/sci/ - Science & Math

>>12703362
Enginigger here
started reading the first one
Got like 4 pages in and stopped. Too much of a hassle.

>>12703362
no, apparently the best stuff requires high level math so i'm self studying math first, beginning with real analysis. I hope to read TAOCP when I'm in grad school.

>>12703835
The first part of the art of computer programming is supposed to basically be a shorter version of concrete math (other way around actually) so should only require some analysis.

>>12703792
Ah fair enough, why is that?

I am quite enjoying them, feels like relearning maths for the most part. I am a Bioinformatician so I was planning on studying through this one (12-18 months) then reading 4A for the combinatorics, which has direct applications in my field. Is skipping the other sound like a bad idea to anyone?

>>12703835
This, SICP is way friendlier

>>12704789
fair enough, cheers for the tip anon.

I am kind of using it more to strengthen (and construct, in many cases) my mathematical foundations. So far I am a few sections in and finding it okay (famous last words!). I have been going through the exercises and can generally do anything sub 20 quickly, 20-25 might take half an hour or so (or not at all, for some) but anything 30 and above I am happy if I can even formulate a strategy or understand how one might go about solving them. As you can see, my maths is still weak, but then again I am not a mathematician. Do you think SCIP would be worth picking up too?

>>12704789
>SICP is way friendlier
It also covers completely different material. SICP is basically just a really good intro to programming course text.
>can generally do anything sub 20 quickly, 20-25 might take half an hour or so (or not at all, for some)
>20-25 might take half an hour
Is that half an hour each?

>>12704841
>Is that half an hour each?
Depends on the question, some take 1 minute, others take half an hour if it is the first time I have come across a question of that kind.

Some examples (though I risk turning this into a thread about how shit my maths is!):

9. [M23] Given that [math]x[/math] and [math]y[/math] are rational, prove the laws of exponents under the assumption that the laws hold when x and y are integers.

This I found very straightforward, and did it in minutes. On this other hand

8. [25] Let [math]m[/math] be a positive integer. Prove that every positive real number [math]u[/math] has a unique positive [math]m[/math]th root, by giving a method to construct successively the values [math]n[/math], [math]d_1, d_2,...[/math] in the decimal expansion of the root.

took me a lot longer, perhaps an hour or so of reading back and fiddling. Really really not competitive times for questions which I am sure are trivial to others, but as I say, I am far from a mathematician. I see improvement though, so I am happy enough.

So, are other volumes in the series skippable or is that just going to cause issues down the line?

I'm going to learn analysis, linear algebra, and algebra first before I dive into Knuth's tome. I have enough mathematical maturity to do some exercises, but my autism to gain more insight is bugging me. Btw, did you do every exercise in the intro? The one where he formally defined what is an algorithm.

>>12703362
I have really successful programmer friends who have never opened, so here's that

>>12704901
>did you do every exercise in the intro?
If you are referring to section 1.1, I did not do the last two, but if I fail on problems I just keep them to come back to later rather than just look up the answer. I was planning on coming back to them on my second read through, where I will hopefully be more prepared.

>>12704911
Not surprised, only a small portion of programmers have even attempted to read these as far as I can see. I am not strictly a programmer (though during my PhD I did a fair bit of dev work, building new genome analysis tools), so I am fairly certain this will be of limited utility in my professional life. Genuinely enjoying my time studying it though! Volume 4A is the only one I can really see being directly useful to me, the rest is just because it's interesting.

>>12704917
Yes, that's what I'm talking about. I can't remember how far I've gotten on TAOCP since I've hands full on working on other maths subjects. What chapter are you on right now?

>>12705078
Still C1 since it takes up most of the first volume, but I am section 1.2.3 Sums & Products, which is a bit more engaging than the previous chapter on exponents and logs. Still right at the beginning of the journey really. I am taking it slowly and trying to make sure that, even if I can't do some of the exercises (which is a given, considering how hard some are), I at least grasp the content of the section enough to do the ones up to 25 ish. I intend to reread this after I have finished it, since I suspect I will discover nuance on the second reading that eluded me on the first, due to my sheer ignorance of some of some of the subjects.

>>12703362
They’re a great source of algorithmic knowledge leading up to the 2000s. Keep in mind though that they aim for a foundational yet technical treatment of the material - so you’ll learn about algorithms related to randomness and producing pseudorandom numbers, but you have to be at least causally comfortable with measure to follow Knuth’s treatment.

I feel like it’s a great read but definitely excessive if you want introductory algorithms. But nobody can deny it’s an incredibly informative text.

>>12704203
I mean kind of? Knuth expects his readers to be able to pull analytic arguments out at the maturity of at least chapters 1-4 of baby Rudin in the first book onward (hell he even takes some of Rudin’s exercises verbatim), but he develops the basic abstract algebra he uses.
He develops the necessary measure theory to talk about randomness in vol II but you ought to have done measure prior to get the full picture.

>>12705556
Without doubt my reading of it is excessive, you are not wrong there! Working on it each evening has turned into a bit of a relaxing ritual now, for whatever reason.

