Its possible that the honors class you are taking can add some units for financial aid consideration. I have done exactly what you are doing and took some classes at a quarter type university as well as some at a semester type community college. I had 10 semester units at the CC and 4 quarter...
I'm not sure if this will work for you, but it does for me. When I read a fact or theorem, I think "How would I explain this to Tony?" I think about how that conversation would go and explain to him in my own words this new concept. Then I imagine him asking a question about it, I would then...
I am almost finished with the Hubbard book and I am also almost done with baby rudin. They both touch the same topics, but Hubbard has pictures and examples whereas Rudin is really dense. For example, Hubbard has a whole chapter on linear algebra while Rudin just has a couple pages. They both go...
Proving something with an algorithm doesn't just prove that a solution exists(which is a common way to prove something), but also gives you a way to compute the answer as well. For example, the proof that ax^2 +bx +c = 0 has zero, one or two solutions is proved using an algorithm which gives you...
Practically everything is proven in that book although that hardest proofs are in the appendix. So you could choose to treat this as a real analysis book, which is a step up from Spivak, if you choose to go over the proofs in the appendix, or not, and if you skip a few sections here and there...
Since your teacher specializes in real analysis, you could learn more about fractals. I, myself, am going to do a reading course on fractals at some point, as well as non-euclidean geometry since they are not offered at my school and they have interested me before I even knew what a derivative was.
That's a good idea. There are two versions of real analysis and abstract algebra. One for applied and theoretical where the theoretical is harder. I am auditing the applied so I can ace the theoretical later.
Also, you can audit at anytime you want, even start in the middle of a semester. I did...
At my college auditing is free. However, you obviously don't get a grade and you don't turn in homework or tests since they won't get graded. You just go there to sit for lectures. Finding information on auditing was very hard for me; there was only a vague paragraph about auditing in my 600+...
If you can, you should audit at least one or two classes per semester. That way you can learn a lot more without it being too much of a time sink. You can do the homework of those classes when you have time or just ignore those classes when you need to prepare for tests in your real classes.
You should definitely take it again. If you can you might want to just audit the class, but if you can't you should take it anyways since you need to know things like span, linear independence, eigenvectors, eigenvalues, inner products, subspaces, projections, and SVD's. Many of these topics are...
Usually honors courses are done in the first two years of a four year education. That being said, I have heard that getting good grades on your last two years is more important than if you did bad on the fist two, since it shows you have improved. Knowing this, doing a few honors courses in the...
I've been to two different colleges and I have done an honors course in both. They are very different from each other. My first one was kinda of unofficial where we mostly had to do an extra paper/presentation and harder tests. On average you had to work about a third harder than normal to get...
I am reading the proof of the Inverse Function Theorem in baby Rudin and I have a question about it. How does associating a function phi(x) (equation 48) with each point y tell us anything about if f(x) is one-to-one? I'll show the proof below. Also, if f'(a) = A, and f(x)=x2, what would A-1 be?
The Answer to the Riddle:
First thing you do is start both hourglasses.
After the 4 minute one runs out of sand, immediately turn it over to start it again.
After the 7 minute one runs out of sand, place the 4 minute one on its side to halt its progress. The 4 minute one should have one...
One thing you can do with the book you have now (probably) is to look at a theorem that the book proves and try to prove it yourself before looking at the proof. If you are stuck you can look at the first line of the proof, then look at each successive line when you are still stuck. Since the...
I do not know if your school supports this, but you could audit the lower class while taking the upper class. That way you do not need to do all the work of the lower class if you do not have enough time.
I will be attempting to get a PhD in statistics eventually though I have yet to get my BS, however, in the mean time I have a few electives I need to fill and I want them to help me in my self study of relativity and quantum mechanics. I will not be surpassing a Master's knowledge of these areas...
I am getting my B.S. in statistics in a few years and will then try for a PhD, and I happen to have 1-4 spots where I can take additional courses. I am taking all my stat courses as well as a year of real analysis and a year of abstract algebra and want to take these other courses, but I may...
This might be a bit too abstract, but if you consider L as a mapping between two spaces, then you can consider its derivative. In this case the derivative of L^2 in the direction of u is Lu + uL.
[D F(L)]u = Lu + uL
where
F(L) = L^2
and [DF(L)] is the "same" as the Jacobian Matrix...
I am studying the multi variable Inverse Function Theorem and the Implicit Function Theorem. I think my brain is rebelling against understanding them and I would appreciate if someone here could explain the two theorems semi rigorously as well as explain when they are used, and why they are...
For E&M A Student's Guide to Maxwell's Equations https://www.amazon.com/dp/0521701473/?tag=pfamazon01-20 has both the integral and differential forms of the 4 Maxwell equations as well as explains why there is a dot product used in certain formulas as well as other del operators. It is at a...
Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard has the same material as Spivak yet and starts earlier with linear algebra, set theory, logic, and ends with the Generalized Stokes Theorem. It is also about 5 times longer, is alot slower in creating the foundations...
For me Calc II boosted my mathematical maturity more than Calc I and Calc III combined and its all because of the substitutions. I went through every u, trig, and generalized substitution problem in the book and it significantly increased my ability to move from algebraic expression to algebraic...
The schools I have looked at around me in San Diego have defined "2 years" as 2 years of high school which translates to only one semester at a community college.
I had an idea and maybe you can tell me if I am right. Since sin and cos are between -1 and 1, and the denominators values of sin and cos is always greater than or equal to 0 then if a + b > max{2c,2d}, then the limit goes to 0, if not then the limit doesn't exist. Am I on the right track?
Well, if a=b=c=d=1, I get a neat little tidbit saying that the limit as r goes to zero is sin(theta)cos(theta) for what ever theta you travel through to get to 0. Though this confirms my assumption that the limit doesn't exist for when a=b=c=d=1, it doesn't tell me anything about for when...
This question came up in a book I am using for self study. I was going to just skip the question but then I remembered I can ask for help here.
Homework Statement
Let a,b,c,d be nonnegative integers. For what values of a,b,c,d does
\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} \frac{x^a...