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6.042

Mathematics for Computer Science

Undergraduate · Historical course

Spring 2015

This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds: 1. Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations. 2. Discrete structures: graphs, state machines, modular arithmetic, counting. 3. Discrete probability theory. On completion of 6.042J, 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. This course is part of the {{% resource_link "70d06f44-b623-42be-9057-dc4b4773a7d6" "Open Learning Library" %}}, which is free to use. You have the option to sign up and enroll in the course if you want to track your progress, or you can view and use all the materials without enrolling.

Readings

Fall 2010

Topics

  • Introduction and proofs
  • Induction
  • Strong induction
  • Number theory I
  • Number theory II
  • Graph theory and coloring
  • Matching problems
  • Graph theory II: minimum spanning trees
  • Communication networks
  • Graph theory III
  • Relations, partial orders, and scheduling
  • Sums
  • Sums and asymptotics
  • Divide and conquer recurrences
  • Midterm
  • Linear recurrences
  • Counting rules I
  • Counting rules II
  • Probability introduction
  • Conditional probability
  • Independence
  • Random variables
  • Expectation I
  • Expectation II
  • Large deviations
  • Random walks

Readings

Fall 2005

Topics

  • Good and Bad Proofs Course Information
  • Propositions and Proofs
  • Proofs by Contradiction and Cases
  • Predicate Logic
  • Sets and Functions
  • Induction I
  • Induction II
  • Relations I
  • Relations II
  • Graph Theory I
  • Graph Theory II
  • Graph Theory III
  • Graph Theory IV
  • Number Theory I
  • Number Theory II
  • Number Theory III
  • State Machines I: Invariants Fallacies with Infinity
  • State Machines II: Derived Variables, Stable Marriage Problem
  • Sums and Series I
  • Sums and Series II Mid-course Survey
  • Asymptotics
  • Counting I
  • Counting II
  • Counting III (with Magic Trick Solution)
  • Counting IV
  • Generating Functions I
  • Generating Functions II
  • Introduction to Probability
  • Conditional Probability and Independence
  • Random Variables
  • Distribution and Density, Binomial Distribution
  • Expectation
  • Linearity of Expectation
  • Variance
  • Sampling and Confidence
  • Law of Large Numbers
  • Random Walks

Readings

Sources