>>12705566
Yeah I have noticed Knuth seems to be rather optimistic about the brain of the reader, it can be a little confusing at times when he just casually throws analysis at you, with "trivial" steps skipped or not explained. Keeps me on my toes.

>>12705722
>Working on it each evening has turned into a bit of a relaxing ritual now, for whatever reason.
I think it's because Knuth has a very distinct personality in his writing. He takes the opposite focus to someone like Rudin, where he devotes a lot of words to explaining technique but only a a few paragraphs to relevant theory. I feel like his textbooks are a response to the terse nature of other math books where the reader is left to their own devices to figure out some of the proof.
Granted, both approaches are valuable (I appreciate Rudin way more now than I did when I started reading him), but I think what makes Knuth work is that he explains a LOT, asks easy questions, and then expects you to answer the harder questions semi-consistently. He doesn't let you off the hook, but he throws you a lot of bones on *how* to think.
>ah I have noticed Knuth seems to be rather optimistic about the brain of the reader
I *wish* Computer Science education went down Knuth's style, where he isn't afraid to throw you harder mathematical structure. I've found that it's because you might not always need the technical results, but the more I look at it, the more I feel it's just 90s computer scientists being lazy discrete mathematicians.

Well, a lot of "classic" nondiscrete math is trickling down from being just relevant if you want to do "serious" CS, so hopefully we see it show up. Or at least
>split CS into the serious CS/CSE major and the software engineering major.

>>12703362
I don't know how to read. Say the word "educaton" out loud to yourself. ed-JEW-caton. Ever since I figured this out, I have not done a day of schooling, and to be honest with you my friends I have actually forgotten what a comma is. So there you have it, I have an IQ of 87 and I am proud to not be one of those smart slaves who have to worry about the world; I can just live a care-free life.

To avoid schooling -- back in the day the law was a bit lighter -- my dad just told the Alabama service workers that I was being "homeschooled". My dad has an IQ of around 84 and even he fooled those (((suit-wearers))). I will keep farming and living the good dumb life. The farm is my garden of Eden and the fertiliser is plant steroids. The sun is my alarm clock and the moon is my bedtime indicator.

>>12705808
based

>>12705794
Yeah I 100% agree. Although I am not particularly experienced with reading other standard works, I really enjoy Knuth's writing style. In particular, he seems to have put in a good amount of thought to what exercises to provide. For the most part they hit the sweet spot of not overly hard if you have carefully studied and understood the preceding section, but seldom so easy that they yield without effort. That is until he throws some kind of mad HM40 research question at you, but I really love that he was not in any way scared to include those since it gives the reader half a chance, and an insight into what a research question actually looks like.

I will re-review this in 6 months time and see if I am still as enthusiastic haha.

>>12706377
Are you interested in making a study group?

>>12707930
Not that anon but I'd be interested in a Concrete Mathematics study group

>>12707930
>>12707978
This. But it should be a general thread here rather than on discord. People get easily distracted there, not to mention that there are lots of tran*ies on that shitty app.

>>12704676
Ehhh, it's not that bad, most of the suff in the books can be learned elsewhere much faster and less obtusely.
If you want to develop as some sort of (actual) computer scientist, then the book does exercise your problem solving skills.

>>12703835
>>12705566
you are wrong. it's just some induction and combinatorics. He even clarifies groups are only used here and there.

it's certainly not easy, but it's not deep abstract math concepts, it's just hard proofs and puzzles.

>>12703362
people don't understand the purpose of these books. the primary purpose of knuth's work is to prove algorithm complexity for basic algorithms in a mathematically rigorous way.

most engineers just want to learn how the algorithm works and the basic complexity. so that information can be acquired more efficiently in other books. (I recommend udi manber)

if you are doing some research and really went to get on the weeds with an algorithm than looking it up in knuth can be helpful.

If I have done most of CLRS is there much reason to read TAOCP?

>>12710097
not unless you are extremely interested in the analysis part, see
>>12710068

>>12710068
Yes and no. It’s primary use case is in fact for research, but Knuth explicitly writes the book knowing that people will selectively choose the depth at which they complete the book. He tiers problems and material in that way, and his aim is to go from highschool level mathematics into full rigor. He fails a bit in this regard (again, he pulls a strong command of real analysis and measure theory almost out of nowhere and with little development within the text) but that was the intent.

I agree that other sources are best for simply learning about an algorithm and its use. But you’d be hard pressed to say you wouldn’t benefit from Knuth’s book even as a programmer - you just have to make the call whether or not you have the energy and maturity to go through it. Though, the obvious is that you’ll want it for research, and this is clear if you look at any algorithmic work today that isn’t purely combinatorial.

>>12703362
>anyone read em?

Waiting on the newer edition

>>12710068
>I recommend udi manber
Why this specifically?

Heckin bumperino.

>>12710751
Legit. I absolutely love my 3rd ed though. It's my baby, don't let it leave my side!

>>12710068
I can see how it would be used most commonly as a reference text. However, the wealth of analysis and presence of exercises does give the reader the opportunity to elevate it to something more than just a reference that spends all it's life on the shelf. Knuth seems to have put a lot of effort into ensuring that people actively engage with his works, rather than buy them to occupy space on a shelf.