Mathematics for Computer Science

“Mathematics for Computer Science” from MIT OpenCourseWare is available in pdf format. Download lecture notes, assignments, exams and solutions.

Book Description

This course offers an 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 this course, 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.

Table of Contents

• What is a proof?
• The well ordering principle
• Propositional 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 and asymptotics
• Counting
• Generating functions
• Introduction to probability
• Random processes
• Random variables
• Deviation from the mean

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