/prog/ - Programming

>>3034

PART 2

Algorithms

Intro to Algorithms aka CLRS https://mitpress.mit.edu/books/introduction-algorithms this will teach you sort of an Art of Programming lite.

NP-hard problems

Concrete Math by Knuth et all (CONtinuous and disCRETE math)

This is chapter 2 of The Art of Computer Programming (TAOCP) "Mathematical Preliminaries" in a format that isn't as terse. Complete this and you can do any of the TAOCP books, and solve any problem using discrete mathematics in computer science.

Bezerker level, how the fuck did they do that tier

Calculus on Manifolds by Spivak. This notation is used by Gerald Sussman (of SICP fame) in all his texts. It's a great fleshing out of multi variable calculus, but you absolutely have to do the exercises, it's a small book but difficult.

Structural Interpretation of Classical Mechanics Aka SICM free online http://mitpress.mit.edu/sites/default/files/titles/content/sicm/book.html

Just read the Intro/First chapter (unless you have a solid understanding of classical mechanics from these lectures: http://theoreticalminimum.com/courses/classical-mechanics/2011/fall then read the whole book)

You write out math equations in scheme. You will get that "aha" moment like when you read SICP but for Math. If you just read the first chapter/intro you will be able to convert math equations into functions whenever you come across them. If you read the whole book you will:

* write a lagrangian as a normal Scheme function

* symbolically take derivatives of that to get equations of motion

* print those equations with LaTeX.

* compile those equations to native code and numerically integrate and plot the motion of the system

It's like magic the first time you see it. You can now write highly advanced physics into game player movements.

Master of the Universe tier

The Art of Computer Programming any volume. I would start with 4.1a Combinatorial Algorithms. 4.1b is out on Knuth's homepage and it contains all new math that isn't even on Wikipedia yet. The exercises are in the book for a reason, it's not just reference it's to help you understand the material so try some of them.

Functional Differential Geometry by Sussman. http://groups.csail.mit.edu/mac/users/gjs/6946/calculus-indexed.pdf SICP is the gold tier for Computer Science, SICM is gold tier for Physics, and Functional Differential Geometry is gold tier for applied mathematics. This again converts equations into scheme functions. Treating data as a distribution in high-dimensional space is at the core of machine learning, and differentiating across those dimensions is typically how learning is done. There's a whole area called Information Geometry which treats the parameter spaces of statistical models as Riemannian manifolds under the Fisher information metric you'll learn in machine learning courses.

In SICM the same authors mention that a computational approach to calculus revealed errors in their own understanding of classical mechanics equations (such as Lagrange's equations), and they introduced new notation to address the problem. Functional Differential Geometry picks up that idea and runs with it, debugging general relativity and quantum mechanics.

Conclusion

This list is about learning base theory, so you can branch off and learn anything you want yourself like a formal course in Statistics http://www.stat.cmu.edu/~larry/all-of-statistics/ or go into number theory for cryptography. With this foundation there is literally no course or advanced field of Compsci you can't take.

I like your suggestions.

For linear algebra I would suggest Shilov, it's a fantastic book, and published very cheaply by Dover books. Of course with all these recommendations, it is never a bad idea to read from a few different authors, some will suit you better than others.

>>3034

>"Advanced Calculus" which is actually easier,

I seem to remember that being the other way around.

Another alternative for calculus/Analysis is the two volume treatise by Zorich.

http://www.amazon.com/Mathematical-Analysis-Universitext-Vladimir-Zorich/dp/3540874518

http://www.amazon.com/Mathematical-Analysis-Universitext-Vladimir-Zorich/dp/3540874534

Of all the analysis books I could find, that one stood out to me as the clear winner, based on the breadth of coverage, and the well explained yet slick proof style.

Your millage may very.

Jesus Christ OP, how long would it take to read all this stuff?

(Saved the thread for future reference.)

>>3040

I'm not OP, but I added the books after his nice list.

I think 3-4 years is a good target. You'll want to read most if not all of the linear algebra and analysis texts, but as you specialize to more advanced topics, you'll just cover things that interest you.

