Fall 2010
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Math 1A - Section 1 - Calculus Instructor: Michael Christ Lectures: MWF 10:00-11:00am, Room 2050 Valley LSB Course Control Number: 53603 Office: 809 Evans Office Hours: Prerequisites: Reasonable mastery of high school trigonometry and analytic geometry, plus sufficient intellectual maturity for a college Mathematics course. An online placement exam is available at: http://math.berkeley.edu/courses_placement.html for diagnostic use; it is not required. Please see professional advisors Thomas Brown or Jennifer Sixt of the Mathematics department ASAP if unsure which of Math 1A, 1B, 16A, 16B, 32 is most appropriate for you. Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 9781-424-05500-5 or 1-424-05500-8. Recommended Reading: Syllabus: Limits, derivatives and applications, inverse functions, integrals and applications. Chapters 1 through 6 of the text. Course Webpage: http://math.berkeley.edu/~mchrist/Math1A/homepage.html Grading: HW 10%, quizzes 15%, first midterm exam 15%, second midterm 20%, final exam 40%. Students will be rank ordered according to total course points. Distribution of letter grades will be consistent with Mathematics department averages for calculus courses. Homework: Weekly problem sets, due on Wednesdays. Assignments posted weekly on course web page. Comments: Math 1A - Section 2 - Calculus Instructor: James Sethian Lectures: TT 8:00-9:30am, Room 155 Dwinelle Course Control Number: 53642 Office: 725 Evans Office Hours: Prerequisites: Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 9781-424-05500-5 or 1-424-05500-8. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 1A - Section 3 - Calculus Instructor: Mark Haiman Lectures: MWF 12:00-1:00pm, Room 155 Dwinelle Course Control Number: 53681 Office: 855 Evans Office Hours: W 1:30-3:00 Prerequisites: Appropriate high school mathematics background Required Text: 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. Recommended Reading: Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~mhaiman/math1A-fall10 Grading: Approximately, Homework 10%, 3 Midterm exams 15% each, Final exam 45%. The exact grading policy will be announced on the course webpage at the start of the semester. Homework: Problems assigned on course webpage, due weekly in discussion sections. Comments: Math 1B - Section 1 - Calculus Instructor: Martin Olsson Lectures: MWF 9:00-10:00am, Room 155 Dwinelle Course Control Number: 53720 Office: 879 Evans Office Hours: TBA Prerequisites: Math 1A. Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 978-1-424-05500-5 or 1-424-05500-8. Recommended Reading: Syllabus: A detailed syllabus will be passed out on first day of class. Course Webpage: Grading: Based on homework, quizzes, two midterms, and a final. Homework: There will be weekly homework. Comments: Second part of the introduction to differential and integral calculus of functions of one variable, with applications. This course is intended for majors in engineering and the physical sciences. Math 1B - Section 2 - Calculus Instructor: Vaughan Jones Lectures: TT 3:30-5:00pm, Room 105 Stanley Course Control Number: 53756 Office: 929 Evans Office Hours: TBA Prerequisites: Math 1A Required Text: Single Variable Calculus, Early Transcendentals for UC Berkeley James Stewart, Cengage Learning, ISBN 978-1-424-05500-5 or 1-424-05500-8. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H1B - Section 1 - Calculus Instructor: George Bergman Lectures: MWF 9:00-10:00am, Room 3 Evans Course Control Number: 53795 Office: 865 Evans Office Hours: Mon., Tues. 11:30-12:30, Fri. 3:30-4:30. Prerequisites: Math 1A or equivalent, and consent of the instructor. Required Text: James Stewart, Single variable calculus: Early Transcendentals, Cengage (custom Berkeley edition 1A/1B) Recommended Reading: None Syllabus: Chapters 7-9, 11, 17: techniques and applications of integration, first and second order differential equations, infinite sequences and series. Course Webpage: Grading: Grades will be based on weekly section quizzes (25%), two midterms (15% + 20%), a final exam (35%), and regular submission of your "daily question" (5%; see last paragraph below). Homework: Weekly; not graded. Comments: I will follow the curriculum for Math 1B, but try to provide greater rigor (real proofs), greater insight, and more interesting exercises. We will also go back to some of the key proofs from 1A and put them on a solid basis. I don't expect the grading scale to be either higher or lower than for 1B, but you will have to do more thinking to get a good grade; hopefully, you will enjoy this. If you start H1B but find in a few weeks that it is not the course for you, it should be possible to transfer to regular 1B and not be at a disadvantage. My discussion of the material in each lecture will be based on the assumption that you have done the assigned reading for that day! You will be expected to submit a question on each day's reading by the start of class; preferably by e-mail the day before. (Details in the first-day course handout. In particular, if you understand the reading thoroughly and have no questions about it, you should submit a pro forma question -- with the answer.) Math 16A - Section 1 - Analytic Geometry & Calculus Instructor: Leo Harrington Lectures: MWF 1:00-2:00pm, Room 155 Dwinelle Course Control Number: 53801 Office: 711 Evans Office Hours: TBA Prerequisites: Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & Its Applications Vol. I (Custom Edition), ISBN# 0-558-37269-4 Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 16A - Section 2 - Analytic Geometry & Calculus Instructor: Theodore Slaman Lectures: TT 11:00-12:30pm, Room 105 Stanley Course Control Number: 53840 Office: 719 Evans Office Hours: TuTh 2-3:30P, beginning with Thursday, August 26, 2010. Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & Its Applications Vol. I (Custom Edition), ISBN# 0-558-37269-4 Recommended Reading: Syllabus: Course Webpage: Further information will be available on bSpace. Grading: Homework: Comments: Math 16B - Section 1 - Analytic Geometry & Calculus Instructor: Thomas Scanlon Lectures: TT 3:30-5:00pm, Room 155 Dwinelle Course Control Number: 53879 Office: 723 Evans Office Hours: TBA Prerequisites: Required Text: Goldstein, Lay, Schneider & Asmar, Calculus & Its Applications Vol. II (Custom Edition), ISBN# 0-558-37274-0 Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 24 - Section 1 - Freshman Seminar Instructor: Jenny Harrison Lectures: Tu 3:00-4:00pm, Room 891 Evans Course Control Number: 53918 Office: 829 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 32 - Section 1 - Precalculus Instructor: Alex Rennet Lectures: MWF 8:00-9:30am, Room 4 LeConte Course Control Number: 53927 Office: 1043 Evans Office Hours: W 11-12 and F 11-12, 1:30-3:30 in the Student Learning Center Prerequisites: Required Text: Cohen, "Fundamentals of Precalculus", Custom Edition Recommended Reading: Syllabus: download at the course webpage Course Webpage: http://math.berkeley.edu/~rennetad/teaching.html Grading: Homework: Comments: Math 53 - Section 1 - Multivariable Calculus Instructor: Denis Auroux Lectures: TT 12:30-2:00pm, Room 155 Dwinelle Course Control Number: 53978 Office: 817 Evans Office Hours: TBA Prerequisites: Math 1B Required Text: Stewart, Multivariable Calculus, (custom edition). Recommended Reading: Syllabus: see course web page Course Webpage: http://math.berkeley.edu/~auroux/53f10/ Grading: homework and quizzes 25%; two midterms 25% each; final exam 25%; lowest midterm can be dropped and replaced by final exam grade. There will be no make-up exams. Grading policy allows you to miss one midterm, but check your schedule to make sure you have no conflict for the final exam. Homework: Homework will be assigned weekly. Comments: Math 53 - Section 2 - Multivariable Calculus Instructor: L. Craig Evans Lectures: MWF 12:00-1:00pm, Room 155 Dwinelle Course Control Number: 54017 Office: 1033 Evans Office Hours: TBA Prerequisites: Required Text: Stewart, Multivariable Calculus, (custom edition). Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 54 - Section 1 - Linear Algebra & Differential Equations Instructor: Olga Holtz Lectures: TT 2:00-3:30pm, Room 155 Dwinelle Course Control Number: 54056 Office: 851 Evans Office Hours: TuTh 10:00-11:00am and by appt. Prerequisites: Math 1B Required Text: 1. Lay, Linear Algebra, Custom Berkeley Edition, Addison-Wesley. 2. Nagel, Saff & Snider, Fundamentals of Differential Equations, Custom Berkeley Edition, Addison-Wesley. Recommended Reading: Syllabus: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations. Course Webpage: http://www.cs.berkeley.edu/~oholtz/54/ Grading: 30% homework, 30% midterm, 40% final Homework: Homework will be assigned on the web once a week, due a week later. Comments: Math 54 - Section 2 - Linear Algebra & Differential Equations Instructor: Dan-Virgil Voiculescu Lectures: MWF 3:00-4:00pm, Room 105 Stanley Course Control Number: 54095 Office: 783 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math H54 - Section 1 - Linear Algebra & Differential Equations Instructor: Staff Lectures: MWF 3:00-4:00pm, Room 71 Evans Course Control Number: 54128 Office: Evans Office Hours: TBA Prerequisites: Math 1B. Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 55 - Section 1 - Discrete Mathematics Instructor: Lauren Williams Lectures: MWF 11:00-12:00pm, Room 10 Evans Course Control Number: 54134 Office: 913 Evans Office Hours: F 12:00pm-1:00pm or by appointment Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B is recommended but not required. Freshman 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, 6th Edition. Recommended Reading: 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 science and engineering disciplines. Course Webpage: http://math.berkeley.edu/~williams/55-fall10.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. Comments: Math 104 - Section 1 - Introduction to Analysis Instructor: Alexandre Chorin Lectures: MWF 12:00-1:00pm, Room 9 Evans Course Control Number: 54218 Office: 911 Evans Office Hours: Prerequisites: Math 53 and 54. Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 2 - Introduction to Analysis Instructor: Christopher Manon Lectures: MWF 3:00-4:00pm, Room 75 Evans Course Control Number: 54221 Office: 1067 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 3 - Introduction to Analysis Instructor: Michael Klass Lectures: MWF 1:00-2:00pm, Room 332 Evans Course Control Number: 54224 Office: 319 Evans Office Hours: TBA Prerequisites: Required Text: Rudin, Principles of Mathematical Analysis, McGraw-Hill; & Ross, Elementary Analysis: The Theory of Calculus, Springer. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 4 - Introduction to Analysis Instructor: Alexander Givental Lectures: TT 3:30-5:00am, Room 75 Evans Course Control Number: 54227 Office: 701 Evans Office Hours: TBA Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 5 - Introduction to Analysis Instructor: Benjamin Dodson Lectures: MWF 10:00-11:00am, Room 3109 Etcheverry Course Control Number: 54230 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 104 - Section 6 - Introduction to Analysis Instructor: Benjamin Stamm Lectures: TT 12:30-2:00pm, Room 6 Evans Course Control Number: 54233 Office: 705 Evans Office Hours: Mon 9:00am - 11:00am and Wed 8:00am - 10:00am Prerequisites: Math 53 and 54 Required Text: Ross, Elementary Analysis: The Theory of Calculus ISBN: 0-387-90459-X Recommended Reading: Syllabus: This course provides an introduction to real analysis. Covered topics: Real and rational numbers, sequences, continuity, sequences and series of functions, differentiation, integration. Course Webpage: http://math.berkeley.edu/~stamm/teaching/math104.html Grading: Homework assignments and quizzes (25%), Midterm Exam 1 (15%), Midterm Exam 2 (20%), Final Exam (40%). Homework: Weekly homework assignments will be posted on the course web page. Comments: Math H104 - Section 1 - Introduction to Analysis/Honors Instructor: Mariusz Wodzicki Lectures: MWF 12:00-1:00pm, Room 81 Evans Course Control Number: 54236 Office: 995 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 110 - Section 1 - Linear Algebra Instructor: Per-Olof Persson Lectures: MWF 1:00-2:00pm, Room 100 Lewis Course Control Number: 54239 Office: 1089 Evans Office Hours: TBA Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: