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Ma 290: Reading
1.00 - 9.00 Credits
California Institute of Technology
Occasionally, advanced work is given through a reading course under the direction of an instructor.
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Ma 290 - Reading
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Ma 390: Research
1.00 - 9.00 Credits
California Institute of Technology
No course description available.
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Ma 390 - Research
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Ma 4: Introduction to Mathematical Chaos
9.00 Credits
California Institute of Technology
An introduction to the mathematics of “chaos.” Period doubling universality, and related topics; interval maps, symbolic itineraries, stable/unstable manifold theorem, strange attractors, iteration of complex analytic maps, applications to multidimensional dynamics systems and real-world problems. Possibly some additional topics, such as Sarkovski’s theorem, absolutely continuous invariant measures, sensitivity to initial conditions, and the horseshoe map. Instructor: Lee.
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Ma 4 - Introduction to Mathematical Chaos
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Ma 5 abc: Introduction to Abstract Algebra
9.00 Credits
California Institute of Technology
Introduction to groups, rings, fields, and modules. The first term is devoted to groups and includes treatments of semidirect products and Sylow’s theorem. The second term discusses rings and modules and includes a proof that principal ideal domains have unique factorization and the classification of finitely generated modules over principal ideal domains. The third term covers field theory and Galois theory, plus some special topics if time permits. This course it to be taught concurrently with Ma 105. Instructors: Flach, Mantovan, Jorza.
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Ma 5 abc - Introduction to Abstract Algebra
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Ma 6 abc: Introduction to Discrete Mathematics
9.00 Credits
California Institute of Technology
First term: a survey emphasizing graph theory, algorithms, and applications of algebraic structures. Graphs: paths, trees, circuits, breadth-first and depth-first searches, colorings, matchings. Enumeration techniques; formal power series; combinatorial interpretations. Topics from coding and cryptography, including Hamming codes and RSA. Second term: directed graphs; networks; combinatorial optimization; linear programming. Permutation groups; counting nonisomorphic structures. Topics from extremal graph and set theory, and partially ordered sets. Third term: elements of computability theory and computational complexity. Discussion of the P=NP problem, syntax and semantics of propositional and first-order logic. Introduction to the Gödel completeness and incompleteness theorems. Instructors: Omar, Wilson, Williams.
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Ma 6 abc - Introduction to Discrete Mathematics
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Ma 7: Number Theory for Beginners
9.00 Credits
California Institute of Technology
Some of the fundamental ideas, techniques, and open problems of basic number theory will be introduced. Examples will be stressed. Topics include Euclidean algorithm, primes, Diophantine equations, including an + bn = cn and a2 - db2 = ±1, constructible numbers, composition of binary quadratic forms, and congruences. Instructor: Ramakrishnan.
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Ma 7 - Number Theory for Beginners
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Ma 8: Problem Solving in Calculus
3.00 Credits
California Institute of Technology
A three-hour per week hands-on class for those students in Ma 1 needing extra practice in problem solving in calculus. Instructor: Staff.
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Ma 8 - Problem Solving in Calculus
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Ma 91 a: Homological Algebra
9.00 Credits
California Institute of Technology
This course will be a first introduction to homological algebra, covering generalities on additive and abelian categories; the category of complexes, and the long exact sequence of cohomology; cones and homotopies; the homotopic category of complexes; projective and injective resolutions, and the derived category; derived functors; double complexes; spectral sequences; and further topics as time permits. Not offered 2012–13.
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Ma 91 a - Homological Algebra
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Ma 92 abc: Senior Thesis
9.00 Credits
California Institute of Technology
Open only to senior mathematics majors who are qualified to pursue independent reading and research. This research must be supervised by a faculty member. The research must begin in the first term of the senior year and will normally follow up on an earlier SURF or independent reading project. Two short presentations to a thesis committee are required: the first at the end of the first term and the second at the midterm week of the third term. A draft of the written thesis must be completed and distributed to the committee one week before the second presentation. Graded pass/fail in the first and second terms; a letter grade will be given in the third term.
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Ma 92 abc - Senior Thesis
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Ma 98: Independent Reading
6.00 Credits
California Institute of Technology
Occasionally a reading course will be offered after student consultation with a potential supervisor. Topics, hours, and units by arrangement. Graded pass/fail.
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Ma 98 - Independent Reading
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