# Maths

## Resources

### Articles

* An animated introduction to Fourier Series - Andrei Ciobanu
  * [Part 1: From the Circle to Epicycles](https://www.andreinc.net/2024/04/24/from-the-circle-to-epicycles)
* [An Interactive Introduction to Fourier Transforms](https://www.jezzamon.com/fourier/) - Jez Swanson
* [Doomsday Algorithm](https://rudy.ca/doomsday.html)
* [How to Study Mathematics](https://www.math.uh.edu/~dblecher/pf2.html) - Lawrence Neff Stout, Illinois Wesleyan University
* [So You Want to Study Mathematics…](https://www.susanrigetti.com/math) - Susan Rigetti
* The Mathematics of 2048 - John Lees-Miller
  * [Minimum Moves to Win with Markov Chains](https://jdlm.info/articles/2017/08/05/markov-chain-2048.html) ([HN](https://news.ycombinator.com/item?id=15327837))
  * [Counting States with Combinatorics](https://jdlm.info/articles/2017/09/17/counting-states-combinatorics-2048.html) ([HN](https://news.ycombinator.com/item?id=15327837))
  * [Counting States by Exhaustive Enumeration](https://jdlm.info/articles/2017/12/10/counting-states-enumeration-2048.html) ([HN](https://news.ycombinator.com/item?id=15894126))
  * [Optimal Play with Markov Decision Processes](https://jdlm.info/articles/2018/03/18/markov-decision-process-2048.html) ([HN](https://news.ycombinator.com/item?id=16790338))

### Books

#### Discrete Mathematics

* [A Logical Approach to Discrete Math](https://smile.amazon.co.uk/dp/1441928359) - David Gries, Fred B. Schneider

* [Concrete Mathematics](https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathematics%202e.pdf) - Ronald Graham, Donald Knuth, Oren Patashnik

* [Discrete and Combinatorial Mathematics](https://smile.amazon.co.uk/dp/1292022795) - Ralph Grimaldi

* [Discrete Mathematics: An Open Introduction](https://discrete.openmathbooks.org/dmoi4.html) - Oscar Levin

* [Discrete Mathematics with Applications](https://smile.amazon.co.uk/dp/0495826162/) - Susanna Epp

* [Discrete Mathematics with Graph Theory](https://smile.amazon.co.uk/dp/8120332989/) - Edgar G. Goodaire, Michael M. Parmenter

* [Mathematics: A Discrete Introduction](https://smile.amazon.co.uk/dp/049501866X) - Edward R. Scheinerman

* [A Gentle Introduction to the Art of Mathematics](https://giam.southernct.edu/GIAM/) - Joe Fields, Southern Connecticut State University

* [Algebraic Topology](https://pi.math.cornell.edu/~hatcher/AT/ATpage.html) - Allen Hatcher
  * [YouTube playlist](https://www.youtube.com/playlist?list=PLpRLWqLFLVTCL15U6N3o35g4uhMSBVA2b)

* [An Infinite Descent into Pure Mathematics](https://infinitedescent.xyz/) - Clive Newstead

* [Calculus](https://www.amazon.co.uk/Calculus-Michael-Spivak/dp/0914098918) - Michael Spivak

* [Calculus for Beginners and Artists](https://math.mit.edu/~djk/calculus_beginners) - Daniel J. Kleitman

* [Calculus Made Easy](https://calculusmadeeasy.org/) - Silvanus P. Thompson

* [Calculus On Manifolds](http://www.strangebeautiful.com/other-texts/spivak-calc-manifolds.pdf) - Michael Spivak

* [Complex Analysis](https://ds.amu.edu.et/xmlui/bitstream/handle/123456789/8538/Complex%20Analysis%20-%20Lang.pdf?sequence=1\&isAllowed=y) - Serge Lang

* [Everything You Always Wanted To Know About Mathematics](https://www.math.cmu.edu/~jmackey/151_128/bws_book.pdf) - Brendan W. Sullivan

* [How To Solve It ](https://press.princeton.edu/books/paperback/9780691164076/how-to-solve-it)- George Polya
  * [Summary by Peter Alfeld](https://www.math.utah.edu/~alfeld/math/polya.html)

* [Immersive Linear Algebra](https://immersivemath.com/ila/index.html) - Jacob Ström, Kalle Åström, and Tomas Akenine-Möller

* [Introduction to Linear Algebra](https://www.amazon.co.uk/Introduction-Linear-Algebra-Gilbert-Strang/dp/1733146679/) - Gilbert Strang

* [Linear Algebra Done Right](https://linear.axler.net/) - Sheldon Axler
  * [YouTube playlist](https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw)

