abstractmath.org 2.0

help with abstract math

Produced by Charles Wells Revised 2017-01-22
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# TABLE OF CONTENTS

This is a list of all the major articles on this site. The index gives a more detailed access to the
topics covered.

Introduction

Index

Background and attitude

Diagnostic Examples

The languages of math

** Mathematical English**

Distinctive features of math English

Assertions and statements

Names

Glossary

**The symbolic language of math**

Symbolic
expressions

Variables

Substitution

Variable objects

Alphabets

Delimiters

Other symbols

**More about math languages**

Context

Embedding

Overloaded
notation

Preconditions
and postconditions.

Redundancy

Suppression
of parameters

Variations in meaning

Scope

** **Conventions

Defaults

Intent
of assertions

Parameters

Mathematical reasoning

And, or, not

Conditional assertions

Universally true assertions

Existence statements

Presentation of proofs

Forms of proof

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

Generalization

The ratchet
effect

Pattern recognition

Cognitive dissonance

Variable objects

Doing math

Useful behaviors

Dysfunctional attitudes and behaviors

Numbers

Natural
numbers

Integers

Rational
numbers

Real numbers

Sets

Sets: Notation

Some specific sets

Sets: Specification

Subsets and inclusion

Sets: Rules of Inference

Sets: Metaphors and images

Functions

Examples of
functions

Specification and definition of function

Notation and terminology for functions

Properties of functions

Images and metaphors for
functions

Representations of continuous functions

Representations of discrete functions

Derivatives

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