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
The Essence of Mathematics, in One Beatles Song
https:/
I've always thought that @doverpubs should do something like this! Can't wait to see what Aurora releases... http:/
Typesetting Mathematics According to the ISO Standard https:/
Paradox at the heart of mathematics makes physics problem unanswerable http:/
Watched: Why mathematics? Richard Brown at TEDxJohnsHopkinsUniversity - YouTube https:/
Voted for "Mathematics Without Apologies" in the Opening Round of the 2015 #GoodreadsChoice Awards https:/
Creative Writing in Mathematics and Mathematical Sciences via @BIRS_Math http:/
Nice profile of John Conway: The world’s most charismatic mathematician | The Guardian http:/
David Spivak's Category Theory for the Sciences [http:/
This argument certainly applies to reading advanced mathematics texts. (Cross reference: http:/
In Pinker's framework, advanced mathematics texts do have the requisite coherence relations, it's just that the distance between the relations are less coherent to some than others (who have more background.)
John, your excellent work certainly isn't going unnoticed!
I thank you not only for originally hosting the workshop, but for continuing to follow up to help it continue it's life online long after the fact. My hypothesis is that because the work entailed here is so cutting edge (and does require some reasonable work on the part of the viewer to watch, read, and cogitate) that your work today is really for the long-tail. I'm sure that there are others, like me, who weren't able to trek to Tennessee for the original, but appreciate that they can relive it online.
I'm sorry some of the videos didn't manage to come out. I'm still distraught over Harte's not being available, though I suppose that his text is a possible stand in.
Sadly, scholarly communication isn't a more sexy profession, but fortunately we have people like you who manage to do it well. I always find myself wishing that I knew 20 more people like you who had the depth and breadth of experience in physics, mathematics, and biology.
If it helps, your influence (both through this workshop and your prior posts) has prompted me to begin delving heavily into <a href="http://cat.boffosocko.com">category theory</a> in the last week, and as a result there are about 20 others who are joining me in studying it over the coming months. I know that Andrew Eckford is also in the same camp.[<a href="https://twitter.com/andreweckford/status/593870544224833538">1</a>][<a href="https://twitter.com/andreweckford/status/593870774655651840">2</a>][<a href="https://twitter.com/andreweckford/status/603705613466673152">3</a>] (Psst.. you might be missing some of the conversation which is taking place on Twitter.)
Thanks, as always, for the effort you've made into these (and many other) fields, which helps pave the way for those following you!
For all the "sad" mathematicians out there,
Combinatorics is the mathematics of counting.
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:/
Math should be taught and approached from a creative, reasearch-like perspective -- which is how it organically developed throughout history anyway. This will help children (and even adults) to know how to better approach problems and figure them out when they get to higher levels. Some of the "rote" memorization of forms and formulas is just silly, and in part is what is keeping anyone from learning any math created after the 18th century until they're a junior in college, by which point most have given up on mathematics entirely.
I maintain that part of the reason that 'geniuses' like Euler and Gauss 'discovered' so much of math is that there was a truly large amount of easy low-hanging fruit for them to find. There's no reason that students couldn't be 'led' to rediscover some of these types of areas for themselves.