Book on maths: MINIMUM MATHEMATICS for future scientists and engineers: An inspiring self-study note

Hello all,

In the spirit of Timoshenko's of one contributes what one can, I am sharing with young students my note on mathematics. 

The link is:

https://www.researchgate.net/publication/360324957_MINIMUM_MATHEMATICS_for_future_scientists_and_engineers_An_inspiring_self-study_note

There are several issues with the traditional mathematics education. First, it focuses too much on technical details. Second, the history of mathematics is completely ignored; textbook exposition usually presents a complete reversal of the usual order of developments of mathematics. Concepts, theorems are given without motivation. And the language is serious, thus not engaging.

I have been selft-studying maths since 2016 when I read Paul Lockhart's A Mathematician’s Lament, and this book is the result of that continuing learning process. The style of the book, as you might guess, is informal. Mostly because I am not a mathematician and also I like a conversational tonne. This is not a traditional mathematics textbook, so it does not include many exercises. Instead it focuses on the mathematical concepts, their origin (why we need them), their definition (why they are defined like the way they’re), their extension. The process leading to proofs and solutions is discussed as most often it is the first step which is hard, all the remaining is mostly labor work (involving algebra usually). And of course, history of mathematics is included by presenting major men in mathematics and their short biographies.

This is a self-studying mathematics notebook covering high school mathematics to university mathematics. Topics include algebra, trigonometry, single variable calculus, vector calculus, variational calculus, differential equations, linear algebra, probability, numerical analysis and introduction to programming using Julia.

Note that this is just a draft because I am still learning (on tensor, differential geometry, AI, statistics).

Bests from Melbourne,

Phu Nguyen

Monash Uni