathematical Problem Solving (Honors)Instructor: William KahanLectures: M 4:00-6:00pm, Room 71 EvansCourse Control Number: 54754Office: 863 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: Math 104 - Section 1 - Introduction to AnalysisInstructor: Dapeng ZhanLectures: MWF 12:00-1:00pm, Room 75 EvansCourse Control Number: 54817Office: 873 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 104 - Section 2 - Introduction to AnalysisInstructor: Jan ReimannLectures: TuTh 9:30-11:00am, Room 70 EvansCourse Control Number: 54820Office: 705 EvansOffice Hours: Tu 11:00am-1:00pm, W 1:00-2:00pmPrerequisites: Math 53, Math 54Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of CalculusRecommended Reading: Rudin, Principles of Mathematical AnalysisPugh, Real Mathematical AnalysisSyllabus: The real number system. Sequences, limits, and
continuous functions in R and R. The concept of a metric space. Uniform
convergence, interchange of limit operations. Infinite series.
Differentiation. Mean value theorem and applications. The Riemann
integral.Course Webpage: http://math.berkeley.edu/~reimann/Fall_06/104.htmlGrading: 20% homework, 20% each midterm, 40% finalHomework: WeeklyComments: Math 104 - Section 3 - Introduction to AnalysisInstructor: Dapeng ZhanLectures: MWF 3:00-4:00pm, Room 75 EvansCourse Control Number: 54823Office: 873 EvansOffice Hours: TBAPrerequisites: Math 53 and Math 54Required Text: Kenneth A. Ross, Elementary Analysis: The Theory of CalculusRecommended Reading:Syllabus: In this course we will study basic notations of real
analysis, limits and convergence, series, continuous functions, power
series, differentiation and integration, and metric spaces.Course Webpage: http://math.berkeley.edu/~dapeng/ma104-S3.htmlGrading: 20% homework, 20% each midterm (2), 40% finalHomework: Homework will be assigned in every class, and due once a week.Comments:Math 104 - Section 4 - Introduction to AnalysisInstructor: Vaughan JonesLectures: TuTh 3:30-5:00pm, Room 71 EvansCourse Control Number: 54826Office: 929 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 104 - Section 5 - Introduction to AnalysisInstructor: Alexandre ChorinLectures: MWF 8:00-9:00am, Room 71 EvansCourse Control Number: 54829Office: 911 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math H104 - Section 1 - Introduction to Analysis (Honors)Instructor: George BergmanLectures: MWF 10:00-11:00am, Room 5 EvansCourse Control Number: 54832Office: 865 EvansOffice Hours: Tu 1:30-2:30pm, Th 10:30-11:30am, F 3:00-4:00pmPrerequisites: Math 1AB, and a GPA of at least 3.3 in math
courses taken over past year; or consent of the instructor. Math 53 is
also recommended. The course is aimed at mathematics majors and other
students with a strong interest in mathematics.Required Text: W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw-Hill.Recommended Reading: None.Syllabus: We will cover Chapters 1-7 of the text.Course Webpage: None.Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam, 35%; regular submission of the daily question (see below), 5%.Homework: Weekly.Comments: This is the course in which the material you saw in
calculus is put on a solid mathematical basis. It begins with the
properties of the real numbers that underlie these results. I will cover
the same material as when I teach regular 104, but the exercises will
be more challenging, and we will be able to discuss the ideas more
deeply.I don't like the conventional lecture system, where students spend the hour copying the contents of the course from the blackboard into their notebooks. Hence I assign readings in the text, and conduct the class on the assumption that you have done the assigned reading and thought about what you've read. In lecture I may go over key proofs from the reading, clarify difficult concepts, give alternative perspectives, discuss points to watch out for in the next reading, etc. If you are unbreakably attached to learning first from the lecture, and only afterward turning to the book, my course is not for you. On each day for which there is an assigned reading, each student is required to submit, in writing or (preferably) by e-mail, a question
on the reading. (If there is nothing in the reading that you don't
understand, you can submit a question marked "pro forma", together with
its answer.) I try to incorporate answers to students' questions into my
lectures; when I can't do this, I usually answer by e-mail. More
details on this and other matters will be given on the course handout
distributed in class the first day, and available on the door to my
office thereafter.Math 110 - Section 1 - Linear AlgebraInstructor: Olga HoltzLectures: TuTh 2:00-3:30pm, Room 100 LewisCourse Control Number: 54835Office: 821 EvansOffice Hours: TuTh 11:00am-12:00pm and by appt.Prerequisites: Math 53, Math 54 Required Text: S.H. Friedberg, A.J. Insel, L.E. Spence, Linear Algebra, 4th Edition, Pearson EducationRecommended Reading: Online lecture notes by C. de Boor (will be posted).Syllabus: Vector spaces. Linear maps and matrices. Linear systems
of equations. Eigenvalues and eigenvectors. Determinants and other
functions of matrices. Inner product spaces. Self-adjoint, normal and
