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

Eligibility and requirements

Prerequisites

Code Name Teaching period Credit Points
MAST30005 Algebra
Semester 1 (On Campus - Parkville)
 12.5

Or equivalent.

Corequisites

None

Non-allowed subjects

None

Recommended background knowledge

Knowledge of basic point-set topology as covered for example in MAST30026 Metric and Hilbert Spaces.

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 4 March 2025

Assessment

DescriptionTimingPercentage

Up to 50 pages of written assignments (three assignments spread evenly)

  • 50 pages
Throughout the teaching period50%

A written examination

  • 3 hours
During the examination period50%

Last updated: 4 March 2025

Dates & times

Not available in 2025

What do these dates mean

Visit this webpage to find out about these key dates, including how they impact on:

  • Your tuition fees, academic transcript and statements.
  • And for Commonwealth Supported students, your:
       -  Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
     

    Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.

Last updated: 4 March 2025

Further information

  • Texts

    Prescribed texts

    Recommended texts and other resources

    Pierre Samuel, Algebraic Theory of Numbers, Dover Publications 2008.

    James Milne, Algebraic Number Theory, online notes.

  • Available through the Community Access Program

    About the Community Access Program (CAP)

    This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.

    Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants

    Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.

  • Available to Study Abroad and/or Study Exchange Students

    This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.

Last updated: 4 March 2025