Spring 2019

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: The sequence Math 10A, Math 10B is intended for majors in the life sciences. Elementary combinatorics and discrete and continuous probability theory. Representation of data, statistical models and testing. Sequences and applications of linear algebra.

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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.

Office: 785 Evans

Office Hours: TBD

Required Text: Lial, Greenwell, and Ritchey.  See CalCentral for specific version.  Online access is NOT required.

Grading: This class will have regular homework, two midterms, and a final exam.  There may be other miscellaneous assignments.

Homework:  Webwork almost every class, plus written HW approximately weekly.

Course Webpage:  All files and announcements will be on bCourses.

Exams: This class has two evening midterms.  Do not plan travel or other conflicts on these dates, as there are no makeup exams.

• Monday, March 11, 8-10pm
• Monday, April 15, 8-10pm

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 or 10B. Mathematics 10B

Description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; orthogonality, symmetric matrices. Linear second-order differential equations; first-order systems with constant coefficients. Fourier series, application to partial differential equations.

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Prerequisites: Mathematical maturity appropriate to a sophomore math class. 1A-1B recommended

Description: Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.

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Description: Directed Group Study, topics vary with instructor.

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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: 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: 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: 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: 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.

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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: 110 and 113, or consent of instructor

Description: Further topics on groups, rings, and fields not covered in Math 113. Possible topics include the Sylow Theorems and their applications to group theory; classical groups; abelian groups and modules over a principal ideal domain; algebraic field extensions; splitting fields and Galois theory; construction and classification of finite fields.

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Prerequisites: 53 and 54

Description: Introduction to signal processing including Fourier analysis and wavelets. Theory, algorithms, and applications to one-dimensional signals and multidimensional images.

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Prerequisites: Math 53, 54, 55

Description: An introduction to computer programming with a focus on the solution of mathematical and scientific problems. Basic programming concepts such as variables, statements, loops, branches, functions, data types, and object orientation. Mathematical/scientific tools such as arrays, floating point numbers, plotting, symbolic algebra, and various packages. Examples from a wide range of mathematical applications such as evaluation of complex algebraic expressions, number theory, combinatorics, statistical analysis, efficient algorithms, computational geometry, Fourier analysis, and optimization. Mainly based on the Julia programming language, but some examples will demonstrate other languages such as MATLAB, Python, C, and Mathematica.

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Course Webpage: http://persson.berkeley.edu/math124

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: 110 and 113

Description: A critical examination of Euclid's Elements; ruler and compass constructions; connections with Galois theory; Hilbert's axioms for geometry, theory of areas, introduction of coordinates, non-Euclidean geometry, regular solids, projective geometry.

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Prerequisites: 104

Description: 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.

Office: 923 Evans

Office Hours: TBA

Required Text: R. Millman and G. Parker, Elements of Differential Geometry

Recommended Reading: M. P. Do Carmo, Differential Geometry of Curves & Surfaces, revised & updated second edition

Grading: TBA

Homework: TBA

Course Webpage: will be linked from math.berkeley.edu/~hutching

Prerequisites: 151; 54, 113, or equivalent

Description: Complex numbers and Fundamental Theorem of Algebra, roots and factorizations of polynomials, Euclidean geometry and axiomatic systems, basic trigonometry.

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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.

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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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Required Text:  T. W. Gamelin "Complex Analysis" ISBN 978-0387-95069-3

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Course Webpage: https://math.berkeley.edu/~art/S19-Math-185.html

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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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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Prerequisites: 104

Description: Honors section corresponding to Math 185 for exceptional students with strong mathematical inclination and motivation. Emphasis is on rigor, depth, and hard problems.

Office: Evans 833

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Recommended Reading: L. Ahlfors "Complex Analysis", also S. Lang "Complex Analysis'' as an optional source.

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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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Course Webpage: the link is on my home page at: math.berkeley.edu/~rieffel

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Description: The course is designed as a sequence with with Statistics C205A/Mathematics C218A with the following combined syllabus. Measure theory concepts needed for probability. Expection, distributions. Laws of large numbers and central limit theorems for independent random variables. Characteristic function methods. Conditional expectations, martingales and martingale convergence theorems. Markov chains. Stationary processes. Brownian motion.

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Description: This semester's topic is "Stochastic Growth and KPZ Equation"

Office:  803 Evans Hall

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Prerequisites: Math 128A/B or equivalent knowledge of basic numerical analysis, programming experience.

Description: Theory and practical methods for numerical solution of partial differential equations. Finite difference methods for parabolic and hyperbolic problems, finite volume methods for hyperbolic conservation laws, finite element methods for elliptic equations, discontinuous Galerkin methods for first and second order systems of conservation laws.

Office: 1081 Evans Hall

Office Hours: See instructor or course website

Required Text: None

Recommended Reading: 

• 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.
• R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge, 2002. ISBN 978-0521009249
• C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover, 2009. ISBN 978-0486469003.

Grading: Letter grade.

Homework: 7 extensive problem sets.

Course Webpage: On bCourses, for registered students only.

Prerequisites: 214

Description: Basic topics: symplectic linear algebra, symplectic manifolds, Darboux theorem, cotangent bundles, variational problems and Legendre transform, hamiltonian systems, Lagrangian submanifolds, Poisson brackets, symmetry groups and momentum mappings, coadjoint orbits, Kahler manifolds.

Office: 923 Evans

Office Hours: TBA

Required Text: D. McDuff and D. Salamon, Introduction to Symplectic Topology, third edition

Recommended Reading: A. Cannas da Silva, Lectures on Symplectic Geometry, https://people.math.ethz.ch/~acannas/Papers/lsg.pdf

Grading: Letter grade.

Homework: TBA

Course Webpage: will be linked from math.berkeley.edu/~hutching

Prerequisites: 254A and 256A; 256B or current enrollment in 256B may be required

Description: Valuations, units, and ideals in number fields, ramification theory, quadratic and cyclotomic fields, topics from class field theory, zeta-functions and L-series, distribution of primes, modular forms, quadratic forms, diophantine equations, P-adic analysis, and transcendental numbers. Sequence begins fall.

Office: 883 Evans

Office Hours: TBD

Required Text: None

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Grading: Letter grade.

Homework: Weekly or biweekly

Course Webpage: https://math.berkeley.edu/~vojta/254b.html

Content for this year's course: Arakelov theory and diophantine geometry (hence the changed prerequisites).  See the course web page.

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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Description:   This 3 unit course will be team-taught by Prof. Suncica Canic of Math and Prof. Shawn Shadden of Mechanical Engineering.  It is also offered as Mechanical Engineering C213/BioEngineering C213 (Fluid Mechanics of Biological Systems)

Office:   Prof. Canic:  911 Evans Hall,  Prof. Shadden: 5126 Etcheverry Hall

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