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| Fall 2003 Course Announcements |
Math 1A - Section 1 - Calculus
Instructor: Garth Dales
Lectures: TuTh 12:30-2:00pm, Room 2050 Valley Life Science
Course Control Number: 54303
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Office Hours: TBA
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Math 1A - Section 2 - Calculus
Instructor: Hung-Hsi Wu
Lectures: MWF 10:00-11:00am, Room 1 Pimental
Course Control Number: 54354
Office: 733 Evans, e-mail: wu@math.berkeley.edu
Office Hours: TBA
Prerequisites: Trigonometry and analytic geometry
Syllabus: Essentially the first six chapters of the text will
be covered.
Required Text: Stewart, Calculus: Early
Transcendentals, Brooks/Cole
Grading: 20% homework and quizzes, 10% Midterm 1, 20% Midterm
2, 50% final.
Homework: Weekly assignments given on the web. Group work
among students is encouraged.
Comments: The lectures will generally follow the text, but
there will be minor deviations. A course schedule giving the sections
of the text that will be covered each week will be made available on
the web. Students are required to read the text in advance of the
lectures. Both mathematical reasoning and techniques for solving
problems will be emphasized. This is emphatically not a cookbook
course. For the exams, students will be responsible for a small
number of proofs in the text, e.g., the proof of the Fundamental
Theorem of Calculus, but about 80% of the exam question will be close
to the assigned homework problems. This means that each student has
almost complete control over his/her grades: just work hard at the
homework problems week in and week out. The course progresses very
rapidly by high school standards. Good work habits are required for
survival in this course.
Math 1A - Section 3 - Calculus
Instructor: Jenny Harrison
Lectures: MWF 3:00-4:00pm, Room 115 Dwinelle
Course Control Number: 54405
Office: 851 Evans, e-mail: harrison@math.berkeley.edu
Office Hours: TBA
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Math 1B - Section 1 - Calculus
Instructor: Ole Hald
Lectures: MWF 9:00-10:00am, Room 155 Dwinelle
Course Control Number: 54438
Office: 875 Evans, e-mail: hald@math.berkeley.edu
Office Hours: TBA
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Math 1B - Section 2 - Calculus
Instructor: Charles Pugh
Lectures: TuTh 2:00-3:30pm, Room 155 Dwinelle
Course Control Number: 54489
Office: 829 Evans, e-mail: pugh@math.berkeley.edu
Office Hours: TBA
Comments: There is a course webpage here.
Math 16A - Section 1 - Analytical Geometry and Calculus
Instructor: Leo Harrington
Lectures: TuTh 3:30-5:00pm, Room 1 Pimental
Course Control Number: 54525
Office: 711 Evans, e-mail: leo@math.berkeley.edu
Office Hours: TBA
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Math 16A - Section 2 - Analytical Geometry and Calculus
Instructor: John Wagoner
Lectures: MWF 11:00am-12:00pm, Room 155 Dwinelle
Course Control Number: 54567
Office: 899 Evans, e-mail: wagoner@math.berkeley.edu
Office Hours: TBA
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Math 16B - Analytical Geometry and Calculus
Instructor: Robin Hartshorne
Lectures: MWF 8:00-9:00am, Room 10 Evans
Course Control Number: 54612
Office: 881 Evans, e-mail: robin@math.berkeley.edu
Office Hours: TBA
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Math 24 - Section 1 - Freshman Seminars
Instructor: Jenny Harrison
Lectures: F 4:00pm-5:00pm, Room 72 Evans
Course Control Number: 54651
Office: 851 Evans, e-mail: harrison@math.berkeley.edu
Office Hours: TBA
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Math 24 - Section 2 - Freshman Seminars
Instructor: Nicolai Reshetikhin
Lectures: M 3:00pm-5:00pm, Room 891 Evans
Course Control Number: 54653
Office: 945 Evans, e-mail: reshetik@math.berkeley.edu
Office Hours: TBA
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Math 32 - Precalculus
Instructor: GSI - TBA
Lectures: MWF 8:00-9:00am, Room 2060 Valley Life Science
Course Control Number: 54654
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Math 53 - Multivariable Calculus
Instructor: Michael Hutchings
Lectures: TuTh 8:00-9:30am, Room 155 Dwinelle
Course Control Number: 54702
Office: 923 Evans, e-mail: hutching@math.berkeley.edu
Office Hours: TBA
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Math 53M - Multivariable Calculus With Computers
Instructor: Mariusz Wodzicki
Lectures: MWF 12:00-1:00pm, Room 390 Hearst Mining
Course Control Number: 54759
Office: 995 Evans, e-mail: wodzicki@math.berkeley.edu
Office Hours: F 1:10-2:30pm
Prerequisites: Math 1B with a grade B or better.
Syllabus: In this course, I will introduce students to the
elements of Theory of Differential Forms. Familiarity with
differential forms is a necessity for students of Mathematics,
Physics and Engineering, yet the subject is rarely taught at the (non
Honors) undergraduate level. An added bonus is that topics that are
complicated and cumbersome in the traditional approach become clear
and transparent when one uses the language of differential forms.
The students should be advised that Multivariable Calculus is a
serious course, much harder than Math 1A/B, which rewards dedication
and discipline. Regular lecture attendance is practically a
requirement. My intention is to make lectures an exciting
experience which opens "windows onto previously unknown worlds".
I will not be using a third party's textbook. My own text will be
available on the course web page to students enrolled in the class.
Prior familiarity with at least basics of Linear Algebra is a clear
advantage in learning Multivariable Calculus. Therefore, it makes
sense to take this course either in parallel with Math54, or
Math54M, or to take Math54, or Math54M, before taking
Math53M.
Computers will be used mostly for visualization purposes. Previous
programming experience is not essential, though helpful.
Since I am expecting a certain minimum level of preparation for this
course, I require grade B, or better, on Math1B (or an equivalent)
from prospective students.
Before enrolling, any student should work through a 12 page
document entitled Preliminaries.
If you struggle with the material it contains, then this course is
probably not for you and you should not enroll in it. All
students will be tested in the second week of the class on this
material.
By enrolling in this class you consent to the fact that you can
take the Final Exam at the date and time prescribed by the
University. No make-up finals will be given.
Required Text: See above.
Recommended Reading: Harley Flanders, Differential Forms
with Applications to the Physical Sciences, Dover Publications,
1989 (originally, Academic Press, 1963).
Grading: Based on two midterms (20 percent) whose dates will
be announced during the first week of classes, the final (30
percent), homework (20 percent), and the work in discussion sections
(10 percent).
Homework: Weekly; collected in your discussion section every Thursday.
Math H53 - Multivariable Calculus - Honors
Instructor: Kevin Hare
Lectures: MWF 12:00-1:00pm, Room 71 Evans
Course Control Number: 54753
Office: 767 Evans, e-mail: kghare@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 1B
Recommended Prerequisite: Math 1B with a grade of B- or higher.
Syllabus: I plan to cover Chapters 10 through 16 of the book
(except for Chapter 11), plus additional material that I think is
interesting.
Chapter 10. Parametric equations and polar coordinates.
Chapter 12. Vectors in R2 and R3
Chapter 13. Vector functions
Chapter 14. Partial derivatives
Chapter 15. Multiple integrals
Chapter 16. Vectors calculus
Required Text: Stewart, Calculus: Early Transcendentals, 4th ed.
Grading: Grades will be based on weekly quizes (ten of which
count) (20%), two in-class midterm (40%), and the Final Exam (40%)
Homework: There will be homework assigned weekly. The homework
will not be due, but quizes will be based on the homework questions.
Comments: There will be a web-page for the Course maintained
at http://www.math.berkeley.edu/~kghare/Courses/MathH53.html
Math 54 - Linear Algebra and Differential Equations
Instructor: Allen Knutson
Lectures: TuTh 11:00am-12:30pm, Room 2050 Valley Life Science
Course Control Number: 54780
Office: 1033 Evans, e-mail: allenk@math.berkeley.edu
Office Hours: TBA
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Math 54M - Linear Algebra and Differential Equations
Instructor: Ming Gu
Lectures: MWF 3:00-4:00pm, Room 10 Evans
Course Control Number: 54831
Office: 861 Evans, e-mail: mgu@math.berkeley.edu
Office Hours: TBA
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Math 55 - Discrete Mathematics
Instructor: John Strain
Lectures: TuTh 2:00-3:30pm, Room 2050 Valley Life Science
Course Control Number: 54849
Office: 1099 Evans, e-mail: strain@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 1AB strongly recommended. Some knowledge
of computer science helpful.
Syllabus: Chapters 1-7 of the text will be covered thoroughly,
plus supplementary notes on probability theory by Prof. Lenstra.
Required Text: K.H. Rosen, Discrete Mathematics and Its
Applications, 5th edition, McGraw-Hill, 2003.
Recommended Reading: Student Solutions Guide for Rosen's text.
Grading: Homework 10%, Quizzes 10%, Midterms 20% each, Final 40%.