unitary maps. Canonical forms.Course Webpage: http://www.cs.berkeley.edu/~oholtz/110/index.htmlGrading: 30% homework, 30% midterm, 40% final.Homework: Homework will be assigned on the web every week, due the week after.Comments: The instructor intends to stress practical applications
of matrix theory and its numerical aspects. To this ends, MATLAB
experiments, demos and animation will be presented in class. However,
there will be no computer homework assignments.Math H110 - Section 1 - Linear Algebra (Honors)Instructor: Jenny HarrisonLectures: MWF 11:00am-12:00pm, Room 70 EvansCourse Control Number: 54862Office: 851 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:Math 113 - Section 1 - Introduction to Abstract AlgebraInstructor: Giulio CavigliaLectures: MWF 3:00-4:00pm, Room 71 EvansCourse Control Number: 54865Office: 805 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 113 - Section 2 - Introduction to Abstract AlgebraInstructor: Sarah MasonLectures: TuTh 12:30-2:00pm, Room 2 EvansCourse Control Number: 54868Office: 765 EvansOffice Hours: Tu 2:00-3:00pm, W 1:00-2:00pm, Th 10:30-11:30amPrerequisites: Linear AlgebraRequired Text: Fraleigh, A First Course in Abstract Algebra, 7th ed.Recommended Reading: Syllabus: The main objects studied in this course are groups,
rings, and fields. We will cover several related topics and include
plenty of examples.Course Webpage: http://math.berkeley.edu/~sarahm/m113.htmlGrading: 40% homework and groupwork, 15% each midterm, 30% final examHomework: Weekly individual homework plus some group work.Comments:Math 113 - Section 3 - Introduction to Abstract AlgebraInstructor: Alexander GiventalLectures: MWF 2:00-3:00pm, Room 71 EvansCourse Control Number: 54871Office: 701 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 113 - Section 4 - Introduction to Abstract AlgebraInstructor: John KruegerLectures: TuTh 8:00-9:30am, Room 75 EvansCourse Control Number: 54874Office: 751 EvansOffice Hours: TBAPrerequisites: Required Text: Dummit and Foote, Abstract Algebra, 3rd ed.Recommended Reading:Syllabus: http://math.berkeley.edu/~jkrueger/syllabus.html Course Webpage: http://math.berkeley.edu/~jkrueger/math113.htmlGrading: Homework:Comments:Math 115 - Section 1 - Introduction to Number TheoryInstructor: Kenneth A. RibetLectures: MWF 2:10-3:00pm, Room 60 EvansCourse Control Number: 54877Office: 885 EvansOffice Hours: TBAPrerequisites: Math 53 and Math 54Required Text: To be announced later. Here are some candidates;
please give me feedback if you have the time and inclination to explore
these books:
- Topics in the theory of numbers by Erdös and Suranyi
- An introduction to the theory of numbers by Niven, Zuckerman and Montgomery
- A computational introduction to number theory and algebra by Victor Shoup
- Elementary number theory by William Stein
Recommended Reading:Syllabus: The catalog suggests a study of "Divisibility,
congruences, numerical functions, theory of primes. Topics selected:
Diophantine analysis, continued fractions, partitions, quadratic fields,
asymptotic distributions, additive problems." One highlight of the
course is the theorem of quadratic reciprocity.Course Webpage: http://math.berkeley.edu/~ribet/115/ (the current version is for an old course; this web page will get fixed up in August)Grading: Based on two midterms,the final exam, and homework, with the exact mix to be announced later.Homework: Substantial problem sets will be assigned weekly.Comments:Math 118 - Section 1 - Mathematical Signal ProcessingInstructor: L. Craig EvansLectures: TuTh 9:30-11:00am, Room 81 EvansCourse Control Number: 54880Office: 907 EvansOffice Hours: TBAPrerequisites: Math 53 and 54 (Math 104 would be very helpful.)Required Text: Boggess and Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice HallRecommended Reading: NoneSyllabus: Fourier analysis (Fourier series and Fourier transform), wavelets, theory and applications Course Webpage: NoneGrading: 25% homework, 25% midterm, 50% finalHomework: Homework will be assigned **every** class, and each assignment is due in one week.Comments: Math 121A - Section 1 - Mathematics for the Physical SciencesInstructor: Shamgar GurevichLectures: TuTh 11:00am-12:30pm, Room 289 CoryCourse Control Number: 54883Office: Office Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments:Math 123 - Section 1 - Ordinary Differential EquationsInstructor: Robert ColemanLectures: MWF 12:00-1:00pm, Room 4 EvansCourse Control Number: 54892Office: 901 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical LogicInstructor: Theodore SlamanLectures: TuTh 2:00-3:30pm, Room 289 CoryCourse Control Number: 54895Office: 719 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 128A - Section 1 - Numerical AnalysisInstructor: Xuemin TuLectures: TuTh 9:30-11:00am, Room 60 EvansCourse Control Number: 54898Office: Office Hours: TBAPrerequisites: Required Text: Recommended Reading:Syllabus: Course Webpage: Grading: Homework: Comments: Math 135 - Section 1 - Introduction to Theory SetsInstructor: Jack SilverLectures: TuTh 9:30-11:00am, Room 39 EvansCourse Control Number: 54919Office: 753 EvansOffice Hours: TBAPrerequisites:Required Text: Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 140 - Section 1 - Metric Differential GeometryInstructor: L. Craig EvansLectures: TuTh 12:30-2:00pm, Room 241 CoryCourse Control Number: 54922Office: 907 EvansOffice Hours: TBAPrerequisites: Math 53 and 54 (Math 104 would be very helpful.)Required Text: R. Millman and G. Parker, Elements of Differential Geometry, Prentice HallRecommended Reading: NoneSyllabus: Theory of curves in the plane and in space, surfaces in
