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https://github.com/nbro/understanding-math

Links to resources talking about how to learn & understand mathematics, and mathematical language, terminology and notation.
https://github.com/nbro/understanding-math

links mathematics understanding

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

Awesome Lists containing this project

README 

        
# Understanding Mathematics [![Awesome](https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg)](https://github.com/sindresorhus/awesome)



## Articles



- [Understanding Mathematics](http://www.math.utah.edu/~pa/math.html), a study guide by [Peter Alfeld](http://www.math.utah.edu/~pa/)

- [How to Develop a Mindset for Math](https://betterexplained.com/articles/how-to-develop-a-mindset-for-math/) at [BetterExplained](https://betterexplained.com)

- [Understanding Math Concepts](https://allkindsofminds.org/understanding-math-concepts/) at [AllKindsOfMinds](http://www.allkindsofminds.org/)

- [What is conceptual understanding?](https://web.archive.org/web/20221218055631/https://www.maa.org/external_archive/devlin/devlin_09_07.html) by Keith Devlin

- [Learning to Learn: Math Abstraction](https://betterexplained.com/articles/learning-to-learn-math-abstraction/) at [BetterExplained](https://betterexplained.com/)

- [How to study math](http://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx) by [Paul](http://tutorial.math.lamar.edu/)



## Papers



- [Teaching Mathematics for Understanding](http://ptgmedia.pearsoncmg.com/imprint_downloads/merrill_professional/Van_de_Walle_9780132824828.pdf) by Van De Walle

- [Can We Make Mathematics Intelligible?](https://www.jstor.org/stable/2321471) (1981) by R. P. Boas

- [A Mathematician's Lament](https://web.archive.org/web/20201210045725/https://www.maa.org/external_archive/devlin/LockhartsLament.pdf) by Paul Lockhart

- [How to Survive Your College Math Class (and Take Home Something of Value)](http://www.math.clemson.edu/~mjs/courses/misc/study.pdf) by Matthew Saltzman and Marie Coffin

- [Mathematics, morally](https://eugeniacheng.com/wp-content/uploads/2017/02/cheng-morality.pdf) by Eugenia Cheng



## Books



- [How to Solve It: A New Aspect of Mathematical Method](https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069116407X/ref=dp_ob_title_bk) by George Polya

- [Measurement](http://www.hup.harvard.edu/catalog.php?isbn=9780674284388) by Paul Lockhart

- [A Mathematician's Lament](http://www.goodreads.com/book/show/6232657-a-mathematician-s-lament) by Paul Lockhart

- [The Art and Craft of Problem Solving](https://kheavan.files.wordpress.com/2010/06/paul-zeitz-author-the-art-and-craft-of-problem-solving-2edwiley20060471789011.pdf) by Paul Zeitz



## Videos



- [Mathematics - The Language of the Universe](https://www.youtube.com/watch?v=S5LuCwZ0bpg)

- [The World of Mathematical Reality](https://www.youtube.com/watch?v=V1gT2f3Fe44) by Paul Lockhart

- [Paul Lockhart teaching Go](https://www.youtube.com/watch?v=vWya5fKwZ38) by Chaelim "Addy" Kim

- [Five Principles of Extraordinary Math Teaching](https://www.youtube.com/watch?v=ytVneQUA5-c) TEDx talk by Dan Finkel



## Online Questions



- [How to study math to really understand it and have a healthy lifestyle with free time?](http://math.stackexchange.com/questions/44704/how-to-study-math-to-really-understand-it-and-have-a-healthy-lifestyle-with-free) at [Math StackExchange](http://math.stackexchange.com/)



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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](https://en.wikipedia.org/wiki/Language_of_mathematics) at Wikipedia

- [Mathematical Words: Origins and Sources](http://web.archive.org/web/20191204152854/http://www.economics.soton.ac.uk/staff/aldrich/Mathematical%20Words.htm) by John Aldrich

- [Communicating in the Language of Mathematics](https://web.archive.org/web/20191202000933/http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics) by David Moursund and edited by Dick Ricketts

- [How to write mathematics clearly](https://workinginuncertainty.co.uk/clearmaths.shtml) by Matthew Leitch

- [How to understand math formulas](http://www.intmath.com/blog/how-to-understand-math-formulas) at [Interactive Mathematics](http://www.intmath.com/)

- [The symbolic language of math](https://abstractmath.org/MM/MMSymLang.htm) by Charles Wells



#### Papers



- [The Language and Grammar of Mathematics](https://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf) by Timothy Gowers

- [Reading Mathematics](https://pi.math.cornell.edu/~hubbard/readingmath.pdf) by [John Hamal Hubbard](https://pi.math.cornell.edu/~hubbard/)

- [A Guide to Writing Mathematics](http://web.cs.ucdavis.edu/~amenta/w10/writingman.pdf) by Dr. Kevin P. Lee

- [Mathematics and the Language of Nature](http://www.fdavidpeat.com/bibliography/essays/maths.htm) by F. David Peat

- [Learning the Language of Mathematics](http://wac.colostate.edu/llad/v4n1/jamison.pdf) by Robert E. Jamison



#### Books



- [Handbook for Spoken Mathematics](https://archive.org/details/handbook-for-spoken-mathematics-larrys-s/mode/2up) by Lawrence A. Chang et al.

