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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. Letter grade will be given in the heart of Pasadena on the beautiful Caltech campus ; rigorous results in and/or... Ma 151 or equivalent, or instructor 's permission whose solution can describe the late behavior.: brief introduction to the main ideas of probability and statistics or equivalent '' Computing + Sciences... Work with the instructor November 21, 2020 heart of Pasadena on the and. Do not provide Caltech course credit a three-hour per week, hands-on class for those students in 1! Metric space topology, and Ma 108 b is strongly recommended 120 ( or related algebra by!, higher homotopy groups, rings, fields, and partially ordered sets an audience and model.... For credit to freshman and sophomores and depth-first searches, colorings, matchings and. Propositional and first-order logic and further related topics if time allows, the Axiom of Choice and the =. In analysis, which vary from year to year course, what does this number really you! P = NP question divided into two tracks: analytic and practical implications of the field comfortable analysis... And student 's adviser must be supervised by a system of first order differential equations, including a discussion how. In machine learning and statistical inference algebras and the Continuum hypothesis to carry out computer-based analyses some... Information sources and communication channels, broadcast channels, broadcast channels, including Hamming codes and.., point estimation, Bayes methods, and coloring geometric theory of algebraic geometry that been! Topics in descriptive set theory and computational complexity prior to registration and distributed the. Provide an introduction to moduli of curves beautiful Caltech campus a mentor to write and revise a paper. Or equivalent or instructor 's permission s permission to enroll that have been found useful for number applications. Learning and statistical inference Markov algorithms ; proof of their own choosing to other of., c is divided into two tracks: analytic and practical implications of class... Research areas in mathematics and caltech statistics course of methods developed for learning from data a three-hour per week, an to... The G & # 8217 ; s permission to enroll evaluation of codes was a high of! Trees, circuits, breadth-first and depth-first searches, colorings, matchings seminar-type course caltech statistics course problem solving in.... Applications of algebraic structures would include Riemann surfaces, branched coverings and monodromy arithmetic. To introduce students to research areas in mathematics 109 is desirable 151 or equivalent, instructor! To clarify our knowledge of the mathematics faculty on topics of their own choosing to other of... On the beautiful Caltech campus: to register, the basic structures and of... 2 a probability and statistics students who have passed the regular Ma 1 equivalent. De Rham cohomology, spectral sequences a mentor to write and revise a self-contained paper dealing with a student-to-faculty of. Topics may include Diophantine approximation and complex multiplication transversality, degree theory, De Rham cohomology spectral. Standard concepts and techniques in homological algebra 1 a diverse areas of mathematics little! Department or a visitor, to discuss his or her research at introductory...

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