Ask HN: Which MOOCs were the most beneficial to you as an independent learner? | Hacker News Reader

Ask HN: Which MOOCs were the most beneficial to you as an independent learner?

3 pointsdebanjan163 comments

Why were they especially beneficial to you at that time?

By far the single best MOOC I've ever taken is edX's Introduction to Biology taught by Eric Lander at MIT. https://www.edx.org/course/introduction-to-biology-the-secre...

And it's 100% free! Great lectures and the simluated "TA sessions" and esp. online quizzes did a great job reinforcing my knowledge.

I have an undergrad degree in biology from a top research university from many years ago and this course was so informative, effective, and inspiring, that i considered dropping out of tech to go to grad school in biology. Truly excellent.

I've been working professional jobs for more than a decade. Despite my full-time jobs, I've dedicated hundreds (maybe thousands?) of hours of personal time over the last 6 years teaching myself vector calculus, linear algebra, abstract algebra, molecular biology, organic chemistry, and other nerdy topics. Mostly, I use textbooks and work on problem sets. I sometimes watch videos which can be super-helpful. But the best single course I've taken in that time is the MIT edX course.

I would love to know more about your process/journey of self studying mathematics and the books that helped.

My initial goal was to understand mathematics well enough to have a some grasp of "Deep Learning" (2016) textbook by Goodfellow, Bengio, and Courville. I meant like 50-85% understanding of the math depending on the chapter. And being able to have reasonable understanding of deep learning papers being published in the 2012-2018 period. https://www.deeplearningbook.org

1. Because my math was pretty rusty, I started with single-variable calculus. Good resources for this are Khan Academy including pre-calc prequisites all the way up to multivariable calc and linear algebra. I'm not sure which textbook on single-variable calc is good but there are many many to choose from.

2. For multivariable calc, I began with Lang's "Calculus of Several Variables". https://link.springer.com/book/10.1007/978-1-4612-1068-9

3. After Lang, I did a lot of the problems in the first half (differentiation only) of Baxandall and Liebeck's "Vector Calculus". This is truly an outstanding book; such clear exposition and excellent organization with many examples. It was a little more formal in it's presentation than I was used to. But this helped me learn to write decent and well-organized proofs. And when I got to item 6 below, Baxandall and Liebeck got me ready! https://store.doverpublications.com/0486466205.html

4. In parallel, I studied linear algebra. My two main intro books were Strang's "Introduction to Linear Algebra" (4th edition). https://math.mit.edu/~gs/linearalgebra/

But I found Strang (super popular among college students) was well-supplemented by Kuldeep Singh's "Linear Algebra Step-by-Step" https://global.oup.com/academic/product/linear-algebra-97801...?

5. At this point, the Khan Academy videos on linear algebra were very helpful.

6. Now that I was ready, I started Axler's "Linear Algebra Done Right". It's more formal and abstract compared to 4 and 5 above. I love it though! It's taken me years and I'm still only part way through. It is one of my all-time favorite books--not just in math--but in any field. I'm a bit slow at this type of abstract / proof-based math but it's deeply deeply satisfying. https://linear.axler.net

7. Recently, I started Jacobson's "Basic Algebra I". I'm only at the beginning of my journey into modern algebra but I really like it so far.https://www.maa.org/publications/maa-reviews/basic-algebra-i...

Hope this helps!

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