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Algebraic Number Theory (MAST90136)
Graduate courseworkPoints: 12.5Dual-Delivery (Parkville)
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About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Overview
| Availability | Semester 1 - Dual-Delivery |
|---|---|
| Fees | Look up fees |
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: 12 November 2022
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30005 | Algebra | Semester 1 (Dual-Delivery - 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: 12 November 2022
Assessment
| Description | Timing | Percentage |
|---|---|---|
Up to 50 pages of written assignments (three assignments spread evenly)
| Throughout the teaching period | 50% |
A written examination
| During the examination period | 50% |
Last updated: 12 November 2022
Dates & times
- Semester 1
Coordinator Alexandru Ghitza Mode of delivery Dual-Delivery (Parkville) Contact hours 3 one-hour interactive lectures per week Total time commitment 170 hours Teaching period 28 February 2022 to 29 May 2022 Last self-enrol date 11 March 2022 Census date 31 March 2022 Last date to withdraw without fail 6 May 2022 Assessment period ends 24 June 2022 Semester 1 contact information
Last updated: 12 November 2022
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.
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: 12 November 2022