space, first and second fundamental forms, Gauss and mean curvature,
Gauss-Bonnet Theorem, introduction to higher dimensional Riemannian
geometryCourse Webpage: NoneGrading: 25% homework, 25% midterm, 50% finalHomework: Homework will be assigned **every** class, and each assignment is due in one week. Comments: Math 141 - Section 1 - Elementary Differential TopologyInstructor: Dagan KarpLectures: MWF 10:00-11:00am, Room 247 CoryCourse Control Number: 54925Office: 1053 EvansOffice Hours: TBA and by appointmentPrerequisites: 104Required Text: Guillemin/Pollack, Differential Topology, Prentice-HallRecommended Reading: Milnor, Top. From Diff. View.; Bott/Tu, Diff. Forms in Alg. Top.Syllabus: The official course description includes: "Manifolds in
n-dimensional Euclidean space and smooth maps, Sard's Theorem,
classification of compact one-manifolds, transversality and intersection
modulo 2." What we actually cover will depend upon the interests and
background of the class as a whole. Differential topology contains some
of the most beautiful and basic ideas in all of mathematics and we will
let our curiosity drive us as much as possible.Course Webpage: http://math.berkeley.edu/~dkarp/courses/141/Grading: Homework will be a very significant part of the total
grade. There will also be one midterm and one final exam (perhaps they
will both be take home).Homework: Will be assigned and collected regularly.Comments: Math 151 - Section 1 - Mathematics of the Secondary School Curriculum IInstructor: Hung-Hsi WuLectures: TuTh 2:00-3:30pm, Room 7 Evans; Discussion: M 4:00-5:00pm, Room 81 EvansCourse Control Number: Lectures: 54927; Discussion: 55822Office: 733 EvansOffice Hours: M 1:00-3:00pm, Tu 10:00-11:00am, Th 11:00am-12:00pmPrerequisites: Math 1A, 1B, 53, or equivalent.Required Text: None. Lecture notes will be made available as the course progresses.Recommended Reading: Syllabus: This course is part of a three-semester sequence, Math
151-152-153, whose purpose is to give a complete mathematical
development of all the main topics of school mathematics in grades 8-12.
A key feature of this presentation is that it would be directly
applicable to the classroom of grades 8-12, and in fact, to middle
school as well. To put this in context, the development of of rational
numbers in Math 113 (Introduction to Abstract Algebra), for example,
would *not* be usable in the school classroom, no matter which grade is
considered.For Math 151, the topics are: theory of rational numbers based on the number line, the Euclidean algorithm and fractions in lowest terms, the concepts of congruence and similarity, equation of a line, linear functions and quadratic functions. This is an upper division course in mathematics. Therefore, like any other upper division mathematics course, the emphasis will be on precision and reasoning (i.e., proofs). The goal is to present school mathematics as part of mathematics
proper, so that when it is your turn to teach in the schools, you will
be able to teach your students honest mathematics rather than the mess
that you witness in most school classrooms.Course Webpage: TBAGrading: Homework 30%, First midterm 10%, Second midterm 20%, Final 40%.Homework: Weekly assignments, due every Monday.Comments: Students are required to form study groups to work on
the homework problems but not to copy from each other. There will be a
Yahoo "groups" chat room for communications to form study groups. The
purpose of the problem session, every monday 4-5 pm, is to discuss the
solutions of the problems *after* the problem set has been handed in.Math 185 - Section 1 - Introduction to Complex AnalysisInstructor: Constantin TelemanLectures: TuTh 9:30-11:00am, Room 7 EvansCourse Control Number: 54928Office: 905 EvansOffice Hours: TuTh 11:00am-12:00pmPrerequisites: Math 104, some linear algebraRequired Text: Tristan Needham, Visual Complex Analysis, see http://www.usfca.edu/vca/Recommended Reading: Donald Sarason, Notes on Complex Function TheorySyllabus: Complex numbers, power series, Moebius transformations,
analytic functions, winding numbers, complex integration, residues and
polesCourse Webpage: Under construction, please check my homepage http://math.berkeley.edu/~teleman/ where a link will be posted.Grading: 15% homework, 25% each for two midterms, 35% finalHomework: Will be assigned on the webpage every week.Comments: We will cover the standard topics in complex analysis
through the eyes of planar geometry. Most of the fundamental results of
complex analysis were obtained by the 1850's and the theory has been
polished into a perfect formalism since then. Many textbooks explain
mostly this finished product, whereas we shall ask 'why' the theory
works and try to find visual answers, usually in the (complex) plane.
