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  • Courseware 
    Number Theory II: Class Field Theory

    Number Theory II: Class Field Theory

    This course is the continuation of 18.785 Number Theory I. It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Galois cohomology Algebraic number theory Class field theory
    Resource Type:
    Courseware
     
  • Courseware 
    Work

    Number Theory I

    This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.

    Subjects:
    Mathematics and Statistics
    Keywords:
    Number theory Algebraic number theory
    Resource Type:
    Courseware