nbro / understanding-math

Links to resources talking about how to learn & understand mathematics, and mathematical language, terminology and notation.

Understanding Mathematics

Articles

• Understanding Mathematics, a study guide by Peter Alfeld
• How to Develop a Mindset for Math at BetterExplained
• Understanding Math Concepts at AllKindsOfMinds
• What is conceptual understanding? by Keith Devlin
• Learning to Learn: Math Abstraction at BetterExplained
• How to study math by Paul

Papers

• Teaching Mathematics for Understanding by Van De Walle
• Can We Make Mathematics Intelligible? (1981) by R. P. Boas
• A Mathematician's Lament by Paul Lockhart
• How to Survive Your College Math Class (and Take Home Something of Value) by Matthew Saltzman and Marie Coffin
• Mathematics, morally by Eugenia Cheng

Books

• How to Solve It: A New Aspect of Mathematical Method by George Polya
• Measurement by Paul Lockhart
• A Mathematician's Lament by Paul Lockhart
• The Art and Craft of Problem Solving by Paul Zeitz

Videos

• Mathematics - The Language of the Universe
• The World of Mathematical Reality by Paul Lockhart
• Paul Lockhart teaching Go by Chaelim "Addy" Kim
• Five Principles of Extraordinary Math Teaching TEDx talk by Dan Finkel

Online Questions

• How to study math to really understand it and have a healthy lifestyle with free time? at Math StackExchange
• How do math geniuses understand extremely hard math concepts so quickly? at Quora

Slides

• Teaching for Conceptual Understanding: Exciting Mathematics by Juanita Copley

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Mathematical Language

Links to resources talking about "the mathematical language" and how to overcome problems encountered when reading, writing, interpreting and listening to mathematics.

Articles

• Language of mathematics at Wikipedia
• Mathematical Words: Origins and Sources by John Aldrich
• Communicating in the Language of Mathematics by David Moursund and edited by Dick Ricketts
• How to write mathematics clearly and keep more readers by Matthew Leitch
• How to understand math formulas at Interactive Mathematics
• The symbolic language of math by Charles Wells

Papers

• The Language and Grammar of Mathematics
• Reading Mathematics by John Hamal Hubbard
• A Guide to Writing Mathematics by Dr. Kevin P. Lee
• Mathematics and the Language of Nature by F. David Peat
• The language and grammar of mathematics by Timothy Gowers
• Learning the Language of Mathematics by Robert E. Jamison

Books

• Handbook for Spoken Mathematics by Lawrence A. Chang, Ph.D. (with assistance from Carol M. White and Lila Abrahamson)
• A Handbook of Mathematical Discourse by Charles Wells

Videos

• Math isn't hard, it's a language TEDx talk by Randy Palisoc

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Mathematical Notation & Terminology

Articles

• List of mathematical symbols at Wikipedia
• Mathematical operators and symbols in Unicode at Wikipedia
• History of mathematical notation at Wikipedia
• Mathematical and scientific symbols at http://www.uefap.com/
• LaTeX Math Symbols prepared by L. Kocbach (on the basis of another document by David Carlisle, Manchester University)
• Mathematical notation at Wikipedia
• Set notation at Wikipedia
• Notation in probability and statistics at Wikipedia
• Notation for differentiation at Wikipedia
• List of mathematical symbols by subject at Wikipedia
• Statistics synonyms at Wikipedia
• Glossary of probability and statistics at Wikipedia
• Glossary of calculus at Wikipedia
• Glossary of set theory at Wikipedia
• Glossary of linear algebra at Wikipedia
• Glossary of graph theory at Wikipedia
• Glossary of game theory at Wikipedia
• Glossary of mathematical symbols at Wikipedia
• List of mathematical constants at Wikipedia
• Glossaries of mathematics (it also includes other glossaries for more advanced topics) at Wikipedia
• LaTeX/Mathematics at Wikipedia

Papers

• Mathematical Operators at http://unicode.org
• Some Common Mathematical Symbols and Abbreviations (with History) by Isaiah Lankham, Bruno Nachtergaele, Anne Schilling

Books

• Mathematical Notation: A Guide for Engineers and Scientists by Edward R. Scheinerman
• The Cambridge Dictionary of Statistics by B. S. Everitt and Anders Skrondal

Videos

• Mathematical Notation - The Language of Mathematics by Sarada Herke

Slides

• Maths in Lectures: Understanding the Notation by Dr. David Butler

Online Questions

• All questions about mathematical notation sorted in descending order of votes at Math StackExchange
• All questions about mathematical notation sorted in descending order of votes at Stack Overflow
• All questions about mathematical terminology sorted in descending order of votes at Math StackExchange
• Where can I learn about mathematical notation? at Math StackExchange
• How to learn mathematical notation? at Stack Overflow
• How to become comfortable with mathematical notation? at Ask MetaFilter
• What is the status of generating LaTeX from handwriting at Tex StackExchange

Websites

• Wolfram Alpha
• Math Words

Github

• math-as-code by Jam3 (Github's repository)

