A typical day in the life of being a scientist.

I feel less stupid today than yesterday.

Bessel function - integral representation, identities

$\boxed{ J_n(z) = \frac{i^{-n} }{ \pi } \int_0^{\pi} e^{iz \cos{t} } \cos{ (n \theta ) } d\theta = \frac{1}{2 \pi} \int_{-\pi}^{ \pi} d\tau e^{in\tau } e^{-ix \sin{\tau } } }$

because

$\begin{gathered} i^{-n} \int_0^{\pi} e^{ i z \cos{\theta} } \cos{ (n\theta ) } d\theta = \ = \frac{ e^{ - i n \pi } }{2} \int_0^{\pi} d\theta e^{ i z \cos{\theta }} ( e^{ i n \theta } + e^{- i n \theta } ) = \underbrace{ \frac{1}{2} \int_0^{\pi} d\theta e^{ i z \cos{\theta } } e^{ in ( \theta - \pi/2 ) } }_{ \text{ do \theta = t + \frac{ \pi} {2}  } } + \underbrace{ \frac{1}{2} \int_0^{\pi} d\theta e^{ i z \cos{\theta } } e^{ - i n ( \theta + \pi/2 ) } }_{ \text{ do \theta = -t - \frac{\pi}{2} }} = \ = \frac{1}{2} \int^{ \frac{ \pi}{2} }_{ \frac{- \pi}{2} } dt e^{ -iz \sin{t } } e^{ int } + \frac{1}{2} \int_{ \frac{ -\pi}{2} }^{ - \frac{ 3 \pi}{2} } (-dt) e^{-iz \sin{t} } e^{int } = \frac{1}{2} \int_{-\pi}^{ \pi/2} dt e^{- iz \sin{t}} e^{ int } + \frac{1}{2} \int_{ -3\pi /2}^{ -\pi} dt e^{ -iz \sin{t} } e^{int} = \ = \frac{1}{2} \int_{-\pi}^{ \pi} dt e^{int} e^{-iz \sin{t}} \end{gathered}$

PS : In Latex, in the begin gathered math environment, I can’t get the \ two backslashes to line break. And I’m running out of time.

It took me two full days to figure out this Bessel function. Sometimes I feel like this song from Glee: http://youtu.be/K3F5rpzo1s4 that my good is never good enough. and nobody cares.

### My first attempt at reblogging, John Skyler. ;)

If you had to learn addition and subtraction, all over again, how would you do it?

I’ll bet on what you wouldn’t do. You wouldn’t take a long table of sums and differences, from single digits into dozens, and memorize them all. What would be the point? There…

John Skyler’s post on pedagogy in biology

Here’s my reply, as I couldn’t find, on tumblr, how to reply directly.

John Skyler: I dig the biology teaching post. I tackled with the same dilemmas you presented when I was taking Molecular Cell Biology. You have any review papers or books to recommend? Even in physics, the pedagogy of Quantum Field Theory has DRASTICALLY improved from circa 2000-2004 to circa 2008 - present with Srednicki’s book. @ernestyalumni PS how do you comment or reply directly to a post in tumblr???! Why isn’t that process as simple as with livejournal?!?!??

Video’s up! I talk about Laura A. King’s paper on the Health Benefits from writing down life goals - (statistically) significant psychological and physical (health) benefits after 5 weeks! A little over a dozen undergraduates were asked to write for 4 days, 20 minutes a day, of their ideal future life they want to live and they saw (statistically) significant psychological and physical (health) benefits! And statistics students - you should know, if you’re taking an exam in statistics or if you’re going to be using statistics in the future, what a p-value is, Type I error, and variance!

My notes and solutions on Zee’s Quantum Field Theory in a Nutshell, particularly on Chern-Simons theory, are up: https://drive.google.com/file/d/0B1H1Ygkr4EWJaGtZMUdyeUplZVk/edit?usp=sharing

igg.me/at/ernestyalumni2014

Write down your goals! On the Health Benefits of Writing down your goals

Would you like to see positive health benefits after 5 weeks? Would you like to see those positive health benefits without any medication or doctor visits? Would you like to feel better and more positive? Do you like science?

I talk about the health benefits of writing down your goals, psychological and ‪#‎physical‬, based upon a research paper by Laura A. King in a youtube video that I’m uploading right now. Stay tuned.

I read a very well researched paper on the #health#benefits of #writing down your #goals by Laura A. King-write down your goals and dreams and #nevergiveup! Here’s the PDF link: http://www.psych.utoronto.ca/users/peterson/selfauthoring/Narrative%20and%20Goal%20Setting/Future%20Authoring%20and%20Goal%20Setting/King%20LA%20Health%20benefits%20of%20writing%20about%20life%20goals%20PSPB%202001.pdf YouTube video coming up soon as I explain the academic paper. #indiegogo campaign dropping before#thanksgiving. Would you like to see more #science #research benefiting the public and expanding what’s humanly possible? Go support the#indiegogo page! #ernesttravels #ernestyalumni #STEM #psychology#TNDO @sleepis4suckers #ethiphoppreacher #ericthomas (at Kačerov)

03 - Towards Fiber Bundles - definition of a Fiber bundle.

And we now come to the climax early of our road towards fiber bundles. I talk about the definition of a fiber bundle and explain bits and pieces of the definition. Again, allow the diagrams to guide your thinking.

I took the definition of fiber bundle off wikipedia, as you budding mathematicians and physicists should consult wikipedia for definitions (sage advice from a very wise Caltech professor).

http://en.wikipedia.org/wiki/Fiber_bundles

Be sure, if you find this video useful, to like it, subscribe, and to check back in on any of your favorite social media platforms! And do you want to help fund science? Check out my indiegogo page!

gmail  : ernestyalumni
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