Math 74 - Transition to Upper Division Mathematics
Instructor: GSI - TBA
Lectures: MWF 3:00-4:00pm, Room 277 Cory
Course Control Number: 54873
Office:
Office Hours: TBA
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Math H90 - Honors Problem Solving
Instructor: Staff
Lectures: M 4:00-6:00pm, Room 31 Evans
Course Control Number: 54876
Office:
Office Hours: TBA
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Math 104 - Section 1 - Introduction to Analysis
Instructor: Laurent Bartholdi
Lectures: TuTh 9:30-11:00am, Room 75 Evans
Course Control Number: 54936
Office: 1073 Evans, e-mail: laurent@math.berkeley.edu
Office Hours: Tu(Th) 1:00-2:00pm at Cafe Strada, Bancroft @ Telegraph
Prerequisites: Math 53 and 54
Syllabus: 1. Introduction: Basic concepts of logic and set
theory. Functions. Natural numbers and induction. Field axioms and
real numbers. Completeness axiom.
2. Sequences: Limit theorems. Cauchy sequences. Metric space
topology. Compactness. Heine-Borel Theorem. Series.
3. Continuity: Basic properties of continuous functions. Uniform
continuity. Limits of functions. Continuity and connectedness in
metric spaces.
4. Sequences and series of functions: Power series. Uniform
convergence. Convergence tests. Weierstrass' Approximation
Theorem.
5. Differentiation: Basic properties of differentiation. The Mean
Value Theorem. Taylor's Theorem.
6. Integration: The Rieman Integral. Fundamental Theorem of
Calculus. Rieman-Stieltjes Integral.
Required Text: Kenneth A. Ross, The Elementary Theory of Calculus
Recommended Reading: Walter Rudin, Principles of
Mathematical Analysis
Grading: 20% min(MID,HW), 40% max(MID,HW), 40% final
Homework: Weekly, graded.
Comments: This is usually a difficult class, that requires
substantial personal effort from students. More information can be
found on the class
website
Math 104 - Section 2 - Introduction to Analysis
Instructor: George M. Bergman
Lectures: MWF 11:00am-12:00pm, Room 71 Evans
Course Control Number: 54939
Office: 865 Evans, e-mail: gbergman@math.berkeley.edu
Office Hours: Tu 1:30-2:30pm, Th 10:30-11:30am, F 4:15-5:15pm
Prerequisites: Math 53 and 54. (Math 74, which may be taken
simultaneously, is also strongly recommended for students not
familiar with proofs.)
Syllabus: We will cover Chapters 1-7 of the text.
Required Text: W. Rudin, Principles of Mathematical
Analysis, 3rd Edition, McGraw-Hill
Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam,
35%; regular submission of the daily question (see below), 5%.
Homework: Weekly, generally due Wednesdays.
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.
It will be for some of you the first course in which you are
expected, not to calculate answers, but to give proofs. This
transition, though intellectually exciting, is difficult for many
students. I will bear in mind that the function of the course is not
just to teach you Real Analysis, but also to introduce you to
mathematical reasoning, and that it is my job to help you with the
one as much as the other. Students who think they will have
particular difficulty with proofs are advised to take Math 74
simultaneously.
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 will assign readings in the text, and
conduct the class on the assumption that you have done this reading
and thought about the 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..
On each day for which there is assigned reading (usually Mondays and
Fridays), 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 may instead answer your question 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.
Many students find Rudin a difficult text. If your response to this
would be to put it aside and try to learn from the lectures alone, I
advise you not to take my section. The author writes clearly, but
writes as a mathematician, and in lecture I will try to help you
understand him, not replace him.
Math 104 - Section 3 - Introduction to Analysis
Instructor: Dan Geba
Lectures: MWF 2:00-3:00pm, Room 75 Evans
Course Control Number: 54942
Office: 837 Evans, e-mail: dangeba@math.berkeley.edu
Office Hours: MW 3:00-4:30pm
Prerequisites: Math 53 and 54
Syllabus: Real number system. Sequences. Series. Metric
spaces. Continuous functions. Differentiation in one variable.
Riemann integral.
Required Text: K.A. Ross, Elementary Analysis
Recommended Reading: W. Rudin, Principles of Mathematical
Analysis
Grading: Homework (30%), Midterm (30%), Final (40%)
Homework: Assigned on Friday, due next Friday. The worst 3
homeworks will not be included in the final grade. No late homeworks.
No make-up exams.
Math 104 - Section 4 - Introduction to Analysis
Instructor: Keith Miller
Lectures: TuTh 12:30-2:00pm, Room 75 Evans
Course Control Number: 54945
Office: 803 Evans, e-mail: kmiller@math.berkeley.edu
Office Hours: TBA
Prerequisites:
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Math 104 - Section 5 - Introduction to Analysis
Instructor: Daniel Tataru
Lectures: TuTh 2:00-3:30pm, Room 75 Evans
Course Control Number: 54948
Office: 841 Evans, e-mail: tataru@math.berkeley.edu
Office Hours: Th 9:30-10:30am, F 10:00-11:00am
Prerequisites: Math 53 and 54
Syllabus: Chapters 1-7 of the text.
Required Text: W. Rudin, Principles of Mathematical
Analysis, 3rd Edition, McGraw-Hill
Grading: 25% homeworks, 25% the midterm, 50% the final
Homework: Homework is assigned on the course web page, and due
once a week.
Comments: For many students this is the first course in which
you learn mathematics in a rigurous way. This means that the emphasis
now is not on computational abilities but instead on giving proofs
and using mathematical reasoning. To ease this transition the course
will start slowly and pick up the pace later on. The textbook I chose
is quite demanding, but it also has the advantage of being one of the
best around.
Math 104 - Section 6 - Introduction to Analysis
Instructor: Donald Sarason
Lectures: MWF 3:00pm-4:00pm, Room 3 Evans
Course Control Number: 54951
Office: 779 Evans, e-mail: sarason@math.berkeley.edu
(Do not contact me by e-mail except in a dire emergency. If you have
a question about the course, see me in my office, preferably during
office hours or by appointment, or try to reach me by phone
(642-3521).)
Office Hours: MW 9:30-11:30am
Prerequisites: Math 53 and 54
Syllabus: Most of the textbook and a certain amount of
supplementary material will be covered. The aim of the course is to
develop rigorously the basic ideas underlying calculus (and much of
the rest of mathematics). This will start with a detailed study of
the system of real numbers. The notions of convergence and
continuity will be examined, and will be shown to apply in a very
general setting, that of metric spaces. The two fundamental
operations of calculus, differentiation and integration, will be
developed from scratch. Along the way one encounters surprises: a
continuous functions that is nowhere differentiable, a space-filling
curve, the Cantor ternary set (the original fractal).
Required Text: Kenneth A. Ross, Elementary Analysis: The
Theory of Calculus, Springer-Verlag, 1980
Grading: Homework, 20%; two midterm examinations, 20% each;
final examination, 40%
Homework: Homework will be due most Wednesdays. It should be
handed in at the beginning of class. Late papers will not be
accepted.
Exams: The final exam is scheduled for Friday, December 12,
12:30-3:30 p.m. (Exam Group 8). The schedule for the midterm exams
is to be decided. There will be no make-up exams. Accordingly, do
not register for this section if you have a conflict.
Comments: A tutor for Math 104 will be available in 891 Evans
each Monday and Tuesday, for five hours each day. The identity of
the tutor and the precise hours will be announced shortly. There is
a class website at http://www.math.berkeley.edu/~sarason/Class_Webpages/Math104_S6.html.
Math H104 - Introduction to Analysis - Honors
Instructor: Vaughan Jones
Lectures: MWF 3:00-4:00pm, Room 51 Evans
Course Control Number: 54954
Office: 929 Evans, e-mail: vfr@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 53 and 54 and an enjoyment of challenging
problems. According to a departmental policy that began in January,
2003, students who take this course should normally be math majors
with a 3.5 GPA in upper-division mathematics courses. Exceptions may
be made by the instructor. Instead of signing up for this course,
students put themselves on the waitlist. Department staff members
will move students into the class incrementally. If you absolutely
wish to take this class but haven't yet been admitted, you may need
to speak with the instructor to plead your case.
Syllabus: I will cover Chapters 1-4 of the book.
Required Text: Charles Pugh, Real Mathematical
Analysis, Springer UTM Series.
Grading: Homework 25%, two midterms, each 15%. Final exam 45%.
Homework: Weekly. Mostly, but not always, taken from the book.
Comments: Math 104 is the defining math course in the
undergraduate curriculum. It is here that one makes rigorous the
concepts underlying calculus. It is here especially that one learns
to think and write carefully about mathematics. It is a difficult
course even for the best students, but the rewards are great. The
emphasis in the honors section will be on more difficult problems,
but only once the basic ideas have been properly assimilated.
Math 110 - Section 1 - Linear Algebra
Instructor: George M. Bergman
Lectures: MWF 3:00-4:00pm, Room 75 Evans
Course Control Number: 54957
Office: 865 Evans, e-mail: gbergman@math.berkeley.edu
Office Hours: Tu 1:30-2:30pm, Th 10:30-11:30am, F 4:15-5:15pm
Prerequisites: Math 54, or a course with equivalent linear
algebra content. (Math 74 is also recommended for students not
familiar with proofs.)
Syllabus: Approximate list of sections of the text that we
will cover: Appendices A, B, D, 1.1-1.6, 2.1-2.6, 4.4-4.5, 5.1, 5.2,
5.4, 6.1-6.6, 6.9, 7.1-7.3.
Required Text: S. H. Friedberg, A. J. Insel and L. E. Spense,
Linear Algebra, 4th Edition, Prentice-Hall.
