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://www.quora.com/Why-arent-math-textbooks-more-straightforward) I'd suggest reading some of my extended answer here: http://boffosocko.com/2015/03/16/why-arent-math-textbooks-more-straightforward/

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://chronicle.com/blognetwork/castingoutnines/) or blogs like http://mathwithbaddrawings.com/ that can be very helpful. Then there's even folks like https://terrytao.wordpress.com/ as well.

On twitter, you might consider following some the people on this list to start: https://twitter.com/ChrisAldrich/lists/mathematicians/members
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://stream.withknown.com/2015/why-you-should-start-a-website-as-a-college-student (Keep in mind that some platforms like WordPress allow you to keep things as "drafts" without publishing them, so they're then available everywhere you might need them.)

Finally, for graduate level math, I highly recommend spending the $100-200 for a Livescribe Pulse pen: http://www.livescribe.com.

Feel free to ping me here or via other means (http://boffosocko.com) for help/questions.

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://arxiv.org/abs/1409.0590) and then take a crack at this popular press article about it in Medium (https://medium.com/the-physics-arxiv-blog/information-theory-and-the-origin-of-life-4cf6b93d156c). If it's something that blows your skirt up, then you can certainly begin to delve more deeply into some of his journal articles over the past decade or so.

For further references, I maintain a nice list of resources at Information Theory and Biology Resources (http://boffosocko.com/itbio/), as well as a "journal club" of sorts at Mendeley: ITBio: Information Theory, Microbiology, Evolution, and Complexity (https://www.mendeley.com/groups/2545131/itbio-information-theory-microbiology-evolution-and-complexity/).

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://www.amazon.com/gp/product/0520271440/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0520271440&linkCode=as2&tag=itbio-20&linkId=R3CFNWGXPDTSA5GG) of the relatively new area known as "Big History" (see http://www.bighistoryproject.org) . There, he posits the universe, the stars, and other structures as living things. Admittedly their structures are much simpler than what we might "traditionally" think of as life, but which when considered deeply, certainly are living by the broadest definition - they have less "complexity" but are far longer lived than human beings.