Basic notions of the sets theory. Functions. Counting methods. Inclusion-exclusion. Generating functions. Recurrence relations. Binomial coefficients. Combinatorial identities. Stirling approximation. Entropy function.

 

Recommended literature:

 

• Brualdi, R.A., Introductory combinatorics. 3rd ed., North-Holland, 1992.

• McEliece, R.J., R.B. Ash and C. Ash. Introduction to discrete mathematics. McGraw-Hill, 1989.

• 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 leact common multiple. Euler and Fermat theorems. Euclid’s algorithm. Solving linear congruences. Chinese remainder theorem. Density of primes.

 

Recommended literature:

 

• Niven, I., H.S. Zuckerman and H.L. Montgomery. An introduction to the theory of numbers. 5th ed., Wiley, 1991.

• Robbins N. Beginning Number Theory 2nd ed. Jones&Bartlett Publishers,2006.

 

3. Groups (week 9)

 

Groups and sub-groups. Normal sub-groups. Cosets. Factor-groups. Lagrange theorem. Cyclic groups. Order.

 

Recommended literature:

 

• Dean, R.A., Elements of abstract algebra. Wiley, 1966.

 

4. Finite fields (weeks 10-14)

 

Rings and fields. Structure of finite fields. Minimal polynomials. Uniqueness of fields. Fermat theorem. Implementation of fields operations.

 

Recommended literature:

 

• Macwilliams F.J.,Sloane N.J.A . The Theory of Error-Correcting Codes. Elsevier Science,1996.

• McEliece, R.J., Finite fields for computer scientists and engineers. Kluwer, 1987.

• Lidl, R. and H. Niederreiter. Finite fields. 2nd ed., Cambridge University Press, 1997.