Grading: Homework, 25%; two Midterms, 15% and 20%; Final Exam,
35%; regular submission of the daily question (see below), 5%.
Homework: Weekly, generally due Fridays.
Comments: In Math 54 you saw elementary linear algebra, with
an emphasis on solving linear equations, and with the abstract
concept of a vector space rather briefly treated. In this course,
the emphasis will be on further development of the properties of
abstract vector spaces, and linear maps among them.
It will be for many of you the first course in which you are expected
not just to calculate, but to give proofs. This transition, though
intellectually exciting, is difficult for some students. I will bear
in mind that the function of the course is not just to teach you
linear algebra, but also to introduce you to mathematical reasoning.
For students who think they will have particular difficulty with
proofs, Math 74 is recommended. Unfortunately, this is scheduled for
the same hour as my section this Fall; so students who need it should
either take it during Summer Session, or take it this Fall but take a
different section of Math 110.
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 will assign readings in the text, and
conduct the class on the assumption that you have done this reading
and thought about the 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..
On each day for which there is assigned reading (usually Mondays and
Wednesdays), each student in my class 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 may instead answer your questions 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 2 - Linear Algebra
Instructor: Ai-Ko Liu
Lectures: TuTh 2:00-3:00pm, Room 71 Evans
Course Control Number: 54960
Office: 905 Evans, e-mail: akliu@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Math 110 - Section 3 - Linear Algebra
Instructor: Arthur Ogus
Lectures: TuTh 11:00am-12:30pm, Room 71 Evans
Course Control Number: 54963
Office: 877 Evans, e-mail: ogus@math.berkeley.edu
Office Hours: MWF 2:00-3:00pm, subject to change.
Grading: The grading will be approximately weighted as
follows: 25% homeowrk, 30% midterms, 40% final, 5% quizzes. I try
to assign grades as follows:
- A thorough understanding of the material, as well as a
demonstration of originality in solving problems and writing proofs.
- Very good understanding of most of the material,
demonstrated by familiarity with definitions and proofs and ability
to solve problems.
- Firm grasp of the main points, including the important
definitions and theorems, ability to solve standard problems.
- Familiarility with major concepts, terminology, and
problem solving technqiues.
- None of the above.
Homework: Weekly assignments, due each Thursday. One or two
midterms, as well as some unspecified number of quizzes given at
unspecified intervals.
Webpage: http://www.math.berkeley.edu/~ogus/Math_110/index.html
Comments: In concrete terms, linear algebra is the study of
systems of linear equations in several variables. Such systems arise
in a vast number of situations in mathematics and other fields, and
it is absolutely crucial to understand them as thoroughly and
conceptually as possible. The solution set to such a system has a
rich geometric structure which is a fundamental part of linear
algebra. The concepts of vector and inner product spaces reveal both
the geometric and algebraic points of view, and a key theme of the
course will be the interplay between the "abstract" linear
algebra and the geometric intuition that it expresses. In the end
(and in fact even in the beginning) this theme will be more important
to us than the algorithmic methods for solving equations covered in
math 54. An important goal of the course is for students to learn to
read and write mathematical proofs, as well as to become comfortable
with the interplay between abstraction and intuition. There will be
a graduate student instructor assigned to help answer questions,
especially with the homework. His office hours will be:
Wednesday: 9-11, 1-2, 4-6
Thursday: 9-12, 4-6,
in 891 Evans.
For information on how to reach me, see my home
page.
Math 110 - Section 4 - Linear Algebra
Instructor: John Steel
Lectures: TuTh 12:30-2:00pm, Room 2 Evans
Course Control Number: 54966
Office: 717 Evans, e-mail: steel@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Math 110 - Section 5 - Linear Algebra
Instructor: Tara Holm
Lectures: MWF 9:00-11:00am, Room 75 Evans
Course Control Number: 54969
Office: 813 Evans, e-mail: tsh@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 54, or a course with equivalent linear
algebra content. (Math 74, which may be taken simultaneously, is also
recommended for students not familiar with proofs.)
Syllabus: TBA
Required Text: S. Axler, Linear Algebra Done Right
Grading: TBA
Homework: Weekly, generally due Wednesdays.
Math 110 - Section 6 - Linear Algebra
Instructor: Ming Gu
Lectures: MWF 12:00-1:00pm, Room 75 Evans
Course Control Number: 54972
Office: 861 Evans, e-mail: mgu@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Comments:
Math 110 - Section 7 - Linear Algebra
Instructor: Donald Sarason
Lectures: MWF 8:00-9:00am, Room 75 Evans
Course Control Number: 54975
Office: 779 Evans, e-mail: sarason@math.berkeley.edu
(Do not contact me by email except in a dire emergency. If you have
questions about the course, see me in my office, preferably during
office hours or by appointment, or try to reach me by phone
(642-3521).)
Office Hours: MW 9:30-11:30am
Prerequisites: Math 53 and 54
Syllabus: It is hoped we can cover the whole book together
with occasional supplementary material. The basic objects of study
will be finite-dimensional vector spaces over the real and complex
numbers, and the linear transformations between them. Of special
concern will be linear transformations from a space to itself,
so-called operators. The deepest theorems in the subject, the
spectral theorem and the Jordan decomposition, describe the structure
of operators.
Required Text: Sheldon Axler, Linear Algebra Done
Right, Second Edition, Springer, 1997.
Grading: Homework, 20%; two midterm examinations, 20% each;
final examination, 40%.
Homework: Homework will be due most Fridays. It should be
handed in at the beginning of class. Late papers will not be
accepted.
Exams: The final exam is scheduled for Thursday, December 11,
8:00-11:00 a.m. (Exam Group 4). The schedule for the midterm exams
is to be decided. There will be no make-up exams. Accordingly, do
not register for this section if you have a conflict.
Comments: A tutor for Math 110 will be available in 891 Evans
every Wednesday and Thursday, five hours each day. The identity of
the tutor and the precise hours will be available shortly. There is
a class webpage at http://www.math.berkeley.edu/~sarason/Class_Webpages/Math110_S7.html.
Math 110 - Section 8 - Linear Algebra
Instructor: Ilan Hirshberg
Lectures: TuTh 3:30-5:00pm, Room 6 Evans
Course Control Number: 54978
Office: 1055 Evans, e-mail: ilan@math.berkeley.edu
Office Hours: TBA
Prerequisites: High school AP math, including a working
knowledge of complex numbers (Math 1B,53 and 54 are not necessary).
Students will be expected to understand and produce proofs.
Students who have a lot of trouble with proofs are advised to take
Math 74 before taking this class.
To help you decide if this course is for you, the first suggested
reading will be posted on the course website (see below). Students
who are unsure if they are prepared to take the course are advised to
try working through the first reading before classes start; that
should give you an idea of what to expect. Feel free to contact me
(by email) if you have any further questions.
Syllabus: Scalars, vector spaces, linear transformations,
determinants, Eigenvalues, characteristic and minimal polynomials,
Jordan form, inner product spaces.
Recommended Reading: P. R. Halmos, Linear Algebra Problem
Book. Before most lectures, I'll give a list of suggested
readings from the book, which may help you understand the lecture if
you do them ahead of time. The readings are purely optional, and I
will not assume that you have done them.
Grading: Homework, two optional midterms and a final. Those
will count as 40% Final, 20% max(Final, Midterm #1), 20% max(Final,
Midterm #2), 20% max(Final,Homework), and will be converted to a
letter grade by: 85-100: A, 70-84: B, 55-69: C (adjusted by +'s and
-'s). The grades will not be `curved'.
Homework: Typically 6-7 problems, due each Thursday. The
problems will mostly be theoretical, and may be quite different from
what you have seen in lower division. It is OK if you can't figure
out how to do some of the problems, as long as you make a serious
effort, learn from your mistakes, study the solutions, and eventually
(before the exam) understand how to do those problems.
Comments: Different instructors have different styles and
emphases, and you should choose the one best for you. Here's some
more information on my approach.
The course will be rigorous and rather abstract. The focus will be on
giving students a good grasp of the theory. I will not discuss any
applications.
My lectures tend to be organized, and I'll write (almost) everything
on the board. The lectures will be self-contained, except for some
things which will be left as exercises or homework. I will not follow
a textbook. Students are expected to attend lecture regularly and
take good notes.
The course will have a webpage: http://www.math.berkeley.edu/~ilan/110/
Math H110 - Linear Algebra - Honors
Instructor: Kenneth Ribet
Lectures: MWF 12:00-1:00pm, Room 7 Evans
Course Control Number: 54981
Office: 885 Evans, e-mail: ribet@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 54 required, Math 53 and experience with
proofs highly recommended. According to a departmental policy that
began in January, 2003, students who take this course should normally
be math majors with a 3.5 GPA in upper-division mathematics courses.
Exceptions may be made by the instructor. Instead of signing up for
this course, students put themselves on the waitlist. Department
staff members will move students into the class incrementally. If you
absolutely wish to take this class but haven't yet been admitted, you
may need to speak with the instructor to plead your case.
Syllabus: The catalog proposes description reads as follows:
"Matrices, vector spaces, linear transformations, inner products,
determinants. Eigenvectors. QF factorization. Quadratic forms and
Rayleigh's principle. Jordan canonical form, applications. Linear
functionals." We will discuss most, but not all, of the topics on
that intimidating list. Because this is an honors course, lectures will
approach linear algebra from an abstract point of view, stressing
theorems and their proofs.
