Spring 2017

Prerequisites: 1A

Description: Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

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Prerequisites: Continuation of 10A

Description: Elementary combinatorics and discrete probability theory. Introduction to graphs, matrix algebra, linear equations, difference equations, and differential equations.

Office: 785 Evans

Office Hours: Mondays 11-12pm, Wednesdays 12:30-2:30pm

Required Text: No textbook required.  Course notes will be provided.

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Course Webpage: https://math.berkeley.edu/~talaska/10B.php

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. Consult the mathematics department for details

Description: This sequence is intended for majors in the life and social sciences. Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions.

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Prerequisites: 16A

Description: Continuation of 16A. Application of integration of economics and life sciences. Differential equations. Functions of many variables. Partial derivatives, constrained and unconstrained optimization.

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Prerequisites: Three years of high school mathematics, plus satisfactory score on one of the following: CEEB MAT test, math SAT, or UC/CSU diagnostic examination

Description: Polynomial and rational functions, exponential and logarithmic functions, trigonometry and trigonometric functions. Complex numbers, fundamental theorem of algebra, mathematical induction, binomial theorem, series, and sequences.

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Prerequisites: Mathematics 1B

Description: Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

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Prerequisites: 1B

Description: Honors version of 53. Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

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Prerequisites: 1B

Description: 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.

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Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

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Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

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Prerequisites: Math 53 and 54

Description: Selected topics illustrating the application of mathematics to economic theory. This course is intended for upper-division students in Mathematics, Statistics, the Physical Sciences, and Engineering, and for economics majors with adequate mathematical preparation. No economic background is required.

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Prerequisites: 53 and 54

Description: The real number system. Sequences, limits, and continuous functions in R and R. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.

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Prerequisites: Calculus 1A-1B

Description: The concept of metric spaces. The real line and the Eucleadean spaces. Limit points, open and closed sets. Compactness. Convergence. Cauchy sequences. Uniform convergence. Continuous functions. Uniform continuity. Infinite series and tests for convergence.The Riemann integral.

Office Hours: Wednesday 10-11 a.m. or by appointment.

Required Text: Rudin " Principles of Math Analysis"

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Grading: The grade will be based 10 % on weekely homework, 25% on quizzes, 25% on a Midterm and 40% on a Final Exam.   

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Prerequisites: 53 and 54

Description: The real number system. Sequences, limits, and continuous functions in R and R. The concept of a metric space. Uniform convergence, interchange of limit operations. Infinite series. Mean value theorem and applications. The Riemann integral.

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Prerequisites: 54 or a course with equivalent linear algebra content

Description: Matrices, vector spaces, linear transformations, inner products, determinants. Eigenvectors. QR factorization. Quadratic forms and Rayleigh's principle. Jordan canonical form, applications. Linear functionals.

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Prerequisites: 54 or a course with equivalent linear algebra content

Description: 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.

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Prerequisites: 54 or a course with equivalent linear algebra content

Description: 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.

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Prerequisites: 54 or a course with equivalent linear algebra content

Description: 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.

Office: 751 Evans

Office Hours: Monday 10:00-11:00, 4:00-5:00, Wednesday 1:00-2:00

Required Text: Dummit & Foote, Abstract Algebra, 3rd edition

Recommended Reading: Homework 20% + Midterm 1 20% + Midterm 2 20% + Final 40%.

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Homework: due weekly on Wednesday 3pm

Course Webpage: http://math.berkeley.edu/~hongbins/m113s17.html

Prerequisites: 54 or a course with equivalent linear algebra content

Description: Honors section corresponding to 113. Recommended for students who enjoy mathematics and are willing to work hard in order to understand the beauty of mathematics and its hidden patterns and structures. Greater emphasis on theory and challenging problems.

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Prerequisites: 53 and 54

Description: Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems.

Office: 883 Evans

Office Hours: TBD

Required Text: Niven, Zuckerman, Montgomery, An introduction to the Theory of Numbers, Wiley, 5th edition

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Grading: Homework 30%, midterms 15% and 20%, final exam, 35%.

Homework: Due weekly

Course Webpage: https://math.berkeley.edu/~vojta/115.html

Prerequisites: 53 and 54

Description: Intended for students in the physical sciences who are not planning to take more advanced mathematics courses. Special functions, series solutions of ordinary differential equations, partial differential equations arising in mathematical physics, probability theory.

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Prerequisites: 53 and 54

Description: Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, and solution of ordinary differential equations. Practice on the computer.

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Prerequisites: Math 110 and 128A or equivalent, and basic MATLAB skills.

Description: Iterative methods for linear systems, approximation theory, iterative solution of systems of nonlinear equations, approximation of eigenvalues and eigenvectors of matrices, applications to simple partial differential equations. Practice on the computer.

Office: Evans 811

Office Hours: Probably Tu 11-12, 1-2:15; Th 8:30-9:15

Required Text: Numerical Analysis, 2nd ed., Timothy Sauer, Pearson Pub., 2011

Comment: This is a mathematics course, and so the emphasis is on how to obtain effective methods for computation, and on analyzing when methods will, and will not, work well (in contrast to just learning algorithms and applying them). 

