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Everything you always wanted to know about mathematics (2013) [pdf]

math.cmu.edu

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Re: Everything you always wanted to know about mathematics (2013) [pdf]

#61
post #3

Beautifull! Is there similar book on physics?

Susskind's series does a pretty decent job walking the reader through topics in (theoretical) physics. At a somewhat more advanced level, you can try Schwichtenberg's No-Nonsense books. I also enjoyed Stevens' The Six Core Theories of Modern Physics.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#62
post #58
post #54

Note that these are 700 pages which could take multiple years (if you're doing it in your spare time) to go through. I'm not sure who would have the motivation and discipline for this.

> Everything you... wanted Far from being "everything" anyone would want or need, it's rather "some (fundamental) things" you must know. A couple of pages a day, on average, would get you there within one year.

Still, I'm in doubt that a significant proportion of us would have the discipline for this. One reason why some things are pretty much only learned in university is that they provide the necessary motivation.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#63

Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.

I love this book: https://www.goodreads.com/book/show/17406856

The explanations are great and the examples and excises are such that you can just do them in your head.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#65
post #62
post #58

Earlier quoted context omitted.

> Everything you... wanted Far from being "everything" anyone would want or need, it's rather "some (fundamental) things" you must know. A couple of pages a day, on average, would get you there within one year.

Still, I'm in doubt that a significant proportion of us would have the discipline for this. One reason why some things are pretty much only learned in university is that they provide the necessary motivation.

I collect interesting problems and learn the math that can solve them. I do best by directly connecting fun and learning.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#66

Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.

At Math Academy (https://mathacademy.com), we created a series of courses, Mathematical Foundations I, II, & III, that will take a student from basic arithmetic through calculus and prepare them for university-level courses like Linear Algebra, Multivariable Calculus, Probability & Statistics, etc. You can jump in at any with an adaptive diagnostic that will custom fit the course to you based on your individual strengths and weaknesses.

https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-iii

We also have courses on Linear Algebra and Mathematics for Machine Learning:

https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/mathematics-for-machine-lear...

It's not free, but our adaptive, AI-driven algorithms makes it the most efficient way to learn math that you're going to find. We've had numerous students master 3-5 years of math in a single year.

We're still in beta and haven't done a proper Show HN yet, but we're getting there!

I'm the founder, so I'd be happy to answer any questions.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#67

Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.

I found this to be a good explanation of Calculus in particular: http://lightandmatter.com/fund/

It assumes you have some algebra, but does not require college algebra.

Re: Everything you always wanted to know about mathematics (2013) [pdf]

#69
post #38

https://pimbook.org/ Read this instead

That book has a completely different focus... breadth instead of understanding argumentation.

I agree that the Programmer's Introduction to Mathematics is more likely to contain useful content (instead of being about how to develop the ability to reason carefully). It also has a LOT more breadth than the OP.

The free part of Chapter 3 "On Pace and Patience" is a key very important attitude toward learning from this book (especially on your own). If you are thinking about studying from this book, make sure you philosophically agree.

I tried to copy and paste a paragraph here, but it looks like it has been ROT-13 encoded in the PDF (or something)!

> [...] mathematical culture requires being comfortable being almost continuously in a state of little to no understanding It's a humble life [...]

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