Required Text: Stephen H. Friedberg, Arnold J. Insel and
Lawrence E. Spence, Linear
Algebra, Fourth Edition.
Recommended Reading: There are quite a few good linear algebra
books in circulation; see the textbook
lists for some examples. You might want to work problems in other
books when studying for exams or to test your own understanding.
Also, whenever you feel stuck when reading our text, feel free to
consult alternative treatments. Reading several discussions of one
topic is often illuminating.
Grading: Homework 25%, midterms 15% each, final 45%.
Homework: See the course web page for
weekly assignments. (This page was begun in Fall, 2002 but will be
updated for Fall, 2003 over the summer.)
Math 113 - Section 1 - Introduction to Abstract Algebra
Instructor: John Wagoner
Lectures: MWF 1:00-2:00pm, Room 75 Evans
Course Control Number: 54984
Office: 899 Evans, e-mail: wagoner@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 113 - Section 2 - Introduction to Abstract Algebra
Instructor: Alexander Givental
Lectures: TuTh 11:00am-12:30pm, Room 2 Evans
Course Control Number: 54987
Office: 701 Evans, e-mail: givental@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Comments:
Math 113 - Section 3 - Introduction to Abstract Algebra
Instructor: Tom Graber
Lectures: MWF 8:00-9:00am, Room 71 Evans
Course Control Number: 54990
Office: 833 Evans, e-mail: graber@math.berkeley.edu
Office Hours: MWTh 10:00am-11:00am
Prerequisites: Math 54 or equivalent knowledge of linear algebra.
Syllabus: We will cover the basic theory of groups, rings, and fields.
Required Text: Beachy and Blair, Abstract Algebra
Grading: Homework, 30%; Midterms 15% each; Final 40%.
Homework: Assigned weekly.
Math 113 - Section 4 - Introduction to Abstract Algebra
Instructor: Mark Haiman
Lectures: TuTh 9:30-11:00am, Room 4 Evans
Course Control Number: 54993
Office: 771 Evans, e-mail:
Office Hours: TuTh 1:00-2:00pm (starting Fall 2003)
Prerequisites: Math 54 or equivalent knowledge of linear algebra.
Syllabus: Abstract algebra is a method of studying diverse
mathematical concepts, to do with geometry, symmetry, numbers, and
arithmetic, by discovering general axiomatic systems that describe
properties they have in common. In this course we will study the
three most important types of these axiomatic systems: groups,
rings and fields. We will see how they can be used to
solve some classical problems dating back to antiquity, such as the
impossibilty of trisecting an arbitrary angle or constructing the
cube root of 2 using only a straightedge and compass, and why there
are formulas for the roots of a polynomial of degree 2, 3 and 4 but
not 5.
Required Text: John B. Fraleigh, A First Course in Abstract
Algebra, 7th edition, Addison-Wesley, 2003.
Grading: Grading policy to be announced.
Homework: Homework assignments will be posted weekly on the
course web page.
Web Page: www.math.berkeley.edu/~mhaiman/math113
Math 113 - Section 5 - Introduction to Abstract Algebra
Instructor: Paul Vojta
Lectures: MWF 3:00-4:00pm, Room 9 Evans
Course Control Number: 54996
Office: 883 Evans, e-mail: vojta@math.berkeley.edu
Office Hours: TBA
Prerequisites: 53 and 54
Syllabus: This course will cover the basics of groups, rings,
and fields, as given in (parts of) Chapters 0, 1, 2, 3, 5, 6, 7, and
8 of the textbook. Details will be announced at the beginning of the
course.
Required Text: Fraleigh, A first course in abstract algebra
Grading: Homeworks, 30%; midterms, 15% and 20%; final exam, 35%.
Homework: Assigned weekly
Web page:
Comments: I tend to follow the book rather closely, but will
try to give more examples this time.
Math 113 - Section 6 - Introduction to Abstract Algebra
Instructor: A. Yong
Lectures: TuTh 3:30-5:00pm, Room 75 Evans
Course Control Number: 54999
Office: 1035 Evans, e-mail: ayong@math.berkeley.edu
Office Hours: TuTh 5:00-6:00pm, Reader's office hours to be posted.
Prerequisites: Math 54 or equivalent knowledge of linear algebra.
Syllabus: (From the course catalog): "Sets and relations. The
integers, congruences and the Fundamental Theorem of Arithmetic.
Groups and their factor groups. Commutative rings, ideals and
quotient fields. The theory of polynomials: Euclidean algorithm and
unique factorizations. The Fundamental Theorem of Algebra. Fields and
field extensions." -- as given in (parts of) chapters 0-10 of the
textbook.
Required Text: John B. Fraleigh, A First Course in Abstract
Algebra, 7th edition, Addison-Wesley, 2003
Recommended Reading: Joseph J. Rotman, A First Course in
Abstract Algebra, 2nd edition, Prentice Hall, 2000
Michel Artin, Algebra, Prentice Hall, 1991
I. N. Herstein, Abstract Algebra, 3rd edition, Prentice Hall, 1996
Grading: Homework (30%), Two midterms (15% each), Final exam (40%)
Homework: Assignments will be posted weekly starting September
2nd on the course webpage and are due in class the following week.
Webpage: http://math.berkeley.edu/~ayong/teaching.html
Exams: There will be two in class midterms; the first will be
on October 14th, covering group theory and some ring theory), the
second on Thursday November 27 covering more ring theory and some
field theory. The final exam will be cumulative, and the date will be
set by the registrar.
Comments: I will spend 1 week on "preliminaries" (chapter 0),
5.5 weeks on "group theory" (chapters 1-3,7), 4.5 weeks on "rings and
polynomials" (chapters 4-5) and 4 weeks on "elements of field theory"
(chapters 6,9-10). Of course there will not be time to cover
**every** aspect of these chapters!
Math 115 - Introduction to Number Theory
Instructor: Richard Borcherds
Lectures: TuTh 3:30-5:00pm, Room 85 Evans
Course Control Number: 55002
Office: 927 Evans, e-mail: reb@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 53 and 54.
Syllabus: Divisibility, congruences, numerical functions,
theory of primes, Diophantine analysis, continued fractions,
partitions, quadratic fields.
Required Text: Niven, Zuckerman, and Montgomery, The Theory
of Numbers
Grading: 40% homework, 15% each midterm, 30% final.
Homework: Homework will be assigned on the web every week.
Comments: See the course home page
www.math.berkeley.edu/~reb/115 for more details.
Math 121A - Section 1 - Mathematical Tools for the Physical Sciences
Instructor: Vera Serganova
Lectures: MWF 11:00am-12:00pm, Room 3 Evans
Course Control Number: 55005
Office: 709 Evans, e-mail: serganova@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
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Math 121A - Section 2 - Mathematical Tools for the Physical Sciences
Instructor: Dan Voiculescu
Lectures: TuTh 12:30-2:00pm, Room 6 Evans
Course Control Number: 55008
Office: 783 Evans, e-mail: dvv@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Math 123 - Ordinary Differential Equations
Instructor: Mehmet Erdogan
Lectures: TuTh 11:00am-12:30pm, Room 3 Evans
Course Control Number: 55011
Office: 805 Evans, e-mail: burak@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Comments:
Math 125A - Mathematical Logic
Instructor: Leo Harrington
Lectures: TuTh 12:30-2:00pm, Room 70 Evans
Course Control Number: 55014
Office: 711 Evans, e-mail: leo@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Math 128A - Section 1 - Numerical Analysis
Instructor: Alexandre Chorin
Lectures: MWF 10:00-11:00am, Room 3 Evans
Course Control Number: 55020
Office: 911 Evans, e-mail: chorin@math.berkeley.edu
Office Hours: TBA
Syllabus: I will cover the syllabus as it is announced in the
catalog, and follow the book loosely.
Grading: Grading will be based on a midterm, a final, and
homework, with emphasis on computing assignments.
Comments: My lecturing style is informal and I enjoy class discussion.
Math 128A - Section 2 - Numerical Analysis
Instructor: Kevin Hare
Lectures: MWF 3:00-4:00pm, Room 85 Evans
Course Control Number: 55026
Office: 767 Evans, e-mail: kghare@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 53 and Math 54
Syllabus: I plan to cover the first six chapters in the text.
1. Number systems and errors: Representation of numbers; error
propagation and error estimation.
2. Solution of nonlinear equations: Bisection, secant method,
Newton's method; fixed point iteration and acceleration.
3. Systems of linear equations: Elimination method - factorization,
pivoting, inverse calculation; iterative methods; eigenvalue problems.
4. Interpolation and Approximation: Interpolating polynomial,
Lagrange form, error formula; spline interpolation; trigonometric
interpolation and Fourier Series.
5. Differentiation and Integration: Numerical differentiation;
numerical quadrature-Romberg scheme, composite rules, Gaussian
quadrature.
6. Initial Value Problems: Euler's method, Taylor and Runge-Kutta
methods; convergence, stability, trapezoid method; stiff equations.
Required Text: Richard L. Burden and J. Douglas Faires,
Numerical Analysis, 7th ed.
Grading: Grades will be based on six Homework assignments
(30%), two in-class midterm (30%), and the Final Exam (40%).
Homework: There will be six assignments. These will be based
on questions from the text, plus occasionally additional questions.
There may be a small number of minor programing questions.
