Meyer A.R. Mathematics for Computer Science

Massachusets Institute of Technology, 2010. — 519 p.Objectives of this book are to explain and apply the basic methods of mathematics in Computer Science, to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.After reading this book you will be able to:
reason mathematically about basic data types and structures (such as numbers, sets, graphs, and trees) used in computer algorithms and systems; distinguish rigorous definitions and conclusions from merely plausible ones; synthesize elementary proofs, especially proofs by induction.
model and analyze computational processes using analytic and combinatorial methods.
apply principles of discrete probability to calculate probabilities and expectations of simple random processes.What is a Proof?
The Well Ordering Principle.
Prepositional Formulas.
Mathematical Data Types.
First-Order Logic.
Induction.
Partial Orders.
Directed graphs.
State Machines.
Simple Graphs.
Recursive Data Types.
Planar Graphs.
Communication Networks.
Number Theory.
Sums & Asymptotics.
Counting.
Generating Functions.
Introduction to Probability.
Random Processes.
Random Variables.
Deviation from the Mean.