Linear Algebra, 4th edition by Friedberg, Insel and Spence. Recommended Reading: Syllabus: Vector spaces. Linear transformations and matrices. Linear systems of equations. Determinants. Eigenvalues and eigenvectors. Inner product spaces. Self-adjoint, normal, and unitary maps. Course Webpage: http://persson.berkeley.edu/110 Grading: Homework assignments and quizzes (25%), Midterm Exam 1 (15%), Midterm Exam 2 (15%), Final Exam (45%). Homework: Weekly homework assignments will be posted on the course web page. Comments: Math H110 - Section 1 - Linear Algebra/Honors Instructor: Jenny Harrison Lectures: MWF 3:00-4:00pm, Room 101 Wurster Course Control Number: 54266 Office: 829 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 1 - Introduction to Abstract Algebra Instructor: STAFF Lectures: TT 8:00-9:30am, Room 71 Evans Course Control Number: 54269 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 2 - Introduction to Abstract Algebra Instructor: Ian Agol Lectures: TT 11:00-12:30pm, Room 6 Evans Course Control Number: 54272 Office: 921 Evans Office Hours: TBA Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th edition, Addison-Wesley. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 3 - Introduction to Abstract Algebra Instructor: Alexander Paulin Lectures: MWF 2:00-3:00pm, Room 71 Evans Course Control Number: 54275 Office: 887 Evans Office Hours: Prerequisites: Required Text: I will not be using a single textbook. I'll give out a complete set of course notes at the beginning. Recommended Reading: Classic Algebra - P.M. Cohn. It's at a higher standard than what we'll do but is the gold standard. I'll also suggest other books to look at at the beginning of the course. Syllabus: Basics of group, ring and field theory. I'll be more precise closer to the time. Course Webpage: Grading: Final: 50%. Two midterms: 15% each. Homework: 20% Homework: Eight or so problems each week. Comments: I'll give out hand written notes at the start of each lecture so you can concentrate on following the material rather than writing the whole time. Math 113 - Section 4 - Introduction to Abstract Algebra Instructor: Ian Agol Lectures: TT 3:30-5:00pm, Room 71 Evans Course Control Number: 54278 Office: 921 Evans Office Hours: TBA Prerequisites: Math 54 or a course with equivalent linear algebra content. Required Text: John B. Fraleigh, A First Course in Abstract Algebra, 7th edition, Addison-Wesley. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 113 - Section 5 - Introduction to Abstract Algebra Instructor: Kate Poirier Lectures: MWF 9:00-10:00am, Room 71 Evans Course Control Number: 54281 Office: 877 Evans Office Hours: TBA Prerequisites: Required Text: Dummit and Foote, Abstract Algebra, 3rd edition (2nd edition is also okay) Recommended Reading: Artin, Algebra Syllabus: Groups, rings and fields Course Webpage: TBA Grading: Homework (20%), two midterm exams (20% each), and a final exam (40%) Homework: Five to ten questions will be assigned and due each week. Comments: Math 115 - Section 1 - Number Theory Instructor: Martin Olsson Lectures: MWF 10:00-11:00am, Room 71 Evans Course Control Number: 54284 Office: 879 Evans Office Hours: TBA Prerequisites: Required Text: Niven, Zuckerman and Montgomery, An Introduction to the Theory of Numbers, Wiley, 5th edition. Recommended Reading: Syllabus: Divisibility, congruences, quadratic reciprocity and quadratic forms, simple continued fractions. Course Webpage: Grading: Based on homework, two midterms, and a final. Homework: There will be weekly homework. Comments: Math 121A - Section 1 - Math Tools For the Physical Sciences Instructor: John Neu Lectures: MWF 11:00-12:00pm, Room 70 Evans Course Control Number: 54287 Office: 1051 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 123 - Section 1 - Ordinary Differential Equations Instructor: John Neu Lectures: MWF 3:00-4:00pm, Room 2 Evans Course Control Number: 54290 Office: 1051 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 125A - Section 1 - Mathematical Logic Instructor: Alice Medvedev Lectures: MWF 3:00-4:00pm, Room 3 Evans Course Control Number: 54293 Office: TBA Evans Office Hours: TBA Prerequisites: Math 113 for two reasons. There will be many algebraic examples in this course. Most importantly, you are expected to be able to write clear, precise proofs. Required Text: Fundamentals of Mathematical Logic by Peter G. Hinman Recommended Reading: The textbook is chosen for clarity; it is a bit advanced. Logic for Mathematics and Computer Science by Stanley N. Burris may be a nice introductory supplement. Syllabus: The goal of this course is Godel's Completeness and Incompleteness theorems. The shortest path is sections 1.1-1.4, 2.1-2.5, 3.1-3.2, 3.5, and 4.1-4.6 of the textbook. I will supplement this with many more examples. If time permits, we will explore other parts of the first five chapters. The following two webpages are for similar courses I have taught in the past; I expect this one to be somewhere in-between. Course Webpage: http://www.math.uic.edu/~alice/math430F08/math430F08.html http://www.math.uic.edu/~alice/math502F07/math502F07.html Grading: Homeworks, 2 to 3 exams, and 0 to 1 projects will be combined in some way. Homework: There will be weekly homework assignments. There may also be a larger collaborative project. Comments: Further information coming in late July. Math 126 - Section 1 - Intro Partial Diff Equations Instructor: L. Craig Evans Lectures: MWF 10:00-11:00am, Room 75 Evans Course Control Number: 54296 Office: 1033 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 128A - Section 1 - Numerical Analysis Instructor: Ming Gu Lectures: MWF 1:00-2:00pm, Room 277 Cory Course Control Number: 54299 Office: 861 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 142 - Section 1 - Elementary Algebraic Topology Instructor: Marc Rieffel Lectures: TT 9:30-11:00am, Room 71 Evans Course Control Number: 54323 Office: 811 Evans Office Hours: TBA Prerequisites: Math 104 and 113 or equivalent. Required Text: M. A. Armstrong, Basic Topology. Recommended Reading: Syllabus: Topology considers how the points of "spaces" hang together, while ignoring distances. (Distances can be considered the concern of "geometry", as