In case you have any questions, please feel free to email me (see page 1 of the lecture notes for my email address).

It seems like you have done very well on the CAT and on the first Home Assignment. You will get them back after the Christmas break.

All lecture notes are now (finally) posted, see below. Make sure you have all pages (page 1 to 77) when preparing for the exam.

Mondays, 11am-12noon. Location: MH1

Wednesdays, 8am-10am. Location: AGRI LAB

- Continuous assessment test (10% of the total grade).
- Home assignment 1. (10% of the total grade). On Induction, Congruences and Factorization.
- Home assignment 2. (10% of the total grade). On RSA cryptography. This is distributed in class on Thursday, Dec 14. Deadline: January 29.
- Final exam (70% of the total grade). It is now confirmed that the final exam will take place in the regular exam period with all your other exams. The final exam will be much harder than the CAT, you are expected to:
- understand all the proofs in the posted lecture notes
- be able to solve nontrivial problems (like the problems in the lecture notes)

- Part 1: Review of sets, relations and functions.
- Lecture notes (page 1 to 9).
- Answers and solutions (page 10 to 11).

- Part 2: Elementary number theory
- Lecture notes, sections 2.1 to 2.3 (page 12 to 24)
- Answers and solutions (page 25 to 26)
- Home assignment 1 (page 27)
- Lecture notes, sections 2.5 to 2.7 (page 28 to 38)
- Lecture notes, Arithmetic mod n (page 39 to 42)
- Answers to exercises (page 43 to 45)
- Solutions to problems (page 46 to 50)

- Part 3: Proofs and problem-solving Lecture notes (page 51 to 58)

- Part 4: Applications to cryptography Lecture notes (page 59 to 65)

- Information on the exam. Information sheet (page 66)

- Part 5: Introduction to abstract algebra Lecture notes (page 67 to 77)

An excellent little book, available for free online, is Paul Garrett's Introduction to abstract algebra. This book covers most of what we will do in this course. If you want an alternative to the lecture notes, you should definitely consult this text.

Some general notes on sets can be found here.

A similar page, which gives you the prime factorization of an integer, is here. When you use these pages, remember that you must also be able to do these kinds of calculations by hand on the exam.

There is an excellent e-book by Robert D. Carmichael covering more or less the same number theory as we do in this course. This book has been made available online for free through the Gutenberg project.

William Chen has written a very good set of notes on Elementary Number theory. These notes cover much more than we will have time for in this course.

You can also have a look at some notes by Bruce Ikenaga. These are in Postscript format.

Another book is Elementary number theory by W. Edwin Clark, also in Postscript format.

To read more about various methods of proof, you can check out these notes.

Here is a list of the RSA labs Challenge numbers which give you from US$ 30,000 if you can find their prime factorization. There is also an associated FAQ.

The well-known number theorist William Stein has written some very good lecture notes on number theory which among other things cover material on factorization and cryptography, more advanced than in this course. These notes also give a very good introduction to Elliptic curves, which is an important and very active number-theoretic research area, with applications in cryptography.

There is also a introductory book by W. Edwin Clark in Postscript format.

Here are some other books that can be found in the library, for the interested students. Most of them are more advanced than this course. They are ordered roughly in increasing order of difficulty, within each category.

Bolker: Elementary number theory: an algebraic approach.

Tattersall: Elementary Number Theory in Nine Chapters.

Rose: A course in number theory.

Davenport: The higher arithmetic.

Jordan and Jordan: Groups.

van der Waerden: Modern Algebra, volume I and volume II.

Bahturin: Basic structures of Modern Algebra.

Reid: Undergraduate commutative algebra.

Reid: Undergraduate algebraic geometry.

Goodaire and Parmenter: Discrete mathematics.