Skip to main content
\(\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \renewcommand{\vec}[1]{\mathbf{#1}} \newcommand{\lt}{ < } \newcommand{\gt}{ > } \newcommand{\amp}{ & } \)


A Coset Counting Formula, Corollary
Abelian Group, Definition
a Limerick, Poem
Adjacency Matrix, Definition
Adjacency Matrix Method, Subsection
Algebraic Systems, Section
Alternating Group, Definition
Andrew Robinson, Poem
Antisymmetric Relation, Definition
Associative Property, Definition
Atom of a Boolean Algebra, Definition
Automata, Section
Inner, Exercise
Basic Law Of Addition:, Theorem
Basic Set Operations , Section
Basis, Definition
Biconditional Proposition, Definition
Bijection, Definition
Binary Conversion Algorithm, Algorithm
Binary Operation., Definition
Binary Representation, Section
Binary Search, Subsection
Binary Tree, Definition
Binary Trees, Section
Binomial Coefficient, Definition
Recursive Definition, Definition
Binomial Coefficient Formula, Theorem
Bipartite Graph., Definition
a Limerick, Poem
Boolean Algebra , Definition
Boolean Algebras, Section
Boolean Arithmetic, Definition
Boolean Expression, Definition
Boolean Expressions, Section
Bounded Lattice, Definition
Breadth-First Search, Subsection, Algorithm
Bridge, Definition
Bubble Sort, Subsection
Cancellation in Groups , Theorem
Cardinality., Definition
Cartesian Product, Definition
Characteristic Equation, Definition
Characteristic function, Exercise
Characteristic Roots, Definition
Chinese Remainder Theorem, Theorem
Chromatic Number, Definition
Closed Form Expression., Definition
Closest Neighbor Algorithm, Algorithm
Closure Property, Definition
Polynomial, Example
Group, Section
Coding Theory, Section
Combinations, Subsection
Commutative Property, Definition
Complement of a Lattice Element, Definition
as an operation, Definition
Complement of a set, Definition
Complemented Lattice, Definition
Complete Undirected Graph., Definition
Composition of Functions, Definition
Composition of Relations, Definition
Concatenation, Definition
Conditional Statement, Definition
Congruence Modulo m, Definition
Conjunction, Logical, Definition
Connected Component, Definition
Connectivity in Graphs, Section
Contradiction, Definition
Contrapositive, Definition
Converse, Definition
Coset, Definition
Coset Representative, Definition
Operation on, Definition
Cosets and Factor Groups, Section
Countable Set, Definition
Counting Binary Trees, Subsection
CRT, Theorem
Cycle, Definition
Cycle Notation, Subsection
Cyclic Group, Definition, Definition
Cyclic Subgroup, Definition
Degree, Definition
Degree Sequence of a Graph, Definition
Derangement, Subsection
Diagonalizable Matrix, Definition
Digraph, Paragraph
Dimension of a Vector Space, Definition
Direct Product, Definition
Direct Products, Section
Direct proof, Example
Directed graph, Paragraph
Disjoint Cycles, Note
Disjoint Sets, Definition
Disjunction, Logical, Definition
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
Eigenvalue, Definition
Eigenvector, Definition
Elementary Operations on Equations., Theorem
Elementary Row Operations, Theorem
Embedding of a graph, Paragraph
Empty set, Paragraph
Equivalence, Definition
Equivalence Class, Item
Equivalence Relation, Definition
Equivalence Relations, Subsection
Euclidean Algorithm, The , Subsection
Euler's Formula, Theorem
Euler's Theorem, Theorem
Koenigsberg Case, Theorem
Eulerian Paths, Circuits, Graphs, Definition
Existential Quantifier, Definition
Exponentiation in Groups, Definition
Expression Tree, Subsection
Factor Group, Definition
Factor Theorem, Theorem
Factorial, Definition
Fibonacci Sequence, Example
Field, Definition
Finite-State Machine, Definition
Finite-State Machines, Section
Five-Color Theorem, Theorem
Flow Augmenting Path, Definition
Forest., Definition
Formal Language, Definition
Four-Color Theorem, Theorem
Free Monoids and Languages, Section
Full binary tree, Item
Function, Definition
Bijective, Definition
Composition, Definition
Equality, Definition
Injective, Definition
One-to-one, Definition
Surjective, Definition
Of two Variables, Subsection
Fundamental Theorem of Group Homomorphisms, Theorem
Gauss-Jordan Algorithm, Algorithm
Generalized Set Operations, Definition
Generate, Definition
Generating Function, Definition
Generating Functions, Section
Closed form expressions for, Subsection
Operations on,, Subsection, Definition
Generation Problem, Problem
George Boole
a Limerick, Poem
Data Structures, Section
Simple Directed, Definition
Graph Coloring, Definition
Graph Optimization, Section
Graphic Sequence, Definition
Greatest Common Divisor (\(\gcd\)) , Definition
Greatest Element, Definition
Greatest Lower Bound, Definition
Group, Definition
Hamiltonian Paths, Circuits, and Graphs, Definition
Homogeneous Recurrence Relation., Definition
Homomorphism, Definition
Group, Section
Howlett,Chris, Poem
Idempotent Property, Definition
Identity Function, Definition
Identity Matrix, Definition
Identity Property, Definition
Image of an Element., Definition
Implication, Definition
Improper subset, Paragraph
Inclusion-Exclusion, Laws of , Theorem
Indirect proof, Paragraph
Induced Subgraph, Definition
Induction and Recursion, Subsection
Injection, Definition
