Mathematics for Computer Science

> I couldn't answer them most of the time, so I'd need an answer key nearby to get unstuck.

This happens with a lot of books out there. It would have been great if the authors of MCS gave solutions for at least some select questions.

[Demo] There is also collection of Gilbert Strang lectures here: http://classmill.com/jennathompson/introduction-to-algebra - You'd have to login to watch the whole series, but lets you mark lectures as "done", ask questions, and track progress etc..

Thanks for the resource. I never really paid attention when I took linear algebra, and I've always regretted it since it seems to rear it's head everywhere.

Looking over the second part of the MIT course, I see that a lot of the same material is covered in this free textbook.

http://cglab.ca/~michiel/DiscreteStructures/

Are there companion solutions for the problem sets available anywhere?

That's not just "reading material" ... it's a frigging 1000-page book! :-D

Thanks for that link! It looks like it was just updated today.

Indicator RVs are introduced on p738 & used all over the book. But on p788, he proves Markov without mentioning indicators. Typically, you create an indicator for the (R>=x) event, compute its expected value & voila Markov! Somewhat atypical.

Learning those topics will not be a waste of time. You'll see them come up time and time again on your path towards more CS topics.

I did something similar last year with Statistics and Probability. The best place I've found for a linear course for online math is https://www.khanacademy.org/

I was able to start at the beginning and get all the necessary math to actually step forward to some of the more complex courses. I'd suggest starting there.

I'm working through that as well, it's excellent.

This may also help you if you're going the autodidactic route:

http://hbpms.blogspot.com/

Hi there and congrats on working through this course. Most students coming into this class are learning all the formalized truth table/mappings/isomorphism/etc stuff for the first time. I took this class after having failed a course in Real Analysis and ended up appreciating it not so much as a math class but as a good intro to how to think about Theoretical Computer Science.

Looking back at the psets, i think it's actually worth looking at them in reverse order just to not get too discouraged: the class ends on some number theory and begins with the Relation/Axiom/Set/Sequence stuff you see in early high level math classes. Some of that number theory/counting stuff is incredibly accessible from the outset, so the class doesn't just get monotonically more obtuse.

That said, if you've worked through vellman and you finish up this class, you're more than ready to do a class in proper number theory, discrete math or even real or complex analysis. Somebody else said that this course was a prereq for clrs, it is sort of, but you could take them both concurrently if you had to, as clrs doesn't have such a strong focus on proofs (if you're interested, 6.045j is a good followup in automata/computability/etc, lots of regexes, state machines and turing machines)

anyhow, i just want to say that it's ok if you don't get it all at once. i think i ended up seeing lots of these ideas two or three times in a variety of classes. probably the first time i was just mechanically spitting out proofs without understanding them. by the third time i came across them, they actually clicked for me. But there was value (for me at least) to exposure early on because you do know the things that are hazy and it's easier to dive deeper on those the next time you encounter them.

have fun!

"Concrete Mathematics" by Knuth is by far the best presented book on maths relevant to CS that I've seen. You could definitely work through it with your background (I did with a similar background), it's challenging but approachable.

I am self-teaching myself mathematics for a few years now and will suggest the following: Algebra and Trig, a subset of which is known as pre-calc. Don't short yourself on this because it is basic and you don't want to be struggling with it at the same you are struggling with the higher level stuff. I cannot recommend Sheldon Axler's Algebra and Trigonmetry highly enough. After much searching I found that and have been through it 3 times.

Next Calculus: I recommend Gilbert Strang's text book which will take you through what in uni is called Caculus 3, 1 being intro, 2 being differential and 3 being integral. I in the midst of this book and so can't speak to further but my plan is to move onto Strang's linear Algebra. After that, where to go depends on particular interest but leaving any of that out, in my opinion, will just handicap your further studies. Moder education does a lot of things wrong but the standard math sequence in use everywhere isn't one of them imo.

In addition to what others are saying I can't stress enough how important combinatorics are as well. Definitely spend some time trying to understand this area. From there move on to stochastic processes.

Epp's Discrete Mathematics with Applications is a nice book that covers much of the same material as this MIT class, but at a slower, easier pace. It's highly suitable to the beginner.

You should know high school algebra and precalculus to be able to read the book. Trigonometry and calculus are not prerequisites, although you will probably want to learn those too.

I haven't looked at the MIT course in detail, but doesn't it seem like Concepts would be more similar to this than 251?

Catalan numbers show up all over the place and are a really useful sequence. My combinatorics course in undergrad had a "Catalan Problem of the Week" where you would have to show that the Catalan sequence solves a particular problem.

One of my favorite math books ever, but definitely not for the faint of heart. It's starts off slow but gets hard fast.

Is thinking obsolete too?