Once a geometric idea is understood, it becomes much easier, and less
mysterious, to work with the corresponding formalism.Math 185 - Section 2 - Introduction to Complex AnalysisInstructor: William KahanLectures: MWF 1:00-2:00pm, Room 289 CoryCourse Control Number: 54931Office: 863 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage:Grading:Homework:Comments:Math 185 - Section 3 - Introduction to Complex AnalysisInstructor: Jason MetcalfeLectures: TuTh 8:00-9:30am, Room 71 EvansCourse Control Number: 54934Office: 837 EvansOffice Hours: TBAPrerequisites: Math 104Required Text: Churchill & Brown: Complex Variables and Applications, 7th edition (McGraw-Hill)Recommended Reading:Syllabus: Main topics: Complex numbers, analytic functions,
integrals, series, residues and poles, and conformal mappings. Please
see the webpage for a detailed syllabus.Course Webpage: http://math.berkeley.edu/~metcalfe/teaching/math185/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 202A - Section 1 - Introduction to Topology and AnalysisInstructor: Justin HolmerLectures: TuTh 8:00-9:30am, Room 150 GSPPCourse Control Number: 55024Office: 849 EvansOffice Hours: TBAPrerequisites: An undergraduate "Intro. to Analysis" course (such
as Math 104 here at Berkeley) with emphasis on writing rigorous
mathematical proofs.Required Text: None (but subject to change)Recommended Reading: Stein & Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert SpacesRoyden, Real AnalysisMunkres, TopologySyllabus: During the first half of the course, we will cover
general point-set topology. During the second half of the course, we
will cover the Lesbesgue measure and integration theory in R^{d}. Math 202b in the spring will pick up on abstract measure and integration theory and then launch into functional analysis.Course Webpage: http://math.berkeley.edu/~holmer/teaching/f202a/. Contains an expanded version of this course announcement.Grading: 50% homework, 25% midterm, 25% final. There will be one
two-day midterm covering point set topology (first half of course).
The final will cover measure theory only (second half of the course).
Both exams will be in-class.Homework: Homework will be assigned once a week and due the
following week, and will consist of about a dozen problems. Plan to
spend a full day preparing your solutions. All problems, even if taken
from a textbook, will be retyped and posted on the web.Comments: This course is recommended for advanced undergraduate
students planning to study math in graduate school, beginning graduate
students who have not yet studied this material, or for students from
other fields of science and engineering with the appropriate background
and motivation. If you are a full time student, plan to devote 1/4 of
your time to this course.Math 204A - Section 1 - Ordinary and Partial Differential EquationsInstructor: Jon WilkeningLectures: TuTh 12:30-2:00pm, Room 5 EvansCourse Control Number: 55027Office: 1091 EvansOffice Hours: TBAPrerequisites: Undergraduate Analysis and Linear AlgebraRequired Text: Coddington and Levinson, Theory of Ordinary Differential EquationsRecommended Reading: Hurewicz, Lectures on Ordinary Differential EquationsCourant and Hilbert, Methods of Mathematical Physics, Vol 1Syllabus: In the first part of the course, we will study
fundamental questions of existence, uniqueness and dependence of
solutions of ODE's on initial conditions and parameters. We will then
study linear systems (e.g. with constant or periodic coefficients),
boundary value problems, adjoint equations, expansion and completeness
theorems, Sturm-Liouville theory, perturbation theory, and the
Poincare-Bendixson Theorem. We fill finish the course with ODE methods
in PDE and the Cauchy-Kowalewski theorem.Course Webpage: http://math.berkeley.edu/~wilken/204A.F06Grading: 75% Homework, 25% Final ExamHomework: 10 assignmentsComments:Math 205 - Section 1 - Theory of Functions of a Complex VariableInstructor: Donald SarasonLectures: MWF 8:00-9:00am, Room 5 EvansCourse Control Number: 55030Office: 779 EvansOffice Hours: TBAPrerequisites: Math 185 or the equivalentRequired Text: No textbook will be followed closely. The classic book of L. V. Ahlfors, Complex Analysis, contains most of the course material. Other possible references will be mentioned in the first lecture.Recommended Reading:Syllabus: Brief review centering on Cauchy's theorem and the
argument principle; conformal mapping, including the Riemann mapping
theorem and distortion theorems; analytic continuation; algebraic
functions; entire functions and functions meromorphic in the entire
plane, including the Weierstrass and Mittag-Leffler representations;
elliptic functions; the modular function; Picard's theorems; Dirichlet
series; Riemann zeta-function; prime number theorem.Course Webpage:Grading: The course grade will be based on homework. There will be no exams.Homework: There will be regular homework assignments.Comments: The lectures will be self-contained except for routine details.Math 206 - Section 1 - Banach Algebras and Spectral TheoryInstructor: Donald SarasonLectures: MWF 10:00-11:00am, Room 41 EvansCourse Control Number: 55033Office: 779 EvansOffice Hours: TBAPrerequisites: Math 185 and Math 202AB, or the equivalentsRequired Text: No textbook will be followed closely. W. Rudin's book Functional Analysis contains much of the course materaial. Other possible references will be mentioned in the first lecture.Recommended Reading:Syllabus: Review of some basic operator theory; operators with
