Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages, and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.
Version 2.3 (Summer 2010) added a section on pushdown automata; aside from that, there were only minor corrections and changes. The most recent version, 2.3.1 (Summer 2011), is a very minor update, with one new proof and a few corrections.
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Foundations Of Computation is available in two free PDF versions, with different page sizes. See the links at the bottom of this page to access the PDFs. A printed version can be ordered from lulu.com for the cost of reproduction ($9.62), plus shipping. Readers are also welcome to print out the PDF themselves. The book can be freely redistributed in unmodified form for non-commercial purposes. This applies to the entire book, as well as to parts of the book, provided that proper attribution to the authors is given.
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(The image on the left is the cover of the print version of the book. The background image is a visualization of a small piece of the famous Mandelbrot set, which has nothing to do with the content of the book -- except for the fact that the Mandelbrot set is an example of a complicated and beautiful structure produced by very simple computational means. The region of the xy-plane that is shown on the cover is approximately 0.35471950 < x < 0.35473217 and 0.09540064 < y < 0.09542001).
Carol Critchlow (email@example.com)