Curriculum Map

Discrete Mathematics

Author:
Ramon A. Mata-Toledo, Professor, James Madison University, Harrisonburg, Virginia

This Curriculum Map provides a list of highly relevant and engaging content from throughout AccessScience for use in enriching your teaching. Site assets such as tables, graphs, diagrams, and biographies have been mapped to standard topics taught in a Discrete Mathematics course. Use the "Copy Link" functionality to paste a direct link from each asset into your school's learning management system for easy incorporation into your curriculum.

Course Topics

Introduction to Logic
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Article Section This section of the Logic circuits article describes logic circuit operations and explains why they use a two-value signal. copy link
Diagram This figure provides symbolic representations of the basic logic circuits (NOT, AND, OR, NAND, and NOR). It also shows the truth tables associated with these logic circuits. copy link
Diagram This figure provides an example of the most commonly used memory element (flip-flop). copy link
Article Section This section of the Logic article defines a proposition, discusses truth-values of propositions, and presents their basic logical connectives (not, and, or, implication, and biconditional). It also defines a tautology. copy link
Article Section This section of the Logic article provides examples of truth tables of the negation (not), conjunction (and), disjunction (or), and implication operators. It also shows how tautologies are recognized. copy link
Article Section This section of the Logic article, entitled Valid inferences, briefly describes the concepts of logical equivalence and inference rules. It also defines the modus tollens and modus ponens and provides a couple of examples. copy link
Article Section This section of the Logic article, entitled Logical deduction, describes the five basic tautological formulas, selected by Whitehead and Russell, from which all other tautologies can be derived. These are part of Principia Mathematica.
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Biography Bertrand Russell was one of two main authors of Principia Mathematica. This monumental work attempted to show that logic is the foundation of mathematics, and its publication is still relevant today.
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Biography Alfred Whitehead was an English mathematician who, along with Bertrand Russell, created Principia Mathematica.
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Biography George Boole was an English logician and author of the Laws of Thought, a book in which he described what is now known as Boolean algebra.
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Sets
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Article Section This section of the Set theory article defines the cardinality of sets for both finite and infinite sets. and explains the notation for denoting cardinality.
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Article Section This section of the Set theory article provides an example and diagram that illustrate the operations of union, intersection, and difference of sets.
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Biography Georg Cantor, a German mathematician, was the creator of set theory.

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Biography Friedrich Frege was a German mathematician credited with advances in logic and set theory.
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Biography John Venn's diagrams, widely used to represent sets, are named after him even though they were initally used by Leonhard Euler.
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Diagram This diagram is a representation of points on a plane using the Cartesian coordinate system. copy link
Biography Creator of analytical geometry, René Descartes was the first to establish the representation of points on a plane. copy link
Functions
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Article Section This section of the Algebra article defines when a relationship between variables is a function. copy link
Graph This graph shows how to represent points in a coordinate system, and provides an example of a function. copy link
Article Section Two sequential sections of the Algebra article describe exponential and logarithmic functions as inverse of one another. copy link
Article Section This section of the Algebra article describes polynomial functions and provides an example. copy link
Article Section This section of the Trigonometry article describes the sine, cosine, tangent, secant, cosecant, and cotangent using the unit circle in a rectangular system of coordinates. copy link
Table This table shows the values of trigonometric functions for sin, cos, sec, csc, tan, and cot in multiples of π/4. copy link
Article Section This section of the Trigonometry article describes the notions of even and odd functions, illustrated with the basic trigonometric functions. copy link
Sequences and Summations
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Article Section This section of the Progression article defines the term arithmetic progression and gives a formula for finding the nth term of the progression. It also gives the formula for calculating the sum of the first n terms of the arithmetic progression. copy link
Article Section This section of the Progression article defines the term geometric progression and provides formulas for calculating the nth term of the sequence and the sum of the terms of the progression depending on the common ration being less or greater than 1. copy link
Article Section This section of the Combinatorial theory article defines Fibonacci numbers and provides both the generating function and the closed formula for Fibonacci numbers. copy link
Matrices
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Article Section This section of the Matrix theory article, Representation of rotations, describes how matrices can be used to represent certain transformations in the Cartesian plane. copy link
Article Section This section of the Matrix theory article describes how to multiply matrices and provides an example. copy link
Article Section This section of the Matrix theory article describes simple axioms that are satisfied by vector addition and scalar multiplication. copy link
Number Theory
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Biography Euclid was a Greek mathematician whose fundamental work, The Elements, served as the foundation for teaching geometry for over 2,000 years. The book also set the foundation for what is now called number theory. copy link
Article Section This section of the article on Euclidean geometry describes the content of each of the 13 books that comprise Euclid's work, The Elements. copy link
Biography Pierre de Fermat contributed greatly to the development of number theory. His most famous conjecture is known as Fermat's last theorem, which remained unproven for more than 300 years until Andrew Wiles proved it correct in 1993. copy link
Article Section This section of the Number theory article describes the notion of congruence between two numbers a and b modulo another positive integer m. This section also defines the Euler phi function and presents Fermat's little theorem. copy link
Article Section Fermat's last theorem is briefly described in this section of the Number theory article, Diophantine equations. copy link
Biography Paul Erdös (1913–1996) is considered to be the most prolific mathematician in history, particularly in number theory. copy link
Biography Carl Friedrich Gauss (1777–1855) developed modular arithmetic. He is considered one of the greatest mathematicians of all times. copy link
Article This concise Division article provides a definition of division in both algebraic and polynomial terms. copy link
Article Section This section of the Algorithm article demonstrates the Sieve of Eratosthenes and Euclid's algorithm for calculating the greatest common divisor (gcd) of two given numbers. copy link
Article Section This section of the Computer programming article, entitled Problem solving, presents Euclid's algorithm for calculating the gcd of two given numbers using the concept of modulus using a computer language pseudo code. copy link
Article This article on numerical representation describes different notations used to represent integer numbers in a computer. copy link
Cryptography
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Article Section In the first section of the Cryptography article, Figures 1 and 2 show the confidentiality and authentication models of cryptography, respectively. copy link
Diagram This figure illustrates the enciphering computation in the Data Encryption Standard process. copy link
Diagram This figure shows the details of the Advanced Encryption Standard round function. copy link
Article Section This section of the Cryptography article provides a description of how the RSA algorithm works and presents its theoretical foundation. copy link
Counting
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Article Section This section of the Combinatorial theory article describes permutations and combinations. copy link
Article Section This section of the Combinatorial theory article provides a brief description of the pigeonhole principle. copy link
Article The Binomial theorem article explains this ubiquitous algebraic identity. copy link