Fundamental Concepts of Algebra

Course title: Fundamental
Concepts of Algebra Course code: Math 1012 Prerequisite: Math 1011 Course
category:
Course description:
The course mainly covers Sets with basic operations,
relations and functions, cardinal numbers, groups, rings, and the system of integers.


Compulsory Course outline

Chapter 1: Set theory

1.1 Review of sets and set operations, ordered pairs, relations and functions

1.2 Order and equivalence relation

1.3 Classification of sets

1.4 Cardinal numbers

Chapter 2: Groups

2.1 Binary operations, algebraic structures

2.2 Identity element and inverses

2.3 Morphisms

2.4 Definition and examples of groups

2.5 Subgroups, cosets, and Lagrange's theorem

2.6 Normal subgroups and quotient groups

2.7 Homomorphisms

Chapter 3: Rings

3.1 Definition of rings and examples

3.2 Subrings and characteristic of a ring

3.3 Ideals and quotient rings

3.4 Homomorphism of rings

3.5 Integral domains and the field of quotients

3.6 Polynomial rings

3.7 Prime fields

Chapter 4: The system of integers

4.1 Properties of addition and multiplication

4.2 Order axioms of the system of integers

4.3 Well-ordering axioms

4.4 Mathematical induction

4.5 Characterization of the system of integers

Teaching materials

Textbook: - Demissu Gemeda and Seid Mohammed, Fundamental Concepts of Algebra, Dept. of Mathematics, AAU, 2008

References: -

-B. Fraleigh John, A First Course in Abstract Algebra, 2nd ed, Addison-Wesley publishing Company, Reading

-J. J Gerald, Introduction to modern algebra(revised), 4th ed; University Bookstall, Reading, 1989

- D. S. Dummit and R. M. Foote, Abstract algebra, 3rded, John Wiley and Sons, 2004.

- P. B. Bhattachara et-al, Basic abstract algebra, 2nded, Cambridge University press, 1995

- N. H. Ma-Coy et-al, Introduction to abstract algebra, Academic Press, 2005