Index Index
Abelian Group Definition
a Limerick Poem
a Limerick Poem
Adjacency Matrix Method Subsection
Algebraic Systems Section
algorithm
a Limerick Poem
Alternating Group Definition
Alternating group
a Limerick Poem
An Glossary
Analog-to-digital Conversion Example
Antisymmetric Relation Definition
Associative Property Definition
Atom of a Boolean Algebra Definition
augmented matrix
a Limerick Poem
Automata Section
Automorphism
Inner Exercise
Basic Law Of Addition: Theorem
Basic Set Operations Section
Basis Definition
Biconditional Proposition Definition
Bijection Definition
Binary Conversion Algorithm Algorithm
binary matrix. See relation matrix
Binary Operation. Definition
Binary Representation Section
Binary Search Subsection
Binary Tree Definition
Binary Trees Section
Binomial Coefficient
Recursive Definition Definition
binomial coefficient Definition
Binomial Coefficient Formula Theorem
Binomial Theorem, The Theorem
Bipartite Graph. Definition
Bipartitie
a Limerick Poem
Bit Glossary
Boolean Algebra Definition
Boolean Algebras Section
Boolean Arithmetic Definition
Boolean Expression Definition
Boolean Expressions Section
Boolean matrix. See relation matrix
Bounded Lattice Definition
Breadth-First Search Subsection
Breadth-first Search Algorithm
Bridge Definition
Bubble Sort Subsection
Byte Glossary
Bézout’s lemma Theorem
Cancellation in Groups Theorem
Cardinality. Definition
Cartesian Product Definition
Center of a Graph Item
Center of a graph Item
Characteristic Equation Definition
Characteristic function Exercise
Characteristic Polynomial Example
Characteristic Roots Definition
Child
of a Root Definition
Chinese Remainder Theorem Theorem
Chromatic Number Definition
Circuit, in a graph Note
Closed Form Expression. Definition
Closest Neighbor Algorithm Algorithm
Closure Property Definition
Code
Polynomial Example
Codes
Linear Section
Coding Theory Section
Cofactor Definition
combinations Subsection
Commutative Property Definition
Compact Minset Notation Definition
Complement of a Lattice Element Definition
as an operation Definition
Complement of a set Definition
Complemented Lattice Definition
Complete Undirected Graph. Definition
Complex Number Glossary
Composite Integer Glossary
Composition of Functions Definition
Composition of Relations Definition
Concatenation Definition
Conditional Statement Definition
Congruence Modulo
conjunction, Logical Definition
Connected Component Definition
Connectivity in Graphs Section
Constant Glossary
Contradiction Definition
Contrapositive Definition
Converse Definition
Coset Definition
Coset Counting Formula Corollary
Coset Representative Definition
Cosets
Operation on Definition
Cosets and Factor Groups Section
Countable Set Definition
Counting Binary Trees Subsection
covering relation Definition
Creative Commons Glossary
Cycle Definition
Cycle Notation Subsection
Cyclic Group Definition Definition
Cyclic Subgroup Definition
data Structure Glossary
degree Definition
degree Sequence of a Graph Definition
derangement Subsection
detachment Table
Determinant Definition
diagonal matrix
a Limerick Poem
diagonalizable Matrix Definition
diagonalization Process, The Section
diameter of a Graph Item
digraph Paragraph
Dihedral Group
Definition Definition
dihedral Group Subsection
dimension of a Vector Space Definition
Direct Product
of Two Groups Definition
direct Product Definition
direct Products Section
direct proof Example
directed Graph Definition
directed graph Paragraph
disjoint Cycles Note
disjoint Sets Definition
disjunction, Logical Definition
distinct Glossary
distributive Lattice Definition
distributive Property Definition
divides Definition
division Property for Integers Theorem
division Property for Polynomials Theorem
divisors of an Integer Definition
duality for Boolean Algebras Definition
Eccentricity of a vertex Item
Edges
of a directed graph Definition
of an undirected graph Definition
Egg, Bob Poem
Eigenvalue Definition
Eigenvector Definition
Elementary Operations on Equations Theorem
Elementary Row Operations Theorem
Embedding of a graph Paragraph
Empty Graph Note
Empty set Paragraph
empty set
a Limerick Poem
Enumeration Paragraph
Equivalence Definition
Equivalence Classes Definition
Equivalence Relation Definition
Equivalence Relations Subsection
Euclidean Algorithm, The Subsection
Euler, Leonhard Subsection
Eulerian Paths, Circuits, Graphs Definition
Euler’s Formula Theorem
Euler’s Theorem Theorem
Koenigsberg Case Theorem
Even Integer Glossary
Existential Quantifier Definition
Exponentiation in Groups Definition
Expression Tree Subsection
Extended Rule Of Products, The Theorem
Factor Glossary
Factor Group Definition