closes ranges; idempotents; compact operators; Fredholm operators;
Banach algebras (basics, spectrum, holomorphic functional calculus,
Gelfand theory of commutative Banach algebras, C*-algebras); basics of
operators theory in Hilbert spaces; various versions of the spectral
theorem (commutative C*-algebras, normal operators, one-parameter
unitary groups); possible additional topics, time permitting.Course Webpage:Grading: The course grade will be based on homework. There will be no exams.Homework: There will be regular homework assignments.Comments: The lectures will be self-contained except for routine details.Math 215A - Section 1 - Algebraic Topology Instructor: Peter TeichnerLectures: TuTh 9:30-11:00am, Room 71 EvansCourse Control Number: 55036Office: 703 EvansOffice Hours: TuTh 11:00am-12:00pmPrerequisites: Linear algebra and point-set topologyRequired Text: Hatcher, Algebraic Topology see http://www.math.cornell.edu/~hatcher/AT/ATpage.htmlRecommended Reading: Bredon, Topology and GeometrySyllabus: Algebraic topology seeks to capture the essence of a
topological space in terms of various algebraic and combinatorial
objects. We will construct and apply three such gadgets: the fundamental
group, homology groups, and the cohomology ring. Much but by no means
all of the course content is in the book by Hatcher. Like in Bredon's
book, the topology of manifolds will play a prominent role in this
course.Course Webpage: Will be linked from http://math.berkeley.edu/~teichnerGrading: The grade will be based on homework.Homework: Yes.Comments:Math 221 - Section 1 - Advanced Matrix Computation Instructor: John StrainLectures: TuTh 9:30-11:00am, Room 61 EvansCourse Control Number: 55042Office: 1099 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus: Course Webpage: Grading:Homework: Comments: Math 222A - Section 1 - Partial Differential EquationsInstructor: Daniel TataruLectures: TuTh 12:30-2:00pm, Room 7 EvansCourse Control Number: 55045Office: 841 EvansOffice Hours: TBAPrerequisites: 105 or 202B 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. (with 222B)Course Webpage: Grading: Homework + take home final exam.Homework: Homework will be assigned every week.Comments: Math 224A - Section 1 - Mathematical Methods for the Physical SciencesInstructor: Fraydoun RezakhanlouLectures: TuTh 11:00am-12:30pm, Room 5 EvansCourse Control Number: 55048Office: 815 EvansOffice Hours: TBAPrerequisites: Math 104Required Text: NoneRecommended Reading:Syllabus: The majority of the fundamental processes of our
natural world are described by differential equations. Some examples are
the vibration of solids, the flow of fluids, the formation of crystals,
the spread of infections, the diffusion of chemicals, the structure of
molecules, etc. These examples are responsible for our interest in
partial differential equations such as Hamilton-Jacobi equation, Euler
equation, Navier-Stokes equation, Diffusion equation, Wave equation and
Korteweg-deVries equation. As the primary goal of the course, I discuss
some of the above equations and explain some mathematicals tools that
are needed to solve them. I also use these equation as an excuse to
introduce students to some basic questions in fluid mechanics and
statistical physics. Some of the topics are:1. Advection, diffusion, Brownian motion, sources, Green's function. 2. Fluid mechanics, Euler equation, incompressible limit, shallow water equation. 3. Shock waves, Rarefaction waves, Riemann invariants. 4. Similarity methods. 5. Scattering theory, Korteweg-deVries equation. There is no required text and I will distribute handwritten notes in the class. Course Webpage:Grading: There will be weekly homework assignments (due Tuesdays) and one take-home exam.Homework: Comments:Math 225A - Section 1 - MetamathematicsInstructor: Leo HarringtonLectures: TuTh 12:30-2:00pm, Room 72 EvansCourse Control Number: 55051Office: 711 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 228A - Section 1 - Numerical Solution of Differential EquationsInstructor: Jon WilkeningLectures: TuTh 11:00am-12:30pm, Room 87 EvansCourse Control Number: 55054Office: 1091 EvansOffice Hours: TBAPrerequisites: Math 128A or equivalent knowledge of basic numerical analysis. Some programming experience (e.g. Matlab, Fortran, C, or C++)Required Text: Iserles, A First Course in the Numerical Analysis of Differential EquationsMorton and Mayers, Numerical Solution of Partial Differential EquationsRecommended Reading: Hairer/Norsett/Wanner, Solving Ordinary Differential Equations (2 Vols)Syllabus: The first half of the course will cover thoery and
practical methods for solving systems of ordinary differential
equations. We will discuss Runge-Kutta and multistep methods, stability
theory, Richardson extrapolation, stiff equations and boundary value
problems. We will then move on to study finite difference solutions of
hyperbolic and parabolic partial differential equations, where we will
develop tools (e.g. Von Neumann stability theory, CFL conditions,
consistency and convergence) to analyze popular schemes (e.g.
