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  • Law 33: Introduction to the Law

    9.00 Credits
    California Institute of Technology

    An introduction to Anglo-American law from both the legal and the social- scientific points of view. Subject can vary from year to year. Available for introductory social science credit. Instructor: McCaffery.
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  • Law 99: Causation and Responsibility

    9.00 Credits
    California Institute of Technology

    This course will examine the interrelationships between the concepts of causation, moral responsibility, and legal liability. It will consider legal doctrines of causation and responsibility, as well as attempts within philosophy to articulate these concepts. Questions to be addressed include: Can you be morally or legally responsible for harms that you do not cause? Is it worse to cause some harm, than to unsuccessfully attempt it? Is it justified to punish those who cause harm more severely than those who attempt harm? When, if ever, can the ends justify the means? What constitutes negligence? Is it worse to cause some harm, than to allow it to happen (when you could have prevented it)? Instructor: Hitchcock.
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  • Ma 1 abc: Calculus of One and Several Variables and Linear Algebra

    9.00 Credits
    California Institute of Technology

    Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Omar, Ramakrishnan, Mantovan, Aschbacher, Ni, Kechris. Prerequisite:    High-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7).
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  • Ma 1 d: Series

    5.00 Credits
    California Institute of Technology

    This is a course intended for those students in the special calculus-intensive sections of Ma 1 a who did not have complex numbers, Taylor polynomials, and infinite series during Ma 1 a. It may not be taken by students who have passed the regular Ma 1 a. Instructor: Staff.
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  • Ma 10: Oral Presentation

    3.00 Credits
    California Institute of Technology

    In this course, students will receive training and practice in presenting mathematical material before an audience. In particular, students will present material of their own choosing to other members of the class. There may also be elementary lectures from members of the mathematics faculty on topics of their own research interest. Instructor: Mantovan.
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  • Ma 104: Elliptic Curves

    9.00 Credits
    California Institute of Technology

    The ubiquitous elliptic curves will be analyzed from elementary, geometric, and arithmetic points of view. Possible topics are the group structure via the chord-and-tangent method, the Nagel-Lutz procedure for finding division points, Mordell’s theorem on the finite generation of rational points, points over finite fields through a special case treated by Gauss, Lenstra’s factoring algorithm, integral points. Other topics may include diophantine approximation and complex multiplication. Not offered 2012-13. Prerequisite:    Ma 5, Ma 3, or equivalents.
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  • Ma 105 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 5. Instructors: Flach, Mantovan, Jorza.
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  • Ma 108 abc: Classical Analysis

    9.00 Credits
    California Institute of Technology

    First term: structure of the real numbers, topology of metric spaces, a rigorous approach to differentiation in R . Second term: brief introduction to ordinary differential equations; Lebesgue integration and an introduction to Fourier analysis. Third term: the theory of functions of one complex variable. Instructors: C. Marx, Demirel.
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  • Ma 109 abc: Introduction to Geometry and Topology

    9.00 Credits
    California Institute of Technology

    First term: aspects of point set topology, and an introduction to geometric and algebraic methods in topology. Second term: the differential geometry of curves and surfaces in two- and three-dimensional Euclidean space. Third term: an introduction to differentiable manifolds. Transversality, differential forms, and further related topics. Instructors: Markovic, Ni, Baba. Prerequisite:    Ma 2 or equivalent, and Ma 108 must be taken previously or concurrently.
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  • Ma 11: Mathematical Writing

    3.00 Credits
    California Institute of Technology

    Students will work with the instructor and a mentor to write and revise a self-contained paper dealing with a topic in mathematics. In the first week, an introduction to some matters of style and format will be given in a classroom setting. Some help with typesetting in TeX may be available. Students are encouraged to take advantage of the Hixon Writing Center’s facilities. The mentor and the topic are to be selected in consultation with the instructor. It is expected that in most cases the paper will be in the style of a textbook or journal article, at the level of the student’s peers (mathematics students at Caltech). Not offered on a pass/fail basis. Instructor: Wilson.
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