article | Chris Aldrich

Algebraic Number Theory | UCLA Extension

Only Me

Like a kid anxiously awaiting Christmas morning, I spent some time refreshing UCLA Extension’s web page over the weekend in hopes of seeing the announcement of Mike Miller’s Fall math course with no results.

I checked again a half hour ago and their site was down!

My salivating hit a fever pitch!

Refreshing, refreshing, refreshing… and now it’s live again with:

Mike Miller is teaching Algebraic Number Theory in the Fall!

Algebraic Number Theory

MATH X 450.8 | 3.00 units

In no field of mathematics is there such an irresistible fascination as in the theory of numbers. This course, the first in a two-quarter sequence, is an introductory, yet rigorous, survey of algebraic number theory, which evolved historically through attempts to prove Fermat’s Last Theorem. Beginning with a quick review of primality and unique factorization for ordinary integers, the course extends these notions to more exotic domains: quadratic, cubic, cyclotomic, and general number fields. This development is then applied to the representation of integers as sums of squares and, more generally, to classic Diophantine equations. Topics to be discussed include: Euclidean, principal ideal, and Noetherian domains; integral bases; binary quadratic forms; algebraic field extensions; and several remarkable theorems/conjectures of Ramanujan.

UCLA: 5137 Math Sciences
Tuesday, 7-10pm,
September 22 – December 8
11 meetings total
(no mtg 11/17)

See you all in just a few weeks!

A Note For the Reticent

Exercise Your Brain

As many may know or have already heard, Dr. Mike Miller, a retired mathematician from RAND and long-time math professor at UCLA, has been offering incredibly inexpensive upper level undergraduate and graduate level math courses for 30+ years through UCLA Extension.

Whether you’re a professional mathematician, engineer, physicist, physician, or simply a hobbyist interested in mathematics you’ll be sure to get something interesting out of this course, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years. Once most new students have taken one class, they’re incredibly prone to want to take them all (and yes, he’s THAT good — we’re sure you’ll be addicted too.)

“Beginners” Welcome!

Even if it’s been years since you last took calculus or linear algebra, Mike (and usually the rest of the class) will help you get quickly back up to speed to delve into what is often a very deep subject. Though there are a handful who will want to learn the subject for specific applications, naturally, it’s simply a beautiful and elegant subject for those who just want to meander their way through higher mathematics for the fun of it (this will probably comprise the largest majority of the class by the way.)

Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past calculus, this is bound to be the most entertaining thing you can do with your Tuesday nights in the fall. If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage to come and join us for at least the first class before you pass up on the opportunity – there’s no need to preregister or prepay if you’re unsure. I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently.

For the reticent, I’ll mention that one of the first courses I took from Mike was Algebraic Topology which generally requires a few semesters of Abstract Algebra and a semester of Topology as prerequisites. I’d taken neither of these prerequisites, but due to Mike’s excellent lecture style and desire to make everything comprehensible to the broadest number of students, I was able to do exceedingly well in the course. Also keep in mind that you can register to take the class for a grade, pass/fail, or even no grade at all to suit your needs/lifestyle.

My classes have the full spectrum of students from the most serious to the hobbyist to those who are in it for the entertainment and ‘just enjoy watching it all go by.’

Mike Miller, Ph.D.

Textbook: Introductory Algebraic Number Theory

Update (8/19/15) Per my email conversation with Dr. Miller, despite that neither the Extension website nor the bookstore have a book listed for the class yet, he’s going to be recommending Introductory Algebraic Number Theory by Saban Alaca and Kenneth S. Williams (Cambridge University Press, 2003, ISBN: 978-0521183048).

César Hidalgo on Why Information Grows | The RSA

I’ve just recently finished the excellent book Why Information Grows by César Hidalgo. I hope to post a reasonable review soon, but the ideas in it are truly excellent and fit into a thesis I’ve been working on for a while. For those interested, he does a reasonable synopsis of some of his thought in the talk he gave the the RSA recently, the video can be found below.

The underlying mathematics of what he’s discussing are fantastic (though he doesn’t go into them in his book), but the overarching implications of his ideas with relation to the future of humankind as a function of our economic system and society could have some significant impact.

“César visits the RSA to present a new view of the relationship between individual and collective knowledge, linking information theory, economics and biology to explain the deep evolution of social and economic systems.

