### MP473 Number Theory IIIH/IVH, Semester 2, 2000

### Prepared by Keith Matthews

Email: webmaster@numbertheory.org

Web: http://www.numbertheory.org/keith.html

### Study Suggestions

Students are encouraged in tutorials to raise any difficulties
encountered with the problem sheets and lecture material.
Students should try to keep up to date with study of their lectures, so as
to be able to understand subsequent lectures. They are also urged to do as many
problems as possible. By doing problems, students will soon discover their
strong and weak points.

The lecture notes will contain enough explanations and examples to make the definitions, theorems and arguments clear. However some students will need further examples and explanations of certain points and I recommend they peruse books from the reading list below. Most of these books have lots of examples and develop the concepts in greater detail than we have time for in our short course of lectures.

The course is an introduction to algebraic number theory, especially quadratic and cyclotomic fields.
### Past exams

### Reference books

No textbook is recommended

There are many books in the PSE and Undergraduate Libraries which touch on the subject. Here are some useful ones:
- P. Samuel,
*Algebraic Theory of Numbers*, QA247.S25131972
*Algebraic Number Theory*, I.N. Stewart and D.O. Tall, (Second Edition), Chapman and Hall/CRC Press 1987
- W.J. LeVeque,
*Topics in Number Theory Vol. II*, QA241.L581956
*A Classical Introduction to Modern Number Theory*, K. Ireland and M. Rosen, (Corrected Second Printing) Graduate Text 84, Springer 1993
- H.B. Mann,
*Introduction to Algebraic Number Theory*, QA241.M31955
- P. Ribenboim,
*Algebraic Numbers*, QA247.R461972
- W. Narkiewicz,
*Elementary and Analytic Theory of Algebraic Numbers*, QA247.N33321990
- D.A. Marcus,
*Number Fields*, QA247.M3461977
*A Course in Computational Number Theory*, (Corrected Third Printing), H. Cohen, Graduate Texts in Mathematics 138, Springer 1996, ISBN 3-540-55640-0 (Errata)

### Computer programs

The subject contains many interesting algorithms. Students can experiment with
an exact arithmetic computer program called **CALC**, written by the lecturer
and which implements some of the algorithms met in the course. CALC can be downloaded from the WWW.

KRM 19th May 2005