User:Jshflynn/Howson Handbook
Chapter $1$: Some Mathematical Language
Connectives
Definition:Equivalent Statements
Axioms
Definition:Contrapositive Statement
Variables and Quantifiers
Definition:Variable/Propositional Logic
Definition:Alphabetic Substitution
Definition:Contingent Statement
Definition:Universal Quantifier
Definition:Existential Quantifier
Equality
Axiom Systems
Definition:Theorem (Formal Systems)
Definition:Independent Statements
Chapter $2$: Sets and Functions
Sets
Sets
Definition:Membership Relation
Definition:Index (Indexing Set)
Definition:Set Intersection/Family of Sets
Definition:Set Union/Family of Sets
Definition:Relative Complement
Definition:Symmetric Difference
Graphs and Functions
Definition:Codomain of Mapping
Definition:Image of Element under Mapping
Definition:Set of All Mappings
Definition:Restriction of Mapping
Definition:Extension of Mapping
Some Special Types of Function
Composition of Functions
Definition:Commutative Diagram
Definition:Preimage of Subset under Mapping
Definition:Left Inverse Mapping
Definition:Right Inverse Mapping
Functions of Several Variables
Definition:Mapping/General Definition
Operations
Definition:Operation/Binary Operation
Definition:Operation/N-Ary Operation
Definition:Commutative Operation
Definition:Associative Operation
Definition:Distributive Operation
Definition:Algebraic Structure
Definition:Closed Algebraic Structure
Chapter $3$: Equivalence Relations and Quotient Sets
Binary Relations
Definition:Relation/General Definition
Definition:Transitive Relation
Definition:Equivalence Relation
Definition:Antisymmetric Relation/Definition 1
Quotient Sets
Definition:Equivalence Relation Induced by Mapping
Definition:Set Partition/Definition 2
Chapter $4$: Number Systems $\text{I}$
Peano's Axioms
A Set-Theoretic Approach
The Rational Integers
The Rational Numbers
Chapter $5$: Groups $\text{I}$
Subgroups
If you would like to take over
I have to stop doing this for a week so I'm turning off the log in page for me. If anyone would like to take over, here you go:
The List
+ Chapter 4: Number Systems I
Definition:Natural Number
++ Peano's Axioms
Definition:Successor Mapping on Natural Numbers
Axiom:Peano's Axioms
Principle of Mathematical Induction
Definition by Induction of Natural Number Addition
Definition:Multiplication/Natural Numbers/Minimal Infinite Successor Set
Definition:Inequality
Definition:Trichotomy
Definition:Relation Compatible with Operation
Definition:Well-Ordering/Definition 1
Definition:Ordered Set
Definition:Totally Ordered Set
++ A Set-Theoretic Approach
Definition:Set Equivalence
Definition:Cardinality
Definition:Cardinal
Definition:Cardinal Number
Definition:Zero (Cardinal)
Definition:One (Cardinal)
Definition:Sum of Cardinals
Definition:Product of Cardinals
Definition:Cardinal Exponentiation
Definition:Finite Set
Definition:Infinite Set
Definition:Finite Cardinal
Definition:Infinite Cardinal
Natural Numbers as Cardinals
Definition:Ordinal/Transfinite
Definition:Countable Set/Definition 1
Definition:Uncountable Set
Continuum Hypothesis
++ The Rational Integers
Definition:Integer
Definition:Addition/Integers
Definition:Multiplication/Integers
Definition:Negative/Integer
Definition:Positive/Integer
++ The Rational Numbers
Definition:Rational Number
Definition:Addition/Rational Numbers
Definition:Multiplication/Rational Numbers
+ Chapter 5: Groups I
Definition:Group
Definition:Multiplicative Notation
Definition:Additive Notation
Definition:Identity (Abstract Algebra)/Two-Sided Identity
Definition:Inverse (Abstract Algebra)/Inverse
Definition:Semigroup
Definition:Monoid
Definition:Magma
Definition:Abelian Group
Definition:Finite Group
Definition:Order of Structure
Definition:Order of Group Element
Definition:Infinite Group
Definition:P-Group
Definition:Periodic Group
Definition:Aperiodic Group
Definition:Cyclic Group
Definition:Power of Element/Group
Definition:Generator of Group
Definition:Group of Permutations
Definition:Symmetric Group
Definition:Alternating Group
Definition:Symmetry Group
Definition:Dihedral Group
++ Subgroups
Definition:Subgroup
Definition:Proper Subgroup
Definition:Permutation Group
Definition:Coset/Left Coset
Definition:Coset/Right Coset
Definition:Index of Subgroup
Definition:Normal Subgroup/Definition 1
++ Chapter 6: Rings and Fields
Definition:Ring
Definition:Additive Group
Definition:Ring with Unity
Definition:Commutative Ring
Definition:Subring
Definition:Unit of Ring
Definition:Group of Units
Definition:Division Ring
Definition:Field
Definition:Subfield
Definition:Ordered Ring
Positive Elements of Ordered Ring
Definition:Integral Domain
Definition:Zero Divisor
Definition:Zero Divisor/Ring
Definition:Characteristic (Ring Theory)
Definition:Ideal (Ring Theory)
Definition:Left Ideal
Definition:Right Ideal
Definition:Maximal Ideal
Definition:Subset Product
Definition:Principal Ideal
Definition:Generator of Ideal
Definition:Principle Ideal Domain
Definition:Greatest Common Divisor/Integral Domain
Definition:GCD Domain
Definition:Coprime/GCD Domain
Definition:Lowest Common Multiple/Integral Domain
Definition:Irreducible (Ring Theory)
Definition:Associate/Commutative Ring
Definition:Unique Factorization Domain
+ Chapter 7: Homomorphisms and Quotient Algebras
Definition:Homomorphism (Abstract Algebra)
Definition:Group Homomorphism
Definition:Ring Homomorphism
Definition:Monomorphism (Abstract Algebra)
Definition:Epimorphism (Abstract Algebra)
Definition:Isomorphism (Abstract Algebra)
Definition:Endomorphism
Definition:Automorphism (Abstract Algebra)
Definition:Homomorphism (Abstract Algebra)/Image
Definition:Kernel of Group Homomorphism
Definition:Exact Sequence
Definition:Short Exact Sequence
Definition:Quotient Group
Definition:Quotient Ring
Definition:Quotient Field