(Part 2) Top products from r/cheatatmathhomework

my pleasure. i too am a grad student in applied math and all we do is diffeq. my first year we had a whole sequence on greens functions and i really really loved it. Its funny how quickly it becomes impossible to find resources for these kinds of problems. I highly recommend this and this. I also think that latex is the best thing since sliced bread. are you in a regular math program or applied?

For proofs in general, I like D'Angelo and West's Mathematical Thinking. http://www.amazon.com/Mathematical-Thinking-Problem-Solving-Proofs-Edition/dp/0130144126

For discrete math, especially combinatorics, I loved Miklos Bona's A Walk Through Combinatorics. http://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9814335231/

For induction proofs, you check your base case, assume the induction hypothesis (true for k), and then check k+1.

You should be able to manipulate the k+1 term into something involving the k term, and that will then lead to the k+1 conclusion.

Example For all n >= 4, 2^(n) < n!

Base case: n = 4. 2^(4) = 16 < 24 = 4!

IH: Assume true for some k >= 4.

Then 2^(k+1) = 2*2^(k)

2*2^(k) < 2*k! (Induction Hypothesis used here)

2*k! < (k+1)k! (k > 3, so k+1 > 2)

(k+1)k! = (k+1)! (definition of factorial)

The first one is a logic question. Specifically propositional logic, though if you are interested in logic you could also study basic predicate logic.

The second one could fall into a few overlapping categories, but I might put it into abstract algebra. I found a very good book that I used to self-prepare for a graduate course was this one by Dan Saracino. You may need to go one level more basic depending on your background, in which case i've been told this book is good.

Yeah, all these questions specifically say to use Cramer's rule. This is from Pre-Calc book by Dugapolski (Amazon LINK) (I think pretty common in US colleges). Probably the worst Math book Ive ever used. Doesnt explain things well, most of the time by just doing examples and not really listing steps of how to do things. You are supposed to look at the steps and figure out how they got there.

The worst offense is that it always uses super easy problems as examples. In this case for example... they use super easy linear equations to show Cramer's rule... not once they show how to handle x^2 or y^2. Yet in homework problems as you can see they ask you to solve them.

Youtube basically taught me everything so far. Class started with 30 people, we're down to 12 now (people dropping the class). There are 2 A's 2B's 4 C's and rest are F's ... because of this stupid book. (I am one of the A's)

http://www.amazon.com/Introduction-Mathematical-Statistics-Applications-Edition/dp/0321693949

I found this book below. Do you think it'd be an overkill to study it?

Linear Geometry by Gutenberg&Weir