This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042J, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.Interactive site components can be found on the Unit pages in the left-hand navigational bar, starting with Unit 1: Proofs.
This page provides quick links to lecture notes that I have written for various classes: CS254: A graduate class on computational complexity (Stanford) [Spring 2010 Class Home Page] [Notes for Lectures 1-8] CS278: A graduate class on computational complexity (Berkeley) [Spring 2001 Class Home Page] [Fall 2002 Class Home Page] [2001 Lecture Notes in book…
H. Xing, G. Nicholls, and J. Lee. Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, page 6912--6920. Long Beach, California, USA, PMLR, (09--15 Jun 2019)
M. Brennan, and G. Bresler. (2020)cite arxiv:2005.08099Comment: 175 pages; subsumes preliminary draft arXiv:1908.06130; accepted for presentation at the Conference on Learning Theory (COLT) 2020.