> TWO PROBLEMS in 1 day

One of the dirty little secrets of studying CS and math is that truly understanding 2 problems of the kind you've never seen before in 1 day is OK and expected. Hell, sometimes mere understanding of one single solution to a problem can take a week or longer. Most anyone who does better has either studied the (adjacent) material before or just trudging along half-understanding this bit and that piece hoping that sometime in the future it might all come together. And that's exactly what happens after you stick with it for awhile (often several years). Your job is to understand the thought process and philosophy of math. It's usually called "math maturity". Math/CS people reuse the same tips and tricks over and over again under many different guises and after a while you'll start seeing this repetition and even start using them yourself. It's very similar to how you learned your own native tongue. Luckily, math folk have methods to rein in this madness.

Check out [0]. It's free and teaches you some basics of structured thought. Then check out [1], [2], [3] to expand on what you've learned.

One really good unpretentious algo book that shows you how to do problems is [4].

[0] BOOK OF PROOF by Richard Hammach

https://www.people.vcu.edu/~rhammack/BookOfProof/

[1] Discrete Mathematics with Applications by Susanna Epp

https://www.amazon.com/Discrete-Mathematics-Applications-Sus...

[2] Pure Mathematics for Beginners by Steve Warner

https://www.amazon.com/Pure-Mathematics-Beginners-Rigorous-I...

[3] Mathematical Proofs by Gary Chartrand et al

https://www.amazon.com/Mathematical-Proofs-Transition-Advanc...

[4] Data Structures and Algorithms: Concepts, Techniques and Applications by G.A.V. Pai

https://www.amazon.com/gp/product/0070699577/ref=ppx_yo_dt_b...

Good Luck and don't f*ck it up!

My answer to your question is math. Learn to read and write proofs. Any intro to proofs will do: those employed in discrete math, the ones in analysis, the diagram chasing ones, whatever...Working with math proofs will definitely straighten out your thinking and whip your mind into shape.

Some suggestions to get you started:

Book of Proof by Richard Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/

Discrete Math by Susanna Epp: https://www.amazon.com/Discrete-Mathematics-Applications-Sus...

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al: https://www.amazon.com/Mathematical-Proofs-Transition-Advanc...

How to Think About Analysis by Lara Alcock: https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0...

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers: https://www.amazon.com/Learning-Reason-Introduction-Logic-Re...

Mathematics: A Discrete Introduction by Edward Scheinerman: https://www.amazon.com/Mathematics-Discrete-Introduction-Edw...

The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Rafi Grinberg: https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr...

Linear Algebra: Step by Step by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...

Abstract Algebra: A Student-Friendly Approach by the Dos Reis: https://www.amazon.com/Abstract-Algebra-Student-Friendly-Lau...

That's probably plenty for a start.

This fall I will be teaching the required "Discrete Math for CS course" to about fifty students at the University of South Carolina. Previously I used Epp's book [1] which in my opinion is an outstanding book but regrettably is $280.44. Many of our students are working minimum wage jobs to make ends meet, and I don't want to make them pay so much if I can at all help it.

Lucky I saw this!!

I do have one reservation though -- many of our students come in with a weaker mathematical background than MIT students; for example we spent several weeks doing proofs by induction (and no other kinds of proofs) and this text doesn't seem to feature a couple of weeks worth of examples.

I think I'll probably go with this and supplement as needed. Really it looks quite wonderful. (And hell, the book seems to be open source which would mean that I could potentially write supplmentary material directly into the book and make my version available publicly as well.)

This thread seems like a particularly good place to solicit advice: experiences with this book or others, what you wished you'd learned in your own undergraduate course on this subject, etc. I've taught this course once before -- I feel I did quite well but I still have room to improve. Thanks!

[1] https://www.amazon.com/Discrete-Mathematics-Applications-Sus...

I recommend learning discrete mathematics, then data structures and algorithms.

I cannot stress enough how important mathematical foundations is. It'll make everything else much easier to learn. I haven't read the book but heard good things about: https://www.amazon.com/Discrete-Mathematics-Applications-Sus... as a beginner text.

Coursera has multiple offerings on Data Structures / Algorithms -- find one that works best for you.

For instance:

https://www.coursera.org/learn/introduction-to-algorithms

https://www.coursera.org/specializations/algorithms

https://www.coursera.org/learn/algorithmic-thinking-1

https://www.coursera.org/learn/algorithmic-toolbox

By doing all of those you'll get a good introductory exposure to the topics.

You should also look at a rigorous course offering of Algorithms. MIT has a few online to view.

Some readings for a beginner are:

https://www.khanacademy.org/computing/computer-science/algor...

https://www.amazon.com/Algorithms-Unlocked-Press-Thomas-Corm...

https://www.amazon.com/Introduction-Algorithms-3rd-MIT-Press... (not beginner level but classic)

After all of this you should be fine with diving into interview books. You'll want to whiteboard solutions and be able to do all the difficult problems. Look into sites like leetcode, glassdoor and be able to do the difficult problems posted there.

These books will kick your teeth in if you're not prepared. You either get a teacher who'll hold your hand or you need to gear up for fight(develop math maturity and learn all the tricks and tips). To the latter end, you can check out the Book of Proof by Richard Hammack[0] and Discrete Math by Susanna Epp[1].

[0] http://www.people.vcu.edu/~rhammack/BookOfProof/

[1] https://www.amazon.com/Discrete-Mathematics-Applications-Sus...

To start from absolute zero, check out Suzanna Epp's Discrete Math[0]. I believe even a motivated high school student could get started with it and even finish it. If your proof-writing is shaky, the book provides a very good workout. From there it will be easy to choose the areas of discrete math to specialize.

[0] http://www.amazon.com/gp/product/0495391328?keywords=susanna...

Would somebody please disrupt the textbook publishing industry?

http://www.amazon.com/Discrete-Mathematics-Applications-Susa...

$264.39, for students that work part time jobs at $7.00 an hour (before taxes).

Not only students are angry about this. Professors are angry, and authors are angry too. Bitter fights between professors and publishers are common.

Everybody wants to see the big players in this industry fail. Please, someone, make it happen.