Fall 2004

MATH 340 / LGIC 210, MWF 12-1, DRL 3C2

Advanced Mathematical Methods in Computer Science

Professor Andre Scedrov

Starting September 15, we will also sometimes meet for extra classes on Wednesdays 3-4 in DRL 4C6.

Next class after Wednesday, November 10 is on Monday, November 29.

Office: Room 4E6 in David Rittenhouse Laboratory
Telephone: eight five nine eight three ( Math. Dept. Office: eight eight one seven eight )
Fax: three four zero six three
E-mail: lastname at math
Office Hours: By appointment


Further References


Counting, Permutations, and Combinations, Binomial Theorem, Multinomial Theorem, Combinations with Repetition [Grimaldi Chapter 1].

Algebra of sets, power set, cartesian product, binary relations, closure properties, equivalence relations, functions, Cantor Theorem, countable sets, equinumeruous sets, uncountability of the set of reals. [Grimaldi Chapters 3 and 5, and Moschovakis Chapters 1 and 2].

Recurrences, sums, and integer functions: Towers of Hanoi, Quicksort recurrence, floor and ceiling functions. [Grimaldi Chapters 10 and 5, and Graham et al. "Concrete Mathematics" Chapters 1-3].

Asymptotic functions, O-notation. [Grimaldi Chapter 5 Section 5.7, Buchmann Chapter 1 Section 1.4, and Graham et al. "Concrete Mathematics" Chapter 9].

Overview of Probability Theory: Probability Distribution, Random Variable, Conditional Probability, Bayes Theorem, Expected Value. [Grimaldi Chapter 3, Buchmann Chapter 4, and Graham et al. "Concrete Mathematics" Chapter 8].

Basic Concepts of Cryptology: Substitution Ciphers, Permutation Ciphers, Vigenere Cipher, Rotor Machines, Attack Models. Symmetric Ciphers, Block Ciphers, One-Time Pad, Information-Theoretic Properties of One-Time Pad, Perfect Secrecy, Misuses of One-Time Pad, Malleability. Stream Ciphers, Linear Feedback Shift Register, Golomb's Randomness Postulates, Linear Complexity, Non-linear Filters, Knapsack Keystream Generator. [Buchmann Chapters 3 and 4].

Introduction to Number Theory: Congruences, Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, Modular Exponentiation by Repeated Squaring. [Buchmann Chapters 1 and 2].

Public-Key Cryptosystems: Diffie-Hellman Key Exchange, Person-in-the Middle Attack. Discrete Logarithm, Giant-Step Baby-Step Algorithm, Pohlig-Hellman Algorithm, ElGamal Public-Key Cryptosystem. RSA Public-Key Cryptosystem. Digital Signatures, Selective Forgery, Existential Forgery, Signature Schemes Based on RSA, Signature Schemes Based on Discrete Logarithm: ElGamal Signature Scheme.

Homework #1 Due in Class on Wednesday, September 29

This is a complete list of homework #1 due September 29, 2004.

Homework #2 Due in Class on Wednesday, October 13

This is a complete list of homework #2 due October 13, 2004.

Take-Home Midterm Exam Due in Class on Wednesday, November 3.

Please show all your work, not just the final result.

This is a complete list of midterm assignments due November 3, 2004.

Take-Home Final Exam Due in DRL 4E6 at 4 p.m. on Friday, December 17.

Please show all your work, not just the final result.

This is a complete list of assignments due December 17, 2004.