Comments: There will be a web-page for the Course maintained
at http://www.math.berkeley.edu/~kghare/Courses/Math128a.html
Math 128A - Section 3 - Numerical Analysis
Instructor: John Neu
Lectures: TuTh 8:00-9:30am, Room 85 Evans
Course Control Number: 55032
Office: 1051 Evans, e-mail: neu@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 130 - Classical Geometries
Instructor: Robin Hartshorne
Lectures: MWF 10:00-11:00am, Room 9 Evans
Course Control Number: 55038
Office: 881 Evans, e-mail: robin@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Math 135 - Introduction to Theory Sets
Instructor: Jack Silver
Lectures: TuTh 2:00-3:30pm, Room 85 Evans
Course Control Number: 55041
Office: 753 Evans, e-mail: silver@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Comments:
Math 141 - Elementary Differential Topology
Instructor: Allen Knutson
Lectures: TuTh 8:00-9:30am, Room 3 Evans
Course Control Number: 55044
Office: 1033 Evans, e-mail: allenk@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
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Math 160 - History of Mathematics
Instructor: Hung-Hsi Wu
Lectures: MWF 1:00-2:00pm, Room 6 Evans
Course Control Number: 55047
Office: 733 Evans, e-mail: wu@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 53, 54, and 113
Syllabus: The first four weeks on the history of mathematics
from Babylonia (circa 1800 B.C.) to Descartes, the remainder of the
semester on the period 1600-1900.
Required Text: John Stillwell, Mathematics and Its
History, Second Edition, Springer-Verlag, 2002.
Recommended Reading: D. J. Struik, A Concise Histroy of
Mathematics, Dover, 1987.
Grading: Homework 20%, Midterm I 15%, Midterm II 25%, Term paper 40%.
Homework: Weekly, problems will be about mathematics AND
history. Working in groups will be encouraged.
Comments: The first thing to make clear is that this is an
upper division course on mathematics. The official prerequisites of
second year calculus and introductory algebra (Math 113) will not be
enough, and new mathematics will have to be introduced. This is
because the course will try to explore the mathematics of the
nineteenth century, which would also overtax the capability of the
instructor. This course is a lot of work, and if past experience is
any guide, students generally do not consider this to be an
acceptable way of learning the history of mathematics. But work it
will be, so please consider carefully before enrolling. For those
who want to learn something about MATHEMATICS, instead of about
calculus or algebra or geometry or complex functions, this course
should be rewarding. You will get to learn about the evolution of
mathematical ideas, for example, the line of thought from Eudoxus to
Euclid, to Abel and Cauchy, to Dedekind, Cantor and Weierstrass. A
term paper will replace the final; a suggested list of topics will be
handed out during the first week. The two midterms will be about both
mathematics and history.
Math 170 - Mathematical Methods for Optimization
Instructor: L. Craig Evans
Lectures: TuTh 3:30-5:00pm, Room 81 Evans
Course Control Number: 55050
Office: 907 Evans, e-mail: evans@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 53 and 54
Syllabus: Topics will include:
1. Linear programming
2. Nonlinear programming
3. Game theory
4. The calculus of variations
5. Control theory (if time permits)
Required Text: Joel Franklin, Methods of Mathematical
Economics (SIAM)
Grading: 25% homework, 25% midterm, 50% final
Homework: I will assign a homework problem, due in one week,
at the start of each class.
Math 185 - Section 1 - Introduction to Complex Analysis
Instructor: Mehmet Erdogan
Lectures: TuTh 8:00-9:30am, Room 71 Evans
Course Control Number: 55053
Office: 805 Evans, e-mail: burak@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 185 - Section 2 - Introduction to Complex Analysis
Instructor: Dan Geba
Lectures: MWF 1:00-2:00pm, Room 71 Evans
Course Control Number: 55056
Office: 837 Evans, e-mail: dangeba@math.berkeley.edu
Office Hours: MW 3:00-4:30pm
Prerequisites: Math 104
Syllabus: Complex numbers. Analytic functions. Elementary
functions. Integrals. Series. Residues and poles. Application of
residues. Mapping by elementary functions. Conformal mapping.
Required Text: J.W. Brown and R.V. Churchill, Complex
Variables and Applications
Recommended Reading: L.V. Ahlfors, Complex Analysis
Grading: Homework (30%), Midterm (30%), Final (40%)
Homework: Assigned on Friday, due next Friday. The worst 3
homeworks will not be included in the final grade. No late homeworks.
No make-up exams.
Math 185 - Section 3 - Introduction to Complex Analysis
Instructor: Dan Voiculescu
Lectures: TuTh 9:30-11:00am, Room 71 Evans
Course Control Number: 55059
Office: 783 Evans, e-mail: dvv@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
|
Math 187 - Fourier Analysis and Applications
Instructor: Michael Christ
Lectures: MWF 2:00-3:00pm, Room 71 Evans
Course Control Number: 55062
Office: 809 Evans, e-mail: mchrist@math.berkeley.edu
Office Hours: Tu 1:30-2:30pm, W 1:10-2:00pm
Prerequisites: Math 104 and 185.
Syllabus: Most undergraduate courses are introductions to
particular branches of mathematics, or to particular sub-subjects. In
this course we seek to link together some of these diverse
sub-subjects. We will begin with a solid introduction to Fourier
analysis, but will thereafter focus on its interconnections with
topics throughout mathematics and science. In the title,
``Applications'' refers especially to applications within
mathematics; this will not be a course in ``applied mathematics'' per
se.
Topics will include:
- Basics of Fourier analysis. Convergence issues.
- Real analysis: Monsters, including nowhere differentiable functions.
- Geometry: The isoperimetric problem (how to enclose the maximal
possible area with a curve of given length).
- Approximation theory: Approximation by simple functions (e.g. polynomials).
- Nature: Tides, wine cellars, crystallography.
- Differential equations: The heat and wave equations. The
Dirichlet problem for Laplace's equation.
- Probability: Random walk and Brownian motion. Sums of random
variables -- the central limit theorem.
- Using Fourier series to do numerical calculations -- the Fast
Fourier Transform.
- Number theory: Prime numbers in arithmetic progressions.
The text is unusual in structure and emphasis. It consists
largely of a series of short mathematical vignettes, interlaced with
commentary, history, biography, and wry humor. Students must be
willing to read.
Required Text: T. W. Korner, Fourier Analysis
Recommended Reading: E. M. Sein and R. Shakarchi, Fourier
Analysis: An Introduction
H. Dym and H. P. McKean, Fourier Series and Integrals
Y. Katznelson, An Introduction to Harmonic Analysis
Homework: Problem sets will be assigned weekly.
Comments: There will be two in-class midterm exams (dates
TBA) and a written final exam.
Math 191 - Section 1 - Experimental Courses in Mathematics
Instructor: Emiliano Gomez
Lectures: MW 4:30-6:00pm, Room 35 Evans Hall
Course Control Number: 55065
Office: 985 Evans, e-mail: emgomez@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 191 - Section 2 - Undergraduate Seminar in Applied Mathematics
Instructor: L. C. Evans/Frances Hammock (For questions,
contact Frances at hammockf@hotmail.com.)
Lectures: M 4:00-5:00pm, Room 9 Evans Hall
Course Control Number: 55068
Prerequisites: Math 1A, 1B, 53, 54
Syllabus: Seminar in applied math. There will be an hour of
lecture by a
speaker once a week on some topic in applied math.
Grading: P/NP
Homework: One two-page paper due at the end of the semester.
Comments: Ever wondered what you can do with a background in
applied mathematics? Come find out from some of the leading minds in
biotechnology, computer science, economics, astrophysics....the list
goes on! Math is used everywhere - to learn more about it come check
out this seminar.
Speakers from around campus and from LBL will be giving undergraduate
level talks about their work. Some speakers include: List some names
James Demmel, Computer Science
Stefano Dellavi, Economics
Richard Plant, Agriculture
Richard Muller, Physics
Math 191 - Section 3 - Experimental Mathematical Modeling
Instructor: Nathaniel Singer
Lectures: MW 8:30am-10:00am, Room 262 Dwinelle
Course Control Number: 55070
Office: e-mail: nathanielsinger@yahoo.com
Office Hours: TBA
Prerequisites: Math 53 and 54
Syllabus: This course will operate with one clearly defined
goal: To have students understand how to build mathematical models. A
very relevant question is how would one most effectively learn to do
this? First you might want to start out by asking why you want to
learn about mathematical models in the first place. Before
approaching that you might want to know what a mathematical model is
and how it fits in to your understanding of the world. You will have
to do that initial inquiry on your own, but to get you started you
might try going to this website: http://www.mathmodeling.com/UMAPissues/2002MCM.pdf.
This class will be taught in a manner that differs from conventional
mathematics classes. Differences include:
- Team-based, in depth projects rather than homework sets
- Making the course fun, interesting, and relevant to your life
- Freedom to become more fully engaged and responsible
- A challenging yet supportive environment.
Beyond expanding their intuitive understanding of how to build
models, it is likely that students will emerge from this class with
(to mention just a few things) a better understanding of why we study
the mathematical subjects that we study, a clearer understanding of
how to tackle problems without a definite solution, and an clearer
idea about how to learn mathematics as well as other subjects on
their own.
Required Text: Ned's will stock the following books: John
Holland, Hidden Order: How Adaptation Builds Complexity;
Edward Bender, An Introduction to Mathematical Modeling.
