Spring 2012

Office: 1073 Evans
Office Hours: TBA
Prerequisites: Math 1A, or its equivalent.
Required Text: James Stewart, Single variable calculus: Early Transcendentals for University of California, (special Berkeley edition), ISBN 978-1-4240-5500-5 or 1-4240-5500-8, Cengage Learning.
Syllabus: See the course web page (coming in December 2011).
Grading: See the course web page.
Homework: Weekly, to be posted on the course web page.

Prerequisites: Math 1A
Required Text: James Stewart, Single variable calculus: Early Transcendentals for University of California, (special Berkeley edition), ISBN 978-1-4240-5500-5 or 1-4240-5500-8, Cengage Learning.

Prerequisites: Math 16A or the equivalent
Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & Its Applications Vol. II (Custom Edition), ISBN# 0-558-37274-0

Office: 829 Evans
Office Hours: TBA
Syllabus: In this seminar, we will discuss the latest
developments in science and math. Students will present short oral
reports from articles of their choice in the Science Times, Scientific
American, Science News, or articles in What is Happening in the
Mathematical Sciences. Discussion and debate are encouraged especially
when controversial or challenging issues arise, e.g., cloning of organs,
string theory, stem cell research, and geopolitics of global warming.
Students are encouraged to think of applications and possibilities of
new research projects. Brainstorming and creative thinking are
encouraged! This seminar is intended for students who love math and
science and want to discuss the latest developments in an atmosphere
that fosters creative thought. Students considering a major in math or
science have found this seminar a useful resource to help clarify their
choice. This seminar is part of the Connections@Cal initiative.
Comments: Jenny Harrison obtained her Ph.D. in mathematics in
Warwick, England. She has taught at Oxford, Princeton, and Yale, as well
as UC Berkeley. Her research interests include a new quantum calculus
that applies equally to charged particles, fractals, smooth surfaces,
and soap films. Applications of this theory to sciences may arise during
this seminar.
Faculty web site: http://en.wikipedia.org/wiki/Jenny_Harrison

Prerequisites: Math 1A and 1B
Required Text: Stewart, Multivariable Calculus (Custom Edition for UCB) ISBN: 978-1-424-05499-2.

Prerequisites: Math 1B

Office: 925 Evans
Office Hours: TBA
Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B is recommended but not required. Freshmen with solid high school math background and a possible interest in majoring in mathematics are strongly encouraged to take this course.
Required Text: Kenneth H. Rosen, Discrete Mathematics and Its Applications, 7th Edition (UC Berkeley Version)
Syllabus: This course provides an introduction to logic and proof techniques, basics of set theory, algorithms, elementary number theory, combinatorial enumeration, discrete probability, graphs and trees, with a view towards applications in engineering and the life sciences. It is designed for majors in mathematics, computer science, statistics, and other related disciplines in the sciences and engineering.
Course Webpage: http://math.berkeley.edu/~bernd/math55.html
Grading: 5% quizzes, 15% homework, 20% each of two midterm exams, 40% final exam
Homework: Weekly homework will be due on Mondays and returned in discussion sections on Wednesdays.

Restrictions:BY CATEGORY; CURRENTLY FULL

Notes:Cross-listed with Economics C103 section 1. Seats have been set aside for Math/Appplied Math majors.

Restrictions:CURRENTLY FULL

Office: 855 Evans
Prerequisites: Math 54 or equivalent preparation in linear
algebra at the lower division level
Required Text: Sheldon Axler, Linear Algebra Done Right,
Springer, 2nd edition (1997)
Syllabus: See course web page.
Course Webpage: math.berkeley.edu/~mhaiman/math110-spring12
Grading: Based on homework, two midterms and final exam.
Homework: Due weekly in discussion sections.

Office: 913 Evans
Office Hours: will be announced on the course webpage
Required Text: John Fraleigh, A First Course in Abstract Algebra, 7th edition, Addison-Wesley.
Syllabus: Groups, rings, and fields.
Grading: Homework, two midterms, and final exam.
Homework: Weekly.

Required Text: Numerical Analysis, 8-th or 9-th edition (by R. L. Burden and J. D. Faires).
Syllabus:
In this course, we will learn some of the most basic concepts and methods in scientific computing.

Many physical phenomena are governed by differential equations. Newton's second law of motion is in general a set of second order time-dependent differential equations. In this course our main goal is to develop a number of tools for solving these and other equations numerically. Our main focus is in developing numerical methods for such purposes. Our text book is Numerical Analysis, 8-th or 9-th edition (by R. L. Burden and J. D. Faires). We will mostly cover the first 6 chapters of the text. There will be emphasis on matlab programming with up to 3 programming assignments.

Office: 897 Evans
Office Hours: MWF 2:00-3:00pm
Prerequisites: Math 104 or Math 121B
Required Text: Pressley, Elementary Differential Geometry, Springer.
Syllabus: Frenet formulas, isoperimetric inequality, local theory of surfaces in Euclidean space, first and second fundamental forms, Gaussian and mean curvature, isometries, geodesics, parallelism, the Gauss-Bonnet-Von Dyck Theorem.
Grading: 1/2 homework, 1/3 final, 1/6 midterm
Homework: Homework will be assigned periodically
Comments: UC students can download the text for free from oskicat.berkeley.edu. You may want to review the material in Appendix 0.

