Biomedical and Electrical Engineer with interests in information theory, evolution, genetics, abstract mathematics, microbiology, big history, IndieWeb, mnemonics, and the entertainment industry including: finance, distribution, representation
I spent most of the night working on the works of Thomas Reid for @boffosockobooks. #philosophy
"Hiring and interviewing are much more akin to literary criticism or philosophy than they are to math.” https:/
I like what you've done with the final product and have always thought about doing something similar myself, particularly after I saw what Martin Fenner (https:/
Another thing I've been playing around with lately has been some tools/toys at http:/
A large part of their philosophy is to own one's own data and then syndicate it out to other social media/external site, but some of their infrastructure allows one to easily make posts on one's own page which then act as replies on another's site. This is particularly interesting from the viewpoint of teaching wherein students and professors can interact with each other, but still have/own all of their individual work. (Incidentally, it also makes for using one's own site as a commonplace book of sorts, which I often find valuable.)
As an exmple, you'll notice on the post on my blog http:/
I find it hard to believe, particularly if you're in financial need, that you'd have a full ride at UT and not have been offered anything at JHU, so double check with the JHU office of financial aid first to see what, if anything, you'd be offered.
More than anything I'd recommend at least visiting both campuses in person and taking a tour and speaking to some students and professors. Asking a question here like you have with only the three data points (two schools and one financial aid package) is not nearly enough to go on for anyone to presume to help you make one of the most influential decisions you're going to make in your life - particularly when the advice is likely to be a terrifically biased and spurious and you're unlikely to delve into the nature of the responses you're getting.
In some sense, you're comparing apples and oranges. A couple of questions you should ask, however, above and beyond the simple ranking portion of the question which most are focusing on in their answers (while the remainder seem to be a bit more biased based on their personal experiences) include:
What are the campus environments like?
How big are the schools and what kind of attention and resources will I have access to?
How big are the cities they're in and what do they offer as part of the undergraduate experience?
What happens after one or two years if you decide to change your major?
Other than the end result of the degree, what do you want out of a college experience?
Are you looking for more diversity or less in terms of culture, religion, etc.?
What are your other interests outside of academics and are those interests actively represented or possible at the school you want to attend? (As an example, are you a musician and want to take classes or have practice time at a college's sister conservatory - perhaps you could get a dual degree? or are there a variety of other music outlets available like bands, symphonies, orchestras, music groups, etc.?)
UT is a humongous place, while Hopkins is significantly smaller, so at UT you're much more likely to be treated like just another number, even within the electrical engineering department. At Hopkins your classes are guaranteed to be much smaller and more intimate which gives you far more access to your professors - particularly when you may need recommendations down the road.
Statistically, if you're planning on going to graduate school, you'll have far more resources for doing research as an undergraduate at Hopkins, which will give you more preparation and a stronger case when you apply. Hopkins excels in undergraduate research experience in part because of its philosophy but also because it gets almost twice the government funding than even the next closest competitor. Additional resources like the proximity of the Applied Physics Lab and the Space Telescope Science Institute (which managed projects like the Hubble Telescope) will give you additional opportunities related to your field while you're in school.
If you do want to play the simple ranking game, keep in mind that only about a third of your course work as an undergraduate will be in the EE department. How highly ranked are all the other programs and departments like mathematics, physics, chemistry, biology, English, and others from which the remainder of your coursework will come? Again, what will things look like if you decide to change major part way through?
[Disclosure: I'm an alum of Johns Hopkins class of 1996 with degrees in both biomedical engineering and electrical engineering. I've been both very active on the Hopkins Society of Engineering Alumni board as well as the board that oversees the University's larger Alumni Association. I'm happy to give you more information about Hopkins, and can be easily found via a variety of social media outlets.]
This brings up, not surpisingly, an old trope in mathematics: "what use is abstract mathematics?" Some of the philosophy is disccussed well in Michael Harris's new book Mathematics without Apologies: Portrait of a Problematic Vocation [http:/
Often courses like analysis and topology seem awfully abstract, but become much more useful when combined with other topics like linear algebra and group theory to build up other abstract topics like Lie groups and Lie algebras which have more specific problem applications. A few years ago I was shocked to see a Birkhauser/Springer text entitled Stochastic Models, Information Theory, and Lie Groups [http:/
I might suggest you sit back and enjoy the abstract portions of the ride for a bit while keeping your eyes out for applied areas for application. You'll find enough applied math as you go along. In general, you may find that many applied areas will become more comprehensible to you because you better understand the abstract math which underpins them.
One bright light at the end of the tunnel for analysis is that it builds up things for measure theory which underpins probability theory.
For resources, you might find Francis Su's (he's the current president of the MAA) online lectures to be interesting/useful. They can be found via http:/
There are also a wealth of materials via India's IIT http:/
I'll turn this question around to suggest that instead of taking notes from your math/physics textbooks, that you're FAR better off PUTTING notes INTO them! Those margins are meant for writing down the parts of problems and examples that the author implicitly leaves out.
One typically wouldn't take notes from a Spanish, French, or Latin textbook would they? Like most languages, mathematics should be read and written to practice it (and maybe even spoken).
Knowing math or physics is best demonstrated by actually doing problems - and the majority of the time, this is what is going to be on the test too, so just pick up a pencil or pen and start working out the answers.
These subjects aren't like history, philosophy, or psychology with multiple choice or essay type questions that might benefit from note-taking, so just jump right in. Give the book a short read and start plugging away at problems.
If you have problems getting started, take a look at some of the examples provided by the author (or in other books), cover up the answer, and try to recreate the solution.
Drafting off of the Quora question "Why aren't math textbooks more straightforward?" (https:/
This sounds a tad like the debate in early Greek philosophy between the relativists (pre-Socratics) and the Platonists.
I'm curious what your calculation would look like to prove that they either contain the same information or that Mount Fuji contains more?
One of the subtleties of Shannon's original paper on information theory is in the second paragraph where he explicitly states that he's leaving out the semantic processing of the message by the receiver and just concentrating on the sending and receipt of the signal. (Put another way we can play the game telephone and you can hear and repeat the exact words I say, but concepts like <i>double entendre</i> and nuance may prevent you from understanding exactly what I meant to say. Shannon is leaving the second problem understanding out of the picture and solely working on the question of did you hear the words I actually said.) The way you're framing your question, it would appear that you're only focusing on the interpretation of the information after it's been received, in which case Shannon's information doesn't really have anything to say.
Now, to take a look at it from a purely mathematical standpoint within a Shannon framework, once could count the totality of the number of atoms and their states in Fuji and compare it to that of Rushmore and the one with more information is simply going to be the larger one.
If we're looking at photos of the two, then the one with more information is going to be the one that doesn't compress down as much under whatever compression algorithm we might choose. (ie, it won't have anything to do with the "information" contained in the faces and whose faces they are, which again is a semantic issue and not a mathematical one.)