λ - programming

I plan to but I am currently in school and work part time so no time.

Ironically, I have to wait till I graduate to educate myself!

I don't plan on following it strictly. Just want a good foundation on:

- Logic
- Discrete math
- Graph theory

At least for now.

I also have a few other books in mind, and a MIT course[1].

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

No. But I studied mathematics so here's my take:

I wouldn't have a clue where to start if I was at high school level (or below) so no comment there. Can't say much about stats either cause I came at probability from the top down (from measure theory).

A lot of the modern "how to prove shit" books are also good intros to discrete maths in general. Sets, basic number theory, graphs, orders, etc.

Spivak's Calculus is a good book but if you are finding that tough then take your pick of the five billion 1st year college calc texts. These aren't the worst place to start.

Similarly with Linear Algebra there are a lot of entry level college texts that will hopefully teach you by making you grind through problems or you could look at Strangs' "Linear Algebra And It's Applications" where the author tries to give you a sense of how it all works at the expense of actual problems to use it on, or Axlers' "Linear Algebra Done Right" which is all theory.

Calc and Linear Algebra have their own uses but the point of them really is to give you a foothold for when you come to abstract mathematics.

CLRS and Concrete Mathematics are probably where I would end my list. If you can make it comfortably through those then you have a good base to build from wherever your CS interests take you.

Logic is surprisingly absent from that list though you will see some in basic discrete math texts, otherwise there are many "Mathematical Logic", "Metamathematics", etc books that cover the same material. I learnt from Alonzo Churchs' book, don't make the same mistake I did.

Some basic point-set topology can be helpful also. If you survived Spivak and with a bit more set theory you should be able to tackle one of the many elementary point-set topology texts out there.

Not sure about the 8chan authors thing for DG either (avoid Calculus on Manifolds altogther unless interested), I guess I could recommend Kocks' "Synthetic Differential Geometry" though you need a lot of background before even thinking about understanding that.

Wish I could have some made better book recommendations.

>differential geometry using scheme
BASED

>>11717
>I plan to but I am currently in school and work part time so no time.

>Ironically, I have to wait till I graduate to educate myself!

this. If I could just spend all my time learning programming and math I would do so but physics, english, work on weekends, etc, etc

I really want to get deeper into graph theory and combinatorics but dont have the time currently.

I find OP's choice of books rather peculiar. As >>11722 noted, he has a strange and not entirely useful affection for Spivak.

CLRS, Concrete Mathematics and most of the other books are great, but I'm missing at least three other important fields necessary for CS that are not covered by those:
* logic,
* computability/complexity theory, and
* graph theory.

>>11762
What would be the important fields to look at when making a mathematical base for CS?

>>11768
Just look at the syllabus of an undergrad CS programme on a well-known uni. What you get should be pretty close to optimal.

>>11775
I was hoping to get a quick and dirty list of all to be covered fields in mathematics important for CS from a pro's point of view, I guess I could assemble a learning list (and I will) but I'm interested in your POW.

>>11781
>your POW
My prisoners of war? How dare you.

OK, I'm not a pro, but here's a very quick and somewhat dirty list of what I have in mind:
>the very basics
language, intuitive geometry, arithmetics, proofs, etc.
>logic
mathematical and computational logic, classical vs. intuitionistic, linear and modal logics, etc.,
>set theory
cardinals, ordinals, AC, axiomatic theories - ZF
>linear algebra
perhaps up to projective spaces
>abstract algebra
rings, lattices, maybe even universal algebra
>analysis
basic multivariable calculus, numerical methods
>number theory
modular arithmetic, primes, primality testing, combinatorics, recurrences, etc.
>statistics and probability
>computability and complexity
>graphs

Some that I wouldn't probably classify as necessary, but might be cool to have:
>topology
some basics are probably covered in analysis, but the more advanced results might not be terribly exciting and are rather removed from the rest of the curriculum at this level
>category theory
same thing, although it leads to some surprising and beautiful relations with logic, computation, sets and algebra

On the other hand, generally, I wouldn't bother with differential geometry, advanced vector analysis, multilinear algebra and many other things. If is data processing is your thing, sure, these might help you; if you're into formal methods, you might instead focus on logic, proof theory, categories; etc. You get the idea.

[a bit off-topic]
The best thing I find are the sporadic connections between various fields, which are especially underlined in the more abstract territories and which are unfortunately not found in vast majority of textbooks. That's one of the reasons I prefer schools to self-studying.

Another thing is that the lecturer might occasionally hint at some advanced topics or recent developments that are not covered in textbooks, and maybe entice the student to dig deeper into that and perhaps even achieve some interesting research results consequently. Textbooks get dated and usually only cover sharply delimited areas of interest, while the lecturer can afford to be a bit fuzzy at times.

Of course, this all depends critically on the lecturer's qualities. If the lecturer is shite, you'd better wander off to the library and spend your precious time there.
[/a bit off-topic]

>>11782
thank u very much, friend

>>11782
In your 'the very basics' section, what do you mean by language? Programming languages?

>>11782
for the unwitting:

completing a course in every subject mentioned in this post is pretty much equivalent to a BA in math.

>>11799
I don't think that's true. In the breadth of topics covered, perhaps, but I'd wager mathematicians go into greater detail and are required to know and conastruct more difficult proofs. I'm pretty sure a mathematician would g deeper in analysis, and algebra (at least) and would cover measure theory, complex analysis, global analysis, differential geometry, and would be required to take a topology course. While a computer scientist would focus on the discrete parts and logic.

>>11796
English

>>11799
definitely not enough for a degree, but a bit much for someone looking to pick up mathematics for the purposes of understanding CS texts/papers.

>>11801
Lain who wrote it here. I may have misunderstood the original objective. If you want to revise and learn math solely for the purpose of reading papers and implementing ides contained therein, then yes, I agree it's a bit too much.

Ugh. I know I should study math, but I just don't want to spend the time I could be programming on it.
Still, I better get to it, specially since I need to for school.

>>11804
Why don't you program along as you learn? You can write programs for most of the concepts you meet in mathematics and it'll help you understand them better.