Grading:  There will be homework and there will be biweekly quizzes, which will each count for 10% of the course grade. There will be programming exercises and there will be one in-class midterm exam, which will each count for 20% of the course grade. There will be a final examination, which will count for 40% of the course grade.  

Makeup midterm exams will not be given; instead, if you tell me ahead of time that you must miss the midterm exam, then the final exam and the other components will count more to make up for it. If you do not tell me ahead of time, then you will need to bring me a doctor's note or equivalent to try to avoid a score of 0. There will be no early or make-up final examination. 

The final examination will take place on WEDNESDAY MAY 10 11:30-2:30 PM.

The midterm exam is expected to take place on Tuesday March 7, 9:30-11 AM.  

Students who need special accommodation for examinations should bring me the appropriate paperwork, and must tell me at least a week in advance of each exam what specific accommodation they need, so that I will have enough time to arrange it.

Homework: Homework will be assigned at almost every class meeting, due at the section meeting the following week. Students are encouraged to discuss the homework and programming assignments with each other, but each student must write their own solutions, reflecting their own understanding, and not copy solutions from anyone else. Even more, if students collaborate in working out solutions or computer code, or get specific help from others, they should explicitly acknowledge this help in the written work they turn in. This is general scholarly best practice. There is no penalty for acknowledging such collaboration or help.

Course Webpage: The link is at:   math.berkeley.edu/~rieffel

Prerequisites: 53, 54, and 55

Description: Functions computable by algorithm, Turing machines, Church's thesis. Unsolvability of the halting problem, Rice's theorem. Recursively enumerable sets, creative sets, many-one reductions. Self-referential programs. Godel's incompleteness theorems, undecidability of validity, decidable and undecidable theories.

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Prerequisites: 104 and 113

Description: The topology of one and two dimensional spaces: manifolds and triangulation, classification of surfaces, Euler characteristic, fundamental groups, plus further topics at the discretion of the instructor.

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Prerequisites: 151, 152 or permission of the instructor

Description: The real line and least upper bound, limit and decimal expansion of a number, differentiation and integration, Fundamental Theorem of Calculus, length and area, characterizations of sine, cosine, exp, and log.

Office: 985 Evans

Office Hours: TBA but will be on M, W and/or F

Required Text: Wu's Math 153 reader - will be available at Copy Central on Bancroft Avenue.

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Grading: There will be one or two midterms, a final exam, and weekly homework.

Homework: Weekly, mostly from the reader.

Course Webpage: we will have a bCourses site.

Prerequisites: 53 and 54

Description: Linear programming and a selection of topics from among the following: matrix games, integer programming, semidefinite programming, nonlinear programming, convex analysis and geometry, polyhedral geometry, the calculus of variations, and control theory.

Office: 925 Evans

Office Hours: Mondays 3-4:30pm; alternatively: before or after the lecture. 

Required Text:  Introduction to Linear Optimization by Dimitris Bertsimas and John N. Tsitsiklis, Athena Scientific 1997.

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Grading: Homework 35%, Midterm 30%, Term Paper 35%.

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Course Webpage: https://math.berkeley.edu/~bernd/math170.html

Prerequisites: Math 104. One might expect that 185 is developed in parallel to its real counterpart 104. In fact this expectation is false, and funderstanding "why" is one of the major goals of this course. So, taking the  two courses concurrently is a bad idea. 

Required Text: "Complex Function Theory" (http://www.ams.org/books/mbk/049/mbk049-endmatter.pdf ) by our own Prof. D. Sarason. It is based on the course taught at UC Berkeley, is only 160 pages long, and is ideally suitable for our aims.

Description: We will closely follow the text (see below) from the very definition of complex numbers, via a proof of the Fundamental Theorem of Algebra, to that of the Riemann Mapping Theorem (which identifies every proper simply-connected subset of the complex plane with the unit disk by means of continuous angle-preserving transformations). 

Office: 701 Evans

Office Hours: to be decided

Grading: based on weekly homework (30%), weekly 5-minute quizzes(30%), and the final exam (40%)

Homework: from the 2nd edition of the textbook.

Course Webpage: https://math.berkeley.edu/~giventh/18517.html (to be created by the beginning of the semester)

Prerequisites: 104

Description: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.

Office: Evans 905

Office Hours: TBA

Required Text: Sarason, Complex Function Theory. Spiegel et.al., Schaum's Outline of Complex Variables, 2nd ed. 

Recommended Reading: Needham, Visual Complex Analysis

Grading: Homework 25%, Exams 75% (in-class tests and a final exam)

Homework: Weekly assignments

Course Webpage: Math 185 Home

Prerequisites: 104

Description: Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.

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Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

Office: 

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Required Text: 

Recommended Reading: 

Grading: 

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Course Webpage: 

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Description: Berkeley Connect is a mentoring program, offered through various academic departments, that helps students build intellectual community. Over the course of a semester, enrolled students participate in regular small-group discussions facilitated by a graduate student mentor (following a faculty-directed curriculum), meet with their graduate student mentor for one-on-one academic advising, attend lectures and panel discussions featuring department faculty and alumni, and go on field trips to campus resources. Students are not required to be declared majors in order to participate.