Lax-Wendroff, leapfrog, Cranck-Nicholson, ADI, etc.)Course Webpage: http://math.berkeley.edu/~wilken/228A.F06Grading: Grades will be based entirely on homework.Homework: 10 assignmentsComments:Math 229 - Section 1 - Theory of ModelsInstructor: Thomas ScanlonLectures: MWF 9:00-10:00am, Room 5 EvansCourse Control Number: 55057Office: 723 EvansOffice Hours: TBAPrerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments:Math 242 - Section 1 - Symplectic GeometryInstructor: Christian BlohmannLectures: TuTh 11:00am-12:30pm, Room 61 EvansCourse Control Number: 55062Office: 898 EvansOffice Hours: TBAPrerequisites: Math 214 or equivalent familiarity with basic material on differentiable manifolds.Required Text: Cannas da Silva, Lectures on Symplectic Geometry, Springer Lecture Notes in MathematicsRecommended Reading:Syllabus: As per the catalog, I will discuss symplectic linear
algebra, symplectic manifolds, Darboux's theorem, cotangent bundles,
variational problems and Legendre transform, hamiltonian systems,
lagrangian submanifolds, Poisson brackets, symmetry groups and momentum
mappings, coadjoint orbits and Kähler manifolds. If time remains at the
end, I will go into advanced topics.Course Webpage: See http://math.berkeley.edu/~blohmann/Grading: The grade will be based class participation, homework,
and an expository paper on some aspect of symplectic geometry or its
applications.Homework: There will be reading assignments from the main text
and homework problems which will be discussed in class. Selected
homework problems will be graded.Comments: This course is meant to equip the student with a
knowledge of the essential definitions, methods, and results in
symplectic geometry, either for the further study of symplectic geometry
itself, or for applications to other fields of mathematics and
mathematical physics (e.g. topology, representation theory, algebraic
geometry, partial differential equations, classical and quantum
mechanics and field theory).Math 249 - Section 1 - Algebraic CombinatoricsInstructor: Vera SerganovaLectures: TuTh 12:30-2:00pm, Room 41 EvansCourse Control Number: 55063Office: 709 EvansOffice Hours: TuTh 11:00am-12:00pmPrerequisites: Math 250A, can be taken at the same time.Required Text: Richard Stanley, Enumerative Combinatorics, Cambridge University Press, v.1,2Recommended Reading: I. Macdonald, Symmetric functions and, W. Fulton, Young tableauxHall polynomials Syllabus: I plan to cover the following topics: posets, lattices,
generating functions, partitions, symmetric functions, Schur
polynomials, representations of symmetric groups, q-binomial
coefficients, geometric lattices, hyperplane arrangementsCourse Webpage: http://math.berkeley.edu/~serganovGrading: Homework: Homework will be assigned on the web every week, and due once a week.Comments:Math 250A - Section 1 - Groups, Rings, and FieldsInstructor: George BergmanLectures: MWF 1:00-2:00pm, Room 70 EvansCourse Control Number: 55066Office: 865 EvansOffice Hours: Tu 1:30-2:30pm, Th 10:30-11:30am, F 3:00-4:00pmPrerequisites: Reasonable mathematical maturity, and/or the
equivalent of Math 113. Undergraduates taking this course should have an
upper division math GPA of at least 3.0, or consent of the instructor.Required Text: Serge Lang, Algebra, 3rd edition (Springer-Verlag, 2002, or Addison-Wesley, 1993).Recommended Reading: TBASyllabus: Main topics: groups, rings, modules, Galois theory.
