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Ma 147 abc: Dynamical Systems
9.00 Credits
California Institute of Technology
First term: real dynamics and ergodic theory. Second term: Hamiltonian dynamics. Third term: complex dynamics. Instructors: Makarov, Lee.
Prerequisite:
Ma 108, Ma 109, or equivalent.
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Ma 147 abc - Dynamical Systems
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Ma 148 abc: Topics in Mathematical Physics
9.00 Credits
California Institute of Technology
This course covers a range of topics in mathematical physics. The content will vary from year to year. Topics covered will include some of the following: Lagrangian and Hamiltonian formalism of classical mechanics; mathematical aspects of quantum mechanics: Schroedinger equation, spectral theory of unbounded operators, representation theoretic aspects; partial differential equations of mathematical physics (wave, heat, Maxwell, etc.); rigorous results in classical and/or quantum statistical mechanics; mathematical aspects of quantum field theory; general relativity for mathematicians. First term: geometric theory of quantum information and quantum entanglement based on information geometry and entropy. Only offered first term 2012-13 Instructor: Marcolli.
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Ma 148 abc - Topics in Mathematical Physics
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Ma 151 abc: Algebraic and Differential Topology
9.00 Credits
California Institute of Technology
A basic graduate core course. Fundamental groups and covering spaces, homology and calculation of homology groups, exact sequences. Fibrations, higher homotopy groups, and exact sequences of fibrations. Bundles, Eilenberg-Maclane spaces, classifying spaces. Structure of differentiable manifolds, transversality, degree theory, De Rham cohomology, spectral sequences. Instructors: Markovic, Liu.
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Ma 151 abc - Algebraic and Differential Topology
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Ma 157 ab: Riemannian Geometry
9.00 Credits
California Institute of Technology
Part a: basic Riemannian geometry: geometry of Riemannian manifolds, connections, curvature, Bianchi identities, completeness, geodesics, exponential map, Gauss’s lemma, Jacobi fields, Lie groups, principal bundles, and characteristic classes. Part b: basic topics may vary from year to year and may include elements of Morse theory and the calculus of variations, locally symmetric spaces, special geometry, comparison theorems, relation between curvature and topology, metric functionals and flows, geometry in low dimensions. Instructors: Baba, Wu.
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Ma 157 ab - Riemannian Geometry
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Ma 160 abc: Number Theory
9.00 Credits
California Institute of Technology
In this course, the basic structures and results of algebraic number theory will be systematically introduced. Topics covered will include the theory of ideals/divisors in Dedekind domains, Dirichlet unit theorem and the class group, p-adic fields, ramification, Abelian extensions of local and global fields. Instructors: Flach, Hedayatzadeh, Jorza.
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Ma 160 abc - Number Theory
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Ma 162: Topics in Number Theory
9.00 Credits
California Institute of Technology
The course will discuss in detail some advanced topics in number theory, selected from the following: Galois representations, elliptic curves, modular forms, L-functions, special values, automorphic representations, p-adic theories, theta functions, regulators. Instructor: Ramakrishnan, Hedayatazadeh.
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Ma 162 - Topics in Number Theory
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Ma 17: How to Solve It
4.00 Credits
California Institute of Technology
There are many problems in elementary mathematics that require ingenuity for their solution. This is a seminar-type course on problem solving in areas of mathematics where little theoretical knowledge is required. Students will work on problems taken from diverse areas of mathematics; there is no prerequisite and the course is open to freshmen. May be repeated for credit. Graded pass/fail. Instructor: Staff.
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Ma 17 - How to Solve It
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Ma 191 abc: Selected Topics in Mathematics
9.00 Credits
California Institute of Technology
Each term we expect to give between 0 and 6 (most often 2-3) topics courses in advanced mathematics covering an area of current research interest. These courses will be given as sections of 191. Students may register for this course multiple times even for multiple sections in a single term. The topics and instructors for each term and course descriptions will be listed on the math option website each term prior to the start of registration for that term. Instructor: Staff.
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Ma 191 abc - Selected Topics in Mathematics
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Ma 2 ab: Differential Equations, Probability and Statistics
9.00 Credits
California Institute of Technology
Ordinary differential equations, probability, statistics. Instructors: Marcolli, Makarov, Border.
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Ma 2 ab - Differential Equations, Probability and Statistics
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Ma 214: Mathematical Finance
9.00 Credits
California Institute of Technology
A course on fundamentals of the mathematical modeling of stock prices and interest rates, the theory of option pricing, risk management, and optimal portfolio selection. Students will be introduced to the stochastic calculus of various continuous-time models, including diffusion models and models with jumps. Not offered 2012–13.
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Ma 214 - Mathematical Finance
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