Short Course Description
1. Combinatorics (weeks 1-5)
Basic notions of set theory. Functions. Counting methods. Inclusion-exclusion Principle. Pigeon hole Principle. Generating functions. Recurrence relations. Binomial coefficients. Combinatorial identities. Stirling approximation. Entropy function.
Recommended literature:
Introductory Combinatorics (3rd Edition) 3rd Edition, by Richard A. Brualdi
Introduction to Discrete Mathematics Hardcover, June 1, 1989
by Robert J. McEliece, Robert B. Ash, and Carol Ash
אקדמיה הוצאה לאור, 2000 ש.גירון וש.דר, מתמטיקה בדידה (מהדורה שניה),
נ.ליניאל ומ.פרנס, מתמטיקה בדידה, בן צבי מפעלי דפוס, 2001
2. Number theory (weeks 6-8)
Prime numbers. Prime factors. Greatest common divisor and least common multiple. Euler and Fermat theorems. Euclid's algorithm. Solving linear congruences. Chinese remainder theorem. Density of primes.
Recommended literature:
An introduction to the theory of numbers. 5th ed., Wiley, 1991. By, Niven, I., H.S. Zuckerman and H.L. Montgomery.
Beginning Number Theory 2nd ed. Jones&Bartlett Publishers,2006. By, Robbins N.
3. Groups (week 9)
Groups and sub-groups. Normal sub-groups. Cosets. Factor-group. Lagrange theorem. Cyclic groups. Order of an element.
Recommended literature:
Elements of abstract algebra. Wiley, 1966. By, Dean, R.A.
4. Finite fields (weeks 10-14)
Rings and fields. Structure of finite fields. Minimal polynomials. Uniqueness of fields. Fermat theorem. Implementation of field operations.
Recommended literature:
The Theory of Error-Correcting Codes. Elsevier Science,1996. Macwilliams F.J.,Sloane N.J.A
Finite fields for computer scientists and engineers. Kluwer, 1987. McEliece, R.J.
Finite fields. 2nd ed., Cambridge University Press, 1997. Lidl, R. and H. Niederreiter.
Full syllabus is to be published