In a radical rethink of what an economy is, one of WIRED magazine’s 50 People Who Could Change the World, César Hidalgo argues that it is the measure of a nation’s cultural complexity – the nexus of people, ideas and invention – rather than its GDP or per-capita income, that explains the success or failure of its economic performance. To understand the growth of economies, Hidalgo argues, we first need to understand the growth of order itself.”

No, It’s Not Your Opinion. You’re Just Wrong. | Houston Press

This has to be the best article of the entire year: “No, It’s Not Your Opinion. You’re Just Wrong.”

It also not coincidentally is the root of the vast majority of the problems the world is currently facing. There are so many great quotes here, I can’t pick a favorite, so I’ll highlight the same one Kimb Quark did that brought my attention to it:

“There’s nothing wrong with an opinion on those things. The problem comes from people whose opinions are actually misconceptions. If you think vaccines cause autism you are expressing something factually wrong, not an opinion. The fact that you may still believe that vaccines cause autism does not move your misconception into the realm of valid opinion. Nor does the fact that many other share this opinion give it any more validity.”

Jef Rouner
in No, It’s Not Your Opinion. You’re Just Wrong | Houston Press

Pictured: A bunch of people who were murdered regardless of someone's opinion on the subject — Pictured: A bunch of people who were murdered regardless of someone’s opinion on the subject

BoffoSocko.com Now Supports Fragmentions!

I’ve been meaning to do it for ages, but BoffoSocko.com now supports fragmentions.

“A fragmention is an extension to URL syntax that links and cites a phrase within a document by using a URL fragment consisting of the phrase itself, including whitespace.”

IndieWebCamp.com

To take advantage of the functionality, append a # and the text you’d like to highlight on the particular page after the address of the particular web page. Add a + to indicate whitespaces if necessary, though typically including a single, unique keyword is typically sufficient to highlight the appropriate section.

Example: http://boffosocko.com/about/website-philosophy-structure/#I+try+to+follow

I’m a sucker for references to math and pastry

hat can I say? I’m a sucker for references to math and pastry.

“One of the wonderful features of math is that, like with pastry, it can use quite simple ingredients to make very complicated situations. This can also make it rather offputting, like making puff pastry. Actually, I don’t think puff pastry is that difficult if you follow the instructions carefully. But even if you don’t want to try doing it yourself, perhaps you can still enjoy the fact that such simple ingredients can turn into delicious puff pastry. Math is about understanding processes and not just eating end results.”

Eugenia Cheng, mathematician, amateur chef
in How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics (Basic Books, 2015)

Chris Aldrich on VH1’s “Dating Naked”!

ver the past couple of months leading up to to the launch of VH1’s new season of “Dating Naked: Playing for Keeps” , I’ve been entertained by friends who have seen little snippets and notices about the show and wondering why and how I got involved in front of the camera. Honestly, it’s mostly been the why question. Ego-bruisingly, only one so far has wanted to know if they could get the “unblurred” cut of the show.

Let’s get one thing straight: the Chris Aldrich on VH1’s Dating Naked is NOT me — first of all, I’m way better looking.

Fortunately as we’re getting closer, there’s now “artwork” to support the fact that it’s not me.

The "other" Chris Aldrich — The “other” Chris Aldrich

It would be nice to have some PR on Hollywood’s busiest corner, but the price was too high.

Once the show launches on the 22nd, I almost can’t wait to see what happens to the Google ranking for my searches on my name. I’m sure I’ll have some further entertainment in relation to my twitter account @chrisaldrich and other parts of my social media presence. I’m almost tempted to make a few changes in the bio sections to increase the ambiguity and cause some trouble.

I’m reminded of Wes Moore’s book “The Other Wes Moore: One Name, Two Fates“, unfortunately I’m not quite sure that my writing a book about my experience with “The Other Chris Aldrich” would be so uplifting or inspiring to others. I’d also be more worried that I’d have to change the subtitle to “One name, One Fate.”

Little Free Library #8424 Progress

Almost the same moment I saw my first Little Free Library, I decided that I wanted to host one of my very own, so I registered with the intent of building one in my free time. The registration arrived and I’d drafted some very serious custom plans, but just never gotten around to purchasing the supplies and building it.

Recently I saw something a bit more quirky and interesting than my original plans that I could up-cycle, so I made the purchase (happy belated birthday to me)! It’s got two spacious shelves with two doors including a glass fronted one, and it’s got the capacity for at least 6 linear feet of books. We’re nearly ready to go.

I’m hoping to get some mounting materials and have the library up and running soon. My plan is to specialize in literary fiction, though I’m sure we’ll also stock a fair amount of popular science and non-fiction as well as thriller, mystery, and suspense as well.