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Prerequisites: 202A and 110

Description: Measure and integration. Product measures and Fubini-type theorems. Signed measures; Hahn and Jordan decompositions. Radon-Nikodym theorem. Integration on the line and in Rn. Differentiation of the integral. Hausdorff measures. Fourier transform. Introduction to linear topological spaces, Banach spaces and Hilbert spaces. Banach-Steinhaus theorem; closed graph theorem. Hahn-Banach theorem. Duality; the dual of LP. Measures on locally compact spaces; the dual of C(X). Weak and weak-* topologies; Banach-Alaoglu theorem. Convexity and the Krein-Milman theorem. Additional topics chosen may include compact operators, spectral theory of compact operators, and applications to integral equations.

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Grading: Letter grade.

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Prerequisites: 206

Description: Basic theory of von Neumann algebras. Density theorems, topologies and normal maps, traces, comparison of projections, type classification, examples of factors. Additional topics, for example, Tomita Takasaki theory, subfactors, group actions, and noncommutative probability.

Office: Evans 851

Office Hours: TBD

Required Text: None.

Recommended Reading: A Course in Operator Theory by John Conway, Theory of Operator Algebras, I by Masamichi Takesaki, and Notes on von Neumann Algebras by Vaughan F.R. Jones.

Grading: Letter grade.

Homework: In class presentation.

Course Webpage: Forthcoming.

Class has been moved to 740 Evans.

Prerequisites: 113 and point-set topology (e.g. 202A)

Description: We’ll first introduce interesting spaces, like manifolds (including knot and link complements) and CW-complexes. Then we’ll discuss the first tools to study qualitatives features of these spaces, namely fundamental group, higher homotopy and homology groups. We’ll end with proving some important consequences, e.g. invariance of dimension, the generalized Jordan curve theorem and the Lefschetz fixed point theorem. Throughout the class, we'll get sidetracked by interesting topics like cobordism groups, fibre bundles, de Rham cohomology, (higher) categories etc. 

Office: 703 Evans

Office Hours: Tu. 2:30 - 3:30 and by appointment

Required Text: Glen Bredon, Topology and Geometry

Recommended Reading: Allen Hatcher, Algebraic Topology

Grading: Letter grade depending on success in homework.

Homework: Weekly homework sessions, homework will be submitted in writing in groups of 2-3 students. 

Course Webpage: http://people.mpim-bonn.mpg.de/teichner/Math/AlgTop.html

Prerequisites: 105 or 202A

Description: 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.

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Prerequisites: 125B and 135

Description: Metamathematics of predicate logic. Completeness and compactness theorems. Interpolation theorem, definability, theory of models. Metamathematics of number theory, recursive functions, applications to truth and provability. Undecidable theories. Sequence begins fall.

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Grading: Letter grade.

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Prerequisites: 250A

Description: This is normally given as a course on commutative algebra, rather than multiplinear algebra. 

Office: 927 Evans Hall

Office Hours: Tu Th 9:30-11:00

Required Text: Commutative algebra by David Eisenbud

Recommended Reading: 

Grading: Letter grade.

Homework: See https://bcourses.berkeley.edu/courses/1456390

Course Webpage: https://bcourses.berkeley.edu/courses/1456390

Prerequisites: 256A

Description: 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.

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Prerequisites: Basic analysis, geometry, topology and algebra.

Description: Participants will give lectures on the theory of - and examples for - physically relevant factorization algebras. 

Office: 703 Evans

Office Hours: Tu. 2:30 - 3:30

Required Text: Kevin Costello and Owen Gwilliam, "Factorization Algebras in Quantum Field Theory”

Recommended Reading: Kevin Costello, “Renormalisation and the Batalin-Vilkovisky formalism”

David Ayala and John Francis, “Factorization homology of topological manifolds”

Grading: Offered for satisfactory/unsatisfactory grade only.

Homework: Prepare one or two lectures throughout the semester.

Course Webpage: http://people.mpim-bonn.mpg.de/teichner/Math/Hot-Topic.html

Prerequisites: Consent of instructor

Description: Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

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Grading: Letter grade.

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Prerequisites: Consent of instructor

Description:In this course we will discuss the relationship between the boundary regularity of the solutions to elliptic second order divergence form partial differential equations and the geometry of the boundary. While in the smooth setting this question uses tools from classical PDEs, in the non-smooth setting tools from harmonic analysis are needed to tackle the problem.

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Description: Topics in foundations of mathematics, theory of numbers, numerical calculations, analysis, geometry, topology, algebra, and their applications, by means of lectures and informal conferences; work based largely on original memoirs.

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Description: Topics in foundations of mathematics, theory of numbers, numerical calculations, analysis, geometry, topology, algebra, and their applications, by means of lectures and informal conferences; work based largely on original memoirs.

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Grading: Letter grade.

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