Fuck, I posted the wrong "Advanced Calculus" book, I meant to post this so-called Honors Calculus pdf who's intro talks about how good Spivak is for self learning, and how difficult some of the problems are http://math.uga.edu/~pete/2400full.pdf

Anybody else with suggestions for theory in CompSci books feel free to dump in this thread

>>3040

I did these books after work, and during an 8 month stretch where I was living off cryptocoin arbitrage, so complete my work by 8am and had nothing to do all day. (I'd still be doing it if it wasn't for blockades put up by governments for getting money into exchanges/irc trading partners).

I spent 2-6hrs per day on each book. It took me a month to do Basic Math, as I was only doing it 2hrs per day. A week to read the other 2 prelim books, about 3 months to do Spivak's Calculus because holy shit it was hard (for me, at the time), about a month each for Discrete Math/Linear Algebra which I did at the same time as Spivak's book, so one day read/do Spivak for about 4-6hrs then do the other book(s) next day.

CLRS took me a while because I did the full MOOC online for it, I think 2-3 months. I wish I had just read the book. While doing it I started reading Concrete Math and used stackexchange to chase down things I didn't know that came up, that took me a good 4 months as it was probably the hardest book I've ever done.

Calculus on Manifolds took a month, it's small but dense and very good. I went back and reread parts of it so many times doing SICM that I can't remember how many times I've done it so let's say 2 months. SICM took awhile, because I had no physics education so had to go and research everything I came across I didn't understand. I think 4 months it took doing p/t. I'm still reading The Art of Computer Programming, I did most of 4A but then went to Vol 1 and started from beginning. I don't read the entire chapters, I skim to get a good reference then try some of the exercises or convert his pseudo-code into Typed Racket for the things I do for money these days. Building a trading engine vol 4 is gold for that.

Functional Differential Geometry I did in less than one month because I was doing it 9hrs a day, it was totally crazy fascinating (just like SICM) and I had a good solid understanding of his notation which is similar to Spivak's Calculus on Manifolds so breezed through it. Right now I'm just reading TAOCP and The Art of Software Security Assessment which is not math related but an awesome read.

Tl;DR it took me about 1.5 years to do this, but I went through some of these books at the same time and some days spent 20 mins on them and others spent 9 hrs.

>>3044

Also note, nobody has to read what I read. There's other ways to get applied mathematical information I just went the theory route http://spin.atomicobject.com/2015/05/15/obtaining-thorough-cs-background-online/

This is an amazing thread. What has prompted you to be such a fucking fantastic gentleman, OP?

There's also this gargantuan reference book, which covers almost everything in Applied Math http://www.derivations.org/ written by a Debian developer.

It gives you to the point definitions of anything you may come across in computer science/engineering courses you forgot, like how Logarithms work. There's no exercises, so you won't get an full understanding of the material but good enough for "brute force learning" which means you start doing any advanced compsci course you wish then go look up any references they assume you already know, like summation or vector calculus.

>>3034

What do you think about Introduction to Algorithms? I got that book with the hope to learn more about math however I can't force myself to read through it. Any advice on that? How does that compare to the other books?

>>3063

Not the person you asked, but I think it is essential reading for any computer scientist. There's another book which gets recommended a lot

> Robert Sedgewick - Algorithms.

I haven't read it, but I did really like ItoA. You're going to need to cover that material at some point, although it's more foundational than practical.

>>3070

The things is that I don't understand a lot of stuff. I downloaded the Basic Math in order to clear a lot of the things I am missing and then I am going to pick up on ItoA.

I feel shame not paying attention in math class. So much wasted time.

P.S.

Finding the Basic Math by Serge Lang wasn't easy so when I found it I decided that I'll seed it for a while on kickass in case someone else wants the knowledge.

>>3075

>I feel shame not paying attention in math class. So much wasted time.

Don't. There's very little chance that you had a great teacher anyways. If the will is there, you'll repair any gaps in your knowledge.