Invitations to the “launch” party should be coming shortly! If you’ve got some books you’d like to donate toward the cause, let me know in the comments below. Be sure to include a Book Crossing ID number on them if you’d like to track where your favorite objects head off to in the future.

Game Theory’s Tit-for-Tat is Just a Mathematically Complete Version of Religion’s Golden Rule

The Golden Rule mandating that you treat others as you want them to treat you is simply a variation on tit-for-tat, one that emphasizes the benefit rather than the harm side. (The Christian principle of returning a favor for a harm in this respect is highly unusual and, one might note, more often than not unimplemented in Christian societies. No society I know of approves returning a harm for a favor as a general moral rule within the group.)

Francis Fukuyama (1952- ), American political scientist, political economist, author
in The Origins of Political Order: From Prehuman Times to the French Revolution (Farrar, Straus and Giroux, 2011)

Cream Scones Recipe

[recipe title=”Cream Scones” servings=”6-8″ time=”25-30mins” difficulty=”easy” image=”http://boffosocko.com/wp-content/uploads/2015/07/20150704_100549.jpg” description=”Light, flaky classic scones with full flavor”]

[recipe-ingredients]
– flour (all purpose generally yields better results than cake)
– sugar
– baking powder
– salt
– unsalted butter (cold)
– fruit: usually dried currants, raisins, chocolate chips, or other fruit
– egg
– heavy cream
– fruit zest (orange, lemon, grapefruit, other)
– cinnamon

[/recipe-ingredients]

[recipe-notes]
Other fats could be substituted for the butter, but butter generally tastes best here. For the small handful of health conscious non-professional home cooks, absolutely do not substitute milk for the cream, otherwise the fat ratio for the recipe will be thrown completely off and your results will be horrifying.

Ratio

5 parts flour : 1 part sugar : 1.5 parts butter : 1 parts egg : 2 parts cream : 1.5 parts fruit

Other ingredients (approximately per part)

1/2 teaspoon salt per part
1 tablespoon baking powder
1/4 oz zest

Professional kitchens scaling the recipe beyond 75 oz of flour, may wish to use 1.25 parts of sugar for more even results.
[/recipe-notes]

[recipe-directions]
1. Preheat oven to 425° F.
2. Whisk together the flour, sugar, baking powder and salt until mixed thoroughly.
3. Cut the cold butter into the flour mixture with a pastry blender until the lumps of butter are just larger than the size of a pea. Any smaller and the scones will be tougher and less flaky.
4. Mix together the cream, egg, (optional currants, raisins, fruit), and the zest, then mix into the flour/butter just until the dough comes together.
5. Do not overwork the scone dough or the resultant scones will not be light and flaky. You should preferably be able to still see small chunks of butter in the dough.
6. Roll the dough out into a disk about 1.5″ thick.
7. Brush a light layer of cream (or milk) onto the top of the disk and sprinkle on a nice layer of cinnamon and sugar.
8. Using a dough scraper cut the dough into eight equal wedges and place onto cooking sheet.
9. Put the sheet of scone dough into the oven at 450 for 12-15 minutes until golden brown, or until an inserted toothpick comes out clean.
10. Cool for a few minutes and then enjoy fresh with clotted cream and fresh fruit.
[/recipe-directions]

[/recipe]

Step-by-step photos

Follow the instructions in the captions below:

Whisk together the flour, sugar, baking powder and salt

Put the cold butter into the flour mixture.

Cut in the butter with a pastry blender until the lumps of butter are just larger than the size of a pea. Any smaller and the scones will be tougher and less flaky.

Mix together the cream, egg, and the zest, then mix into the flour/butter JUST until the dough comes together. — Mix together the cream, egg, (optional currants, raisins, fruit), and the zest, then mix into the flour/butter JUST until the dough comes together.

Do not overwork the scone dough. — Do not overwork the scone dough or the resultant scones will not be light and flaky.

Roll the dough out into a disk about 1.5" thick. — Roll the dough out into a disk about 1.5″ thick.

Brush a light layer of cream (or milk) onto the top of the disk.

Close up of the dough disk with cream. You should preferably be able to still see small chunks of butter in the dough.

Sprinkle on a nice layer of cinnamon and sugar.

Using a dough scraper cut the dough into eight equal wedges and place onto cooking sheet.

Put the sheet of scone dough into the oven at 450 for 12-15 minutes, or until an inserted toothpick comes out clean. — Put the sheet of scone dough into the oven at 450 for 12-15 minutes until golden brown, or until an inserted toothpick comes out clean.