Other topics: Sets, categories, transcendental field extensions. This
is the basic ``what every mathematician needs to know about algebra''
course.Course Webpage: Grading: Homework: 50%, Midterm 17%, Final Exam 33%Homework: There is a lot of material to cover; expect a heavy
course. I try to assign interesting and challenging exercises; however, I
have all students hand in anonymous weekly estimates of the time spent
on study and on homework, and I use this feedback to keep the total time
from running too high.Comments: As in my other courses, I will not waste your time and
mine by putting material from the book on the blackboard for you to
copy. Rather, we will use assigned readings from Lang as the primary
``teacher'', and devote the classroom time to motivation of material in
the forthcoming reading, clarification of points that students ask about
or that I feel needs it, supplementary material, alternative
approaches, discussion of homework exercises, etc. To make this work, I
require each student to submit, on each day for which there is an
assigned reading, a question on that reading. Details (including
what to submit if you understood everything perfectly) will be given on
the first-day handout.Math 254A - Section 1 - Number TheoryInstructor: Paul VojtaLectures: MWF 11:00am-12:00pm, Room 72 EvansCourse Control Number: 55069Office: 883 EvansOffice Hours: MWF 12:30-1:30pmPrerequisites: Math 250A or equivalentRequired Text: Neukirch, Algebraic Number Theory, SpringerRecommended Reading: Syllabus: This is the standard first-year graduate course on
number theory. In the fall semester the course will cover the basics of
number theory over a Dedekind domain: completions, fractional ideals,
ideles and adeles, etc., as in the catalog description or the first
three chapters of the textbook. Basically, the idea is to study finite
algebraic extensions of Z or Q and determine which
properties still hold in this more general setting, because often the
structure of a system of diophantine equations over Z or Q is more apparent after extending the field of definition.The course will also include some introductory material on analytic number theory and class field theory. The second half of this course, Math 254B, will be taught by Ken Ribet. Course Webpage: http://math.berkeley.edu/~vojta/254a.htmlGrading: Grading will be based on homework assignments, including a take-home final.Homework: Weekly or biweekly; assigned in class.Comments: This is my first time using this textbook, but I plan to emphasize its material on the analogy with the function field case.Math 256A - Section 1 - Algebraic GeometryInstructor: Brian OssermanLectures: TuTh 2:00-3:30pm, Room 103 MoffittCourse Control Number: 55072Office: 767 EvansOffice Hours: TBAPrerequisites: 250A; 250B strongly encouragedRequired Text: Hartshorne, Algebraic GeometryRecommended Reading: Eisenbud and Harris, The Geometry of SchemesSyllabus: This is the first semester of an integrated, year-long
course in algebraic geometry. Although the primary source text will be
Hartshorne's Algebraic Geometry, we will start from the beginning with
schemes to emphasize their close connection with classical varieties and
geometry, and we will supplement the text heavily with additional
topics from both modern and classical algebraic geometry.Course Webpage: http://math.berkeley.edu/~osserman/classes/256A/Grading: Primarily homework-based, with the possibility of a takehome final exam or final paper.Homework: Homework will be assigned roughly weekly.Comments:Math 258 - Section 1 - Classic Harmonic AnalysisInstructor: Michael ChristLectures: MWF 12:00-1:00pm, Room 3 EvansCourse Control Number: 55075Office: 809 EvansOffice Hours: TBAPrerequisites: Math 202AB (graduate real/functional analysis) or equivalent.Required Text: M. Christ, Lecture notes Euclidean Harmonic Analysis. (These typewritten notes will be distributed in installments throughout the term at no charge.)Recommended Reading: Y. Katznelson, An Introduction to Harmonic Analysis. This award-winning classic costs only $12.95.E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory IntegralsSyllabus: This introductory course will treat harmonic analysis
in Euclidean spaces and allied topics in real and, to a lesser extent,
complex analysis.Topics: Most but not all of:
- Fourier transform and series. Functorial properties, inversion, Poisson summation, localization, symmetry, identities. Fourier transform on finite cyclic groups.
- Schwartz space, tempered distributions, approximations to the identity.
- Convergence and divergence. Uniform, L
^{p}, almost everywhere convergence. Pointwise divergence. Maximal operators. Decay of Fourier coefficients. - Convolution. The algebras of L
^{1}functions and finite measures. Inequalities, Wiener's theorem. - Connections with complex analysis and harmonic functions. Boundary values, Dirichlet problem, conjugate function. F. and M. Riesz theorem.
- Hardy-Littlewood maximal function, stopping time constructions, L
^{1,∞}, John-Nirenberg inequality, Carleson's inequality, sharp function, good-λ inequality. - Singular integral operators. Principal-value distributions. Multilinear singular integrals.
- Interpolation of operators. The real and complex methods. Lorentz spaces. Analytic families of operators.
- Almost orthogonality. A phase plane Bessel inequality.
- Littlewood-Paley theory. Connection with Carleson measures.
- Fourier multiplier operators.
- Comparison of the Fourier basis with other orthonormal bases and frames: Haar, wavelet, Hermite, Gabor.
- Paley-Wiener theorem and uncertainty principle.
- Oscillatory integrals. Stationary phase, van der Corput's lemma, connections with curvature.
- Sobolev and Hölder classes. Fractional integrals, potentials, embedding, compactness.
- Convergence of multiple Fourier series: Introduction to the Kakeya and Bochner-Riesz problems.
- Restriction and Strichartz inequalities. Connections with dispersive and hyperbolic PDE.
