2014 - 2015

  Discrete Mathematics                                                                                 
Prof. Simon LitsynEngineering Studies - Classrooms001Sun1500-1800 Sem  1
University credit hours:  3.0

Course description
1. Combinatorics (weeks 1-5)
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.

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