Math Education using SageMathCell in an open book

[bookofproofs]

I'm a professional mathematician, but not a practicing one because of my actual employment. However, I run a free and non-commercial website dedicated to mathematics and the axiomatic method. My goal is to promote the competency of thinking logically and of formulating proofs as basic skills rather than something reserved for academia. I want to achieve this goal by developing and complementing (at least the basics) in the theory of different mathematical disciplines and provide these results under the CC BY-SA 3.0 license to the public for educational purposes.

Although - strictly applying the axiomatic method - I have developed some basic theory in analysis, algebra, topology, probability, and geometry since 2014, this is a mammoth project for just one person like me. Therefore, I hope that I will find in this mailing list co-authors willing to actively join my project. 

The project is located at https://www.bookofproofs.org/. It allows integrating SageMathCell in each article. This is as simple as typing in your text 

§§§<div class='sage'>.....</div>§§§ 

with "...." standing for some Sage code you like. 

I think that SageMathCell would definitely make existing contents (e.g. theorems, definitions, examples) of the project more interactive and encourage the readers to "experiment" with mathematics in the context of all articles. 

 

You could support the project by enriching existing articles with SageMathCell or sharing your expertise in a specific mathematical discipline if you like.

It would be great to read about your opinion and to welcome at least some of you as co-authors of the project. Cheers!

bookofproofs

[kcrisman]

I'm a professional mathematician, but not a practicing one because of my actual employment. However, I run a free and non-commercial website dedicated to mathematics and the axiomatic method. My goal is to promote the competency of thinking logically and of formulating proofs as basic skills rather than something reserved for academia. I want to achieve this goal by developing and complementing (at least the basics) in the theory of different mathematical disciplines and provide these results under the CC BY-SA 3.0 license to the public for educational purposes.

Hi!  Welcome to Sage.  Here are two potential links of high interest to a project like yours - there are many which take advantage of the Sage cell technology you might enjoy discussing your own goals for your project with.  Interactivity is good, and these both should be relevant.

https://curatedcourses.org - some commonalities in trying to provide SageMath cells for many situations

http://mathbook.pugetsound.edu - the PreTeXt processor, which allows for writing open books with one input, many formats, and of course interactive SageMath cells

Good luck in sharing your love of mathematics and finding some collaborators - there are more people than ever interested in providing good free resources for mathematics.

[bookofproofs]

Hi!  Welcome to Sage.  Here are two potential links of high interest to a project like yours - there are many which take advantage of the Sage cell technology you might enjoy discussing your own goals for your project with.  Interactivity is good, and these both should be relevant.

Thank you for adding me to your mailing list and for the links with further Sage cell resources. Very interesting places to get involved with!

By the way, bookofproofs.org is somewhat different. While it also uses a TeX processor (Mathjax) and Sage cell, it also integrates other interactive tools (e.g.JSXGraph). The most important difference is probably that it is actually one integrated open book with different parts dedicated to different mathematical disciplines crossreferencing to each other. One advantage of this is that the same axioms and concepts (e.g. sets, vector spaces, equivalence relations, natural, real, complex numbers, ...) do not have to be re-defined or presumed to be known by the reader in each open book separately. The other advantage is that it is easily possible to navigate through the book not only following the hyperlinks back (i.e. the direction from theorems back to axioms) but also to follow them the other way round (i.e. the direction from axioms to theorems across different disciplines).