Cool for a few minutes and then enjoy fresh with clotted cream and fresh fruit.

Collective learning has potentially been growing at the expense of a shrinking body of diverse language

Yesterday, I saw an interesting linguistic exercise:

Short activity to show how flexible our language is and how difficult collective learning would have been for our non sapiens ancestors.

Step 1: As a class, choose 200 random words. (I had 15 kids choose 14 words each)

Step 2: Answer the following questions using only the words listed:

How should we try to kill that mammoth?

Explain why you should marry me.

Give directions for a simple task.

Come up with a plan to improve our cave.

Describe a physical landscape.

Come up with your own question!

Chris Scaturo
on February 3 at 8:44am in Yammer Group on Big History: Unit 6 – Early Humans Group

I have to imagine that once the conceptualization of language and some basic grammar existed, word generation was a much more common thing than it is now. It’s only been since the time of Noah Webster that humans have been actively standardizing things like spelling. If we can use Papua New Guinea as a model of pre-agrarian society and consider that almost 12% of extant languages on the Earth are spoken in an area about the size of Texas (and with about 1/5th the population of Texas too), then modern societies are actually severely limiting language (creation, growth, diversity, creativity, etc.) [cross reference: A World of Languages – and How Many Speak Them (Infographic)]

Consider that the current extinction of languages is about one every 14 weeks, which puts us on a course to loose about half of the 7,100 languages on the planet right now before the end of the century. Collective learning has potentially been growing at the expense of a shrinking body of diverse language! In the paper “Global distribution and drivers of language extinction risk” the authors indicate that of all the variables tested, economic growth was most strongly linked to language loss.

To help put this exercise into perspective, we can look at the corpus of extant written Latin (a technically dead language):

“It is a truly impressive fact that, simply by knowing that if one can memorize and master about 250 words in Latin, it will allow them to read and understand 50% of most written Latin. Further, knowledge of 1,500 Latin words will put one at the 80% level of vocabulary mastery for most texts. Mastering even a very small list of vocabulary allows one to read a large variety of texts very comfortably.”

BoffoSocko.com
with data from Dickinson College Commentaries

These numbers become even smaller when considering ancient Greek texts.

Another interesting measurement is the vocabulary of a modern 2 year old who typically has a 50-75 word vocabulary while a 4 year old has 250-500 words, which is about the level of the exercise.

As a contrast, consider the message in this TED Youth Talk from last year by Erin McKean, which students should be able to relate to:

[ted id=2158]

And of course, there’s the dog Chaser, which 60 minutes recently reported has a vocabulary of over 1,000 words. (Are we now destroying variants of “dog language” for English too?!)

Hopefully the evolutionary value of the loss of the multiple languages will be more than balanced out by the power of collective learning in the long run.

How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics | Category Theory

For those who are intimidated by the thought of higher mathematics, but are still considering joining our Category Theory Summer Study Group, I’ve just come across a lovely new book by Eugenia Cheng entitled How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics.

Eugenia Cheng's book How to Bake Pi — Eugenia Cheng’s book How to Bake Pi

It just came out in the U.S. market on May 5, 2015, so it’s very new in the market. My guess is that even those who aren’t intimidated will get a lot out of it as well. A brief description of the book follows:

“What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.

At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.”

Dr. Cheng recently appeared on NPR’s Science Friday with Ira Flatow to discuss her book. You can listen to the interview below. Most of the interview is about her new book. Specific discussion of category theory begins about 14 minutes into the conversation.

Dr. Eugenia Cheng can be followed on Twitter @DrEugeniaCheng. References to her new book as well as some of her syllabi and writings on category theory have been added to our Category Theory resources pages for download/reading.

The Category Theory Site Is Now Live

Platform Choice

I’ve made a few posts here [1] [2] about a summer study group for category theory. In an effort to facilitate the growing number of people from various timezones and differing platforms (many have come to us from Google+, Tumblr, Twitter, GoodReads, and friends from Dr. Miller’s class in a private Google Group), I’ve decided it may be easiest to set up something completely separate from all of these so our notes, resources, and any other group contributions can live on to benefit others in the future. Thus I’ve built Category Theory: Summer Study Group 2015 on WordPress. It will live as a sub-domain of my personal site until I get around to buying a permanent home for it (any suggestions for permanent domain names are welcome).

