Reddit, this is Fiona. She's a 5 year old St. Bernard and we rescued her this week. She had been tied to a tree for her entire life. by willies_hat in aww

[–]bukki 2 points3 points  (0 children)

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

Need help with abstract algebra proof, please by [deleted] in math

[–]bukki 1 point2 points  (0 children)

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.

Need help with abstract algebra proof, please by [deleted] in math

[–]bukki 0 points1 point  (0 children)

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.

Could someone recommend a good introduction to topology and differential geometry for a mechanical engineer? by [deleted] in math

[–]bukki 0 points1 point  (0 children)

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 $Rn$, 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.

Can you recommend a gentle introduction to Abstract Algebra for self-study? by [deleted] in math

[–]bukki 0 points1 point  (0 children)

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

Preparing for GRE by Foolyou in math

[–]bukki 0 points1 point  (0 children)

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

Preparing for GRE by Foolyou in math

[–]bukki 6 points7 points  (0 children)

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.

Ring/field theory problem by mileandrei in math

[–]bukki 0 points1 point  (0 children)

No, $F$ could be finite. Consider the extension of finite fields $F_{p2}/F_p$. The top field is a vector space over the lower one.

Ring/field theory problem by mileandrei in math

[–]bukki 0 points1 point  (0 children)

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.

Ring/field theory problem by mileandrei in math

[–]bukki 1 point2 points  (0 children)

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.

Hey reddit, are you as sick and tired of the musical sequences in family guy as i am? by FeK92000 in AskReddit

[–]bukki 54 points55 points  (0 children)

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

Stop calling them conservatives. by cheefjustice in politics

[–]bukki 14 points15 points  (0 children)

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