discrete mathematics problems and solutions

Prove that a complete graph with n vertices contains n(n )/ edges. Show that if n people attend a party and some shake hands with others (but not with themselves), then at the end, there are at least two people who have shaken hands with the same number of people. Show that every simple graph has two vertices of the same degree. Prove that the sum of the degrees of the vertices of any finite graph is even. Lovász and K.1 raph Theory Problems and Solutions Tom Davis November, 005 Problems.

Supplementary discrete mathematics Lecture notes by L.

How to Write Proofs, from Professor Larry Cusick's page at California State University, Fresno.

A collection of logic resources intended for homeschoolers.

Nic Ford's personal webpage, which contains a tutorial on logic, set theory and the foundations of mathematics.

Columbia University's Spring 2009 course in discrete mathematics, offered by the Department of Computer Science.

Forum for proposing and solving math problems.Alcumus - interactive problems and solutions for counting and probability.Wiki pages for number theory articles and problems, and counting articles and problems.MIT (ADUni) Discrete Mathematics course.Full set of lecture videos and notes from the University of Colorado.Introduction to Counting and Probability.

Schaum's Outline of Discrete Mathematics by Lipschutz and Lipson is another possible resource. You may also buy a copy of the following text, which is used in the Columbia University course: Discrete Mathematics and its Applications, 6th ed.

Notes on Discrete Mathematics, by James Aspnes, which is used in the Yale University CPSC 202 class.

Discrete Mathematics with Algorithms, by M.

A Short Course in Discrete Mathematics, by Edward A.

MIT Assignments and Solutions Exams Įxams are open notes, as they are in Columbia University's COMS 3203 course in Discrete Mathematics (as of Spring 2009). Generating functions, Number Theory, Cryptography Logic, Proofs, and Mathematical Reasoning

Video: The pigeonhole principle and examples inclusion/exclusion theorem and examples a combinatorial card trick.

Video: Counting problems using combinations, distributions.

Video: Solving recurrence equations (cont.).

Video: Basic arithmetic and geometric sums, closed forms.

Video: Equivalence Relations and Partial Orders.

Video: Functions 1, Video: Functions 2, Video: Functions 3.

Video: Diagonalization, functions and sums reviewįunctions and Relations.

Lesson 1.8: Compound Propositions and Useful Rules.

Lesson 1.1: Introduction to boolean logic.

Video: More logic: quantifiers and predicates (no audio).

Video: Boolean Algebra and formal logic (no audio).

Discrete mathematics problems and solutions