Mathematics for Computer Science

Livro digital

Título:
Mathematics for Computer Science

Autor:
Eric Lehman, F. Thomson Leighton, Albert R. Meyer

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Proving programs correct, designing efficient algorithms, and reasoning about data structures all demand a solid grasp of discrete mathematics. This MIT textbook opens with proofs and the Well Ordering Principle, then builds through logical formulas, induction, and recursive data types before tackling infinite sets—equipping you with the rigorous foundation that separates competent coders from those who can formally verify their own work. The book's five parts methodically cover every essential domain. Part I establishes proof techniques and mathematical data types. Part II dives into number theory (including RSA encryption), directed graphs, communication networks, and planar graphs. Part III develops counting skills through generating functions and asymptotic analysis. Part IV introduces probability spaces, random variables, and deviation from the mean. Part V closes with recurrences from Towers of Hanoi to divide-and-conquer analysis. Unexpected highlights include the Stable Marriage algorithm, the SAT problem, Turing's codes, and a chapter on Gambler's Ruin that directly connects probability to real-world risk. This is the same text used in MIT's renowned Mathematics for Computer Science course—freely available under Creative Commons and thoroughly class-tested. You gain not just mathematical literacy but a framework for thinking about computation itself: how to model problems, prove properties of systems, and reason under uncertainty. Whether you are a self-taught programmer seeking theoretical depth or a student preparing for advanced CS work, this book delivers lasting conceptual tools.