MH4728 — Abstract Algebra
This module is not taught at the moment
Next time it will be taught in the spring semester 2020, which commences on 27 January 2020.
Contact Information
| Name | Dr. Bernd Kreussler |
| Office | N29 |
| Internal Telephone | 4578 |
| bernd.kreussler@mic.ul.ie | |
| WWW | www.maths.mic.ul.ie/kreussler/ |
Some Links of interest
- The Math Forum
- Notes on Abstract Algebra
- R. Ash: Abstract Algebra - The Basic Graduate Year
- David Surowski: Workbook in Higher Algebra (PDF file)
- Edwin H. Connell: Elements of Abstract and Linear Algebra
- Dog School of Mathematics: An Elementary Introduction to Group Theory
- History of Group theory
- The Calendar FAQ
- www.timeanddate.com
- Plus, an internet magazine which aims to introduce readers to the beauty of mathematics.
- On September 8, 22, and 29, 2001, three articles about modern
cryptography had been published in the Portuguese weekly newspaper
Expresso. The
European Mathematical Society
awarded them in 2003 the First Prize in the article competition
Raising Public Awareness of Mathematics.
English versions of these award-winning articles can be found here:
Contents of the lecture delivered during the spring semester 2014
- Integers
- Basic rules (Axioms)
- Divisibility, Euclid's algorithm, mathematical induction
- Prime numbers
- Diophantine equations
- Congruences
- Arithmetic of remainders
- Equivalence relations
- The additive group Z/nZ
- Divisibility and applications of Euclid's algorithm
- Chinese Remainder Theorem
- RSA, ISBN and EAN
- Groups
- Definitions and examples
- Basic results about groups in general
- Applications
- Subgroups, homomorphisms, injectivity, surjectivity, isomorphisms
- Factor groups
- Rings and Fields
- Definitions and examples
- Polynomials
Textbooks
Section 512 on the shelves in the library contains several useful books. Some of them are listed below.
- DURBIN, J.R., Modern Algebra, (Wiley), 1979.
- FRALEIGH, J.B., A First Course in Abstract Algebra, (Addison Wesley), 1976.
- HUMPHREYS, J.F., PREST, M.Y., Numbers, groups and codes, (Cambridge University Press), 1989
- IRVING, R., Integers, Polynomials, and Rings: A Course in Algebra, (Springer), 2004.
- KEMPF, G., Algebraic Structures, (Vieweg Verlag) 1995.
- KIM, K.H., ROUSH, F.W., Applied Abstract Algebra, (Ellis Horwood), 1983.
- LAURITZEN, N., Concrete Abstract Algebra, (Cambridge University Press) 2003.
- LEDERMANN, W., Introduction to Group Theory, (Oliver and Boyd), 1973.
- WHITELAW, T.A., Introduction to Abstract Algebra, (Blackie), 1988.