Grading: Class participation and presentations (30%), Homework
(40%), Final Project (30%).
Comments: For more information I suggest that you go to the
course website, www.mathmodeling.com.
Math 191 - Section 4 - Topics in Discrete and Computational Geometry
Instructor: Jesus De Loera and Francis Su
Lectures: Th 3:30-5:00pm, Room 72 Evans Hall
Course Control Number: 55917
Office: MSRI, e-mail: fsu@msri.org
Office Hours: TBA
Prerequisites: A first course in linear algebra, and an
excitement for discrete mathematics as well as geometry.
Grading: Attendance and participation will be crucial. Each
student will be expected to produce a nice detailed set of notes for
a topic of his/her choice at least once in the semester.
Credit: 2 units of pass-fail credit.
Comments: This course will cover a selection of topics in
discrete and computational geometry with the aim to introduce
undergraduates to some of the exciting ideas at the heart of the
"Discrete and Computational Geometry" Fall program at the
Mathematical Sciences Research Institute (MSRI) at UC-Berkeley. The
general format of the seminar each week will be to explore an
attractive problem in the areas of discrete geometry and
computational geometry. We will facilitate a fun environment in which
active participation will be valued and encouraged.
Here is a tentative sample of topics:
1) Guarding art galleries and polygons.
2) Who are the Platonic and Archimedean solids?
3) Combinatorial fixed points and splitting the rent with roommates.
4) Computing volumes and areas.
5) Zonotopes and hyperplane arrangements.
6) Computational origami.
7) Cash registers, coin exchanges, and geometry.
8) Pick's theorem, areas, and polygons.
9) A taste of the Geometry of Numbers.
10) Euler's formula and its generalizations.
Math 191 - Section 5 - Undergraduate Research Seminar
Instructor: Kenneth A. Ribet
Lectures: Th 11:10am-12:30pm, Room 939 Evans Hall
Course Control Number: 55920
Office: 885 Evans, e-mail: ribet@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus: The goal of the seminar will be to study rational
points on elliptic curves.
Required Text: Joseph H. Silverman and John Tate, Rational
Points on Elliptic Curves, Springer-Verlag
Credit: 2 units; Letter grade or P/NP
Comments: Our textbook will be "Rational Points on Elliptic
Curves" by Joseph H. Silverman and John Tate (Springer-Verlag
Undergraduate Texts in Mathematics). Students may enjoy reading the
review of this book by William R. Hearst III and Kenneth A. Ribet
that was published in the April, 1994 issue of the Bulletin of the
American Mathematical Society. (The review is available as http://modular.fas.harvard.edu/edu/Spring2003/21n/papers/hearst.pdf.)
The textbook is based loosely on lectures that Tate gave to
undergraduates at Haverford College in 1961.
What is this subject about? Take a cubic equation like y^2 + y = x^3
-x^2 and look for solutions in which x and y are rational numbers.
As has been known for at least 100 years, the set of solutions
acquires the structure of an abelian group after one adds in the
extra "point at infinity" that one sees when looking at solution in
the projective (rather than affine) plane. This abelian group is
"finitely generated" in the sense that there exists a finite set of
solutions from which one can obtain all other solutions. The finite
generation is a theorem that L. E. J. Mordell proved in 1923.
Incredibly, there are still a host of open problems that have been on
the table since Mordell's work. For example, the conjecture of Birch
and Swinnerton-Dyer, which posits an analytic formula for the number
of independent rational solutions, is one of the million-dollar
Millenium Prize Problems that were stated by the Clay Mathematics
Institute three years ago. On the other hand, it is quite easy to
compute with elliptic curves using the software package "gp" (and
some other symbolic manipulation programs). One can get gp from http://www.parigp-home.de/, by
the way.
Elliptic curves occur prominently in the proof of Fermat's Last
Theorem. Students may wish to read Ribet's article on FLT that
appeared in the Bulletin of the AMS in October, 1995. This article
can be downloaded as http://www.ams.org/journals/bull/pre-1996-data/199510/199510001.pdf.
Math 202A - Topology and Analysis
Instructor: Charles Pugh
Lectures: TuTh 11:00am-12:30pm, Room 102 Moffitt
Course Control Number: 55131
Office: 829 Evans, e-mail: pugh@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Webpage: http://math.berkeley.edu/~robmyers/math202a.html
Grading:
Homework:
Comments:
Math 204A - Ordinary and Partial Differential Equations
Instructor: Alberto Grunbaum
Lectures: MWF 9:00-10:00am, Room 31 Evans
Course Control Number: 55134
Office: 903 Evans, e-mail: grunbaum@math.berkeley.edu
Office Hours: TBA
Syllabus: This is a one semester graduate level class on ODEs.
The emphasis will be on analytical treatment of differential
equations with a heavy emphasis at the beginning on linear systems,
including the standard material on constant coefficients, periodic
coefficients, the theory of regular and irregular singular points,
etc. We will make a rather detailed study of Gauss' hypergeometric
equation with 3 regular singular points as well as its confluent
versions, leading to Bessel's equation. We will have some discussion
of the important notion (due to Poincare) of asymptotic solutions as
well as the notion of the monodromy group associated to a linear
equation with meromorphic coefficients in the Riemann sphere. Very
important nonlinear equations like those of Painleve will appear in
the latter part of the course in the study of the "isomonodromic
deformations". I will use a very classical text, Coddington and
Levinson to insure a solid foundation for the basic material. The
latter part of the material is not covered in the book and I will
attempt to prepare lecture notes based in some cases on recent
literature in connection with integrable systems. This class
provides a solid bridge between very classical and very current
topics in analysis, mathematical physics, combinatorics, probability,
etc. The main prerequisites are linear algebra (eigenvalues,
eigenvectors, Jordan form, etc) and complex variables (meromorphic
functions, analytic continuation) at the undergraduate level.
Required Text: Coddington and Levinson, Theory of Ordinary
Differential Equations, McGraw Hill.
Recommended Reading: Einar Hille, Ordinary Differential
Equations in Complex Domain, Wiley.
Math 207 - Unbounded Operators
Instructor: Paul Chernoff
Lectures: MWF 10:00-11:00am, Room 65 Evans
Course Control Number: 55140
Office: 933 Evans, e-mail: chernoff@math.berkeley.edu
Office Hours: MWF 10:10am-12:00pm
Prerequisites: Math 202AB
Syllabus: Spectral theorem for unbounded self-adjoint
operators; symmetric operators; one parameter groups and semigroups,
generation of one-parameter unitary groups by self-adjoint operators;
applications to quantum mechanics, including the Stone-von Neumann
theorem on the Heisenberg commutation relations; Schrodinger
operators.
Grading: Based on homework assignments.
Math 214 - Differentiable Manifolds
Instructor: Alan Weinstein
Lectures: TuTh 9:30-11:00am, Room 85 Evans
Course Control Number: 55143
Office: 825 Evans, e-mail: alanw@math.berkeley.edu
Office Hours: Tu 11:15am-12:30pm and 2:15-3:30pm
Prerequisites: Math 202A or equivalent
Required Text: John M. Lee, Introduction to Smooth
Manifolds, Springer, 2003
Grading: The grade will be based on weekly homework
assignments and a take-home final exam.
Comments: I will cover the basic theory of differentiable
manifolds, mappings, vector fields, differential forms, Lie groups,
etc., as preparation for further study of differential geometry,
topology, geometric analysis, and applications. My lectures tend to
be on the informal side, with students referred to the text and other
references for details of some proofs. Since my research interests
center around symplectic geometry and its physical applications, some
of the examples in lecture will come from these fields.
Math 215A - Algebraic Topology
Instructor: Michael Hutchings
Lectures: TuTh 11:00am-12:30pm, Room 85 Evans
Course Control Number: 55146
Office: 923 Evans, e-mail: hutching@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 219 - Ordinary Differential Equations and Flows
Instructor: Fraydoun Rezakhanlou
Lectures: MWF 1:00-2:00pm, Room 85 Evans
Course Control Number: 55149
Office: 815 Evans, e-mail: rezakhan@math.berkeley.edu
Office Hours: MWF, 2:00-3:00pm
Prerequisites: Some analysis and measure theory.
Syllabus: The main goal of the theory of dynamical system is
the study of the global orbit structure of maps and flows. This
course reviews some fundamental concepts and results in the theory of
dynamical systems with an emphasis on differentiable dynamics.
Several important notions in the theory of dynamical systems have
their roots in the work of Maxwell, Boltzmann and Gibbs who tried to
explain the macroscopic behavior of fluids and gases on the basic of
the classical dynamics of many particle systems. The notion of
ergodicity was introduced by Boltzmann as a property satisfied
by a Hamiltonian flow on its constant energy surfaces. Boltzmann also
initiated a mathematical expression for the entropy and the
entropy production to derive Maxwell's description for the
equilibrium states. Gibbs introduced the notion of mixing
systems to explain how reversible mechanical systems could
approach equilibrium states. The ergodicity and mixing are only two
possible properties in the hierarchy of stochastic behavior of a
dynamical system. Hopf invented a versatile method for proving the
ergodicity of geodesic flows. The key role in Hopf's approach is the
hyperbolic behavior of dynamical systems. Lyapunov exponents and
Kolmogorov--Sinai entropy are used to measure the hyperbolicity of a
system.