Office: 875 Evans Hall
Prerequisites: Math 104
Required Text: C.H. Edwards, Jr. The Historical Development of the Calculus, Springer Verlag.
Syllabus: A serious study of the history of calculus would require knowledge of Greek, Latin, Arabic, Italian, French, English, German and Russian. The book chosen for this course drags the reader through the original arguments, but uses English and modern notation. The work will consist of filling in the gaps and solving the exercises. The grade will be based on homework, essays, and bi-weekly oral presentations.

Prerequisites: Math 104

Office: 887 Evans
Office Hours: MW 10:00-11:30am and by appointment
Prerequisites: Math 104
Required Text: "Complex Analysis" by Bak and Newman
Syllabus: I will mostly follow the text, with additional material added as necessary.
Course Webpage: http://math.berkeley.edu/~oeding/math185.html
Grading: 20% homework, 20% midterm I, 20% midterm II, final 40%
Homework: weekly homework

Office: 741 Evans
Office Hours: TBA
Prerequisites: Ability to write proofs and willingness to work on
open-ended problems a must. Math 55 required and at least one 100 level
math course strongly preferred.
Syllabus: Inspired by the knots that appear in daily life, knot theory is the
study of mathematical knots. Today, mathematical knots are of
fundamental importance to modern geometry and have found applications in
biology, chemistry, and physics as well. Moreover, easily stated open
questions about knots abound, and much of the theory can be explained at
an elementary level. As such, knot theory provides an ideal gateway
into mathematical research.

This class will take advantage of this to give students experience doing
research-type mathematics. Students will learn about knot theory and
then apply their knowledge to hard, open-ended problems. Many of the
problems will be very visual and hands-on in nature.
Course Webpage: To be announced.
Grading: One short and one long project. Weekly progress
reports, an in-class presentation, and a final write-up using LaTex will
be required for each project. Exercises will occasionally be assigned.
Comments: Each student will have considerable latitude in finding
problems that fit his or her interest. Students will work in small
groups on these problems, with the majority of this work completed
outside of class. Each group will be expected to discuss its progress
weekly during office hours.

Restrictions:JR, SR

Office: 811 Evans
Office Hours: TBA
Prerequisites: Math 202A or equivalent preparation in analysis. Notice that some measure and integration will have been covered in Math 202A.
Recommended Reading:
Real and Functional Analysis 3rd ed. by Serge Lang, Springer-Verlag
Basic Real Analysis by Anthony Knapp.
Advanced Real Analysis by Anthony Knapp.
Through an agreement between UC and Springer, chapters of the Knapp texts are available for free download by students. You can find the chapters here, and here.
You may need to use campus computers to authenticate yourself to gain access. It is my impression that, at least on-line, one can purchase the two Knapp books together as a package at a more attractive price than if they are purchased singly.
Syllabus: We will continue the study of measure and integration begun in Math 202A. My treatment of integration will be closer to that given in the text by Lang than in the text by Knapp. Topics that will be discussed include product measures and Fubini theorems, signed measures, the Radon-Nikodym theorem, measure and integration on locally compact spaces. This will be followed by an introduction to functional analysis. Banach spaces, closed-graph theorem, Hahn-Banach theorem and duality, duals of classical Banach spaces, weak topologies, Alaoglu theorem, convexity and Krein-Milman theorem. In my lectures I will try to give well-motivated careful presentations of the material.
Grading: I plan to assign roughly-weekly problem sets. Collectively they will count for 50% of the course grade. Students are strongly encouraged to discuss the problem sets and the course content with each other, but each student should write up their own solutions, reflecting their own understanding, to turn in.
There will be a final examination on Monday May 7, 8-11 AM, which will count for 35% of the course grade. There will be a midterm exam. It will count for 15% of the course grade. There will be no early or make-up final examination. Nor will a make-up midterm exam be given; instead, if you tell me ahead of time that you must miss the midterm exam, then the final exam will count for 50% of your course grade. If you miss the midterm exam but do not tell me ahead of time, then you will need to bring me a doctor's note or equivalent in order to have the final exam count for 50% of your course grade.
Homework:They will be posted at Homework as they are assigned.
Comments: Students who need special accommodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance what specific accommodation they need, so that I will have enough time to arrange it.
The above procedures are subject to change.

Course Webpage: http://math.berkeley.edu/~zworski/math212.html

Notes:Cross-listed with Statistics C205B section 1.

Office: 1033 Evans
e-mail: evans [at] math [dot] berkeley [dot] edu
Office Hours: TBA
Prerequisites: Math 222A
Required Text: Partial Differential Equations, by Lawrence C Evans (American Math Society).
Syllabus:
The theory of boundary value and initial value problems for partial differential equations, with emphasis on nonlinear equations. Second-order elliptic equations, parabolic and hyperbolic equations, calculus of variations methods, additional topics selected by instructor.