Factor Theorem Theorem
Factorial Definition
Fibonacci Sequence Example
Matrix Representation Example
Fibonacci sequence
a Limerick Poem
Field Definition
field extension
a Limerick Poem
Finite-State Machine Definition
Finite-State Machines Section
Five-Color Theorem Theorem
Flow Augmenting Path Definition
Forest. Definition
Formal Language Definition
formal logic
a Limerick Poem
Four-Color Theorem Theorem
Frankovich, Jesse Poem
Free Monoids and Languages Section
Function Definition
Bijective Definition
Composition Definition
Equality Definition
Injective Definition
One-to-one Definition
Onto Definition
Surjective Definition
Functions
Of two Variables Subsection
Functions Between Two Sets
Set of Definition
Fundamental Theorem of Group Homomorphisms Theorem
Gauss-Jordan Algorithm Algorithm
genealogical terms List
Generalized Set Operations Definition
Generate Definition
Generating Function Definition
Generating Functions Section
Closed form expressions for Subsection
Operations on Subsection Definition
Generation Problem Problem
Generator Definition
George Boole
a Limerick Poem
Glossary Glossary
Graph
Data Structures Section
Multigraph Definition
Simple Directed Definition
Simple Undirected Definition
Graph Coloring Definition
Graph Optimization Section
Graphic Sequence Definition
Gray Code Example
Gray Code Decoder Exercise
Greatest Common Divisor (
Greatest Element Definition
Greatest Lower Bound Definition
Group Definition
Hamiltonian Paths, Circuits, and Graphs Definition
Hamming Distance Definition
Hasse Diagram Paragraph
Homogeneous Recurrence Relation. Definition
Homomorphism Definition
Group Section
Howlett,Chris Poem
Idempotent Property Definition
Identity Function Definition
Identity Matrix Definition
Identity Property Definition
Iff Glossary
Image of an Element. Definition
Implication Definition
Improper subset Paragraph
Inclusion-Exclusion, Laws of Theorem
Indirect proof Paragraph
Indirect Reasoning Table
Induced Subgraph Definition
Induction and Recursion Subsection
Injection Definition
Integer Glossary
Integers Modulo
Additive Group Definition
Multiplicative Group Definition
Integral Domain Definition
Intersection Definition
Into Glossary
Inverse
Logical Definition
Matrix Definition
Inverse Function
of a function on a set Definition
Inverse Property Definition
Involution Property Definition
Irrational Number Glossary
Irreducibility of a Polynomial Definition
Isomorphic Graphs Definition
Isomorphism
Group Definition
Isomorphisms Section
Join Definition
Karnaugh map Paragraph
Kernel Definition
kernel of a function Exercise
Kruskal’s Algorithm Algorithm
Lagrange’s Theorem Theorem
LaTeX Glossary
Lattice Definition
Lattice Paths Exercise
Lattices Section
Laws of Matrix Algebra Section
Leaf of a binary tree Item
Leaf, of a binary tree Item
Least Element Definition
Least Upper Bound Definition
Left Distributive Property Definition
Level of a vertex Paragraph
Levels of Abstraction Subsection
Limerick
countably infinite Poem
Enumerative Combinatorics Poem
Linear Code Paragraph
Linear Combination. Definition
Linear Dependence Definition
Linear Equations
over the Integers Mod 2 Section
Linear Equations in a Group Theorem
Linear Independence Definition
Logarithm
General Base Definition
Logarithm, base 2 Definition
Logarithms Subsubsection
Properties Theorem
Logic Design Section
logical matrix. See relation matrix
Lower Bound Definition
Machine of a Monoid Section Definition
Many Faces of Recursion, The Section
Matrix Addition Definition
Matrix Inversion Section
Matrix Multiplication Definition
Matrix Oddities Section
Maximal flow Paragraph
Meet Definition
Merge Sort Subsection
Mesh Graph Exercise
Minimal Spanning Tree Definition
Minimum Diameter Spanning Tree Definition
Minor Definition
Minset Definition
Minset Normal Form Definition
Minterm Definition
Minterm Normal Form Definition
Modular Addition Definition
Modular Arithmetic Subsection
Properties Subsection
Modular Multiplication Definition
Modus Ponens
see Detachment Table
Modus Tollens
see Indirect Reasoning Table
Monoid Definition
of a Finite-State Machine Section
Monoids Section
Multigraph Definition
Multiple Pop and Push Definition
Multiples Glossary
Multiplicative Inverses Definition
N-cube Definition
Natural Homomorphism Definition
Natural Numbers Glossary
Negation, Logical Definition
Network Definition
Networks Subsection
Ngai, Steve Poem
Nim Exercise
Nonhomogeneous of Finite Order Linear Relations
Solution Subsection
Nonnegative Number Glossary
Normal Subgroup. Definition
Normal Subgroups Section Subsection
Odd Integer Glossary
Operation Tables Subsection
Operations Section
Order
