Here is my collection of experimental mathematical games, simulations, and other apps I have written (or supervised) over the years.

— Algebra —

- A preliminary demo of an algebra game in Scratch (discussion here), solving a single (randomly selected) linear equation in one unknown using two operations.
- A more developed version of the same game, still programmed in Scratch, with 12 levels, with a focus on making challenging and entertaining problems rather than on basic algebra skills. (Discussion here)
- A variant of the above game with 12 random levels, with the n^th level formed by performing n moves in reverse.

— Logic —

- A solver for Lewis Carroll logic puzzles in Scratch (discussion here).
- An interactive textbook for first-order logic in Javascript (and also CSS and HTML); discussion here and here, and code here.

— Linear algebra —

These Java apps were coded by Kim Chi Tran under my supervision.

- Vector calculator
- Gaussian elimination
- Matrix calculator
- Linear transformations in R^2
- Eigenvalues and Eigenvectors
- The Gram-Schmidt orthogonalisation process

— Complex analysis —

- The complex plane
- Elementary complex maps
- Mobius transforms
- Multi-valued functions
- The complex derivative
- The complex integral
- Taylor and Laurent series
- The fundamental theorem of calculus
- The residue theorem
- The argument principle

— Miscellaneous —

Some miscellaneous Java applets:

- Besicovitch sets
- Conformal compactification
- Honeycombs (with Allen Knutson)
- Exponent Calculator
- Multiple choice applet (now a wiki; see also these two discussions).

Source code for the java applets can be found here.

## 6 comments

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18 September, 2016 at 11:36 pm

Bhargav BaruahHi Terry, This is Bhargav from India…..

You are truly one of the most outstanding, mind-blowing mathematician the world has ever produced.

3 July, 2017 at 7:42 am

Michael M. RossFour Excel calculators/graphing tools (written in VBA):

–Collatz Odd Number Calculator (with Factors and Graphing)

–Goldbach “Stress Test”

–Legendre’s (Linear Parity)

–Legendre’s (Fractional Elimination)

These are macro-enabled worksheets (enable content, enable macros).

https://mathrodite.quora.com/Excel-Calculators-Visualizations

28 January, 2018 at 4:18 pm

David BinnerHi, Professor Tao.

You’ve started building a nice selection of applets here, and work seems to be ongoing; the “Vector calculator” page includes the statement, “We’re still ironing out the kinks in the code, so bear with us for the moment!” I look forward to seeing more of this work as it progresses.

I write similar applets that may be of interest to you and your readers:

http://www.akiti.ca/Mathfxns.html

Presently, JavaScript programs are posted that solve N Equations in N Unknowns, compute Eigenvalues and Eigenvectors of a real general matrix, and perform a Cholesky Decomposition on a real symmetric matrix, to name a few. Source code is viewable (I have done nothing to obfuscate the JavaScript code; furthermore, C++ source code for the programs is being posted on GitHub.) Several more programs are in the works and I am open to suggestions as to what other sorts of discrete math applets could be written that would be useful.

26 May, 2020 at 9:39 pm

Usman NizamiCan you give me link of c++ code ?

28 September, 2018 at 11:34 am

KipperockDear Prof. Tao,I took the liberty of checking most links(but not all of them), and the following are broken/out of date/other problem:

-“Encyclopedia of mathematics” webpage is empty

-MAA MinuteMath have ceased to update their page

-LMFDB is posted twice:between “Libres pensées . . ” and “LMS blog page”, and between “The Geomblog” and “The mathematics literature project”

-“Patterns of Ideas” has been moved to GitHub, and there’s a link at the old one.

-The mathematics literature project shows a 404 error.

-The blog by James Colliander is down.

-“The capacity to be alone” has been deleted.

-“London number theory” has been deleted.

-“Blog on mathematical journals” is down.

-“PDE blog” webpage is empty,seems it’s been deleted.

-All blogs in “tosio.math.utoronto.ca” are down, including: “Analysis and PDE conferences”, “DispersiveWiki”, and the blog by James Colliander.

-Mathonline blog is currently down, perhaps temporarily

-“Mixedmath” has been moved to http://davidlowryduda.com/ (in 2014).

I didn’t know where to post this other than in this less crowded section.

Also, there may be other lemons.

[Links corrected/deleted, thanks – T.]21 June, 2019 at 8:31 am

KipperockDear prof. Tao, when one presses the “Subscribe to RSS feed” button there is a bug, and instead of a window which allows one to enter an email address and sign up for the feed, there pops up a window full of code and nothing can be done – besides going back to the blog.