abstractmath.org 2.0

help with abstract math



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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