by Karl Petersen
Publisher: University of North Carolina 2008
Number of pages: 65
These notes provide an introduction to the subject of measure-preserving dynamical systems, discussing the dynamical viewpoint; how and from where measure-preserving systems arise; the construction of measures and invariant measures; some basic constructions within the class of measure-preserving systems; and some mathematical background on conditional expectations, Lebesgue spaces, and disintegrations of measures.
Download or read it online for free here:
by Oded Goldreich - Cambridge University Press
The book gives the mathematical underpinnings for cryptography; this includes one-way functions, pseudorandom generators, and zero-knowledge proofs. Throughout, definitions are complete and detailed; proofs are rigorous and given in full.
by Martin Tompa
Lecture notes for a graduate course on computational complexity taught at the University of Washington. Alternating Turing machines are introduced very early, and deterministic and nondeterministic Turing machines treated as special cases.
by Leslie Lamport - Addison-Wesley Professional
This book shows how to write unambiguous specifications of complex computer systems. It provides a complete reference manual for the TLA+, the language developed by the author for writing simple and elegant specifications of algorithms and protocols.
by Sanjeev Arora, Boaz Barak - Cambridge University Press
The book provides an introduction to basic complexity classes, lower bounds on resources required to solve tasks on concrete models such as decision trees or circuits, derandomization and pseudorandomness, proof complexity, quantum computing, etc.