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Mathematical Proofs

Articles

• Some Help on Reading Mathematics and Creating Proofs

understanding-math's Issues

Fix the link `Mathematical Words: Origins and Sources` by John Aldrich

Add link to Wikipedia article `Glossary of set theory`

https://en.wikipedia.org/wiki/Glossary_of_set_theory

Include link to paper `Can We Make Mathematics Intelligible?` by Boas

Terminology

A few resources dedicated to mathematical terminology

Articles

• https://en.wikipedia.org/wiki/Dependent_and_independent_variables#Statistics_synonyms
• https://en.wikipedia.org/wiki/Glossary_of_probability_and_statistics
• https://en.wikipedia.org/wiki/Glossary_of_areas_of_mathematics [not included because this Wikipedia article doesn't currently seem to be reliable, given the notice at the topi)
• https://en.wikipedia.org/wiki/Glossary_of_calculus

Books

• The Cambridge Dictionary of Statistics by B. S. Everitt and Anders Skrondal.

What's the goal of this project?

A few questions and sentences which may help to better define the goal of this project:

0. What's the goal of this project? Why does it exist? What does "understanding of mathematics" even mean?

1. Who's the target audience of this project?

   • So far, this repository seems useful only to people with a decent mathematical education, i.e. high-school or higher.

2. Which topics should or not be covered, i.e. which topics are related to the understanding of mathematics?

3. Topics covered so far

   • Notation
   • Formulas
     • How are formulas different from notation?
       - [x] Terminology
       - [x] "Mathematical language"
       • What is it, btw?
         - [x] Proofs
         - [x] "Understanding mathematics"
     • Resources without a more specific categorization.
       - [ ] Problem-solving
     • There are already links which point to resources related to this topic, but are not under a category or section called problem-solving.

4. Which links should be included?

   1. Should we include links only to online immediately and freely accessible resources or can we also have links to websites like Amazon?

5. Should this project include sections for sub-areas of mathematics?

6. Should this project include an advanced searching tool to facilitate its users to obtain a resource (to satisfy their needs) as fast as possible?

7. Is this project also concerned with the history of mathematics in the context of understanding it (e.g. history of mathematical notation, terminology, etc)?

8. What about websites like https://math.stackexchange.com?

Notation

A few resources dedicated to mathematical notation

Articles

• https://en.wikipedia.org/wiki/Set_notation
• https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics
• https://en.wikipedia.org/wiki/Notation_for_differentiation
• https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject

Fix the link `Handbook for Spoken Mathematics` by Lawrence A. Chang, Ph.D. (with assistance from Carol M. White and Lila Abrahamson)

Fix the link `LaTeX Math Symbols` at http://web.ift.uib.no/ and prepared by L. Kocbach

Blogs

A few blogs dedicated to mathematics:

• https://terrytao.wordpress.com/

Broken link in the Video section

"Understanding the Language of The Universe, documentary by World Documentary Movies" points to a video uploaded by a channel that no longer exists.

Fix the link `Communicating in the Language of Mathematics` by David Moursund (and Dick Ricketts)

Fix the link `MathsNotation2013` by https://www.adelaide.edu.au

Fix the link `Mathematics, morally` by Eugenia Cheng

Proofs

• https://math.berkeley.edu/~hutching/teach/proofs.pdf

Add links to Wikipedia glossaries of mathematics

https://en.wikipedia.org/wiki/Category:Glossaries_of_mathematics

Fix the link `Understanding Math Concepts` at AllKindsOfMinds

How to structure this project?

While more seriously addressing the issue #3 (regarding the goal of this project), it may be a good idea to think about how to structure this project.

A few questions/statements which may help to structure this project:

1. Should we categorize the resources based on their format?

   • We may also categorize them based on their format

2. Should we differentiate between online (freely or not) accessible texts vs not online accessible ones?

3. Should we include links to websites like Wolfram Alpha?

4. It may be a good idea to split this repository into multiple directories to better support the scaling of the project

5. Should we use the Github Wiki (or maybe a more "sophisticated" way of presenting the links)?

Problem-solving

A few resources dedicated to improving your problem-solving techniques (mainly in the context of mathematics)

Books

• How to Solve It: A New Aspect of Mathematical Method by Polya

Teaching Math Resources

A few resources dedicated to teaching mathematics

Videos

• Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainier

• Can we make mathematics intelligible? by R. P. Boas

Books

• Adding It Up: Helping Children Learn Mathematics.
• Becoming a Better Math Tutor by David Moursund and Bob Albrecht
• Good Math Lesson Planning and Implementation

Fix the link `Mathematics - The Language of the Universe`

Add the links to the Wikipedia articles on mathematical notation for the most common math subfields

https://en.wikipedia.org/wiki/Category:Mathematical_notation

More clear classification of the topics useful to understand mathematics

So far I'm including links to articles, papers, etc, based on my intuition, but I should define what can be included in this list based on the final goal.