yakeyglee
Name:
Trevor Kafka
School:
Brandeis University
About:
2010 High School graduate who ventured off the year after to pursue aerial circus arts and floor acrobatics. Will be attending Brandeis University in the spring. I have always loved physics and mathematics with a burning passion and frequently pursue it in my spare time. Web: www.trevorkafka.com (website), www.facebook.com/trevor.kafka (FB profile), www.facebook.com/circus.trev (FB page).
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Questions Asked
yakeyglee:
Consider the convergent infinite series \(\displaystyle S = \sum_{i=0}^\infty a_i\).
If we restrict \(a_0, a_1 a_2, \ldots \in \mathbb R\),…
updated 11 months ago
2 replies
No Medals Yet
Mathematics
yakeyglee:
How would one show that the polynomial \(x^4 + x^3 + x^2 + x + 1\) is irreducible in \(\mathbb Q[x]\)?
updated one year ago
No Medals Yet
Mathematics
yakeyglee:
For an infinitely differentiable function \(f : \mathbb R \rightarrow \mathbb R\) and arbitrary choice of \(a \in \mathbb R\), is the follow…
updated one year ago
4 replies
No Medals Yet
Mathematics
yakeyglee:
Let \(a, b\) be elements of a NON-abelian group of orders \(m, n\) respectively. What can you
say about the order of their product \(ab\)?…
updated one year ago
2 replies
No Medals Yet
Mathematics
yakeyglee:
How do we know that any normal subgroup of a group \(G\) can be expressed as the disjoint union of certain conjugacy classes of \(G\)? (I t…
updated one year ago
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Mathematics
yakeyglee:
Here is a question from my Homework (Intro to College Algebra):
"Show that \(\left( \mathbb Z_{2^n} \right)^*\) is not cyclic for any \(n…
updated one year ago
6 replies
No Medals Yet
Mathematics
yakeyglee:
Show that if \(C=\{(x,y) : (x-a)^2+y^2=b^2\}\) for some \(b<a\) (in other words, \(C\) is the circle in the plane centered at \((a,0)\) of r…
updated one year ago
1 reply
No Medals Yet
Mathematics
yakeyglee:
In a spherical electromagnetic wave, what is the configuration of the electric and magnetic fields? I was thinking perhaps the electric fie…
updated one year ago
4 replies
1 Medal
Mathematics
yakeyglee:
What's a simple example of a bijection of \(\mathbb R \rightarrow \mathbb R^2\)? How about for \(\mathbb R \rightarrow \mathbb R^n\)?
updated one year ago
2 replies
No Medals Yet
Mathematics
yakeyglee:
What is the value of this integral? \[\int\limits_{\mathbb Q \cap [0,1]} dx\]Here, \(\mathbb Q \cap [0,1]\) is the set of rational numbers b…
updated one year ago
9 replies
1 Medal
Mathematics
yakeyglee:
What's a simple example of a bijection of \(\mathbb R \rightarrow \mathbb R^2\)? How about for \(\mathbb R \rightarrow \mathbb R^n\)?
updated one year ago
2 replies
No Medals Yet
Mathematics
yakeyglee:
How about a search feature so we can look back on old questions?
updated one year ago
9 replies
2 Medals
Mathematics
yakeyglee:
I read somewhere online that the formula for time dilatation for a static object at a distance \(R\) away from the center of a planet of mas…
updated one year ago
17 replies
1 Medal
Mathematics
yakeyglee:
What's a simple proof of the parallel-axis theorem?
updated one year ago
2 replies
1 Medal
Mathematics
yakeyglee:
If electromagnetic (light) waves from the sun are (essentially) randomly polarized, then why doesn't their superposition average out and can…
updated one year ago
8 replies
2 Medals
Mathematics
yakeyglee:
What is the difference between a matrix and a tensor?
updated one year ago
12 replies
1 Medal
Mathematics
yakeyglee:
In special relativity, to derive the four-velocity from the four-position, one generally needs to do something of this manner:\[\vec V = \fr…
updated one year ago
7 replies
1 Medal
Mathematics
yakeyglee:
Since the magnetic field is simply an interpretation of the effects of length contraction on charges and the electric field (see en.wikipedi…
updated one year ago
25 replies
2 Medals
Mathematics
yakeyglee:
How can one prove that electromagnetism is conservative? (Can this be done directly from Maxwell's equations?)
updated one year ago
17 replies
2 Medals
Mathematics
yakeyglee:
Why is center of mass defined in the way that it is?\[x_{\text{cm}}=\frac{\sum_i m_i x_i}{\sum_i m_i}\]How would we have known, for instance…
updated one year ago
3 replies
No Medals Yet
Mathematics
yakeyglee:
Could someone give me an example of the notions of phase velocity and group velocity?
updated one year ago
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Mathematics
yakeyglee:
How does one derive the Lorentz force from Maxwell's equations?
updated one year ago
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Mathematics
yakeyglee:
What is a (relatively) simple proof that a complex number of modulus greater than two is not an element of the Mandelbrot set \(\mathcal M\)…
updated one year ago
3 replies
1 Medal
Mathematics
yakeyglee:
I have a question regarding electromagnetic waves hitting a conducting surface. It's too long to post here, so check the first comment. If…
updated one year ago
2 replies
3 Medals
Mathematics
yakeyglee:
Does this site tend to run slow for anyone else? I use the latest version of Google Chrome, and while all of its high-tech web features are…
updated one year ago
16 replies
2 Medals
Mathematics
yakeyglee:
Why does the wave equation involve second partial derivatives? If it were \[\frac{\partial f}{\partial x} = \frac{1}{v}\frac{\partial f}{\p…
updated one year ago
9 replies
No Medals Yet
Mathematics
yakeyglee:
What is the magnetic field \(\vec B\) about a point charge \(Q\) at the origin travelling at velocity \(\vec v\)?
updated one year ago
17 replies
1 Medal
Mathematics
yakeyglee:
I know that if you have two probabilities \(P_A\) for event A and \(P_B\) for event B, the probability of event A or event B happening is \(…
updated one year ago
8 replies
4 Medals
Mathematics
yakeyglee:
Is conservation of angular momentum a direct consequence of the conservation of linear momentum?
updated one year ago
4 replies
No Medals Yet
Mathematics
yakeyglee:
Is conservation of angular momentum a direct consequence of the conservation of linear momentum?
updated one year ago
10 replies
1 Medal
Mathematics
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