Credits: 10 | Convenor: Dr. J. C. Ault | Semester: 2 (weeks 7 to 12) |
Prerequisites: | desirable: MC144, MC145, MC147, MC241 | |
Assessment: | Computer project/course work: 20% | One and a half hour exam: 80% |
Lectures: | 18 | Classes: | 10 |
Tutorials: | 6 | Private Study: | 47 |
Labs: | none | Seminars: | none |
Project: | none | Other: | none |
Total: | 75 |
The main aim is to lay down a firm foundation in the basic concepts of the theory ready for development in later (third and fourth year) modules, but it is also intended that this course should be self-contained and lead to its own interesting conclusions.
The lectures, computer workshops and problem sheets are all designed with the above aims in mind. In particular, it is hoped that the workshops will encourage experimentation with the examples of small groups provided and that the projects will give an opportunity for practice with the presentation of abstract mathematical material. You will be expected to become familiar with various particular examples of groups and to know how to prove some of the theorems. You should also be able to apply your newly learned knowledge in unfamiliar but similar situations. The course begins with the general concept of a binary operation and the various properties that such an operation may enjoy leading to the definition of a group. These ideas are investigated in greater detail through use of the computer package ``Exploring Small Groups''. Apart from those provided by the package, there is a standard list of examples derived from symmetries of geometrical shapes, matrices and modular arithmetic. These are used to illustrate the results an ideas introduced in later chapters.
C. R. Jordon and D. A. Jordon, Groups, Edward Arnold.
J. A. Green, Sets and Groups: a First Course in Algebra, RKP.
Walter Ledermann and Alan J. Weir, Introduction to Group Theory, 2nd edition, Addison Wesley Longman.
J. R. Durbin, Modern Algebra: an Introduction, 3rd edition, Wiley.
J. B. Fraleigh, A First Course in Abstract Algebra, 5th edition, Addison-Wesley.
I. N. Herstein, Topics in Algebra, 2nd edition, Wiley.