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

math.cmu.edu

81–90 of 153 posts

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

#81

One thing I've always wanted is a comprehensive guide to mathematical notation, which tells you what symbols mean or at least what field of mathematics they come from. I frequently come across all sorts of weird mathematical symbols in papers, and of course these symbols are virtually never explained, so I have no idea what they mean. Even better would be if there was some way an LLM could read through a paper itself…

RE: math symbols

Check out this excerpt of definitions of basic math notation I use in my books: https://minireference.com/static/excerpts/set_notation.pdf It has some examples of the "alien symbols" ∀ (for all), ∃ (there exists), etc.

One problem (feature?) of math notation is that paper authors don't follow a consistent convention for symbols, so what you're asking might not even be possible... It doesn't help that different math domains might use different symbols for the same concept! That being said, there is the ISO 80000-2 standard that defines recommendations for many of the math symbols, with mentions of other variations, see https://web.archive.org/web/20210705180417/https://people.en... You might want to read through that as a starting point.

Unfortunately, just knowing the notation (being able to read the symbols) is not usually enough. Understanding each symbol/concept usually requires knowing the math context and other related definitions of the domain where the notation is used. In other words, knowing the notation is not a shortcut for learning math... But still, I hear you about the need to select some symbols then right-click and choose "read this to me" or "explain this to me."

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

#82

As a CS major who went to CMU years ago, my favorite book from all of my professors was for my 15-213 class called Computer Systems: A Programmers Perspective I remember at the time the book was in loose leaf paper so it warms my heart to see the book has a 3rd edition. It was used as a core part of teaching assembly, memory representations, and getting students ready for the operating systems class. When I help peop…

We used this for my Computer Architecture class in college and it's one of the few textbooks that I wish I had kept around. I had a used copy so not selling/returning it to the bookstore really wouldn't have been too impactful at the time. Now that I'm wanting to get back into low-level programming, I miss it even more.

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

#83
post #48

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.

It's not one book, but for everything before calculus it would be difficult to beat the books in Israel Gelfand's High School Mathematics Correspondence Curriculum [0]. These are designed for self study and give a fresh perspective on topics they cover. [0] https://www.goodreads.com/series/318605-gelfand-corresponden...

Excellent recommendation; they are very good books to start with. Concepts are clearly explained and I wish every mathematics textbook was structured like this. Some people are biased against these books because they're Soviet, but I find that attitude parochial. If we're judging textbooks on their merits alone, these will get you to Calculus.

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

#85
post #8

If I remember correctly, Brendan Sullivan had a reputation as a TA for Concepts of Mathematics at CMU as "Math Jesus", not sure if that was a testament to his pedagogical skills or just due to the long hair and beard...

Where is he now? Why doesn't he write more books like this? I mean in this lucid explanatory style.

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

#86

As a CS major who went to CMU years ago, my favorite book from all of my professors was for my 15-213 class called Computer Systems: A Programmers Perspective I remember at the time the book was in loose leaf paper so it warms my heart to see the book has a 3rd edition. It was used as a core part of teaching assembly, memory representations, and getting students ready for the operating systems class. When I help peop…

Is there a book or resource you'd recommend for operating systems? I recently finished CS:APP and really enjoyed it. Though I've been programming for ~7 years and felt that made it easier to digest.

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

#88

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.

Check out Kahn Academy, they have a gamified course to guide you through the equivalent of a high school and early college math curriculum. AFAIK it's free?

Specifically these three courses [0][1][2] will take you from basic algebra to precalc. They're very thorough and I've found them extremely useful in upgrading my high school level math skills. I have heard that their calculus courses aren't sufficient though, and that it should be learned from somewhere else.

[0]https://www.khanacademy.org/math/math1 [1]https://www.khanacademy.org/math/math2 [2]https://www.khanacademy.org/math/math3

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

#89
post #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 str…

Looks great and was ready to sign up but I surely wasn't expecting that price! I am not saying it is not worth that, but as someone who has tried to start learning math on my own only to quit afterwards for whatever reason, it's a big risk to take.

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

#90
post #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 b…

Its using ROT25 ¯\_(ツ)_/¯
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