Registration

We’ve actually had a few people already find the new site and register before I’ve announced it, but for those who haven’t done so yet, please go to our participant registration page and enter your preferred username and email address. We’ll email you a temporary password which you can change when you login for the first time. Those who want to use their pre-existing WordPress credentials are welcome to do so.

Once you’ve registered, be sure to update your profile (at least include your name) so that others will know a little bit more about you. If you’d like you can also link your WordPress.com account [or sign up for one and then link it] so that you can add a photo and additional details. To login later, there’s a link hidden in the main menu under “Participants.”

You can also add your details to the form at the bottom of the Participants page to let others know a bit more about you and where you can be reached. Naturally this is optional as I know some have privacy issues. In the notes, please leave your location/timezone so that we can better coordinate schedules/meetings.

Category Theory Blog

Your username/password will allow you to post content directly to the study group’s blog. This can be contributed notes, questions, resources, code, photos, thoughts, etc. related to category theory and related areas of mathematics we’ll be looking at. Initially your posts will be moderated (primarily only to prevent spam), and over time your status will be elevated to allow immediate posting and editing. If you have any questions or need administrative help, I’m easy to find and happy to help if you get into trouble. Most of the interface will hopefully be easy to understand.

For those with questions, please try to read posts as you’re able and feel free to comment with hints and/or solutions. I’ve created “categories” with the chapter titles from the text we’re using to facilitate sorting/searching. Depending on the need, we can granularize this further as we proceed. There is also the ability to tag posts with additional metadata or upload photos as well.

As appropriate, I’ll take material out of the blog/posts stream and place it into freestanding pages for easier reference in the future. As an example, I’ve already found some material on YouTube and MIT’s Open Course Ware site (Spivak posted his 2013 class using our same text, though it unfortunately doesn’t include video or audio) that may be relevant to many.

For those interested, WordPress supports most basic LaTeX, though I doubt it supports any of the bigger category theory diagramming packages, so feel free to draw out pictures/diagrams, photograph them, and upload them for others to see if necessary.

As an advocate of the open web and owning one’s own data, I highly recommend everyone publish/post their content here as well as to their favorite site/platform of choice as they see fit.

Textbook

In emails and chatter around the web, I haven’t heard any major objections to the proposed textbook so far, so unless there are, I’m assuming that it should serve most of us well. Hopefully everyone has a copy by now (remember there are free versions available) and has begun reading the introductory material. Those requiring a bit more mathematical rigor and challenge can supplement with additional texts as I’m sure I and many others will. If you’re posting questions to the site about problems/questions from other texts, please either state them explicitly or tag them with the author’s last name as well as the problem/exercise number. (I’ll try to make them all canonical on the back end as we progress, so don’t worry too much if you’re not sure how or what to tag them with.)

Conference Call Tool

At the moment, most people have been fairly open to the three big platforms, though a few on either Linux or Chromebooks don’t have access to be able to install/operate anything but Google Hangouts, so I’m presently proposing that we adopt it for our group. Nearly everyone in the group already has a gmail account, so I don’t expect it to be an undue burden. If you haven’t used it before, please download/install any plugins you may require for your platform in advance of our first “call.”

Meeting Times

I’ve only heard back from a small handful of people on availability so far, but it doesn’t look like it will be difficult to find an appropriate time. If you haven’t already done so, please fill out the “survey,” so we can determine a good call time for next week. If necessary, we can do additional times to help serve everyone’s needs. We don’t want to leave out any who sincerely want to participate.

Office Hours

As most of the participants are spread over the United States, Europe, and Asia, I’m suggesting that everyone carve out a standing block of time (we can call them “office hours”) that they can use to be available (via Google Hangouts or otherwise) to help out others having difficulty or who have questions. Since there isn’t a “professor” I’m hoping that we can all serve each other as unofficial teaching assistants to get through the process, and having standing office hours may be the easiest way to catch others for help in addition to the web site itself.

Questions? Comments? Snide Remarks?

If you have any questions, or I’ve managed to miss something, please don’t hesitate to make a comment below. I’m hoping to get enough responses by Friday/Saturday this week to post our first meeting time for next week.

Commutative Diagrams in LaTeX

Overview

With my studies in category theory trundling along, I thought I’d take moment to share some general resources for typesetting commutative diagrams in $\LaTeX$ . I’ll outline below some of the better resources and recommendations I’ve found, most by much more dedicated and serious users than I. Following that I’ll list a few resources, articles, and writings on some of the more common packages that I’ve seen mentioned.

