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Ask HN: How or where to begin learning mathematics from first principles?

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Ask HN: How or where to begin learning mathematics from first principles?

#1
A little bit of background:

As I've become more skilled with programming and electronics I have felt myself begin to near a wall. My knowledge of and skills in math is relatively poor and all the interesting things that make up the more advanced programming and electronics pursuits seem to be heavily based on math.

When I butt heads with these more advanced topics I find I resort to scouring the internet to cobble together pieces of various tutorials and guides. While it does feel good in a way to hack together limited understandings to make satisfactory solutions I'm beginning to feel less like a hacker and more like a hack. The knowledge I gain is shallow and I don't think my tactics will get me much further.

Instead of working backwards from implementation I would like to start from the beginning and learn math the proper way. Unfortunately most of the resources I find online seem to more focused on teaching me how to solve math problems. I have no interest in solving specific math problems on a test, I'm not going to school and I doubt I will ever take a math test again in my life. I want to work up from first principles and gain the tools to reason about the world mathematically and understand the cool things that are currently out of my reach like antenna design, machine learning, electromagnetism, cryptography etc.

Unfortunately I so know so little I have no idea how where to start. What websites are helpful, what books I should buy, etc. I was hoping someone here could share. Thank you.

Re: Ask HN: How or where to begin learning mathematics from first principles?

#3
I'm in a not too different situation from yourself as a self taught developer. I spent about 6 months and taught myself most of the mathematics concepts I forgot or never tried hard enough to learn from the Khan Academy. Their mathematics tutorials are excellent.

http://khanacademy.org

Re: Ask HN: How or where to begin learning mathematics from first principles?

#4
Try http://www.khanacademy.org (free), their math series starts from basic arithmetic and walks all the way through to undergrad-level mathematics.

I personally preferred khanacademy to my math teaching at school and it's been handy during my degree.

For more advanced stuff i've found Stanford's online courses (https://www.youtube.com/user/StanfordUniversity/playlists) and MIT OpenCourseWare (http://ocw.mit.edu/index.htm) to have the best material for Physics

Re: Ask HN: How or where to begin learning mathematics from first principles?

#5
There is some distance from this to antenna design, electromagnetism, etc, but I think you have to be fluent in proofs to actually follow along on those. Math is a big subject; ymmv.

A Transition to Advanced Mathematics by Douglas Smith (Author), Maurice Eggen (Author), Richard St. Andre (Author)

ISBN-13: 978-0495562023 ISBN-10: 0495562025 Edition: 7th

It shows up on Abebooks which could help with the price. It's a small book, exceedingly well-crafted and worth every nickel.

Re: Ask HN: How or where to begin learning mathematics from first principles?

#6
Learn how to prove theorems. "How to Prove It" by Velleman is the best book for this (imho). (Amazon link http://www.amazon.com/How-Prove-It-Structured-Approach/dp/05...)

More good advice at http://scattered-thoughts.net/blog/2014/11/15/humans-should-...

Re: Ask HN: How or where to begin learning mathematics from first principles?

#7

There is some distance from this to antenna design, electromagnetism, etc, but I think you have to be fluent in proofs to actually follow along on those. Math is a big subject; ymmv. A Transition to Advanced Mathematics by Douglas Smith (Author), Maurice Eggen (Author), Richard St. Andre (Author) ISBN-13: 978-0495562023 ISBN-10: 0495562025 Edition: 7th It shows up on Abebooks which could help with the price. It's a s…

>There is some distance from this to antenna design, electromagnetism, etc, but I think you have to be fluent in proofs to actually follow along on those. Math is a big subject; ymmv.

I'm only 20 years old and hopefully I have a long life ahead of me so I'm not too worried about how long it takes, I just want to get on the right track.

Thank you on the book recommendation, that looks like it is exactly the type of resource I was looking for!

Re: Ask HN: How or where to begin learning mathematics from first principles?

#9
I have found the below links excellent pathways to mastering mathematics. I actually was in the same place as you and started with Spivak Calculus. Now I am back at school studying mathematics :P

http://www.amazon.com/gp/richpub/syltguides/fullview/20JWVDE...

http://www.amazon.com/gp/richpub/syltguides/fullview/R1GE1P2...

Re: Ask HN: How or where to begin learning mathematics from first principles?

#10
Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, and Lavrent'ev

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...

Covers something like three years of an undergraduate degree in mathematics. Lots of words - but that text is used to develop an understanding of the concepts and images. Considered a masterpiece. An enjoyable read.

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