I was once in the same boat as you, but now I've read pretty much all of the books OP listed. Math classes in school are horrible for generating motivation, so it seems little more than busy work. Besides, as a high school student there are other priorities, like getting the attention of the hot girl in the class.

Stick with it.

>>3075

I've heard some good things about this book too, but I cannot attest its level of difficulty

http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025

It's Knuth though, so I'm sure it is top quality.

>>3075

If you are still lurking this thread, there is this website: http://gen.lib.rus.ec/

Just type the name of the book (excluding "by" when including the author's name) and you'll find many books that aren't on torrent websites. Follow one of the mirrored links and you're pretty much set.

>>3034

Btw, thanks for the guide op, I appreciate this so much.

>>3081

Thanks a lot dude. I am in the process of getting my shit sorted out.

>>3085

You could do a double major in math/comsci.

Or a masters in either one of those subjects. That separates you from the average blub programmer.

I'm reading Basic Mathematics right now, and there's an exercise like this:

Justify each step, using commutativity and associativity in proving the following identities.

I don't know what is meant by "identity" here, but I get the idea of what I'm supposed to do. Trouble is I've no idea what I'm actually supposed to write down. Could someone give me an example please?

Here's the first one for example's sake:

(a + b) + (c + d) = (a + d) + (b + c)

Also, could someone tell me how to use the $$ tags? I couldn't get them to work.

>>3090

It's mainly moving stuff around. Since addition is the only operation in the expression, you can manipulate what's being added first :

(a + b) + (c + d) = (a + d) + (b + c)

= (a + c) + (b + d)

= (a + b + c) + d

= a + (b + c + d)

= (a + b + c + d)

= (a + b) + (c + d)

I might be wrong but that's what I did.

>>3090

>I don't know what is meant by "identity"

An identity is any kind of transform which leaves the operand unchanged. It's a fancy way of saying both sides are equal. You could also say, "equalities".

That example you are showing is demonstrating two identities of addition which must hold in a field.

commutativity: a + b == b + a

associativity: (a + b) + c == a + (b + c)

>>3090

An identity is basically an equation, except you can use it anywhere.

To prove an identity, you need to show that both sides of the equation are the same. You usually do this using expansion, simplification, and even other identities.

See below for a proof.

>>3092

You've got the right idea, but that's not a proof since you're using the thing you're trying to prove to prove it. You'd get marked wrong in an exam (unless you're like me and you bitch to your professor for half marks. Needless to say I won't make that mistake again)

What you'd want is something more like:

Proposition: (a + b) + (c + d) = (a + d) + (b + c)

Proog:

Take the LHS

(a + b) + (c + d)

= a + (b + c) + d (associative laws)

= a + d + (b + c) (commutative laws)

= (a + d) + (b + c) (associative laws)

Which equals RHS.

Therefore, (a + b) + (c + d) = (a + d) + (b + c) holds.

qed

I should probably also specify which mathematical objects a, b, c, and d are.

ie:

let a, b, c, d be particular but arbitrary real numbers.

[…]

Therefore, (a + b) + (c + d) = (a + d) + (b + c) holds for numbers a, b, c, d in the reals.

>>3090 here, is it okay to ask for more help in this thread? I was an idiot when I was younger, and I didn't pay attention in maths class. I'm trying to catch up now, but I no longer have teachers who I can ask for help.

For now I'll just ask.

The third exercise asks me to prove the identity (a - b) + (c - d) = (a + c) + ( - b - d). Here's how I did it:

Proposition: (a - b) + (c - d) = (a + c) + ( - b - d)

Proof:

Take the LHS

(a - b) + (c - d)

= (a + (- b)) + (c + (- d))

= a + ((- b) + c) + (-d) (by associativity)

= a + (c + (- b)) 0 (-d) (by commutativity)

= (a + c) + (-b - d) (by associativity

Which equals the RHS, and therefore the proposition holds.

QED

I have two questions. First, is this correct? Two, am I supposed to note what I did in each step, as I did with the last three steps, but not with the first?