Here is an outline of the course:
1. Existence and uniquesness of solutions to ODEs. Poincare-Bendixon Theorem.
2. Examples: Linear systems. Translations on Tori. Arnold can map.
Baker's transformation. Geodesic flows. Sinai's billiard. Lorentz
gas.
3. Invariant measures. Ergodic theory. Kolmogorov-Sinai Entropy.
Lyapunov exponents. Hyperbolic systems. Smale horseshoe.
4.Thermodynamic formalism. Perron-Frobenius operator.
Bowen-Ruelle-Sinai measures.
5. Pesin's theorem. Ruelle's inequality. Escape rates.
Gallavoti--Cohen fluctuation formula.
Homework: There will be some homework assignments.
Math 221 - Applied Numerical Linear Algebra
Instructor: Keith Miller
Lectures: TuTh 9:30-11:00am, Room 5 Evans
Course Control Number: 55152
Office: 803 Evans, e-mail: kmiller@math.berkeley.edu
Office Hours: TBA
Teaching Assistant: Jiang Zhu, e-mail: zhujiang@math.berkeley.edu
Prerequisites: Good knowledge of linear algebra (such as Math
110), coding experience, numerics equivalent to the level of Math
128AB.
Syllabus: The standard problems we will consider are linear
systems of equations, least squares problems, eigenvalue problems,
and singular value problems - for full and sparse matrices and by
direct and iterative methods. General concepts emphasized include (1)
matrix factorizations, (2) perturbation theory and condition numbers,
(3) effects of roundoff errors, (4) the speed of an algoritm, (5)
choosing the best algorithm for your problem, and (6) engineering
numerical software.
Required Text: James Demmel, Applied Numerical Linear
Algebra, SIAM, 1997
Recommended Reading: L. N. Trefethen, Numerical Linear
Algebra, SIAM, 1997.
This book is more purely mathematical in flavor than Demmel, but its
exposition is sometimes more easily readable.
Grading: Homework (about 25%), Programs (about 25%), Final
(about 50%). Programs will be of two kinds - those in Fortran or C,
and those in Matlab.
Homework: Homework will be due every 1 or 2 weeks.
Exams: 3-hour final (Exam Group 7).
Math 222A - Partial Differential Equations
Instructor: L. Craig Evans
Lectures: TuTh 12:30-2:00pm, Room 7 Evans
Course Control Number: 55155
Office: 907 Evans, e-mail: evans@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 105 or Math 202A
Syllabus: 1. Introduction
2. Four important linear PDE
3. Nonlinear first-order PDE
4. Sobolev spaces
5. Introduction to second-order linear elliptic PDE
Required Text: Lawrence C. Evans, Partial Differential
Equations (American Math Society)
Grading: 25% homework, 25% midterm, 50% final
Homework: I will assign a homework problem, due in one week,
at the start of each class.
Math 224A - Methods of Mathematical Physics
Instructor: Alberto Grunbaum
Lectures: MWF 8:00-9:00am, Room 5 Evans
Course Control Number: 55158
Office: 903 Evans, e-mail: grunbaum@math.berkeley.edu
Office Hours: TBA
Syllabus: The beauty and the challenge of this class is that
of presenting material that has been around in one form or another
for a long time in a way that is fresh and attractive to students. I
will try hard to walk this narrow line. In the first semester I will
try to stick to the material in the book: intuitive ideas about Green
functions, Fourier analysis and distribution theory, one dimensional
boundary value problems, Hilbert spaces, Operator theory and integral
equations. Spectral theory of second order differential operators. In
the second semester, I will have to do some unfinished material from
the first one, and then we will see how this classical stuff plays a
crucial role in problems of current interest. Among the topics that
I would like to touch upon, either during the main part of the course
or towards the end are Tridiagonal matrices, i.e., discrete versions
of second order differential operators. The classical orthogonal
polynomials: Hermite, Laguerre, Bessel and Jacobi. Spectral theory
for finite, semiinfinite and doubly infinite tridiagonal matrices.
The Toda equation for coupled unharmonic oscillators. Beyond
orthogonal polynomials. The relativistic Toda chain and Laurent
orthogonal polynomials. Birth and death processes. Uses of the
spectral theorem in examples. The Schroedinger equation, including
the main examples: the free particle, the harmonic oscillator, the
hydrogen atom etc. to give a concrete discussion of H. Weyl's limit
point-limit circle classification of separated boundary conditions.
Regular and irregular singular points for linear differential
equations in the complex plane. Gauss' linear second order
hypergeometric equation. The Bessel equation. Sampling, aliasing and
all that. The relation between the Fourier transform, the Fourier
series and the DFT. Heisenberg's principle. The problem of double
concentration. Some basic ideas behind the construction of "wavelet
basis". Random walks on integer lattices, discrete time and
continuous time. The issue of recurrence in different dimensions.
Brownian motion. Integration in function space, the Feynman-Kac
formula. Paul Levy's arcsine law. The scattering transform as an
important nonlinear version of the Fourier transform. Reflectionless
potentials, solitons, recovering a potential from scattering data,
the Korteweg-de Vries equation. Some matrix valued versions of the
Schroedinger equation.
Required Text: I. Stakgold, Green's functions and boundary
value problems. (I consider this book as required, since it
contains a lot of the basic material.)
Recommended Reading: The following is a partial list of
recommended books, covering different aspects of the class. G. Lamb,
Elements of soliton theory. M. Toda, Theory of nonlinear
lattices. S. Karlin and H. Studden, A second course in
Stochastic Processes.
Grading: It will be based solely on homework.
Homework: A weekly assignment.
Math 225A - Metamathematics
Instructor: Jack Silver
Lectures: TuTh 11:00am-12:30pm, Room 31 Evans
Course Control Number: 55161
Office: 753 Evans, e-mail: silver@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 228A - Numerical Solution of Differential Equations
Instructor: John Strain
Lectures: TuTh 11:00am-12:30pm, Room 5 Evans
Course Control Number: 55164
Office: 1099 Evans, e-mail: strain@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 128A, or equivalent knowledge of
elementary numerical analysis. Previous or concurrent experience with
Matlab, C or Fortran programming will be helpful.
Syllabus: The course will cover theory and practical methods
for solving one-dimensional differential and integral equations.
1. Methods for solving initial value problems for systems of ordinary
differential equations: construction, convergence and implementation.
1.1 Classical multistep (Adams and BDF) and Runge-Kutta methods.
1.2 Stable high-order deferred correction methods.
2. Solution of boundary value problems for systems of ordinary
differential equations.
2.1 Classical shooting and finite difference techniques.
2.2 Divide and conquer algorithms for integral equations.
Required Text: 1. E Hairer, S.P. Norsett and G. Wanner,
Solving Ordinary Differential Equations I and II (2 vols).
Second edition, Springer, 1993 and 1996.
2. U.M. Ascher, R.M.M. Mattheij, and R.D. Russell, Numerical
Solution of Boundary Value Problems for Ordinary Differential
Equations. SIAM Publications, 1995.
Grading: Grades will be based on regular homework assignments.
Math 229 - Theory of Models
Instructor: Thomas Scanlon
Lectures: MWF 3:00-4:00pm, Room 5 Evans Hall
Course Control Number: 55166
Office: 723 Evans, e-mail: scanlon@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 240 - Riemannian Geometry
Instructor: Alan Weinstein
Lectures: TuTh 12:30-2:00pm, Room 5 Evans
Course Control Number: 55167
Office: 825 Evans, e-mail: alanw@math.berkeley.edu
Office Hours: Tu 9:40-11:00am and 2:10-3:30pm
Prerequisites: Math 214 or equivalent
Required Text: John M. Lee, Riemannian Manifolds, An
Introduction to Curvature, Springer, 1997
Grading: The grade will be based on homework and an expository
paper on some aspect of riemannian geometry and its applications.
Comments: Riemannian geometry, besides being a subject of
great intrinsic interest, is an essential tool in all areas of
differential geometry, as well as in topology and other areas of
mathematics and its applications. (Even in probability theory,
riemannian manifolds of probability distributions have made their
appearance; riemannian geometry is also turning out to be a useful
tool in the study of some aspects of computer vision.) The textbook
covers the basics, and I will lecture on additional topics, such as
the theory of connections on is the gauge theory of connections on
principal bundles.
Math 250A - Groups, Rings and Fields
Instructor: Bjorn Poonen
Lectures: TuTh 8:00-9:30am, Room 70 Evans
Course Control Number: 55170
Office: 703 Evans, e-mail: poonen@math.berkeley.edu
Office Hours: TBA
Prerequisites: Math 114 (or equivalent undergraduate abstract
algebra) or consent of instructor.
Syllabus: We will cover most of Chapters I-VI in Lang's text:
groups (including the Sylow theorems and the Jordan-Holder Theorem),
rings, modules, polynomials, algebraic field extensions, Galois
theory (including infinite Galois theory, and an introduction to
Galois cohomology, if there is time). There is a lot of material, so
students will be expected to read the text for definitions and topics
not covered in class. Class time will serve to emphasize important
points, to clarify difficult topics, and to supplement the text as
needed.
Required Text: Lang, Algebra (revised third edition,
Springer, 2002)
Grading: There will be no exams. Grades will be based on
weekly homework.
Homework: Assignments will be due in class on Tuesdays. Late
homeworks will not be accepted.
