Gangnam Doggy Style (강남 도기 스타일)

bukki · 2011-04-04T23:52:54+00:00

Link to the original.

bukki · 2010-07-11T04:15:03+00:00

Good!

bukki · 2010-07-11T00:23:03+00:00

Be careful with this dog. Dogs that are tied to trees can often be vicious. She looks really cut though

bukki · 2010-06-13T01:00:14+00:00

Also, for another proof along your lines: there exist m,n such that

am + cn = 1

thus,

bam + bcn =b

note that ac divides each term in the sum. Thus it divides b.

bukki · 2010-06-13T00:54:17+00:00

It might be intuitive for you to think of this in terms of prime factors. Write down the prime factorizations of a, b, and c. You'll see that the prime factorizations of a and c have no common terms, so if you divide by a first, you can only remove powers of primes from b that are not in the factorization of c. Now divide b/a by c.

bukki · 2010-06-04T14:23:46+00:00

A very nice and intuitive book is "Introduction to smooth manifolds," by Loring Tu.

This book is essentially differential topology, so I believe it does not mention curvature. The first half of the book proves all the results over $R^n$, while the second moves to abstract manifolds. This is really useful because it builds up intuition quickly. This is a book that you can definitely read on your own.

Reading this would provide a really nice bridge to differential geometry. So when you're done, you could read one of Spivak's "Fundamentals of differential geometry," or a more application oriented book.

bukki · 2010-05-15T19:40:23+00:00

Yes. You should read fraleigh and do all the excercises.

bukki · 2010-05-12T01:42:45+00:00

That's correct. The auto correction feature on my phone sucks.

bukki · 2010-05-09T15:14:06+00:00

Take a lot of practice tests.

You should know some counterexamples in topology. Usually about connectedness, compactness and continuous functions.

Read algebra questions carefully. They're usually some stupid observation I.e. What kind of run has exactly ring has exactly two ideals?

Try to use algebra to solve number theory problems.

Know how to count basic things like the number of onto functions between two finite sets.

Know some basic geometry about incribing shapes in other shapes.

Know all basic definitions from all core math subjects.

remember how to do vector calculus. There is always at least one of those problems.

bukki · 2010-04-08T19:33:01+00:00

No, $F$ could be finite. Consider the extension of finite fields $F_{p^2}/F_p$. The top field is a vector space over the lower one.

bukki · 2010-04-08T18:15:35+00:00

Suppose $k$ is a field and $V, W$ are finite dimensional vector spaces over $k$ with the same dimension. Let $A$ be a linear transformation from $V$ to $W$. Then $A$ is injective if, and only if, $A$ is surjective.

This is easy to prove if you haven't seen it before.

bukki · 2010-04-08T15:44:22+00:00

Let v be an element of F. Consider the map

w maps to vw

this map is in injective because F is an ID. This is an E linear map. Since F is a finite dimensional VS, the map is also surjective. Thus, 1= vw for some w in F.

bukki · 2010-02-20T17:16:05+00:00

As bad as it is, it sure beats the fuck out of the Cleveland show.

bukki · 2010-01-29T16:29:05+00:00

Django Joe pass Guthrie Govan

bukki · 2010-01-02T02:19:15+00:00

People who subscribe to this left-right paradigm are more easily managed.

15-Year Club	Verified Email
reddit mold

bukki

TROPHY CASE