MATH439-16S1 (C) Semester One 2016

Rings and Fields

15 points

Details:
Start Date: Monday, 22 February 2016
End Date: Sunday, 26 June 2016
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 4 March 2016
  • Without academic penalty (including no fee refund): Friday, 20 May 2016

Description

Rings and Fields

This course formally introduces rings and fields, which have been encountered at 100- and 200-level in special situations, and investigates their algebraic structure. It gives a deeper understanding of these algebraic concepts and thus provides a thorough grounding in the algebraic theory which underpins modern applications like cryptography, error-correcting codes, number theory or finite mathematics. If you are interested in any of these subjects or if you want to see how algebraic theory can be applied to solve certain geometric construction problems or prove their impossibility, then this is the course to take.

The topics covered by this course are:

• fundamentals of ring theory: subrings, ideals, factor rings, ring homomorphisms;  
• special rings: integral domains and polynomial rings and factorizations of elements therein;  
• fundamentals of field theory: field extensions, constructions of fields, in particular finite fields, and their uses, like the impossibility of certain geometric constructions such as trisecting the angle.
• Extension topics: Euclidean domains, Galois theory


For a full list of Honours courses, please refer to the School of Mathematics and Statistics Honours Booklet Mathematics and Statistics Honours Booklet

Learning Outcomes

  • Students successfully completing this course should:

  • understand a range of basic algebraic concepts.
  • have developed a high level of competence at core algebraic skills.
  • be able to confidently apply algebraic concepts in practical settings.
  • be able to present clear and logical mathematical arguments.

Prerequisites

Subject to approval of the Head of School.

Restrictions

Course Coordinator

Gunter Steinke

Assessment

Assessment Due Date Percentage 
Assignments 50%
Final Examination 50%

Indicative Fees

Domestic fee $913.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH439 Occurrences

  • MATH439-16S1 (C) Semester One 2016
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