Discrete Math: Functions

Define: Functions

Let A and B be nonempty sets. A function f   from A to B, which is denoted f: A –> B, is a relation from A to B such that all a ∈ Dom(f), f(a), the f-relative set of a, contains just one element of B. Naturally, if a is not in Dom(f), then f(a) = ∅. If f(a) = {b}, it is traditional to identify the set {b} with the element b and write f(a) = b.

Simplified Definition: Functions

Definition 1.a: ...

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The Pigeonhole Principle

The following excerpt was taken from:
Kolman, Busby, & Ross(2009), Discrete Mathematical Structures, 6th ed. Upper Saddle River, NJ: Pearson Prentice Hall

“Theorem: The Pigeonhole Principle

The Pigeonhole Principle is a proof technique that often uses discrete math’s counting methods.

If n pigeons are assigned to m pigeonholes, and m < n, then at least one pigeonhole contains two or more pigeons.

Pigeonhole Principle – Proof

Suppose each pigeonhole contains at most 1 pigeon. Then at most m pigeons have been assigned. But since m ...

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Discrete Math Resources

This post was created to list resources for undergraduate students who are taking a course related to discrete mathematical structures. The links listed here should be used for to learn the fundamentals of discrete mathematical structures.

Discrete Math – Text Based Tutorials

Sets:
http://www.mathsisfun.com/sets/sets-introduction.html

Matrices:
http://home.scarlet.be/math/matr.htm

Propositions & Logical Operations:
http://www.stat.berkeley.edu/~stark/SticiGui/Text/logic.htm

Methods of Proof:
http://www.mathpath.org/proof/proof.methods.htm

Mathematical Induction:
http://people.richland.edu/james/lecture/m116/sequences/induction.html

Combinations and Permutations:
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Pigeonhole Principle:
http://www.cut-the-knot.org/do_you_know/pigeon.shtml

New York State University – Power Point Presentation:
http://cs.nyu.edu/courses/summer03/G22.2340-001/index.htm
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Fundamentals of Discrete Math

Fundamentals of Discrete Mathematical Structures

This post contains a synopsis of the fundamentals of discrete mathematical structures. This post was created during my second year of college while studying to attain a Bachelors of Science in Computer Science.  The discrete math course is a necessary requirement in attaining a B.S. in Computer Science.

“The origins of matrices goes back to approximately 200 B.C.E, when they were used by the Chinese to solve linear systems of equations” (Kolman, Busby, & Ross, 2009).

Are you interested in ...

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Six Trigonometric Functions in Terms of Others

Trigonometric Identities

“In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle with radius 1, where a triangle is formed by a ...

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