Integral Domain, Definition
Intersection, Definition
Matrix, Definition
Inverse Function
of a function on a set, Definition
Inverse Property, Definition
Involution Property, Definition
Irreducibility of a Polynomial, Definition
Isomorphic Graphs, Definition
Group, Definition
Isomorphisms, Section
Kernel, Definition
Kruskal's Algorithm, Algorithm
Lagrange's Theorem, Theorem
Lattice, Definition
Lattices , Section
Laws of Matrix Algebra, Section
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
Linear Combination., Definition
Linear Dependence, Definition
Linear Equations in a Group, Theorem
Linear Independence, Definition
General Base, Definition
Logarithm, base 2, Definition
Logarithms, Subsubsection
Properties, Theorem
Lower Bound, Definition
Machine of a Monoid, Definition
Matrix Addition, Definition
Matrix Inversion, Section
Matrix Multiplication, Definition
Matrix Oddities, Section
Maximal flow, Paragraph
Merge Sort, Subsection
Minimal Spanning Tree, Definition
Minimum Diameter Spanning Tree, Definition
Minset, Definition
Minset Normal Form, Definition
Minterm, Definition
Minterm Normal Form, Definition
Modular Addition, Definition
Modular Arithmetic, Subsection
Properties, Subsection
Modular Multiplication, Definition
Monoid, Definition
of a Finite-State Machine, Section
Monoids, Section
Multigraph, Definition, Definition
Multiple Pop and Push:, Definition
Multiplicative Inverses., Definition
N-cube, Definition
Natural Homomorphism, Definition
Negation, Logical, Definition
Network, Definition
Networks, Subsection
Nonhomogeneous of Finite Order Linear Relations
Solution, Subsection
Normal Subgroup., Definition
Normal Subgroups, Section, Subsection
Operation Tables, Subsection
Operations, Section
of elements of a finite cyclic group, Theorem
Order of a Recurrence Relation, Definition
Partial Ordering, Definition, Definition
Partially ordered set, Definition
of a group by cosets, Theorem
Partition., Definition
Path Graph, Definition
Permutation, Definition, Definition
Permutation Counting Formula, Theorem
Permutation Groups, Section
Composition, Note
Phrase Structure Grammar, Definition
Pigeonhole Principle, Theorem
Planar Graph, Definition
Plane Graph, Definition
Irreducible, Definition
Polynomial Addition, Definition
Polynomial Code, Example
Polynomial Expression
Non-recursive). , Definition
Recursive definition, Definition
Polynomial Multiplication, Definition
Polynomial over a Ring, Definition
Polynomials, Subsection
Polynomials and their evaluation, Subsection
Poset, Definition
Posets Revisited, Section
Power Series, Definition
Power Set , Definition
Power Set Cardinality Theorem, Theorem
Powers of Functions, Definition
Proper subset, Paragraph
Properties of Functions, Section
Properties of Operations, Subsection
Proposition, Definition
Quantifiers, Section
Multiple, Subsection
Negation, Subsection
Range of a Function., Definition
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
Reducibile Polynomial, Definition
Reflexive Relation, Definition
Regular Grammar, Definition
Relation, Definition
Relation Notation, Paragraph
Relation on a Set, Definition
Relatively Prime, Definition
Right Distributive Property, Definition
Commutative, Definition
Ring Isomorphism., Definition
Ring with unity, Definition
Rooted Tree, Definition
Rooted Trees, Section
Row Equivalent Matrices, Definition
Rule Of Products, The, Subsection
Sage Note
bridge hands, Subsection
Cartesion Products and Power Sets, Subsection
Functions, Subsection
Graphs, Subsection
Kruskal's Algorithm, Subsection
Matrix Diagonalization, Note
Matrix Exponential, Note
Matrix Reduction, Note
Modular Arithmetic, Subsection
Power Series, Subsection
Search in a Graph, Subsection
Scalar Multiplication, Definition
Sequence, Definition
Sequences, Section
Operations on,, Definition
Recursively Defined, Subsection
Set-Builder Notation, Paragraph
Sheffer Stroke, Definition
Solution Set, Definition
Some General Properties of Groups, Section
Spanning Subgraph, Definition
Spanning Tree, Definition
Spanning Trees, Section
Spindel, Howard, Poem
Strings over an Alphabet, Definition
Subgraph, Definition
Generated by a Set, Definition
Subsystem, Definition
Subsystems, Section
Summation Notation and Generalizations , Section
Surjection, Definition
Symmetric Relation, Definition
Symmetric Difference, Definition
Symmetric Group, Definition
Systems of Linear Equations, Section
Tautology, Definition
The Binomial Theorem, Theorem
The Diagonalization Process, Section
The Machine of a Monoid, Section
The Many Faces of Recursion, Section
The Traveling Salesman Problem, Subsection
Three Utilities Puzzle, Paragraph
Tournament Graph, Definition
Transitive Closure, Definition
Transitive Relation, Definition
Transposition, Definition
Traversals of Binary Trees, Subsection
Traversals of Graphs, Section
Truth Set, Definition
Unary Operation. , Definition
Undirected Graph. , Definition
Union, Definition
Unity of a Ring, Definition
Universal Quantifier, Definition
Universe, Definition
Upper Bound, Definition
Value of a Flow, Definition
Vector Space, Definition
Vector Spaces, Section
Weighted Graph, Definition
What Is a Tree? , Section
Zero Divisor, Definition