Trying out Oyster's subscription service for the next few months. #netflixforbooks http:/
Why digital natives prefer reading in print. Yes, you read that right. http:/
I would suggest that, at best, real digital natives (at least the reading kind) aren't older than 10 yet.
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.)
Great start so far! I'm relatively new to the subject (but not to math), but have recently been reading Spivak's "Catetory Theory for the Science" with a group via http:/
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:/
This morning I saw someone reading Schulberg's What Makes Sammy Run in public. It's Hollywood's tradecraft verison of the CIA's 'red rose'.
I came to your article in a terrifically circuitous fashion (via a serendipitous Google Image search), but am so glad that I did. Now it appears I'll end up spending the rest of my day reading all your links and references. I work in areas of information theory and molecular biology and have been filling in my knowledge of mathematics over time. Having just finished up six months of work in Lie groups and algebras, it would appear that category theory is the next sandbox in which I should play. Thanks especially for the textbook references as well as the journal articles!
#categorytheory #mathematics #abstractalgebra #topology
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:/
At the most basic level [book:Getting What You Came For: The Smart Student's Guide to Earning an M.A. or a Ph.D.|460669] has some relatively sound advice. If you need something entertaining my friend Adam Ruben's book [book:Surviving Your Stupid, Stupid Decision to Go to Grad School|7769479] is pretty good.
For some of the other topics you mention, start reading The Chronicle of Higher Education. Most of it is available online without a subscription, but they've got lots of current faculty writing regularly on the topics you mentioned.
Slowly you'll find a community of online professors like Robert Talbert (http:/
On twitter, you might consider following some the people on this list to start: https:/
Within twitter, there are a handful of hashtags you might following/comment along with including: #mathchat, #PhDchat, #PhDLife and likely a handful of others.
On the practical side, consider creating accounts on mendeley.com, academica.com, researchgate.com, etc. as a way to find people, help, material, etc. You might also consider starting yourself a blog (aka Commonplace book) to collect all your thoughts: http:/
Finally, for graduate level math, I highly recommend spending the $100-200 for a Livescribe Pulse pen: http:/
Feel free to ping me here or via other means (http:/
Interestingly, Erwin Schrödinger's seminal paper "What is Life?" came out in 1944, almost contemporaneously with the creation of information theory in 1948. Unbeknownst to most Claude Shannon's (the researcher who created the field of information theory and whose Masters thesis literally launched the digital revolution) Ph.D. thesis (1940) was entitled: "An Algebra for Theoretical Genetics," so he could certainly be said to be the god-father of the entire area.
Since then, certainly dozens of researchers have looked at the potential of using information theory to create a better hard core definition of what life really is (certainly the place where any self-respecting Platonist would begin.)
One of the best definitions and frameworks I've seen thus far has to be that of Christoph Adami. To start, and depending on your level of sophistication, take a look at his recent arXiv paper (Information-theoretic considerations concerning the origin of life - http:/
For further references, I maintain a nice list of resources at Information Theory and Biology Resources (http:/
If you really want to blow the top off of your definitions, you might also consider taking a much broader look at the universe (a distant reading, so-to-speak) and read through David Christian's conceptualization (Maps of Time: An Introduction to Big History: David Christian, William H. McNeill http:/