Naturally, just reading through some of the 20+ page user guides to some of these packages can be quite daunting, much less wading through the sheer number that exist. Hopefully this one-stop-shop meta-overview will help others save some time trying to figure out what they’re looking for.

Feruglio Summary

Gabriel Valiente Feruglio has a nice overview article naming all the primary packages with some compare/contrast information. One will notice it was from 1994, however, and misses a few of the more modern packages including TikZ. His list includes: AMS; Barr (diagxy); Borceux; Gurari; Reynolds; Rose (XY-pic); Smith (Arrow); Spivak; Svensson (kuvio); Taylor (diagrams); and Van Zandt (PSTricks). He lists them alphabetically and gives brief overviews of some of the functionality of each.

Feruglio, Gabriel Valiente. Typesetting Commutative Diagrams. TUGboat, Volume 15 (1994), No. 4

Milne Summary

J.S. Milne has a fantastic one-page quick overview description of several available packages with some very good practical advise to users depending on the level of their needs. He also provides a nice list of eight of the most commonly used packages including: array (LaTeX); amscd (AMS); DCpic (Quaresma); diagrams (Taylor); kuvio (Svensson); tikz (Tantau); xymatrix (Rose); and diagxy (Barr). It’s far less formal than Feruglio, but is also much more modern. I also found it a bit more helpful for trying to narrow down one or more packages with which to play around.

Milne, J.S. Guide to Commutative Diagram Packages.

Spivak Pseudo-recommendations

David Spivak, the author of Category Theory for the Sciences, seems to prefer XY-pic, diagXY, and TikZ based on his website from which he links to guides to each of these.

Resources for some of the “Bigger” Packages

Based on the recommendations given in several of the resources above, I’ve narrowed the field a bit to some of the better sounding packages. I’ve provided links to the packages with some of the literature supporting them.

Diagxy: Michael Barr

CTAN Package
Brief four page introduction
Barr, Michael. A new diagram package. (Version 2011-06-18)

XY-pic: Kristoffer Rose & Ross Moore

CTAN Package
XY-pic User Guide
Blaga, Paul A. Commutative Diagrams with XY-pic I. Kernel Functions and Arrows. The PracTEX Journal, Draft of November 16, 2006.

Diagrams: Paul Taylor

TikZ-CD: Florêncio Neves

CTAN Package
TikZ-CD Package Documentation: {tikzcd} Commutative diagrams with TikZ. Version 0.9e; October 30, 2014.
Lenders, Felix. Commutative Diagrams using TikZ. April 12, 2012.

Is there a particular package you recommend? Feel free to add your thoughts, comments, and additional resources in the comments below.

Category Theory Summer Study Group 2015

Syllabus

Initial details for putting the group together can be found at http://boffosocko.com/2015/05/21/category-theory-anyone/.

Below is a handful of suggestions and thoughts relating to the study group in terms of platforms to assist us in communicating as well as a general outline for the summer. I’m only “leading” this in the sense that I put my foot forward first, but I expect and sincerely hope that others will be active leaders and participants as well, so please take the following only as a suggestion, and feel free to add additional thoughts and commentary you feel might help the group.

Primary resources:

General Communication

Since many within the group are already members of the Google Group “Advanced Physics & Math – Los Angeles.” I suggest we use the email list here as a base of communication. I believe the group is still “private” but am happy to invite the handful of participants who aren’t already members. Those actively participating are encouraged to change their settings so that they receive emails from the group either as they’re posted, or in batches once a day. Those subscribed only once a week or less frequently are likely to miss out on questions, comments, and other matters.

Alternately we might also use the GoodReads.com discussion group within the “Mathematics Students” group. I believe only about three of us so far may already be goodreads members, so this may require more effort for others to join.

If anyone has an alternate platform suggestion for communicating and maintaining resources, I’m happy to entertain it.

I wouldn’t be opposed to setting up a multi-user WordPress site that we could all access and post/cross-post to. Doing this could also allow for use of $\LaTeX$ as well, which may be useful down the line. This would also have the benefit of being open to the public and potentially assisting future students. It also has built-in functionality of notifying everyone of individual posts and updates as they’re entered.

Meetings

I’ll propose a general weekly meeting online via Google Hangouts on a day and time to be determined. It looks like the majority of respondents are in the Pacific timezone, so perhaps we could shoot for something around 7pm for an hour or so if we do something during weekdays so that East coasters can join without us running too late. If we decide to do something during the weekend, we obviously have a good bit more flexibility.