* [Mathematical Handbook - Higher Mathematics](https://archive.org/details/vygodsky-mathematical-handbook-higher-mathematics-mir/mode/2up) - M. Vygodsky

* [Mathematics for Computer Science](https://courses.csail.mit.edu/6.042/spring18/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
  * [YouTube playlist (Fall 2010)](https://www.youtube.com/playlist?list=PLB7540DEDD482705B)
  * [YouTube playlist (Spring 2024)](https://www.youtube.com/playlist?list=PLUl4u3cNGP61VNvICqk2HXJTonnKgAc9d)

* [Topics in Algebra](https://marinazahara22.files.wordpress.com/2013/10/i-n-herstein-topics-in-algebra-2nd-edition-1975-wiley-international-editions-john-wiley-and-sons-wie-1975.pdf) - I. N. Herstein

* [Understanding Analysis](https://homel.vsb.cz/~ulc0011/Abbott%20-%20Understanding%20Analysis.pdf) - Stephen Abbott

### Courses

* [Calculus Applied!](https://www.edx.org/course/calculus-applied) - John Wesley Cain, Juliana Belding, Peter M. Garfield
* Calculus: Single Variable - Robert Ghrist
  * [Part 1 - Functions](https://www.coursera.org/learn/single-variable-calculus)
  * [Part 2 - Differentiation](https://www.coursera.org/learn/differentiation-calculus)
  * [Part 3 - Integration](https://www.coursera.org/learn/integration-calculus)
  * [Part 4 - Applications](https://www.coursera.org/learn/applications-calculus)
* [College Precalculus](https://www.youtube.com/watch?v=Y8oZtFYweTY) - freeCodeCamp
* [Introduction to Complex Analysis](https://www.coursera.org/learn/complex-analysis) - Petra Bonfert-Taylor
  * [YouTube playlist](https://www.youtube.com/playlist?list=PLi7yHjesblV0sSfZzWdSUXGO683n_nJdQ)
* [Introduction to Discrete Mathematics for Computer Science](https://www.coursera.org/specializations/discrete-mathematics)
* [Linear Algebra](https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/) - Gilbert Strang
* [Physics and Mathematics Self-Study Project](https://www.diegovera.org/projects) - Diego Vera

### GitHub Repositories

* [Awesome Math Books](https://github.com/valeman/Awesome_Math_Books)
* [Math As Code](https://github.com/Jam3/math-as-code)

### Hacker News threads

* [Can you recommend me a book to (re)learn math?](https://news.ycombinator.com/item?id=33859823)
* [Math books that made you significantly better at math?](https://news.ycombinator.com/item?id=34439828)
* [Serious mathematics books that can replace a good teacher?](https://news.ycombinator.com/item?id=31488608)

### Websites

* [Desmos](https://www.desmos.com/calculator)
* [Easing Functions Cheat Sheet](https://easings.net/)
* [Khan Academy](https://www.khanacademy.org/)
* [Math Academy](https://mathacademy.com/)
* [Setosa](https://setosa.io/#/) - data visualization and visual explanations
* [Symbolica](https://symbolica.io/)
* [teachyourselfmath](https://teachyourselfmath.app)

### YouTube Channels

* [3Blue1Brown](https://www.youtube.com/c/3blue1brown/videos)
* [Aleph 0](https://www.youtube.com/c/Aleph0/videos)
* [blackredpen](https://www.youtube.com/c/blackpenredpen/videos)
* [Eddie Woo](https://www.youtube.com/c/misterwootube/videos)
* [Mathologer](https://www.youtube.com/c/Mathologer/videos)
* [Michael Penn](https://www.youtube.com/c/MichaelPennMath/videos)
* [Mind Your Decisions](https://www.youtube.com/c/MindYourDecisions/videos)
* [Numberphile](https://www.youtube.com/user/numberphile/videos)
* [vcubingx](https://www.youtube.com/vcubingx)
* [Vsauce](https://www.youtube.com/c/vsauce1/videos)

### YouTube Playlists

* [Abstract Algebra](https://www.youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5) - Harvard
* [Calculus Revisited: Single Variable Calculus](https://www.youtube.com/playlist?list=PL3B08AE665AB9002A) - MIT
* [Coding the Matrix - Linear Algebra through Computer Science Applications](https://www.youtube.com/playlist?list=PLEhMEyM9jSinRHXJgRCOLZUiu9847V2g0)
* [Linear Algebra](https://www.youtube.com/playlist?list=PL49CF3715CB9EF31D) - Gilbert Strang, MIT
* [Real Analysis](https://www.youtube.com/playlist?list=PL0E754696F72137EC) - Francis Su, Harvey Mudd College