I am a working programmer (mainly freelance). I am planning to go to grad school and I have heard that for a programmer knowing mathematics makes things n times easier. I have studied electrical engineering in an Indian college. Due to my math averseness (for whatever reason) I have only sketchy memories of what math was taught in college.<p>For the context, in India, mathematics is taught in a mechanical way. I remember integrals are used to find area, volume, etc. and derivatives to find rate of change. I remember doing meaningless and complicated integration problems on end and hating them. I was taught matrix algebra and remember how to multiply them and calculate determinants, but, no recollection of why and where to use them. I remember little multivariable calculus. I see people say that linear algebra should always come before multivariable calculus to get its real taste.<p>That is what I really want. I want the real taste of mathematics and how to apply it fruitfully in situations. I want to learn how to prove something and what it means to prove a thing in mathematics. I also want to learn why some theorem came about (the intuition) and then the rigor. I want both. I want to learn how to solve interesting problems.<p>I want to learn the base of the mathematical pyramid i.e. the foundations. I am listing a few topics that come to mind:<p>1. Calculus<p>2. Linear Algebra<p>3. Probability and Statistics<p>4. Approximation Math<p>5. Numerical methods<p>6. Proofs<p>I have ofcourse miss things. That is why I am asking help here. I will prefer resources that don't water down things (I have already learned that way in school and college) and those that are suitable for self study.<p>If for some cases you think an online course may serve better than a course then don't hesitate to list that, too.
The best book, 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.<p>I used these books from First year to Masters level in Mechanical Engineering, it covers simple arithmetic to Laplace transforms and Fourier Analysis.<p>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.<p><a href="https://www.goodreads.com/book/show/2145638.Engineering_Mathematics" rel="nofollow">https://www.goodreads.com/book/show/2145638.Engineering_Math...</a><p>Here's a review I found:<p>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.<p>It's been the 'staple' diet for such courses for decades for a reason: it has few if any peers!
I’ve heard many good things about <i>Essence of Mathematics</i> by Borovik and Gardiner. I’ve flipped through a copy of the book, and can confirm it’s well-written.
imo Paul Dawkins' series of books are very well written, helpful and free:<p><a href="https://tutorial.math.lamar.edu/" rel="nofollow">https://tutorial.math.lamar.edu/</a>