Comments: The up-to-date course website is at http://math.berkeley.edu/~poonen/math250a.html
Math 252 - Representation Theory
Instructor: Vera Serganova
Lectures: MWF 1:00-2:00pm, Room 4 Evans
Course Control Number: 55173
Office: 709 Evans, e-mail: serganova@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 254A - Number Theory
Instructor: CheeWhye Chin
Lectures: MWF 2:00-3:00pm, Room 9 Evans
Course Control Number: 55176
Office: 705 Evans, e-mail: cheewhye@math.berkeley.edu
Office Hours: TBA
Prerequisites: Strong foundation in abstract algebra (250A)
and commutative algebra (250B).
Syllabus: The goal of this course is to present the key
results in class field theory for number fields, using the tools of
Galois cohomology. The course can be roughly divided into three
parts. The first part covers the basics of local fields and global
fields: valuations, completions, extensions, ramification, adeles,
ideles, approximation theorems, etc. The second part will be about
cohomology: of finite groups, of profinite groups, of Galois groups.
The final part will be focused on class field theory: both for local
fields and for global (number) fields.
Recommended Reading: Algebraic number theory, edited by
J. W. S. Cassels and A. Frohlich, Academic Press, Inc., London, 1986.
J. Neukirch, Algebraic number theory, Springer-Verlag, Berlin,
1999. The proceedings edited by Cassels and Fr–hlich is an excellent
source of study material; the first seven chapters of the book will
be especially relevant for this course. Neukirch's book will be used
as a reference from time to time.
Grading: There will be no exams. Grades will be based on
weekly homework.
Math 255 - Algebraic Curves
Instructor: Robert Coleman
Lectures: MWF 12:00-1:00pm, Room 9 Evans
Course Control Number: 55179
Office: 901 Evans, e-mail: coleman@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 256A - Algebraic Geometry
Instructor: Arthur Ogus
Lectures: TuTh 2:00-3:30pm, Room 51 Evans
Course Control Number: 55182
Office: 877 Evans, e-mail: ogus@math.berkeley.edu
Office Hours: MWF 2:00-3:00pm, subject to change.
Prerequisites: Students will need some background in
commutative algebra, in particular with localization and tensor
products. Some experience with the methods of global geometry (e.g.
differential or algebraic topology), and the language of category
theory, will also be helpful.
Recommended Reading: Qing Liu, Algebraic Geometry and
Arithmetic Curves, Oxford University Press
Grothendieck's EGA
Webpage: http://www.math.berkeley.edu/~ogus/Math_256A/index.html
Comments: There are many foundations on which algebraic
geometry can be built. Probably the most natural is Grothendieck's
theory of schemes, which provides a uniform framework for calculus,
geometry and arithmetic and has led to spectacular advances in all of
these fields. My main goal is to introduce students to the basic
ideas and techniques of schemes in a way that is general enough to
apply to arithmetic and number theory, without neglecting the
geometry that comes from studying varieties over algebraic closed
fields. In the course of the two semesters I hope to cover the main
parts of chapters II and III of Hartshorne's classic text, as well as
selected topics from chapters IV and V, although I will not follow
the text closely. Hartshorne's book and this course are notorious
for their difficult and time-consuming homework, which is absolutely
essential for mastery of the subject.
Math 257 - Group Theory
Instructor: Laurent Bartholdi
Lectures: TuTh 2:00-3:30pm, Room 5 Evans
Course Control Number: 55185
Office: 1073 Evans, e-mail: laurent@math.berkeley.edu
Office Hours: (Tu)Th 1:00-2:00pm at Cafe Strada, Bancroft @ Telegraph
Prerequisites: Math 250A (Groups, Rings and Fields)
Syllabus: 1. The theory of groups acting on trees with "small"
stabilizers, with as model the celebrated theorem "A group acting
freely on a tree is free"
2. The theory of groups acting on rooted trees, with a special
emphasis on closed (profinite) groups and groups generated by
automata
3. The connection between these topics, and in particular the
construction of lattices in products of simple Lie groups due to Marc
Burger and Shahar Mozes
Required Text: None -- notes will be handed out.
Recommended Reading: Jean-Pierre Serre, Trees, Amalgams, SL2
Hyman Bass and Alex Lubotzky, Tree lattices
Laurent Bartholdi, Rostislav I. Grigorchuk and Zoran Sunik, Branch
groups
Grading: A or A+, I haven't decided yet
Homework: Exercises will be handed out; because of the amount
of material to cover, I will expect students to read some selected
papers so that they can be discussed in class.
Comments: There is a class
website.
Math 261A - Lie Groups and Lie Algebras
Instructor: Nicolai Reshetikhin
Lectures: MWF 10:00-11:00am, Room 85 Evans
Course Control Number: 55188
Office: 945 Evans, e-mail: reshetik@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
Math 274 - Rational Curves in Algebraic Varieties
Instructor: Tom Graber
Lectures: MWF 9:00-10:00am, Room 51 Evans
Course Control Number: 55191
Office: 833 Evans, e-mail: graber@math.berkeley.edu
Office Hours: MWTh 10:00am-11:00am
Prerequisites: Math 256
Syllabus: The ostensible goal of the course will be to study
the geometry of rational curves in projective varieties, with an
emphasis on those varietiesw which contain many rational curves.
This will also serve as a pretext for introducing representable
functors (especially the Hilbert scheme and close relatives) and
their infinitesimal study via deformation theory. The core material
of the course will be roughly what is covered in chapters 2-5 of
Debarre's text, Higher-Dimensional Algebraic Geometry.
Recommended Reading: O. Debarre, Higher-Dimensional
Algebraic Geometry. J. Koll'ar, Rational Curves on Algebraic
Varieties.
Math 275 - Combinatorial Game Theory
Instructor: Elwyn Berlekamp
Lectures: TuTh 2:00-3:30pm, Room 81 Evans
Course Control Number: 55193
Office: 847 Evans, e-mail: berlekamp@math.berkeley.edu
Office Hours: TBA
Syllabus: We will study combinatorial game theory, according
to the first volume of "Winning Ways." The theory makes powerful use
of recursion, although there are no formal prerequisites beyond an
understanding of proof by induction and an interest in working
through a few sequences of specific examples. We will use this
theory to find explicit winning strategies for many positions in a
wide variety of playable games, including Hackenbush, Domineering,
Toads & Frogs, Ski Jumps, Konane, Kayles, Dawson, Dots-and-Boxes,
Amazons, and Clobber. We will investigate some operators which map
games into games, and extensions of this theory which extend the
original group into a monoid and now provide rigorous and precise
solutions to many hard endgame problems in a variety of games,
including the classical Asian board game of Go, and some rare
applications of chess and checkers. We will encounter several "NP"
and "PSPACE" complexity results. We will also study the
relationships between these mathematical theorems and the heuristic
search methods of artificial intelligence used by many computer
game-playing programs.
There will be at least two quizzes and probably three midterms (one
oral and two written) and a written final exam.
This is a subject in which it is possible for graduate students
rather quickly to acquire sufficient background to tackle some
unsolved but relatively tractable research problems. Extra credit
for original work. For examples of significant original
contributions which originated when they were students in earlier
versions of this course, see papers by the following authors in
"Games of No Chance": David Wolfe, David Moews, Dan Garcia, Mike
Zieve, Jeff Erickson and Yonghoan Kim, and in "More Games of No
Chance" by Alice Chan and Alice Tsai.
Required Text: Berlekamp, Conway and Guy, Winning Ways,
Vol. 1, AKPeters, Ltd, 2001
Recommended Reading: Don Knuth, Surreal Numbers, 1974,
Addison Wesley
R. Nowakowski (Editor), Games of No Chance, 1996, 1999,
Cambridge University Press
R. Nowakowski (Editor), More Games of No Chance, 2002, which
is available online at msri.org.
Math 279 - Topics in Partial Differential Equations
Instructor: Daniel Tataru
Lectures: TuTh 11:00am-12:30pm, Room 7 Evans
Course Control Number: 55194
Office: 841 Evans, e-mail: tataru@math.berkeley.edu
Office Hours: By appointment
Prerequisites: Real analysis. Some pde background would also be useful.
Syllabus: The aim of the course is to provide an overview of
microlocal analysis, oriented toward problems in nonlinear partial
differential equations. Following are some topics I have in mind:
The Fourier transform
Phase space transforms (i.e. Bargman and FBI)
Littlewood-Paley theory
Pseudodifferential operators,
The Garding and Fefferman-Phong inequalities
Fourier integral operators (following Bony)
Paradifferential calculus
Coherent states and wave packets
All this will be interwoven with applications to problems in linear
and then nonlinear partial differential equations.
References: Jean Marc Delort, FBI Transformation
Charles Fefferman, The Uncertainty Principle (AMS Bulletin)
Gerard Folland, Harmonic Analysis in Phase Space
Lars Hormander, The Analysis of Linear Partial Differential Operators
Elias Stein, Harmonic Analysis
Michael Taylor, Pseudodifferential operators and Nonlinear PDE's
Math 300 - Teaching Workshop
Instructor: Ole Hald
Lectures:
Course Control Number: 55845
Office: 875 Evans, e-mail: hald@math.berkeley.edu
Office Hours: TBA
Prerequisites:
Syllabus:
Required Text:
Recommended Reading:
Grading:
Homework:
Comments:
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