- [A Handbook of Mathematical Discourse](https://abstractmath.org/Books/handbkhyper.pdf) by Charles Wells



#### Videos



- [Math isn't hard, it's a language](https://www.youtube.com/watch?v=V6yixyiJcos) TEDx talk by Randy Palisoc



---



### Mathematical Notation & Terminology



#### Articles



- [History of mathematical notation](https://en.wikipedia.org/wiki/History_of_mathematical_notation) at Wikipedia

- [Mathematical and scientific symbols](http://www.uefap.com/speaking/symbols/symbols.htm) at [http://www.uefap.com/](http://www.uefap.com/)

- [LaTeX Math Symbols](https://web.archive.org/web/20190423203742/http://www-ph.postech.ac.kr/~bimin/Latex.htm) prepared by L. Kocbach (on the basis of [another document](https://web.archive.org/web/20190810123256/http://web.ift.uib.no/Fysisk/Teori/KURS/WRK/TeX/latexsource.html) by David Carlisle, Manchester University)



##### Wikipedia



- [Statistics synonyms](https://en.wikipedia.org/wiki/Dependent_and_independent_variables)

- [LaTeX/Mathematics](https://en.wikibooks.org/wiki/LaTeX/Mathematics)



###### Symbols



- [List of mathematical symbols by subject](https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject)

- [List of mathematical constants](https://en.wikipedia.org/wiki/List_of_mathematical_constants) 

- [List of mathematical symbols](https://en.wikipedia.org/wiki/List_of_mathematical_symbols)

- [Mathematical operators and symbols in Unicode](https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode)



###### Notation



- [Mathematical notation](https://en.wikipedia.org/wiki/Mathematical_notation)

- [Mathematical notation (category)](https://en.wikipedia.org/wiki/Category:Mathematical_notation)

- [Set notation](https://en.wikipedia.org/wiki/Set_notation)

- [Notation in probability and statistics](https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics)

- [Notation for differentiation](https://en.wikipedia.org/wiki/Notation_for_differentiation)



###### Glossaries



- [Glossary of probability and statistics](https://en.wikipedia.org/wiki/Glossary_of_probability_and_statistics) 

- [Glossary of calculus](https://en.wikipedia.org/wiki/Glossary_of_calculus)

- [Glossary of set theory](https://en.wikipedia.org/wiki/Glossary_of_set_theory)

- [Glossary of linear algebra](https://en.wikipedia.org/wiki/Glossary_of_linear_algebra)

- [Glossary of graph theory](https://en.wikipedia.org/wiki/Glossary_of_graph_theory)

- [Glossary of game theory](https://en.wikipedia.org/wiki/Glossary_of_game_theory)

- [Glossary of mathematical symbols](https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols)

- [Glossaries of mathematics](https://en.wikipedia.org/wiki/Category:Glossaries_of_mathematics) 



#### Papers



- [Mathematical Operators](http://unicode.org/charts/PDF/U2200.pdf) at [http://unicode.org](http://unicode.org)

- [Some Common Mathematical Symbols and Abbreviations (with History)](https://www.math.ucdavis.edu/~anne/WQ2007/mat67-Common_Math_Symbols.pdf) by Isaiah Lankham, Bruno Nachtergaele, Anne Schilling



#### Books



- [Mathematical Notation: A Guide for Engineers and Scientists](http://www.amazon.com/Mathematical-Notation-Guide-Engineers-Scientists/dp/1466230525/ref=sr_1_1?s=books&ie=UTF8&qid=1355100927&sr=1-1&keywords=mathematical+notation) by Edward R. Scheinerman

- [The Cambridge Dictionary of Statistics](http://www.stewartschultz.com/statistics/books/Cambridge%20Dictionary%20Statistics%204th.pdf) by B. S. Everitt and Anders Skrondal



#### Videos



- [Mathematical Notation - The Language of Mathematics](https://www.youtube.com/watch?v=Y-c_CgxxPF0) by Sarada Herke



#### Slides



- [Maths in Lectures: Understanding the Notation](https://www.adelaide.edu.au/mathslearning/ua/media/210/MathsNotation2013.pdf) by Dr. David Butler



#### Online Questions



- [All questions about mathematical **notation** _sorted in descending order of votes_](http://math.stackexchange.com/questions/tagged/notation?sort=votes&pageSize=30) at [Math StackExchange](http://math.stackexchange.com)

- [All questions about mathematical **notation** _sorted in descending order of votes_](http://stackoverflow.com/questions/tagged/mathematical-notation?sort=votes&pageSize=50)  at [Stack Overflow](http://stackoverflow.com/)

- [All questions about mathematical **terminology** _sorted in descending order of votes_](http://math.stackexchange.com/questions/tagged/terminology?sort=votes&pageSize=30) at [Math StackExchange](http://math.stackexchange.com)

- [Where can I learn about mathematical notation?](http://math.stackexchange.com/questions/70080/where-can-i-learn-about-mathematical-notation) at [Math StackExchange](http://math.stackexchange.com)

- [How to become comfortable with mathematical notation?](http://ask.metafilter.com/117088/How-to-become-comfortable-with-mathematical-notation) at [Ask MetaFilter](http://ask.metafilter.com/)

- [What is the status of generating LaTeX from handwriting](http://tex.stackexchange.com/questions/1443/what-is-the-status-of-generating-latex-from-handwriting-i-e-ocr) at [Tex StackExchange](http://tex.stackexchange.com/)



#### Websites



- [Wolfram Alpha](http://www.wolframalpha.com/)

- [Math Words](http://www.mathwords.com/)



#### Github



- [math-as-code](https://github.com/Jam3/math-as-code) by Jam3 (Github's repository)



---



### Mathematical Proofs



#### Articles



- [Some Help on Reading Mathematics and Creating Proofs](http://www.math.ucsd.edu/~ebender/proofs.html)