MAT236: Elementary Abstract Algebra Subject Profile


Summary: This handout describes basic course information such as meeting times and locations, subject content and format, assessment materials, and the names and contact details of the lecturer.

Lecturer: Dr Abdollah Khodkar

Office: STV 312F     E-mail: ak@maths.uq.edu.au     Web Site: www.maths.uq.edu.au/~ak

Tel Numbers: 438-7365 (W), 452-2705 (H), 438-8781 (Math Department)

Lectures: Monday, Wednesday, Thursday and Friday 10:00am. - 10:50am. in Room STV 211.

Office hours: 11am. - 12noon. Monday, Wednesday, Thursday and Friday or by appointment.

Prerequisites: A grade C or better in MAT175 is required. MAT236 is a 4 semester hours course.

Objective

This course uses abstract algebra as the vehicle for developing the ability to read and write proofs. In this course we

  1. present the subject matter of abstract algebra in a manner that is understandable to students, and
  2. develop in students a confidence in their ability to read and write mathematical proofs.

In this course we study the structure of the fundamental number systems encountered in high school algebra. The principal topics to be studied include: preliminary material on sets, functions, and operations; abstract rings; integral domains, and fields including the ring of integers; the fields of real and complex numbers; quotient rings; polynomial rings; homomorphisms and ideals.

Resources

The set text for this course is

Elementary Abstract Algebra by Lawrence E. Spence and Charles Vanden Eynden, Harper Collins College Publishers.

Assignments will be set from this book. It will be expected that you obtain access to a book either through purchase or use of the reserve copies.

If you wish to read more books on Abstract Algebra, then the following ones are recommended for reference. They are all available in the library.

  1. A. Feil, A First Course in Abstract Algebra: Rings, Groups, and Fields, QA162 A53 1995.

  2. R.B.J.T. Allenby, Rings, Fields and Groups: An Introduction to Abstract Algebra, QA162 A45 1991.

  3. J.A. Beachy and W.D. Blair, Abstract Algebra With a Concrete Introduction, QA162 B4 1990.

  4. G. Ehrlich, Fundamental Concepts of Abstract Algebra, QA162 E37 1991.

  5. I.N. Herstein, Abstract Algebra, QA162 H47 1999b.

  6. J.R. Durbin, Modern Algebra: An Introduction , QA162 D87 2000.

  7. C.M. Bundrick and J.J. Leeson, Essentials of Abstract Algebra, QA266 B79 1972.

Tentative Schedule

  1. Chapter 1: Mathematical Preliminaries (1.5 week)

    2. Logic and Proof; Sets; The Real and Complex Numbers; Functions; The Algebra of Functions; Relations; Matrices and Polynomials.

  2. Chapter 2: The integers (2 weeks)

    3. Divisibility; The Principle of Mathematics Induction; Prime Factorization; Congruence;

  3. Chapter 3: Rings (4 weeks)

    4. Some Examples of Rings; More Examples of Rings; Elementary Ring Properties; Subrings and Direct Sums; Properties of Multiplication; Homomorphisms and Isomorphisms; Ordered Rings.

  4. Chapter 4: Fields (3 week)

    5. Fields and Integral Domains; Fields of Quotients; The Rational and Real Numbers; The Complex Numbers; Powers and Roots of Complex Numbers.

  5. Chapter 5: Polynomials (3 weeks)

    6. Polynomial Rings; Divisibility; Roots and Irreducible Polynomials; Polynomials of Rational Numbers; Polynomials over Real Numbers and Complex Numbers; Geometric Constructions.


Assessment

Course assessment will consist of the following components:

  1. A comprehensive final examination worth 30% of the final grade.
  2. Four one-hour tests conducted during the scheduled teaching session worth 50% of the final grade.
  3. A set of two weekly assignments worth 20% of the final grade.

Test One: 10:00am. - 10:50am. Friday September 14, Room STV 211.

Test Two: 10:00am. - 10:50am. Friday October 5, Room STV 211.

Test Three: 10:00am. - 10:50am. Friday November 2, Room STV 211.

Test Four: 10:00am. - 10:50am. Wednesday November 21, Room STV 211.

Final Exam: 7:50am. - 10:30am. Thursday December 13, Room STV 211.

Attendance at exams is required. If you must miss an exam for a legitimate reason, you must notify me in adnvance either by calling my office before class or leaving a message in the Math Department Office.

Students with disability

Any student needing to arrange a reasonable accommodation for documented disability should contact Disability Concerns at 350 Fell Hall, 438-5853 (voice) or 438-8620 (TDD).