studied in Math 140, which will be offered next Spring.). Thus the surface of a donut is topologically "the same" as the surface of a one-handled teacup. General relativity tells us that distances in our universe change with time, as masses warp space while they move. But maybe in a global way the topology of our universe does not change. In the early weeks of the course we will discuss how to define "topological spaces" so that all of this has a precise meaning. The considerations strongly involve the ideas of continuity, so the material of Math 104 will be quite important. How then to prove such things as "the surface of a donut is topologically not the same as the surface of a ball", as well as many less intuitive facts? Algebraic topology provides the main tools for handling this and many related questions. These tools consist of various methods for systematically attaching algebraic objects (groups and rings as in Math 113, and the homomorphisms between them) to topological spaces and the continuous functions between them. Then one can compute with these algebraic objects to try to answer the topological questions. The latter part of the course will consider some elementary versions of these tools, and apply them to surfaces and other spaces. In my lectures I will try to give well-motivated careful presentations of the material. I encourage class discussion. Course Webpage: Grading: The final examination will take place on Tuesday December 14, 2010, 3-6 PM. It will count for 50% of the course grade. There will be no early or make-up final examination. There will be two midterm examinations, which will each count for 20% of the course grade. Make-up midterm exams will not be given; instead, if you tell me ahead of time that you must miss a midterm exam, then the final exam and the other midterm exam will count more to make up for it. If you miss a 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 and the other midterm exam count more to make up for it. If you miss both midterm exams the circumstances will need to be truly extraordinary to avoid a score of 0 on at least one of them. Homework: Homework will be assigned at nearly every class meeting, and be due the following class meeting. Students are strongly encouraged to discuss the homework and the course content with each other, but each student should write up their own solutions, reflecting their own understanding, to turn in. Comments: Students who need special accomodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance of each examination what specific accomodation they need, so that I will have enough time to arrange it. The above procedures are subject to change. This course description was last updated on 07/08/2010. Math 143 - Section 1 - Elementary Algebraic Geometry Instructor: John Lott Lectures: MWF 12:00-1:00pm, Room 70 Evans Course Control Number: 54326 Office: 897 Evans Office Hours: W F 3-4PM Prerequisites: Math 113 Required Text: 1. Reid, Undergraduate Commutative Algebra 2. Reid, Undergraduate Algebraic Geometry Recommended Reading: Syllabus: Algebraic geometry looks at the relationship between the geometry of solution sets of equations, i.e. vanishing sets of polynomial equations, and the algebraic properties of the equations. We will begin with an introduction to commutative algebra and then proceed to algebraic geometry proper. Course Webpage: http://www.math.berkeley.edu/~lott/math143.html Grading: 2/3 homework, 1/3 final Homework: See the course webpage. Comments: Math 152 - Section 1 - Math Of the Secondary School Curriculum Instructor: Ken Ribet Lectures: TT 11:00-12:30pm, Room 72 Evans Required discussion section: W 11AM-12PM, 321 Haviland Course Control Number: 54329 and 54332 (sign up for both) Office: 885 Evans Office Hours: To be announced Prerequisites: Math 151; also Math 54 and Math 113, or the equivalent Required Text: Notes by H. Wu, "Mathematics of the Secondary School Curriculum, II" Recommended Reading: Syllabus: Complex numbers and Fundamental Theorem of Algebra, roots and factorizations of polynomials, Euclidean geometry and axiomatic systems, basic trigonometry. Course Webpage: http://math.berkeley.edu/~ribet/152/; this web page does not yet exist, but it will be created over the summer. Grading: My usual mix is to have two midterms that count 15% each, a final exam that is worth roughly 50% of the grade, and a homework/quiz component for the remaining 20%. I may adjust this mix a bit after consulting with previous instructors of Math 151 and Math 152. Homework: My impression is that this course has a fair bit of homework and that the 1-hour section on Wednesday is used for discussions about past and current homework assignments. Comments: I have never taught a course even remotely like this before. I will rely on your good will and hope that we all have a great time together. Math 170 - Section 1 - Mathematical Methds for Optimization Instructor: Ming Gu Lectures: MWF 11:00-12:00pm, Room 47 Evans Course Control Number: 54335 Office: 861 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 1 - Complex Analysis Instructor: Vera Serganova Lectures: TT 11:00-12:30pm, Room 71 Evans Course Control Number: 54338 Office: 709 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 2 - Complex Analysis Instructor: Paul Vojta Lectures: MWF 9:00-10:00am, Room 75 Evans Course Control Number: 54341 Office: 883 Evans Office Hours: TBD Prerequisites: Math 104 Required Text: Brown & Churchill, Complex variables and applications, 8th edition Recommended Reading: None. Syllabus: The course will cover the first seven chapters of the textbook, and parts of Chapters 8 and 9. Course Webpage: http://math.berkeley.edu/~vojta/185.html Grading: Midterms, 15% and 20%; homework 30%; final exam 35% Homework: Homework will be assigned weekly. Comments: This is a basic introductory course in complex analysis, including analytic (holomorphic) functions, derivatives, elementary functions, contour integrals, power series, residues and applications of residues, linear fractional transformations, and a little bit on conformal mappings. I tend to follow the book rather closely, but try to give interesting examples. Math 185 - Section 3 - Complex Analysis