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Mathematics for Computer Science (2018) [pdf]

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Re: Mathematics for Computer Science (2018) [pdf]

#51
post #6

Earlier quoted context omitted.

Screen reader which is able to read PDF with Latex formulas? I will be surprised if this is possible at all. I can not even name most of the symbols from that formulae.

Give https://www.paper2audio.com/ a try; it is targeted at just this use case. It’s a Seattle-local startup.

I'm the Paper2Audio founder and I'm thrilled to see you recommending us here. Paper2Audio specializes in narrating complex documents like research papers to you. It is free for personal use.

This PDF exceeds our page limit, so you would have to split it up. We're working on increasing our page limits.

Re: Mathematics for Computer Science (2018) [pdf]

#52
post #50

Earlier quoted context omitted.

I looked into this book before and without solutions it makes it much harder to use for self-study. Maybe LLMs do change that now but I'm not sure I'd trust their output if I were learning the topic Susanna Epp's Discrete Mathematics With Applications is also a really good option

The logical skills to evaluate the output of a LLM are the same skills brought to bear reading any book. What makes you trust this textbook then? Textbooks are not infallible.

Good textbooks have gone through expert reviews and multiple iterations of improvement. That can't be said of an LLM answering your personalized questions or the book problem

But why not both?

Re: Mathematics for Computer Science (2018) [pdf]

#54
post #43
post #40

I took a look at the table of contents and found that the second chapter is about the well-ordering principle. That’s surprising to me because I’ve only heard of the well-ordering theorem by Zermelo, which is a fundamental theorem in set theory, stating that any set has a well-ordering assuming the axiom of choice. It’s amazing and mind-bending in its own right (imagine a well-ordering for reals), but is clearly not…

The well ordering principle, the axiom of choice, and Zorn's Lemma are all "equivalent", meaning you can pick any one as an axiom and prove the other two. So some text books may pick one as the axiom and others pick a different axiom. The crazy thing about the well-ordering principle: It states that a well ordering exists on the reals, which means that you can find an ordering such that any open set has a minimum. Ap…

You are talking about the well-ordering theorem, not the similarly named well-ordering principle. That’s exactly my confusion when I first opened this PDF.

Re: Mathematics for Computer Science (2018) [pdf]

#55
post #54
post #43

Earlier quoted context omitted.

The well ordering principle, the axiom of choice, and Zorn's Lemma are all "equivalent", meaning you can pick any one as an axiom and prove the other two. So some text books may pick one as the axiom and others pick a different axiom. The crazy thing about the well-ordering principle: It states that a well ordering exists on the reals, which means that you can find an ordering such that any open set has a minimum. Ap…

You are talking about the well-ordering theorem, not the similarly named well-ordering principle. That’s exactly my confusion when I first opened this PDF.

Different folks use different conventions. When I was taught it, they called it the principle, not theorem. You can find similar comments on the Internet (e.g. math subreddit).

Here's one that acknowledges it:

https://math.stackexchange.com/questions/1837836/well-orderi...

> The "well-ordering principle" has (at least) two different meanings. The first meaning is just another name for the well-ordering theorem. The second meaning is the statement that the usual relation < on the set N is a well-ordering. This statement is equivalent to the statement that ordinary induction on the natural numbers works.

Re: Mathematics for Computer Science (2018) [pdf]

#56

I'm not such a fan of trying to cram everything-mathematically-relevant into a single huge book (and it is huge - 1048 pages). Anyway, this reminds me of a rather different initiative in the same vein: The building of Mathematical principles based on the expediences of Computer Science: CONCRETE MATHEMATICS by Donald Knuth, Ronald Graham and Oren Patashnik. https://www-cs-faculty.stanford.edu/~knuth/gkp.html https://…

Graham/Knuth/Patashnik is a lot less "basic discrete maths you're most likely to need" and a lot more "number sequences we've known and loved". Almost more useful for physicists due to the amount of summation fu you'll learn there.

The book Concrete Mathematics started as course notes for a class whose textbook initially was the (dense) "Mathematical Preliminaries" chapter of The Art of Computer Programming (Chapter 1 and roughly the first half of Volume 1), so it can be seen as an expanded and leisurely (and even more delightful, because of all the student jokes and other marginalia) version of that chapter. This is mathematics that Knuth needed for the rest of TAOCP.

So it's more "mathematics for the analysis of algorithms" (incidentally the title of another book by Greene and co-authored by Knuth), and so probably most applicable to the field of "AofA" rather than physics or computer science in general.

Lovely book, very few math books fill one with as much joy as this one.

Re: Mathematics for Computer Science (2018) [pdf]

#57
post #48
post #45

Earlier quoted context omitted.

Not to say it isn't useful to a CS education, but the only time I've ever ran into the well-ordering principle was to establish the foundation for mathematical induction proofs. Students usually learn this in discrete math for CS in undergrad. Then in many future undergrad courses that are algorithms focused, the proofs tend to use induction and no one really thinks of the WOP

Yeah. I have had several different courses teach induction, and nobody really thinks of the WOP. I’m pretty sure most of them skips the WOP when introducing induction.

I’ve seen it used when people show a proof of induction as a theorem. Sometimes they just take the technique of induction as given and don’t prove it.

Re: Mathematics for Computer Science (2018) [pdf]

#58
post #17

I always see lists of like 100 MUST HAVE books for Computer Science. Is there like a top 5 must have books for Computer Science?

Top 5 will never cover the field. Here's my top 10 * Brookshear and Brylow - Computer Science - An Overview * Forta - Teach yourself SQL in 10 minutes * Stallings - Computer Organization and Architecture * Stallings - Operating Systems - Internals and Design Principles * CLRS * Kurose, Ross - Computer Networking - A Top Down Approach * Sipser - Introduction to The Theory of Computation * Stallings, Brown - Computer S…

SICP still deserves to be on such lists.

I also love Concrete Mathematics.

I prefer the Tanenbaum OS books over Stallings. In particular the design and implementation book, although it is more than a decade old now.

Re: Mathematics for Computer Science (2018) [pdf]

#60

I always see lists of like 100 MUST HAVE books for Computer Science. Is there like a top 5 must have books for Computer Science?

It's more useful to practice programming through projects. Then once you feel you're missing the knowledge for a particular problem you're trying to solve, read up about that one.

Projects are essential, but I've found there is a huge problem with your advice: you have no clue about the possible solution surface.

My advice to learners has been "try to learn as much about a topic as someone who has taken the subject in college and forgotten about it".

For example consider calculus: Someone who took calc 20 years ago and hasn't used it since will probably forget exactly how to compute most derivatives and integrals. But if someone mentions an optimization problem "we need to know when this curve peaks" or asks something involving finding the area under a curve, alarm bells should start ringing. They'll know this can be done, and likely go grab a calc book to refresh.

Another example I run across all the time, which is the opposite scenario: Survival analysis. I have been on countless teams where somebody needs to understand something like churn or the impact of a offering a discount that hasn't expired yet, etc. These are all classic survival analysis problems, yet most people are ignorant that this field of study even exists! Because of this I've seen so many times where people complain that "we'll have to wait months or years to see if these changes impact customer lifetime!" (note: if anyone out there is doing Churn or LTV analysis and aren't familiar with survival analysis, you are most certainly approaching it incorrectly).

I've seen a lot of people get frustrated with self study because they try to learn the material too well. If you aren't going to be using survival analysis soon, it's not really worth remembering all the details of how to implement a Kaplan Meier curve. But if you even have a vague sense of what problem this solves, when you encounter that problem in a project, you know where to go back to. Then you typically walk away with a much stronger sense of the subject then if you had studied it harder in the first place.

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