of elements of a finite cyclic group Theorem
Order of a Group Element Definition
Order of a Recurrence Relation Definition
Order Sequence Definition
Ordering Diagram Paragraph
Oslan, Steven Item
Parent of a vertex Definition
Partial Ordering Definition Definition
Partially ordered set Definition
Partition
of a group by cosets Theorem
partition Definition
Path Graph Definition
Path, in a graph Note
Perfect Codes Exercise
Perfect Graph Exercise
Permutation Definition Definition
Permutation Counting Formula Theorem
Permutation Groups Section
Permutations
Composition Note
Phrase Structure Grammar Definition
Pigeonhole Principle Theorem
Planar Embedding of a Graph Definition
Planar Graph Definition
Plane Graph Definition
Polynomial
Irreducible Definition
Polynomial Addition Definition
Polynomial Code Example
Polynomial Expression
Non-recursive). Definition
Recursive definition Definition
Polynomial Multiplication Definition
Polynomial over a Ring Definition
Polynomial Units Theorem
Polynomials Subsection
Polynomials and their evaluation Subsection
Poset Definition
Posets Revisited Section
Positive Number Glossary
Power Series Definition
Power Series Units Theorem
Power Set Definition
Power Set Cardinality Theorem Theorem
Powers Glossary
Powers of Functions Definition
Predicate Paragraph
PreTeXt Glossary
Prime Glossary
Prime number Paragraph
Prim’s Algorithm Algorithm
Products
Extended Rule of Theorem
Rule of Theorem
Proper subset Paragraph
Properties of Functions Section
Properties of Operations Subsection
proposition Definition
Propp, Jim Paragraph
psheil Poem
Radius of a graph Item
Range of a Function. Definition
Rational Number Glossary
Real Number Glossary
Recognition Problem Problem
Rectangular codes Exercise
Recurrence Relation Definition
Recurrence Relations
Solving Subsection
Recurrence Relations Obtained from “Solutions” Subsection
Recursive Language Definition
Recursive Searching Subsection
Reducible Polynomial Definition
References References
Reflexive Relation Definition
Regions of a Planar Graph Paragraph
Regular Grammar Definition
Relation Definition
relation matrix Definition
Relation Notation Paragraph
Relation on a Set Definition
Relatively Prime Definition
Right Distributive Property Definition
Ring Definition
Commutative Definition
Ring Isomorphism. Definition
Ring with unity Definition
Robinson, Andrew Poem
Rooted Tree Definition
Rooted Trees Section
Row Equivalent Matrices Definition
Rule Of Products, The Theorem
SageMath Glossary
SageMath Note
bridge hands Subsection
Cartesian Products and Power Sets Subsection
Functions Subsection
Graphs Subsection
Kruskal’s Algorithm Subsection
Matrix Diagonalization Subsection
Matrix Exponential Subsection
Matrix Reduction Subsection
Modular Arithmetic Subsection
Power Series Subsection
Search in a Graph Subsection
Sets Subsection
Scalar Multiplication Definition
Sequence Definition
Sequences Section
Operations on Definition
Recursively Defined Subsection
Set of Functions Between Two Sets Definition
Set-Builder Notation Paragraph
Sheffer Stroke Definition
SheilaB Poem
Simple Undirected Graph Definition
Solution Set Definition
solutions Appendix
Some General Properties of Groups Section
Span Definition
Spanning Subgraph Definition
Spanning Tree Definition
Spanning Trees Section
Spindel, Howard Poem
Stack Subsection Glossary
Strings over an Alphabet Definition
STT. See Sun Tzu’s Theorem
Subgraph Definition
Subgroup Item
Conditions Theorem
Submonoid
Generated by a Set Definition
Subsystem Definition
Subsystems Section
Subtraction Glossary
Summation Notation and Generalizations Section
Sun Tzu’s Theorem Theorem
Surjection Definition
Switching Theory Section
Symmetric Difference Definition
Symmetric Group Definition
Symmetric Relation Definition
Syndrome Example
Systems of Linear Equations Section
Tautology Definition
Term Glossary
The Integers Modulo
Three Utilities Puzzle Paragraph
To Glossary
Tournament Graph Definition
Transitive Closure Definition
Transitive Relation Definition
Transposition Definition
Traveling Salesman Problem, The Subsection
Traversals of Binary Trees Subsection
Traversals of Graphs Section
Tree Definition
Triple Repetition Code Example
Truth Set Definition
Unary Operation. Definition
Union Definition
Unique Glossary
Units
of a ring Definition
of Polynomial Rings Theorem
of Power Series Rings Theorem
Unity of a Ring Definition
Universal Quantifier Definition
Universe Definition
Upper Bound Definition
Value of a Flow Definition
Variable Glossary
Vector Space Definition
Vector Spaces Section
Venn, John Subsection
Weighted Graph Definition
What Is a Tree? Section
XOR linked list Example
Zero Divisor Definition
zqms Poem