Instructor: Benjamin Dodson Lectures: MWF 8:00-9:00am, Room 75 Evans Course Control Number: 54344 Office: Evans Office Hours: Prerequisites: Math 104 Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 185 - Section 4 - Complex Analysis Instructor: Benjamin Stamm Lectures: TT 8:00-9:30am, Room 75 Evans Course Control Number: 54347 Office: 705 Evans Office Hours: Mon 9:00am - 11:00am and Wed 8:00am - 10:00am Prerequisites: Math 104 Required Text: Brown & Churchill, Complex Variables and Applications, 8th edition. Recommended Reading: Syllabus: This course provides an introduction to complex analysis. Covered topics: Complex numbers, analytic functions, elementary functions, integrals, series, residues and poles, applications of residues. Course Webpage: http://math.berkeley.edu/~stamm/teaching/math185.html Grading: Homework assignments and quizzes (25%), Midterm Exam 1 (15%), Midterm Exam 2 (20%), Final Exam (40%). Homework: Weekly homework assignments will be posted on the course web page. Comments: Math 191 - Section 1 - Advanced Problem Solving Instructor: Olga Holtz Lectures: TT 3:30-5:00pm, Room 81 Evans Course Control Number: 54350 Office: 821 Evans Office Hours: TuTh 10:00-11:00am and by appt. Prerequisites: Math 16A-B, 53, 54, 55, or equivalent background. Required Text: Lozansky and Rousseau; Winning solutions. Problem Books in Mathematics. Springer-Verlag, New York, 1996. ISBN 0-387-94743-4 Recommended Reading: 1. Gleason, Greenwood, and Kelly; The William Lowell Putnam Mathematical Competition. Problems and solutions: 1938--1964. Mathematical Association of America, Washington, D.C., 1980. ISBN 0-88385-428-7 2. The William Lowell Putnam mathematical competition. Problems and solutions: 1965--1984. Edited by Alexanderson, Klosinski and Larson. Mathematical Association of America, Washington, DC, 1985. ISBN 0-88385-441-4 3. Kedlaya, Poonen, and Vakil; The William Lowell Putnam Mathematical Competition, 1985--2000. Problems, solutions, and commentary. MAA Problem Books Series. ISBN 0-88385-807-X Syllabus: Mathematical induction. Integer and prime numbers. Congruence. Rational and irrational numbers. Complex numbers. Progressions and sums. Diophantine equations. Quadratic reciprocity. Basic theorems and techniques from algebra. Polynomials. Inequalities. Extremal problems. Limits. Integrals. Series. Differential equations. Combinatorial counting. Recurrence relations. Generating functions. The inclusion-exclusion principle. The pigeonhole principle. Combinatorial averaging. Course Webpage: http://www.cs.berkeley.edu/~oholtz/191/ Grading: based on homework and class participation. Homework: Homework will be assigned on the web once a week, due a week later. Comments: This is an advanced class intended to improve students' problem solving skills. A sub-goal of this class is to prepare UC-Berkeley competitors for the Putnam competition in December 2010. The class will be taught in an informal, problem-oriented way. Homework problems will require hard work, ingenuity, and good mathematical writing. Math 191 - Section 2 - Introduction to Research via Combinatorial Game Theory Instructor: Dan Gardiner Lectures: TT 12:30-2pm, Room 740 Evans Course Control Number: Office: 1062 Evans Office Hours: TBD Prerequisites: Ability to write proofs and willingness to work on open-ended problems a must. Math 55 required. Math 113, at least concurrently, preferred; if not, at least one other 100 level Math course all but required. Required Text: Recommended Reading: Syllabus: Combinatorial games are two-player, perfect information games like Chess or Go. This class will use selected topics from the theory of these games to give students experience doing research-type mathematics. Students will learn various techniques from this theory and then apply this knowledge to open-ended projects --- the analysis of a particular game, for example, or an investigation of patterns that emerge in families of games. A highlight of the course will be an introduction to the surreal number system and its role in the theory. Course Webpage: http://sites.google.com/site/math191fall2010/ 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. For more specific information, see the course webpage. Homework: 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. Math 202A - Section 1 - Intro. To Topology & Analysis Instructor: Atilla Yilmaz Lectures: MWF 10:00-11:00am, Room 70 Evans Course Control Number: 54461 Office: 796 Evans Office Hours: TBA Prerequisites: Math 104 or equivalent, plus familiarity with basic set theory and linear algebra. Required Text: G. B. Folland, Real Analysis, Second Edition, Wiley Interscience, 1999. Recommended Reading: H. L. Royden, Real Analysis, Third Edition, Prentice Hall, 1988. Syllabus: Chapters 1-5 of Folland. (Measures; integration; signed measures and differentiation; point set topology; elements of functional analysis.) Additional topics if time permits. Course Webpage: http://math.berkeley.edu/~atilla/ Grading: 40% homework, 20% midterm, 40% final. (Exams will be in class.) Homework: Weekly homework sets will be posted to the webpage. Comments: Students might want to read Chapter 0 of Folland before the first lecture. Math 204 - Section 1 - Ordinary & Partial Differential Equations Instructor: Fraydoun Rezakhanlou Lectures: MWF 11:00-12:00pm, Room 5 Evans Course Control Number: 54464 Office: 803 Evans Office Hours: Prerequisites: Math 104 Required Text: Typed notes will be distributed in the class. Recommended Reading: Syllabus: This course reviews some fundamental concepts and results in the theory of ordinary differential equations and dynamical systems. Here is an outline of the course: 1. Fundamental existence theorem for ordinary differential equations. 2. Linear systems and Floquet theory. 3. Poincare-Bendixson Theorem. 4. Rotations numbers and twist maps. 5. Chaotic systems and horseshoes. Course Webpage: Grading: Weakly homework assignments and a final take-home exam. Homework: Comments: Math 205 - Section 1 - Theory of Functions of a Complex Variable Instructor: Dan-Virgil Voiculescu Lectures: MWF 12:00-1:00pm, Room 39 Evans Course Control Number: 54467 Office: 783 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 206 - Section 1 - Banach Algebras & Spectral Theory Instructor: Steve Evans Lectures: TT 11:00-12:30pm, Room 101 Wheeler Course Control Number: 54470 Office: 329 Evans Office Hours: TuTh 2:00-3:00pm Prerequisites: Math 202A-202B, or the equivalent. Required Text: None Recommended Reading:
