and other important topics. Geometric theory of quantum information and quantum entanglement based on information geometry and entropy. Division of Engineering & Applied Science, Department of Computing + Mathematical Sciences, Applied Probability & Stochastic Analysis, Computational Neuroscience & Neural Engineering, Molecular Programming & Synthetic Biology, Scientific Computing & Numerical Analysis, Nivetha Karthikeyan Awarded Chang Career Exploration Prize, Professor Bouman Receives GSC Teaching Award, Oscar Bruno Elected to the National Academy of Sciences of Argentina. Graded pass/fail in the first and second terms; a letter grade will be given in the third term. However, under a steady state hypothesis, they reduce to a simpler equation, whose solution can describe the late time behavior. the symmetric group) and unitary representations (and structure theory) of compact groups. Occasionally a reading course will be offered after student consultation with a potential supervisor. Prerequisites: To register, the student must obtain permission of the mathematics undergraduate representative. Cathy Light, secretary of the corporation and advisor to the president at Carnegie Mellon University, will join Caltech January 4. Fulfills the Institute scientific writing requirement. Students are encouraged to take advantage of the Hixon Writing Center's facilities. Randomness is not anarchy-it follows mathematical laws that we can understand and use to clarify our knowledge of the universe. The mathematical theory of ordinary and partial differential equations, including a discussion of elliptic regularity, maximal principles, solubility of equations. Undecidable problems: word problems for groups, solvability of Diophantine equations (Hilbert's 10th problem). This course will cover core concepts in machine learning and statistical inference. First term: integration theory and basic real analysis: topological spaces, Hilbert space basics, Fejer's theorem, measure theory, measures as functionals, product measures, L^p -spaces, Baire category, Hahn- Banach theorem, Alaoglu's theorem, Krein-Millman theorem, countably normed spaces, tempered distributions and the Fourier transform. Not offered 2020-21. Second term: brief introduction to ordinary differential equations; Lebesgue integration and an introduction to Fourier analysis. Prerequisites: Freshmen must have instructor's permission to enroll. The course is aimed at providing an introduction to the theory of ordinary differential equations, with a particular emphasis on equations with well known applications ranging from physics to population dynamics. Computing + Mathematical Sciences faculty The course deals with aspects of algebraic geometry that have been found useful for number theoretic applications. Instructors: Burungale, Ni, Parikh, Karpukhin, Smillie, Szumowic. The course focuses on the mathematics and statistics of methods developed for learning from data. Not offered on a pass/fail basis. Not offered 2020-21. Caltech Mourns the Passing of … The Computing + Mathematical Sciences (CMS) Department is nestled in the heart of Pasadena on the beautiful Caltech campus. An elementary introduction to the theory of algebraic curves. Students registering for more than 6 units of Ma 97 must submit a brief (no more than 3 pages) written report outlining the work completed to the undergraduate option rep at the end of the term. Third term: harmonic analysis; operator theory. The CMS Partners program provides opportunities for individuals, startups, and companies to engage with Caltech Computing and Mathematical Sciences faculty and researchers in order to support educational and outreach programs and to initiate research collaborations. This course introduces standard concepts and techniques in homological algebra. Prerequisites: Open for credit to freshman and sophomores. Not offered 2020-21. Church's thesis. Prerequisites: Ma 130 or instructor's permission. ©2020 Caltech. Prerequisites: Ma 151 or equivalent, or instructor's permission. Instructors: Karpukhin, Rains, Angelopoulos. Second term: basic complex analysis: analytic functions, conformal maps and fractional linear transformations, idea of Riemann surfaces, elementary and some special functions, infinite sums and products, entire and meromorphic functions, elliptic functions. Comprehensive presentation of linear algebra. Prerequisites: Ma 108; Ma 109 is desirable. Decision problems. Shannon's mathematical theory of communication, 1948-present. First term: Introduction to first-order logic and model theory. Complexity of decision procedures. Approval from the research supervisor and student's adviser must be granted prior to registration. 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