If we could have everyone start by indicating which days/times absolutely won’t work for them and follow up with their three to four preferred days/times, then we might be able to build a consensus for getting together.

Alternate videoconference options could include Skype, ooVoo, or others, in some part because I know that most participants are already part of the Google ecosystem and know that one or more potential participants is using Google Chromebooks and thus may not be able to use other platforms. Is anyone not able to use Google Hangouts? If we opt for something else, we want something that is ubiquitous for platform, allows screen sharing, and preferably the ability to record the sessions for those who aren’t present.

Ideally the videoconference meetings will be geared toward an inverted classroom style of work in which it would be supposed that everyone has read the week’s material and made an attempt at a number of problems. We can then bring forward any general or specific conceptual problems people may be having and then work as a group toward solving any problems that anyone in the group may be having difficulty with.

I’ll also suggest that even if we can’t all make a specific date and time, that we might get together in smaller groups to help each other out. Perhaps everyone could post one or two regular hours during the week as open “office hours” so that smaller groups can discuss problems and help each other out so that we can continue to all make progress as a group.

Primary Textbook

Spivak, David I. Category Theory for the Sciences. (The MIT Press, 2014)

Given the diversity of people in the group and their backgrounds, I’ll suggest Spivak’s text which has a gentle beginning and is geared more toward scientists and non-professional mathematicians, though it seems to come up to speed fairly quickly without requiring a large number of prerequisites. It also has the benefit of being free as noted below.

The textbook can be purchased directly through most book retailers. Those looking for cheaper alternatives might find these two versions useful. The HTML version should be exactly in line with the printed one, while the “old version” may not be exactly the same.

Old version: arxiv.org/abs/1302.6946
HTML version: mitpress.mit.edu/books/category-theory-sciences

Following this, I might suggest we use something like Awody’s text or Leinster’s which are slightly more technical, but still fairly introductory. Those who’d like a more advanced text can certainly supplement by reading portions of those texts as we work our way through the material in Spivak. If all of the group wants a more advanced text, we can certainly do it, but I’d prefer not to scare away any who don’t have a more sophisticated background.

Additional References

Adámek, Jirí & Herrlich, Horst & Strecker, George E. Abstract and Concrete Categories, The Joy of Cats. (Wiley, 2000) & (Dover, 2009) & (Free downloadable version from authors, 2004)
Awody, Steve. Category Theory (Oxford Logic Guides, #52). (Oxford University Press, 2nd Edition, 2010)
Lawvere, F. William & Schanuel, Stephen H. Conceptual Mathematics: A First Introduction to Categories. (Cambridge University Press, 2nd Edition, 2009)
Leinster, Tom. Basic Category Theory (Cambridge Studies in Advanced Mathematics, #143). (Cambridge University Press, 2014)
Mac Lane, Saunders. Categories for the Working Mathematician (Graduate Texts in Mathematics, #5). (Springer, 2nd Edition, 1998)

Proposed Schedule

The following schedule takes us from now through the end of the summer and covers the entirety of the book. Hopefully everyone will be able to participate through the end, though some may have additional pressures as the beginning of the Fall sees the start of other courses. Without much prior experience in the field myself, I’ve generally broken things up to cover about 35 pages a week, though some have slightly more or less. Many, like me, may feel like the text really doesn’t begin until week three or four as the early chapters provide an introduction and cover basic concepts like sets and functions which I have a feeling most have at least some experience with. I’ve read through chapter two fairly quickly already myself. This first easy two week stretch will also give everyone the ability to settle in as well as allow others to continue to join the group before we make significant headway.

If anyone has more experience in the subject and wishes to comment on which sections we may all have more conceptual issues with, please let us know so we can adjust the schedule as necessary. I suppose we may modify the schedule as needed going forward, though like many of you, I’d like to try to cover as much as we can before the end of the summer.

Week One: May 24 (24 pages)

Administrative tasks

Purchase Textbook
Decide on best day/time for meeting
Decide on platform for meetings: Google Hangouts /Skype /ooVoo /Other

1 A brief history of category theory
1.2 Intention of this book
1.3 What is requested from the student
1.4 Category theory references
2 The Category of Sets 9
2.1 Sets and functions
2.2 Commutative diagrams

Week Two: May 31 (50 pages)

2.3 Ologs
3 Fundamental Considerations in Set 41
3.1 Products and coproducts
3.2 Finite limits in Set

Week Three: June 7 (40 pages)

3.3 Finite colimits in Set
3.4 Other notions in Set

Week Four: June 14 (31 pages)