Course Webpage: See bSpace. Grading: Homework: Comments: Math 214 - Section 1 - Differential Manifolds Instructor: Jonathan Dahl Lectures: TT 9:30-11:00am, Room 85 Evans Course Control Number: 54473 Office: TBA Office Hours: TBA Prerequisites: Math 202A Required Text: Michael Spivak, A Comprehensive Introduction to Differential Geometry, Volume 1, 3rd edition, Publish or Perish. Recommended Reading: Syllabus: Smooth manifolds and maps, tangent and normal bundles. Sard's theorem and transversality, Whitney embedding theorem. Morse functions, differential forms, Stokes' theorem, Frobenius theorem. Basic degree theory. Flows, Lie derivative, Lie groups and algebras. Course Webpage: Grading: 50% homework, 50% take-home final exam. Homework: Homework will be assigned roughly every 1-2 weeks. Comments: Math 215A - Section 1 - Algebraic Topology Instructor: Christian Zickert Lectures: MWF 10:00-11:00am, Room 61 Evans Course Control Number: 54476 Office: 1053 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math C218A - Section 1 - Probability Theory Instructor: David Aldous Lectures: MW 5:00-6:30pm, Room 334 Evans Course Control Number: 54479 Office: 351 Evans Office Hours: TBA Prerequisites: Required Text: Durrett, Probability Theory and Examples, 3rd Edition. Recommended Reading: Syllabus: Course Webpage: www.stat.berkeley.edu/~aldous/205A/index.html Grading: Homework: Comments: For up to date information see the course webpage. Math 219 - Section 1 - Dynamical Systems Instructor: Maciej Zworski Lectures: TT 12:30-2:00pm, Room 81 Evans Course Control Number: 54482 Office: 801 Evans Office Hours: Tu 2:10-3:30pm Prerequisites: Firm background in real and complex analysis: Math 202AB. Required Text: Recommended Reading: On-line lecture notes by F. Rezakhanlou and by S. Nonnenmacher. Syllabus: The course provides an introduction to dynamical systems with an emphasis on Hamiltonian systems and chaotic dynamics. Topics will include: 1. Introduction and examples of dynamical systems, 2. Complete integrability, Liouville-Arnold theorem, 3. Invariant measures and ergodic theory, 4. Recurrance in topological dynamics, periodic orbits, 5. Weak and strong mixing, 6. Uniformly hyperbolic systems, 7. Transfer operators. Course Webpage: Grading: The grade will be based on a final project. Homework: Comments: Math 221 - Section 1 - Advanced Matrix Computations Instructor: James Demmel Lectures: TT 9:30-11:00am, Room 31 Evans Course Control Number: 54485 Office: 831 Evans Office Hours: Prerequisites: Required Text: Demmel, Applied Numerical Linear Algebra. Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 222A - Section 1 - Partial Differential Equations Instructor: Daniel Tataru Lectures: MWF 1:00-2:00pm, Room 71 Evans Course Control Number: 54488 Office: 841 Evans Office Hours: M 9:30-11:00am and by appointment. Prerequisites: 202A or equivalent Required Text: Partial Differential Equations, by L.C. Evans, and Partial Differential Equations, vol. 1, by L. Hormander. Recommended Reading: Syllabus: This is the first semester of a two semester sequence in Partial Differential Equations. It is assumed you are familiar with undergraduate real analysis and have some knowledge of ordinary differential equations. For the second half of the semester some measure theory is also needed. Complex analysis is useful but not required. The course roughly follows at first Hormander (theory of distributions and Fourier Analysis) and continues the first part and the beginning of the second part Evans but with various omissions/additions. Topics to be covered include (in this order): • Theory of distributions • Fourier analysis • Linear first order equations • The Laplace equation • The heat equation • The Schrodinger equation • The wave equation • Nonlinear first order equations • Sobolev spaces Course Webpage: Grading: Homework, end of term project Homework: Comments: Math C223A - Section 1 - Stochastic Processes Instructor: E. Mossel Lectures: TT 5:00-6:30pm, Room 241 Cory Course Control Number: 54490 Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 224A - Section 1 - Mathematical Methods For the Physical Sciences Instructor: Alberto Grunbaum Lectures: TT 8:00-9:30am, Room 81 Evans Course Control Number: 54491 Office: 903 Evans Office Hours: Prerequisites: Required Text: Stakgold, I., Green's Functions and Boundary Value Problems Recommended Reading: Syllabus: The material in this class could be described as "functional analysis with applications" or "infinite dimensional linear algebra". It will include a discussion of Fourier analysis, distributions as well as the spectral analysis that goes with operators similar to the continuous and discrete Laplacian, i.e. Jacobi matrices and the corresponding orthogonal polynomials on the real line. All of this is used in studying problems such as heat diffusion as well as random walks. We will also discuss some of the more recent and analogous developments involving unitary operators (as the one that appear in dealing with the classical wave equation or in quantum mechanics) and Szego's theory of orthogonal polynomials in the unit circle and CMV matrices. If time allows it we will make a connection with Quantum Random Walks, a subject that has attracted the attention of workers in computer science. chemistry and physics. Course Webpage: Grading: Homework: Comments: Math 225A - Section 1 - Metamathematics Instructor: Thomas Scanlon Lectures: TT 2:00-3:30pm, Room 35 Course Control Number: 54494 Office: 723 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 228A - Section 1 - Numerical Solutions of Differential Equations Instructor: Per-Olof Persson Lectures: MWF 10:00-11:00pm, Room 9 Evans Course Control Number: 54497 Office: 1089 Evans Office Hours: TBA Prerequisites: Math 128A or equivalent knowledge of basic numerical analysis, some MATLAB programming experience. Required Text: TBD Recommended Reading: