abstractmath.org 2.0
help with abstract math
Revised 2013-05-22 Introduction to this website website TOC website index blog
TABLE OF CONTENTS
This is a list of all the major sections on this site. Each
section (in most cases) has its own table of contents. The index gives a more detailed access to the
topics covered.
Introduction
Background and attitude
Diagnostic Examples
The languages of math
Mathematical English
Assertions
Names
Glossary:
A B
C D
E F
G H
I J
K L M
N O
P Q
R S
T U
V W
X Y Z
The symbolic language of math
Symbolic
expressions
Grammar of the
symbolic language
Variables
Substitution
Some symbols used in math
Alphabets
Delimiters
Other symbols
More about math languages
Context
Conventions
Defaults
Displayed symbolic expressions
Embedding
Incomplete
notation
Intent
of assertions
Overloaded
notation
Parameters
Parenthetic assertions
Preconditions
and postconditions.
Redundancy
Scope
Suppression
of parameters
Synecdoche
Variations in meaning
Proofs
The nature of proofs
The role of proofs in math
Presentation of proofs
Forms of proof
Mathematical
Logics
Translation
problem
Mathematical reasoning
Logical
Constructions
And, or, not
Conditional assertions
Universally true assertions
Existence statements
Methods of
Deduction
Understanding math
Definitions
Mathematical
objects
Mathematical structures
Representations and models
Images and metaphors
Conceptual
and Computational
Other aspects of
understanding math
Abstraction
The
axiomatic method
Cognitive dissonance
Pattern recognition
The ratchet
effect
Doing math
Useful behaviors
Self-monitoring
Zooming and chunking
More useful behaviors
Useful behaviors for proofs
Dysfunctional attitudes and behaviors
Numbers
Natural
numbers
Integers
Rational
numbers
Real numbers
Decimal representation of real
numbers
Irrational numbers
Density of the reals
Sets
Sets: Notation
Some specific sets
Sets: Specification
Sets: Rules of Inference
Sets: Metaphors and images
Russell's paradox
Functions
Examples of
functions
Specification and definition of function
Images and metaphors for
functions
Objects associated with a function
The
name of a function
Domain and codomain
The
value of a function
The image of a function
The quotient of a function
Properties of functions
Composition of functions
Inverses of functions
Relations
Relations: Basics
Relations: Examples
Operations on relations
Properties of relations
Equivalence Relations
Derivatives
(some nice illustrative graphs but nothing else so far)
Index
Astounding
Math Stories
The unreliability
of numerical evidence
Finding
factors, or not
Sizes of
infinity