Book of Mathematical Tricks/Manipulations

[hogspogs]

Hi,

I am wondering if anyone knows of a comprehensive book with tips/tricks/examples for manipulating various expressions. Things such as changing summation indices,
$$\sum_{i,j,k=1}^{n}|a_{ik}b_{kj}|<=(\sum_{i,k=1}^{n}|a_{ik}|)^2(\sum_{j,m=1}^{n}|b_{mj}|)^2$$

or common(and not so common) series expansions, etc. but not limited to series. These things always take a long time to find and are often very specific to a certain discipline. Hope this eqn shows right as it's my first post.

 

[fresh_42]

These things always take a long time to find and are often very specific to a certain discipline.

That's the point: they are specific to the application. I wouldn't call them tricks, but there are certain techniques depending on the branch which are repeatedly used. I'm afraid there is no shortcut to learn them other than read a lot of proofs in the corresponding fields. Such a book would also require to set up the language of each branch before "tricks" can be explained. That would occupy more room than the techniques themselves.

It is as it always is: practice, practice, and not to forget: practice.