Foundations Are there handbooks compiling math techniques to solve problems?

[jonjacson]

Let me explain what I mean.

When you try to solve an algebraic equation, or even sometimes a differential equation it is useful to change variables so the new form of the equation is easier to solve, or takes the form of an equation that has already been solved.

Another technique is making your equation equal to a possible solution in the form of an infinite series and computing what are the coefficients.

There are many of these techniques that we all know, but my question is if there is anybody compiling them into a book format. What about mathematics historians? Do the compile them?

Thanks for your time.

 

[jedishrfu]

Following WW1, there was a program in France to run seminars and to create a set of volumes authored under the pseudonym N. Bourbaki called the Elements of Mathematics that collectively brought together the best mathematicians of the era to share and record their knowledge.

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

https://en.wikipedia.org/wiki/Séminaire_Nicolas_BourbakiThe best popular collection of Mathematical recipes would be the Schaum's Outlines series which covers a lot of applied math with problems and solutions.

 

[jedishrfu]

There are several other practical Math Handbooks to consider:

- Arfken and Weber Mathematical Physics https://www.amazon.com/dp/9381269556/?tag=pfamazon01-20

- Boaz Mathematical Physics https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

- Nearing Mathematical Tools for Physics https://www.amazon.com/dp/048648212X/?tag=pfamazon01-20

which is also available from the author's website online at http://www.physics.miami.edu/~nearing/mathmethods/

- Princeton Companion to Mathematics https://www.amazon.com/dp/B005N8WNT0/?tag=pfamazon01-20

- Princeton Companion to Applied Mathematics https://www.amazon.com/dp/B013ET08FA/?tag=pfamazon01-20

- Handbook of Mathematics authored by

• I.N. Bronshtein
• K.A. Semendyayev
• Gerhard Musiol
• Heiner Mühlig

https://link.springer.com/book/10.1007/978-3-662-46221-8

and my favorites:
- Math 1001 by Elwes light-weight short descriptions of various math topics that you can later investigate online
- Mathematical Bible by Beveridge light-weight treatment of various math topics and history