Required work: Either solve and hand in a reasonable number of
exercises from the text, or write a short report on a topic relevant to
the course. Typically this will involve reading one or several research
or expository articles, and writing a summary (5-10 pages). A list of
suggested topics and references will be distributed by October. Students
are welcome to find their own topics, subject to instructor's approval.Course Webpage: http://math.berkeley.edu/~mchrist/Grading:Homework:Comments: Math 270 - Section 1 - Hot Topics Course in MathematicsInstructor: Peter TeichnerLectures: Th 2:00-3:30pm, Room 71 EvansCourse Control Number: 55077Office: 703 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: http://math.berkeley.edu/~teichner/Courses/270-Derived.htmlGrading: Homework: Comments:Math 271 - Section 1 - Topics in FoundationsInstructor: John AddisonLectures: MWF 2:00-3:00pm, Room 39 EvansCourse Control Number: 55828Office: 763 EvansOffice Hours: TBAPrerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 274 - Section 1 - Topics in AlgebraInstructor: Tsit-Yuen LamLectures: MWF 10:00-11:00am, Room 31 EvansCourse Control Number: 55078Office: 871 EvansOffice Hours: TBAPrerequisites: Math 250ABRequired Text: Kaplansky, Commutative Rings, Polygonal Publishing House, Washington, New JerseyRecommended Reading: Atiyah-MacDonald, Introduction to Commutative Algebra, Addison-Wesley, MassachusettsHutchins, Examples of Commutative Rings, Polygonal Publishing House, Washington, New JerseyLam, First Course in Noncommutative Rings, Springer, New YorkSyllabus: I will teach a course in commutative algebra, in memory of Professor Irving Kaplansky who passed away in July, 2006.The main text will be Kaplansky's book "Commutative Rings". The course will be taught in the main spirit of this text, namely, more from the viewpoint of algebra than from the viewpoint of algebraic geometry. In particular, students need not have taken Math 256A prior to taking this course. I will, however, assume that students have a very thorough grounding in abstract algebra, as is typically taught in Math 250AB. To save time in re-developing the basic material from scratch, I'll assume my audience is familiar with exact sequences, tensor products and "Hom", basic localization theory, behavior of primes under localization, existence lemmas on prime and maximal ideals, integrality notions, Hilbert Basis Theorem, and a few facts about modules and rings with chain conditions (such as the Jordan-Hölder Theorem and the (composition) length of modules). Assuming these prerequisites will enable us to start off on a slightly higher ground. The course will start with Chapter I, covering some theorems of McCoy, nilradical and Jacobson radical, associated primes of modules and rings, noetherian rings and artinian rings, primary decompositions, etc. This will be followed by chapters on integral extensions and dimension theory, and other standard material in commutative algebra. We may not get to the more advanced topics in the field, but it is hoped that whatever the course covers will be well covered. The textbook will not be followed closely, although students are expected to have a copy of it, as well as some of the other reference books listed. Occasionally, class notes will be provided. Many homework problems will be assigned. It will be best if students can start a course webpage, to which they can write up and post their homework problem solutions. Grades will be based on class attendance, HW performance, and possible seminar talks and class projects. I will not intimidate people with exams! The textbook is available only through Polygonal Publishing House, and costs a modest $18, with a possible discount if we order multiple copies. We are planning to place a class order, hopefully BEFORE classes start. Thus, if you want to add your name to the class order, please stop by my office (871 Evans) ASAP to sign up and pay for a copy. Course Webpage:Grading: Grades will be based on class attendance, HW performance, and possible seminar talks and class projects.Homework: Many homework problems will be assigned.Comments:Math 279 - Section 1 - Semiclassical AnalysisInstructor: Maciej ZworskiLectures: MWF 11:00am-12:00pm, Room 39 EvansCourse Control Number: 55081Office: 897 EvansOffice Hours: TBAPrerequisites: Math 222A or equivalent.Required Text: L.C. Evans and M. Zworski Lectures on Semiclassical Analysis http://math.berkeley.edu/~zworski/semiclassical.pdfRecommended Reading:Syllabus: The course will provide a broad introduction to many
aspects of semiclassical/microlocal analysis. A basic graduate course in
real and functional analysis is the only prerequisite. The material
will follow notes by L.C. Evans and M. Zworski (available on line, see
above): 1. Symplectic geometry 2. Fourier transform and the method of stationary phase 3. Quantization of classical observables 4. Semiclassical defect measures and their applications 5. Eigenvalues and eigenfunctions: Weyl laws 6. Exponential estimates for eigenfunctions: Agmon and Carleman 7. Quantum ergodicity 8. Quantization of symplectic transformation: normal forms, Strichartz estimates etc. 9. Semiclassical/microlocal generalizations of the Selberg trace formula Course Webpage:Grading: Homework:Comments:Math 300 - Section 1 - Teaching WorkshopInstructor:Jameel Al-AidroosLectures: W 5:00-7:00pm, Room 3109 EtcheverryCourse Control Number: 55756Office:Office Hours:Prerequisites:Required Text:Recommended Reading:Syllabus:Course Webpage:Grading:Homework:Comments: |