A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Second Edition, Cambridge University Press, 2008. ISBN 978-0521734905. E. Hairer, S. P. Norsett and G. Wanner, Solving ordinary differential equations, Second Edition (2 vols.), Springer, 2008. ISBN 978-3540566700, 978-3540604525. R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, SIAM, 2007. ISBN 978-0-898716-29-0. Syllabus: Theory and practical methods for numerical solution of differential equations. Runge-Kutta and multistep methods, stability theory, stiff equations, boundary value problems. Finite element methods for boundary value problems in higher dimensions. Direct and iterative linear solvers. Discontinuous Galerkin methods for conservation laws. Course Webpage: http://persson.berkeley.edu/228A Grading: Grades will be based entirely on the problem sets. Homework: 7 problem sets. Comments: Math 236 - Section 1 - Metamathematics of Set Theory Instructor: John Steel Lectures: TT 3:30-5:00pm, Room 31 Evans Course Control Number: 54500 Office: 717 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 242 - Section 1 - Symplectic Geometry Instructor: Denis Auroux Lectures: TT 3:30-5:00pm, Room 35 Evans Course Control Number: 54503 Office: 817 Evans Office Hours: TBA Prerequisites: Math 214 (Differentiable Manifolds) and 215A (Algebraic Topology) Required Text: McDuff and Salamon, Introduction to symplectic topology, Oxford Mathematical Monographs Recommended Reading: Syllabus: About 2/3 of the course will be standard material (symplectic manifolds, symplectomorphisms, submanifolds, Darboux and Moser theorems, contact manifolds, almost-complex structures, Kähler manifolds, Hamiltonian group actions and quotients, ...). The rest of the course will consist of an introduction to Floer homology, and to various constructions of symplectic manifolds. Course Webpage: http://math.berkeley.edu/~auroux/242f10 Grading: Based on homework. Homework: Every two weeks. Comments: Math 250A - Section 1 - Groups, Rings & Fields Instructor: Arthur Ogus Lectures: MWF 11:00-12:00pm, Room 75 Evans Course Control Number: 54509 Office: 877 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 254A - Section 1 - Number Theory Instructor: Robert Coleman Lectures: MWF 12:00-1:00pm, Room 4 Evans Course Control Number: 54512 Office: 901 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 256A - Section 1 - Algebraic Geometry Instructor: Richard Borcherds Lectures: TT 11:00-12:30pm, Room 81 Evans Course Control Number: 54515 Office: 927 Evans Office Hours: TuTh 3:30-5:00 Prerequisites: 250A-250B (250B is not essential) Required Text: Hartshorne, Algebraic Geometry Recommended Reading: Syllabus: Affine and projective algebraic varieties. Theory of schemes and morphisms of schemes. Smoothness and differentials in algebraic geometry. Coherent sheaves and their cohomology. Riemann-Roch theorem and selected applications. Sequence begins fall. e will cover Hartshorne chapters 1-3. The goal is to learn how to calculate the cohomology of a coherent sheaf over a scheme. Course Webpage: http://math.berkeley.edu/~reb/256A Grading: Possibly based on homework. Homework: Assigned on course web page. Comments: See course web page for updates. Math 261A - Section 1 - Lie Groups Instructor: Mark Haiman Lectures: MWF 10:00-11:00am, Room 45 Evans Course Control Number: 54521 Office: 855 Evans Office Hours: W 1:30-3:00 or by appointment Prerequisites: Background in algebra and topology equivalent to 202A and 250A. Any differential geometry needed will be reviewed in the lectures. Required Text: None Recommended Reading: See course webpage. Syllabus: See course webpage. Course Webpage: http://math.berkeley.edu/~mhaiman/math261A-fall10 Grading: Based on homework. Homework: Problems assigned as the course proceeds. Comments: Math 273F - Section 1 - Topics in Numerical Analysis Instructor: John Strain Lectures: TT 11:00-12:30pm, Room 7 Evans Course Control Number: 54524 Office: 1099 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments: Math 275 - Section 2 - Topics in Applied Mathematics Instructor: Bernd Sturmfels Lectures: TT 8:00-9:30am, Room 6 Evans Course Control Number: 54530 Office: 925 Evans Office Hours: Tu 10-11, We 11-12, and by appointment. Prerequisites: Optimization and Algebraic Geometry at the undergraduate level (e.g. Math 170 and Math 143). Prior experience with mathematical software. Required Text: The material will be drawn from several books and articles, to be listed on the course webpage. Recommended Reading: Syllabus: Convexity, Semidefinite Programming, Linear Matrix Inequalities, Polynomial Optimization, Computational Algebra, and Real Algebraic Geometry. Course Webpage: www.math.berkeley.edu/~bernd/math275.html Grading: The course grade will be based on homework and a final term project. Homework: Weekly homework will be assigned during the first half of the semester. Comments: During the second half of the semester, students will primarily work on their course projects. Math 275 - Section 4 - Topics in Applied Mathematics Instructor: Richard Borcherds Lectures: TT 2:00-3:30pm, Room 75 Evans Course Control Number: 54536 Office: 927 Evans Office Hours: TuTh 3:30-5:00 Prerequisites: None. Required Text: None. We will use notes that should be available on the course web page. Recommended Reading: Syllabus: This course will explain quantum field theory, including topics such as renormalization, regularization, BRST symmetry, and so on, in a mathematically rigorous way that is general enough to cover physically realistic perturbative models. Course Webpage: http://math.berkeley.edu/~reb/275 Grading: Homework: Comments: See course web page for updates. Math 275 - Section 5 - Topics in Applied Mathematics Instructor: Fraydoun Reakhanlou Lectures: MWF 9:00-10:00am, Room 81 Evans Course Control Number: 54538 Office: 803 Evans Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: The main goal of this course is to give a detailed presentation of some recent developments on the universality conjectures for random matrices and random growth models. Wigner proposed to study the statistics of eigenvalues of large random matrices as a model for the energy levels of heavy nuclei. For a Wigner ensemble