Department of Mathematical Sciences

Mathematics

MATHEMATICS 314: ALGEBRA

Summary

The aim of this introductory algebra course is to introduce and study various axiomatic algebraic structures and concepts. These structures provide the natural setting used to describe and study many of the most important classical and modern results in number theory, algebraic geometry, computational algebra as well as those from other mathematical areas. These algebraic structures are also applied in many other disciplines such as cryptography, coding theory, physics and chemistry.  Topics we investigate include groups, rings, residue classes modulo n, factor rings and fields, polynomial rings, Euclidean domains, unique factorisation domains, field extensions, applications to straight edge and compass constructions, finite fields and applications.

Module information

  • 21539 314 (16) Mathematics 314
  • Third year, first semester, in the Programme in the Mathematical Sciences.
  • Three lectures and one three hour tutorial per week.
  • Prerequisite modules: A pass in Mathematics 214, 244.
  • Language specification : E

Lecturers

  • Dr C Naude, Office:  Industrial Psychology/Mathematics  Building 1023A (e-mail:  cnaude@sun.ac.za)

Course material

  • Textbook:  A Book of Abstract Algebra, C Pinter, 2nd ed. Dover Publ.

Course presentation

The course material is dealt with in detail during the lectures. Tutorials provide the opportunity to work on problems and discuss coursework under the supervision of the lecturer.

Assessment

The class mark will be determined using mainly the mid-semester test. The mid-semester test is graded and returned to students as soon as possible. The final mark is determined from the class mark and the examination mark – the class mark has weight 0.4 and the examination mark 0.6. A class mark of at least 40% is required in order to write the examination. To pass the module the final mark should be at least 50%.

Rationale

This module is presented within the programme in the mathematical sciences. It contributes to providing a basic training in mathematics and is one of the core modules required in order to obtain the BSc degree with a major in mathematics. This module is also useful for those interested in the teaching profession.

Outcomes

Students who have successfully followed this module will be equipped with knowledge of the introductory algebraic concepts necessary in a wide variety of advanced mathematical fields, as well as areas of application. Areas of application which benefit from exposure to, and an understanding of, elementary algebra include theoretical physics, dynamical systems, cryptography, coding theory, discrete mathematics and topics in Computer Science. Students following this module will aquire the ability to work comfortably with abstract and formally defined concepts and axioms. They will also aquire problem solving skills, in particular those where a number of degrees of abstraction are needed.