Intersesting Integrals - A Math Book Review.

     Overall, Interesting Integrals is a book I want to recommend, yet it falls short of being that useful in terms of teaching the few tricks it possesses. In chapters 1-4 of the book, the book performs pretty well, delivering, albeit easy, problems which really drive home the essence of the tricks and demonstrate their uses well. The introduction on Feynman’s trick, in particular, really drives home how well the author can deliver on making a trick both easy and usable. However, afterwards the book strives to get ahead of itself without a decent understanding of the level at which it is asking some readers to go for it. While the occasional step missing is not too big of a draw, the book fails at presenting the solutions in such a way to aid the reader’s learning. There were a few times where the book managed to simply, through some weird notation, become hard to decode without the assistance of Wolfram Alpha to pick up the slack. However, such practices pale in comparison to the text’s problem at providing clear solutions in the dedicated solution section of the book. After chapter 5, I honestly stopped working through the problems since half of the time I could not even get to see the solution to know if I was on the right track or if I was headed in a way contrary to my hope of solution. While I do understand that these are “challenges”, and thus should be attempted in an untimely manner, the challenge of some of these problems varies to the point where I would like to know if I used an hour of time to get to something unsolvable. Lastly, the book’s latter half tries to squeeze a lot of different tricks in the latter half all at once. Without a proper subdivision between tricks and application, it became hard to see what the point of each part was, making intuition increase rather limited unfortunately. It’s why I ended up skipping the penultimate and ultimate chapters altogether, as I feared that his method of explanation would simply cloud my intuition when I try to get a better understanding of contour integration. Altogether, this book seems unfinished and the problems are really weirdly designed. The main draws from it are the following:

1. The old tricks really work. U-subs and integration by parts can really do miracles for a problem, so long as you remember the bounds and change them accordingly.

2. Feynman’s trick is a pretty fun way to waste an afternoon and a great way to integrate stuff. It’s a good jumping off point for me too as I need to really study Calc III this year.

3. The gamma and beta functions. These definitions are some of the cooler ones and really demonstrate some of the cool new functions integration kinda brings to the table.

4. Integration can be done with power series on a higher level, and that power series can be figured out algebraically through taking the integral of a derivative.

5. Integration can also lead to diffeqs, and thus the subjects are closer than I imagined. This gets even better when you realize that such equations can also use recursion in a cool manner.

6. That I need to learn more Calc 3 and contour integration in particular.

7. That I need a good book on Fourier stuff to really understand it.

8. Never fully trust a math book that is this unpolished, and that its okay to leave a book till I have some more experience and / or find a better on.