Also, one of the later exercises says to "Show that - (a + b + c) = - a + ( - 6) + ( - c)." What's the difference between this and the earlier exercises where you're asked to justify steps?

>>3097

What does it mean to say that variables are particular but arbitrary?

>>3106

>What does it mean to say that variables are particular but arbitrary?

Basically just a way of saying "It works for any number". You can pick any numbers within the constraints I gave you (in my case, they have to be real numbers), and it will work for any of those.

Take the following with a grain of salt: I'm still learning myself

I'm fairly sure it's dependent on how unrestrictive the constraints are - in particular if those constraints don't refer to another variable.

You wouldn't say:

Let a and b be particular but arbitrary integers, such that a = 2b.

Though, you might say

Let b be a particular but arbitrary integer, and a be an integer satisfying a = 2b

I couldn't tell you why they word it like that, but that's how my textbooks and my professors tend to do it, so I just immitate it.

>>3034

Can you explain your learning process?

How did you manage to completely read 6 math books that have more 500+ pages in them in less than 2 years and understand all the material :/.

>>3108

All the while running cryptocurrency trading algos that he wrote from scratch.

>>3086

>double major in math/comsci

This is what I'm doing. I'm hoping it will give me better opportunities to do work in academic/research oriented areas, as opposed to enterprise stuff.

>>3119

Be sure to practice questions. Don't just read or you won't learn half of it. Also, it often helps to get it explained in different words - khanacademy is pretty good for that. He explains it and then goes through a couple examples.

>>3106

>I have two questions. First, is this correct? Two, am I supposed to note what I did in each step, as I did with the last three steps, but not with the first?

>Also, one of the later exercises says to "Show that - (a + b + c) = - a + ( - 6) + ( - c)." What's the difference between this and the earlier exercises where you're asked to justify steps?

Could someone please help me with these?

Maths books .pdfs:

>>>/freedu/92

Of varying skills levels. Share any you have there.

Found one of the books mentioned in OPs post on /freedu/, Basic Mathematics by Serge Lang. I'm posting it in this thread so you guys can check it out. If you find any other books mentioned in this thread, make sure to post 'em and share 'em around.

Big thanks to the Anon on /freedu/ for finding this.

>>3130

Unfortunately the PDF will not upload here, so I've uploaded the book to the following link:

http://docdro.id/K1VENuF

>>3128

The first step seems to just be a definition. In other words a - b is short hand for a + (-b), or at least that's how the book seems to do things considering one of it's examples.

Maybe you don't have to keep everything on the same side and can add the minus of the LHS to the right one. He does that in some of his earlier examples, and it would make sense since -(a + b + c) doesn't seem as easy to use as (a + b + c).

Or you could use No.4 or No.5.

I want to say you can't really do it with just associativity and commutativity since -(a + b) only makes sense based on (a + b). They proved -(a + b) = -a - b by adding (a + b) to both sides and getting everything to zero, which I'm pretty sure uses more than associativity and commutativity (axioms involving zero)…I think.

It's funny how adding numbers can be so hard, while taking derivatives is easy as fuck.

Math's weird

>>3168

Forgot to add, you do not need to read the whole text if you don't want to. You can look up courses on MIT Open Courseware (such as, Linear Algebra) and just read their lecture notes and do their assigned reading out of the book for bare minimum effort to learn a subject good enough to be adequate at rolling your own algorithms or understanding math concepts. There's no need to do every single chapter unless you're interested in it like I was

>>3106

The answers are in the back of the book for some questions. An identity is a relation that means that whatever the number or value may be, the answer stays the same. You can also start with Lial's Basic College Mathematics, it's a little more clearer than Lang's book as he assumes you know identities. I'll attempt to attach it to this post if not this (spammy, use ublock origin/adblock) link has it http://www.uploadable.ch/file/uBDeWscyUnRV/d3mlr.Basic.College.Mathematics.9th.edition.pdf

Lial's book covers even earlier stuff, like fractions which I had forgotten. Associative laws will come into play when you do Linear Algebra later and learn Rings.