we take a large symmetric or hermitian N by N matrix [h_] where ${h_:ile j}$ are independent identically distributed random variables of mean zero and variance 1/N. The central question for Wigner ensemble is the universality conjecture which asserts that the local statistics of the eigenvalues are independent of the distributions of the entries as $N$ gets large. This local statistics can be calculated when the entry distribution is chosen to be Gaussian. The density of eigenvalues in large $N$ limit is given by the celebrated Wigner semicircle law in the interval [-2,2]. Joint distribution of eigenvalues away from the edges $pm 2$ has a determinantal structure and is obtained from a sine kernel. The sine kernel is replaced with the Airy kernel near the edges $pm 2$ after a rescaling of the eigenvalues. The largest eigenvalue obeys a different universality law and is governed by the Tracy-Widom distribution. It is a remarkable fact that many of the universality laws discovered in the theory of random matrices appear in a variety of different models in statistical mechanics. A prominent example is the planar random growth models which belong to Kardar-Parisi-Zhang universality class. In these models, a stable phase grows into an unstable phase through aggregation. The rough boundary separating different phases is expected to obey a central limit theorem and its universal law is conjectured to be the Tracy-Widom distribution. This has been rigorously established for two models; simple exclusion process and Hammersley process. Course Webpage: Grading: Homework: There will be some homework assignments. Comments: Math 276 - Section 1 - Topics In Topology Instructor: Michael Hutchings Lectures: TT 9:30-11:00am, Room 81 Evans Course Control Number: 54539 Office: 923 Evans Office Hours: TBA Prerequisites: algebraic topology, differential geometry Required Text: Kronheimer-Mrowka: Monopoles and three-manifolds Recommended Reading: Additional references will be provided during the course. Syllabus: The goal of the course is to understand the basic ideas of Seiberg-Witten Floer theory and its applications to low-dimensional topology. At the beginning of the course, after an introductory overview, we will slowly and gently review the background necessary for Seiberg-Witten theory. Then we will try to understand as much as we can (but certainly not all) of Kronheimer Mrowka's book. Finally we will discuss applications. At the end of the course there will be opportunities for (optional) student presentations. Course Webpage: to be linked from verb=math.berkeley.edu/~hutching= Grading: Homework: Comments: Math 277 - Section 1 - Topics In Differential Geometry Instructor: John Lott Lectures: MWF 2:00-3:00pm, Room 81 Evans Course Control Number: 54542 Office: 897 Evans Office Hours: W F 3-4PM Prerequisites: Math 240 or equivalent Required Text: Villani, Topics in Optimal Transportation. Recommended Reading: Villani, Optimal Transport : Old and New. Syllabus: Optimal transport is the study of the most efficient way to transport dirt from a "before" pile to an "after" pile. The problem was first posed by Monge in 1781. One can pose the problem on a quite general class of spaces. In recent years, it has turned out that understanding optimal transport leads to a good notion of Ricci curvature bounds for metric-measure spaces. In the class we will go through the theory of optimal transport on Euclidean space and Riemannian manifolds, as presented in Villani's book. We will then discuss optimal transport on length spaces, along with the relationship between optimal transport and Gromov-Hausdorff limits. Course Webpage: http://www.math.berkeley.edu/~lott/math277.html Grading: The grade will be based on homework. Homework: Occasional homework problems will be given. Comments: Math 279 - Section 1 - Calderon's Inverse Problem and Cloaking Instructor: Lectures: TT 9:30-11:00am, Room 55 Evans Course Control Number: 54544 Office: Office Hours: TBA Prerequisites: A course in Real Analysis, including the Fourier transform, at the level of G. Folland's book on Real Analysis. An introduction to PDE course is desirable but not necessary. Required Text: 1) Notes by M. Salo on Calderon's problem: http://www.rni.helsinki.fi/~msa/teaching/calderon/calderon_lectures.pdf 2) The book in preparation on Calderon's problem by J. Feldman, M. Salo and G. Uhlmann. A preview can be found at http://www.math.ubc.ca/ feldman/ibook/ This is being updated and notes will be distributed. 3) A. Greenleaf, Y. Kurylev, M. Lassas, G. Uhlmann: Invisibility and Inverse Problems. Bulletin of the American Mathematical Society 46 (2009), 55-97. Recommended Reading: Syllabus: Calderon's inverse problem is an example of an inverse boundary value problem for a partial differential equation (PDE). In general terms the physical situation at hand is modeled by a PDE. The inverse boundary value problem is to determine the internal parameters of a medium (the coefficients of the PDE) given some information at the boundary of the medium. Calderon's problem, also called Electrical Impedance Tomography, consists in the determination of the electrical conductivity of a body by making current and voltage measurements at the boundary. We will discuss progress that has been made in understanding this problem especially in the three dimensional case. We will also apply the methods developed to study other inverse problems including optical tomography and thermoacoustic and photoacoustic tomography. We will also discuss the subject of cloaking and invisibility. The question is how to cloak objects to make them invisible to different types of waves including electromagnetic waves, acoustic and quantum waves. There has been recent theoretical and practical exciting developments in this subject and we will discuss the mathematics behind these developments for the case of electrostatics. Course Webpage: Grading: Homework: Comments: Math 300 - Section 1 - Instructor: Staff Lectures: 0:00-00:00am, Room 0 Course Control Number: Office: Office Hours: Prerequisites: Required Text: Recommended Reading: Syllabus: Course Webpage: Grading: Homework: Comments:
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