4 Categories and Functors, Without Admitting It 115
4.1 Monoids
4.2 Groups

Week Five: June 21 (38 pages)

4.3 Graphs
4.4 Orders

Week Six: June 28 (19 pages)

4.5 Databases: schemas and instances

Week Seven: July 5 (36 pages)

5 Basic Category Theory 203
5.1 Categories and functors

Week Eight: July 12 (28 pages)

5.2 Common categories and functors from pure math

Week Nine: July 19 (48 pages)

5.3 Natural transformations
5.4 Categories and schemas are equivalent, Cat » Sch

Week Ten: July 26 (45 pages)

6 Fundamental Considerations of Categories
6.1 Limits and colimits

Week Eleven: August 2 (15 pages)

6.2 Other notions in Cat

Week Twelve: August 9 (26 pages)

7 Categories at Work 375
7.1 Adjoint functors

Week Thirteen: August 16 (32 pages)

7.2 Categories of functors

Week Fourteen: August 23 (19 pages)

7.3 Monads

Week Fifteen: August 30 (23 pages)

7.4 Operads

Additional resources

Requested/Required Responses from participants:

Preferred platform(s) for communications:

Email and/or online discussions

Platform	Can use	Can’t use	Prefer Not to Use
Google Group
WordPress Site
GoodReads Group
Other:

Videoconferences

Platform	Can use	Can’t use	Prefer Not to Use
Google Hangouts
Skype
ooVoo
Other

Dates and times you absolutely CAN’T make for meetings (please include your local time zone):

Weekdays:

Weekends:

Dates and times you prefer (please include your local time zone):

Weekdays:

Weekends:

One or two time periods during the week you could generally/reliably be available for “office hours”:

Any other thoughts on the material above:

Textbooks
Schedule
Additional resources for the group
Other

If you’d like to join us, please fill out the contact information and details below based on the material above:

The Information Universe Conference

Yesterday, via a notification from Lanyard, I came across a notice for the upcoming conference “The Information Universe” which hits several of the sweet spots for areas involving information theory, physics, the origin of life, complexity, computer science, and microbiology. It is scheduled to occur from October 7-9, 2015 at the Infoversum Theater in Groningen, The Netherlands.

I’ll let their site speak for itself below, but they already have an interesting line up of speakers including:

Keynote speakers

Erik Verlinde, Professor Theoretical Physics, University of Amsterdam, Netherlands
Alex Szalay, Alumni Centennial Professor of Astronomy, The Johns Hopkins University, USA
Gerard ‘t Hooft, Professor Theoretical Physics, University of Utrecht, Netherlands
Gregory Chaitin, Professor Mathematics and Computer Science, Federal University of Rio de Janeiro, Brasil
Charley Lineweaver, Professor Astronomy and Astrophysics, Australian National University, Australia
Lude Franke, Professor System Genetics, University Medical Center Groningen, Netherlands

Conference synopsis from their homepage:

The main ambition of this conference is to explore the question “What is the role of information in the physics of our Universe?”. This intellectual pursuit may have a key role in improving our understanding of the Universe at a time when we “build technology to acquire and manage Big Data”, “discover highly organized information systems in nature” and “attempt to solve outstanding issues on the role of information in physics”. The conference intends to address the “in vivo” (role of information in nature) and “in vitro” (theory and models) aspects of the Information Universe.

The discussions about the role of information will include the views and thoughts of several disciplines: astronomy, physics, computer science, mathematics, life sciences, quantum computing, and neuroscience. Different scientific communities hold various and sometimes distinct formulations of the role of information in the Universe indicating we still lack understanding of its intrinsic nature. During this conference we will try to identify the right questions, which may lead us towards an answer.

Is the universe one big information processing machine?

Is there a deeper layer in quantum mechanics?

Is the universe a hologram?

Is there a deeper physical description of the world based on information?

How close/far are we from solving the black hole information paradox?

What is the role of information in highly organized complex life systems?

The Big Data Universe and the Universe : are our numerical simulations and Big Data repositories (in vitro) different from real natural system (in vivo)?

Is this the road to understanding dark matter, dark energy?

The conference will be held in the new 260 seats planetarium theatre in Groningen, which provides an inspiring immersive 3D full dome display, e.g. numerical simulations of the formation of our Universe, and anything else our presenters wish to bring in. The digital planetarium setting will be used to visualize the theme with modern media.

The Information Universe Website

Additional details about the conference including the participants, program, venue, and registration can also be found at their website.