To find any of these books this link includes a custom ebook search engine https://nl.reddit.com/r/trackers/comments/hrgmv/tracker_with_pdfsebooks_of_college_textbooks/c1xrq44

My question is. When it's too late? I'm 25 years old, almost 26. Also I have to go to work (7-8) hours a day. I'm no lifer (not bitter about that) so this can(?) be an advantage. Do you think I can make it? My main interest are algorithms. I would skip that hard mathematical stuff like those differential things. I have some rusty knowledge of high school math (I can easily solve equations, quadratic theorem, I know about sets and operations with it, equality and ordering relations, basic vector calculus, also I can integrate and derivate… but not in 'proofs' way, I just have more practical, rote knowledge. Thanks for answer, anybody.

>>3276

its not too late m8 but you do need to understand how to do some basic logic and proof to understand certain algorithms involving trees and asympotic analysis, etc

I dont know you or how self-motivated you are so I cant say whether or not you can make it but start learning and programming in your off time and youll figure that out. It never hurts to try.

also muh dubs

What scheme implementation is better for SICM and Functional Differential Geometry?

Programming mathematics yet no type theory, nor cat theory?

>>3276

It's not too late, but you need to be willing to put the work in. What's there to lose?

Cross posting since this board better fits.

http://8ch.net/tech/res/181463.html#q398212

>>3330

>Is SICP wrong here? Isn't A(0,0) supposed to be 1 and not 0

How so?

(A 0 0) means that (= y 0) holds and thus the function returns 0. Or am I missing something?

>>3085

I majored in MIS and got a nice 70k after graduation. But it was only because of previous internship experience. Take some internships along with your courseware and you'll do fine. Save up form the paid internships and you will get both experience and money saved up to pay of your school loans.

>>3427

On what school did you go ?

If someone know where to torrent Linear Algebra by Friedberg, Insel and Spence ; it's nowhere and that shit expensive

>>3440

http://bookzz.org/md5/7a1b2f1d2f02d0d2263b2b9346b33eb9

>>3452

Thanks you so much but the quality is bad, where do you think I can have something better ? I have troubles reading

Does anyone know of a good introduction to vector algebra? I'm trying to learn the basics.

>>3453

Use this search engine

https://cse.google.com/cse/home?cx=00661023013169144559:a1-kkiboeco

>>3063

Try Algorithms Unlocked. It's by one of the authors of CLRS, but a bit easier.

I know OP prefers books but this was pretty good, you can download the videos if you want:

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/index.htm

>>3474

T H A N K S

H

A

N

K

S

>>3482

I just checked the book you said you had trouble reading. It's a djvu file, and it's actually better quality than most pdf scans. You need a djvu reader, try sumatrapdf on windows.

can anyone post fucking torrent or other links to download these books?

I must disagree strongly with giving Basic Mathematics by Lang as first book for those who start.

While it is a great book, it is not a book for beginners and/or those who are not gifted.

When I started it was useless since I didn't have a gift for math nor I had the proper preparation and ability to manage it.

A great book to start instead is Algebra & Trigonometry by Sullivan, since:

>you only need to be able to do the basic operations and know like what is a triangle and a square

>it has been made to teach normal, ungifted people

>it has a lot of exercises made to learn and practice with solutions in the back

>it has extensive and detailed coverage of almost all math needed for pre-calculus

>you can pirate it

After I did that book I was able to understand and learn something from Lang. Despite the name, it is not a book for beginners.

I noticed that many of this guides online on programming/math always advise people to get the "best book", where "best" is the "best" for people who already know/are gifted and not best as in best for normal people and beginners.

>>3582

What do you think of Stewart's 'Precalculus'? I recently started it and I intend on completing the whole book so I can patch up my shitty high school math knowledge

>>3602

I guess it is similar to Sullivan's Algebra & Trig (or Sullivan's Precalculus, which is pretty similar to A&T with just some differences in chapters).