1. Second order elliptic, parabolic and hyperbolic PDE

2. Calculus of variations

3. Nonvariational methods

4. Hamilton-Jacobi PDE

5. Systems of conservation laws
Grading: 25% homework, 25% midterm, 50% final
Homework: I will assign a homework problem, due in one week, at the start of each class.

Office: 923 Evans
Office Hours: TBA
Prerequisites: 214 and 215a or equivalent
Required Text: none
Recommended Reading: references (most of them freely available online) will be provided throughout the course
Syllabus: The first part of the course will introduce the basic structures of symplectic geometry (Lagrangians, Hamiltonians, moment maps, etc.) and also contact geometry (the odd-dimensional counterpart of symplectic geometry). The second part of the course will introduce holomorphic curves and some of their applications to symplectic and contact geometry.
Course Webpage: will be linked from math.berkeley.edu/~hutching
Grading: The only course requirement is a final project, which can be either a short expository paper or a presentation, on any topic related to the course.

Office: 855 Evans
Prerequisites: Algebra background equivalent to 250A.
Required Text: Richard P. Stanley, Enumerative Combinatorics, Vols. I & II. Cambridge Univ. Press 1999, 2000.
Recommended Reading: See course web page.
Syllabus: See course web page.
Course Webpage: math.berkeley.edu/~mhaiman/math249-spring12
Grading: Based on homework.
Homework: Problems assigned for each lecture.

Office: 901 Evans

Office Hours: MF 300-4:00PM

Prerequisites: Math 254a 185

Required Text: Lang, Borevich-Shafarevich

We will begin to look at zeta and L functions of number fields. Prove the Chebotarrev density theorem and the class number formula. We will talk about Stark'ss conjecture and the Riemann hypothesis.

Office: 999 Evans
Office Hours: TBA
Prerequisites: Math 256
Required Text: none
Recommended Reading: Vladimir Berkovich, Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Syllabus: Non-Archimedean geometry is motivated by the desire to develop a theory of analytic spaces over non-Archimedean (for example p-adic) fields analogous to the classical theory of complex manifolds (or, more generally, complex analytic spaces). There are several different approaches to the subject, including Tate's theory of rigid analytic spaces, Raynaud's theory of admissible formal schemes, Berkovich's theory of non-Archimedean analytic spaces, and Huber's theory of adic spaces. We will touch on all of these, focusing mainly on Berkovich's theory. We will also discuss (in varying levels of detail) applications of non-Archimedean geometry to areas such as Galois representations, tropical geometry, and dynamical systems. Students will be expected to be familiar with the basics of scheme theory (as covered in Chapter II of Hartshorne) and we will present many of the foundational results concerning affinoid algebras without proof, but otherwise we will try to keep the material relatively self-contained.
Grading: Students will be expected to help write lecture notes which will be made available to the public at the end of the course. Grades will be based on class participation, assistance in writing up notes based on the lectures, and suggested improvements to the lecture notes.
Homework: see above

Office: 735 Evans
Prerequisites: NB Only students enrolled in Part A of this course in Fall 2011, and who pass the exam, may enroll in Part B.
Recommended Reading:
Landau, L. D. and Lif*bleep*s, E. M., Fluid Mechanics (Pergamon Press, London, Yew York, 1987);
Landau, L. D. and Lif*bleep*s, E. M., Theory of Elasticity (Pergamon Press, London, Yew York, 1986);
Chorin, A. J. and Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (Springer, 1990);
Barenblatt, G. I. Scaling (Cambridge University Press, 2003);
Batchelor, G. K., An Introduction to Fluid Dynamics (Cambridge University Press, 1998).
Syllabus: Fluid Mechanics, including Turbulence and Mechanics of Deformable Solids, including Fracture Mechanics are fundamental disciplines, playing an important and ever-growing role in applied mathematics, including computing, and also physics, and engineering science. The models of fluid flow, deformation and fracture of solids under various conditions appear in all branches of applied mathematics, engineering science and many branches of physical science. Among the problems of these sciences which are under current active study there are great scientific challenges of our time such as turbulence, fracture and fatigue of metals, damage accumulation and nanotechnology.

The proposed course will present the basic ideas and methods of fluid mechanics, including turbulence, mechanics of deformable solids, including fracture as a unified mathematical, physical and engineering discipline. The possibility of such a unified presentation is based on the specific 'intermediate-asymptotic approach' which allows the explanation of the main ideas simultaneously for the problems of fluid mechanics and deformable solids. The basic distinction of this year-long course will have special emphasis on turbulence. The instructor expects to present the basic ideas and to evaluate the current state of the turbulence studies. In particular, scaling laws for the shear flows and local structure of the developed turbulent flows will be presented and discussed.
Homework: There will be no systematic homework. Some problems will be presented shortly at the lectures, their solutions will be outlined, and interested students will be offered the opportunity to finish the solutions. This will not be related to the final exams.
Comments: In the end of the course the instructor will give a list of 10 topics. Students are expected to come to the exam having an essay (5-6 pages) concerning one of these topics which they have chosen. They should be able to answer questions concerning the details of these topics. After that general questions (without details) will be asked concerning the other parts of the course.

Restrictions:GR