I used these books from First year to Masters level in Mechanical Engineering, it covers simple arithmetic to Laplace transforms and Fourier Analysis.
Warning they are Plug and Chug methods, you might also want to take a course on logic and proofs. But if you want to really nail the mechanics of solving typical problems you can't go wrong.
https://www.goodreads.com/book/show/2145638.Engineering_Math...
Here's a review I found:
This book represents a masterpiece in clear exposition. It takes the patient reader from quite basic mathematics through to that required by third year undergraduates in engineering and physical science courses in planned, frame-based, systematic and methodical steps. Each chapter has revision summaries, revision exercises and quizzes together with answers. Even mathematics undergraduates would probably benefit from it as part of their reading diet.
It's been the 'staple' diet for such courses for decades for a reason: it has few if any peers!
https://www.lesswrong.com/posts/xg3hXCYQPJkwHyik2/the-best-t...
some updates here: https://www.lesswrong.com/posts/tJrEDkbS76xX96YDR/update-the...
It's quite old at this point, but most recommendations should be fairly evergreen.
For plug and chug mathematics from 0 to graduate level try, because it is full of worked examples and exercises, is K.A Stroud Engineering Mathematics, and the Advanced Engineering Mathematics book by the same author. Warning they are Plug and Chug methods, you might also want to take a course on logic and proofs. But if you want to really nail the mechanics of solving typical problems you can't go wrong.
I personally used 4 books to learn Linear Algebra last year, and ever since then I hated math textbook so much that I think I will never read any of them again, despite the fact that my HDD is full of math books. Because those authors usually leave blanks on somewhere maybe it is important, and I am so nervous to fill in any gap that may exist.
Some books are just objectively worst written. Like famous Strange's linear algebra textbook. That seems easy at the first glance, and then the learning curve is just skyrocketed to nowhere a beginner can make sense. I mean, how would someone teaching LU decomposition in the INTRODUTION part of the book???
And many recommends 3B1B's linear algebra series, but I don't think that is a great material. He is a great animator but definitely not even a good teacher. Those who experiencing the same frustration watching his videos may understand what I mean.
The problem of major math textbook is that notorious "leave it as an exercise" or "you should prove it yourself". I am here to learn, not "self-taught" self-taught. If I knew how to do that, then I don't need you. I need you (the book) because I want to know. But in order to learn a thing, first I need to learn how to prove. Then I need to learn how to prove a proof. Then again learn how to prove a proof of a proof... You get the point, it is a dead loop that is so obvious to any programmer.
Yes, I even read logic and set theory book and it told me to prove everything myself. But somehow I don't know if it is a typo or what, the LOGIC BOOK is showing wrong thing to me. So bye-bye. Typo is fatal to a math textbook.
There are few books that I don't hate thus far.
One is the Mathematics of Quantum Computing from Springer written by a Dutch guy. He proved that yes we can have a book that is so comprehensive and "author-proof". There is none unproved theorem inside the 800 pages book. All steps are printed there explicitly.
And Stroud Engineering Mathematics is exceptionally best written for the narrative and educational approach.
And maybe the Openstax Calculus. Author provided all important proofs and for those omitted, I never feel any loss.
Especially in mathematics, books are written in Latex, mostly words. Only words are in the book. I wish they can draw more venn diagram and flow chart or something like that, to augment the intuition.
I think it is non sense to set up barricade against learners. Every non harmful knowledge should be accessible to anyone and this will aid the society and the world also reduce climate effect (no one ever need to spend 6 hours googling to find out the solution).
So IMO making math harder than what it is and what it should be is basically pointless and it is causing damage to the humanity. Those professors thinking the opposite should stop writting anything.
- Biggs: Discrete Maths
- Stroud: Engineering Mathematics
- Solkolnikoff: Mathematics of Physics and Modern Engineering
- Sommerville: Software Engineering
- Aho: Compilers
- Kernighan and Ritchie: The C Programming Language
- Kernighan and Pike: The UNIX Programming Environment
- Ben Ari: Principles of Concurrent Programming
- Clements: Microprocessor Systems Design
- Tannenbaum: Distributed Operating Systems
- Dean, Allen, Aloimonos: Articficial Intelligence
- Knuth: The Art of Computer Programming
- Yourdon: Object Oriented Systems Design
- Abelson and Sussman: Structure and Interpretation
Maybe the one that ones that changed me most:
- Polya: How to Solve it - Hofstadter: Godel Escher Bach