I've done the whole Algebra & Trig, it worked for me: I didn't find any mistakes in the book's answer key (very important for self-study), that's why I advised that book.

I had to go online from time to time to understand some concepts better, but that's that.

Of course, there are probably other books that are just as valid.

The important thing I think is to have book that is made for normal people going to college, that covers almost all the arguments, and has a lot of exercises and grunt work.

>>3582

>I must disagree strongly with giving Basic Mathematics by Lang as first book for those who start.

This.

I hate to be the one to discourage but the presented study material is way, WAY beyond the mental capacities of any average person. You seriously need to be principally gifted in mathematics to be able to work through something like concrete math or the Spivak textbook.

>>3582

which version do you reccomend? I'm planning on buying a used copy soon

>>3572

ok FBI over TOR:

books.google.com

>>3572

Why are you here?

>>3637

I used the 9th edition.

Usually this kind of books don't have many differences between editions, but sometimes they skip putting the answers in the book between editions, so make sure the book you get has the answers to odd-numbered exercises.

>>3034

Thank you immensely for all this advice and the good books.

Just a question: you linked youtube classes along with the Discrete Math book but apparently while the book is from Michiel Smid's and based on his second-year

course COMP 2804 (Discrete Structures II), the Youchoob lectures are from his colleague John Howat COMP 1805 (Discrete Structures I).

Since I have no formal education on the subject I'll just start with the lectures and related material on Howat's website, but I assume you linked Michiel's book because it is his more adv topics that should be studied?

Khan Academy, up to Algebra II (1d-3m)

Stewart's Calculus, 1ch-2ch/d odd & 7/d review

How to Prove It

Spivak's Calculus

Calculus On Manifolds (3m-4m)

Strang's Linear Algebra and Its Applications

Apostol's Calculus, vols. 1-2

Foote's Abstract Algebra

Lay's Linear Algebra and Its Applications

Baby Rudin (2m-4m)

Papa Rudin (6m-1y)

[2y]

>>3732

Ignore this.

>been browsing /g/ weekly for years

>no /g/ on front page

>search for "tech"

>before hitting link, realize I don't actually want to see threads about hardware

>search "computer science", no results

>search programming

>/programming/

>right before clicking, notice total posts and pph counters

>/prog/ highest in all stats

>sticky on front page is a thread about the topic I've been most concerned with for the last few months: ACTUAL COMPUTER SCIENCE

Definitely going to keep coming back here

>do a search for perl

>3 hits

This board. You guys. I needed you

>Why would you want to learn math? Because it will change your thinking.

Literally what I've been thinking for the last half a year or longer

>>3034

>Serge Lang

>>3732

>Baby Rudin (2m-4m)

>Papa Rudin (6m-1y)

>>3733

>Ignore this.

why?

>>3810

I didn't mean to post that.

>>3582

I have the same problem as you, I don't even understand the first few pages with the proofs. I'm downloading Sullivan rn as you recommended.

I'll post results if you guys want.

>>3823

would love too, I'm college right now at year and half for getting my BS thus i feel pretty ignorant on maths and plus in my curricular agenda, i dont get any progamming subject and im applying for electronic and telecoms carrer, i do understand some of the basis when it comes to electronic,electrical and telecoms but i do really want to program, i have this goal in my head since highschool, i don't want to be hax0r or anything i just want to be able to code, understand it, and develope shit… so I'm going to start with this guide too and see where it leads at the end hope the treath is still alive, also i want to learn on i2p stuff since I have some basis on the network field, can someone just help me out on pointing the right direction on where should i just start on i2p

thanks in advanced.

English it ain't my native tongue so i hope i made myself clear, and thank you OP for the guide!

>>3921

Cryptocoin trading is still sort of profitable, even if mining isn't that efficient anymore. The 2013 bubble burst seriously proved the doubts of Bitcoin's critics.

I would advise browsing some forums and reading up on economics, if you're new to the field that is. Other than reselling clearance stuff/auctioning off your weebshit there aren't many other (legal) get-rich-quick schemes.