Algebraic Number Theory (MAST90136)

Graduate courseworkPoints: 12.5Not available in 2025

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Overview

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This course is an introduction to algebraic number theory. Algebraic number theory studies the structure of the integers and algebraic numbers, combining methods from commutative algebra, complex analysis, and Galois theory. This subject covers the basic theory of number fields, rings of integers and Dedekind domains, zeta functions, decomposition of primes in number fields and ramification, the ideal class group, and local fields. Additional topics may include Dirichlet L-functions and Dirichlet’s theorem; quadratic forms and the theorem of Hasse-Minkowski; local and global class field theory; adeles; and other topics of interest. 

Intended learning outcomes

After completing this subject, students will:


  • be able to demonstrate understanding of basic number theoretic concepts through analysing examples;
  • find and explain in writing minor proofs of number theoretic results independently;
  • demonstrate the ability to explain proofs of, and identify core ideas behind, the major foundational results of algebraic number theory;
  • have the ability to pursue further studies in number theory and related areas.

Generic skills

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 4 March 2025