CS 70. Discrete Math & Probability
Current Schedule (Fall 2015)
Catalog Description: (4 units) Logic, infinity, and induction; applications include undecidability and stable marriage problem. Modular arithmetic and GCDs; applications include primality testing and cryptography. Polynomials; examples include error correcting codes and interpolation. Probability including sample spaces, independence, random variables, law of large numbers; examples include load balancing, existence arguments, Bayesian inference.
Prerequisites: CS 61A (or equivalent familiarity with basic programming) and sophomore mathematical maturity (that is: at least a rock solid understanding of Math 1A, Math 1B (or equivalents), and the math maturity that comes along with taking Math 53/54 --- possibly concurrently)
Course objectives: The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in Electrical Engineering and Computer Sciences. The course aims to present these ideas "in action"; each one will be geared towards a specific significant application. Thus, students will see the purpose of the techniques at the same time as learning about them.
- Propositions and Proofs
- Mathematical Induction: recursion, the stable marriage problem
- Arithmetic Algorithms: gcd, simple finite fields, primality testing, the RSA cryptosystem
- Polynomials and their Applications: error-correcting codes, secret sharing
- Probability and Probabilistic Algorithms: laws of large numbers, load balancing, probabilistic constructions, conditional probability, Bayesian inference, intro to continuous probability
- Diagonalization, Self-Reference and Uncomputability