Recent content by cwatki14

I have the following question on metric spaces Let (X,d) be a metric space and x1,x2,...,xn ∈ X. Show that d(x1, xn) ≤ d(x1, x2) + · · · + d(xn−1, xn2 ), and d(x1, x3) ≥ |d(x1, x2) − d(x2, x3)|. So the first part is simply a statement of the triangle inequality. However, the metric...

I think the identity element does exist. The problem statement defines N as including 0 as an element. As far as including the negative numbers, obviously these are not included. I think the definitions just define the operations performed on N in different cases of even, odd properties of 2...

I am trying to answer the following question: Determine whether (N,*) is a group or not. N={0,1,2,3,...} and n*m= n+m if n,m even, -(n+m)-2 if n,m odd, and m-n-1 if n odd, m even. I know that the properties of a group are associativity, existence of an identity, and inversiblity. If I...

Currently, I am a bioengineering major, but I have been taking math electives the past year and a half, and now I am finding myself liking pure mathematics much more than engineering and only two classes away from a degree. The two courses I need are Real Analysis and Abstract Algebra...

As a ChemE, well actually a ChemBe (Chemical and Biomolecular), I can say ChemE has little to do with chemistry. If you can convert between mass and moles, then you're set.

Currently, I am a bioengineering major, but I have been taking math electives the past year and a half, and now I am finding myself liking pure mathematics much more than engineering and only two classes away from a degree. The two courses I need are Real Analysis and Abstract Algebra...

Sounds like a huge kick in the butt. At my university, algebra is the most difficult course for math majors. I have heard from other students that the homework alone takes 20-30 hours a week, and very few people get above a C since it isn't curved. I also know that at my university you can't...

I am doubtful that a Diff Eq course will be that heavy in Fourier anyways. We touched a bit on it in my linear algebra course, but it was bare minimal. Maybe after taking analysis, Fourier would be more sequence heavy. When I went into college environment (my senior year of high school) , I...

I used a book called "Problems In Algebraic Number Theory", which is a graduate text. It has a lot of problems, and the second half of the book has all the solutions. Also, if you are not familiar with number theory it has a crash course in elementary number theory at the beginning.

The only two required courses for the major are Advanced Algebra I and Analysis I. Beyond that it is just about filling distribution requirements. So I need to take 1 more course in analysis (beyond Analysis 1), and I have already fulfilled my other upper level Algebra requirement. Ideally...

I claimed that study habits are a completely personal choice! Not everyone needs to study the same. I have no idea what the undergraduate environment is like in China or India, but sometimes I wonder why so many international students come to my university if it is not for the stellar...

Biochemistry and thermodynamics for biomolecular engineers are two very brutal courses for my major, which both require a lot of time for studying. It's really a matter of how much time do I have. Last semester, I took 12 credits of chemistry and chemical engineering courses and eight credits...

Stewart's book usually has an odd question that is very similar to the even one before/after it. So see how that odd one is solved, and apply similar methods to your even one. Stewart's book is not proof heavy, no idea what you're talking about there. Also if you haven't been reading the text...

I personally chose to double major in Chemical and Bioengineering and pure Mathematics. The fact you have doubts on your intellect is a good sign. I have met so many kids at my university (I suppose is considered top tier) who thought they were math and science kids until they got to the...

It's worth it when you realize that graduate school is in jeopardy. For that I'll pay with my sanity, whatever that's worth anymore.