An Asterisk Does Not Denote a Hard Problem†

Richard Millman & George Parker in Elements of Differential Geometry

 

Dagger Graveyard by Natalie Slack
Dagger Graveyard by Natalie Slack

 

Book Review of Dominic O’Brien’s “Quantum Memory Power”

Quantum Memory Power by Dominic O'Brien
Quantum Memory Power by Dominic O’Brien

I’ve read many of the biggest memory related books over the past three decades and certainly have my favorites among them.  I’ve long heard that Dominic O’Brien’s Quantum Memory Power: Learn to Improve Your Memory with the World Memory Champion! audiobook was fairly good, and decided that I’d finally take a peek having known for a while about O’Brien and his eponymous Dominic System.

General Methods

Overall, I was fairly impressed with his layout and positive teaching style, though I don’t particularly need some of the treacly motivation that he provided and which is primarily aimed at the complete novice.  While I appreciate that for some, hearing this material may be the most beneficial, I would have preferred to have some of it presented visually.  In general, I wouldn’t recommend this as a something to listen to on a commute as he frequently admonishes against doing some of the exercises he outlines while driving or operating heavy machinery.

Given the prevalence of and growth of memory systems from the mid-20th century onwards, I personally find it difficult to believe all of his personal story about “rediscovering” many of the memory methods he outlines, or at least to the extent to which he tempts the reader to believe.

Differences from Other Systems

Based on past experience, I really appreciate his methods for better remembering names with faces as his conceptualizations for doing this seemed better to me than the methods outlined by Bruno Furst. I do however, much prefer the major mnemonic system’s method for numbers over the Dominic system for it’s more logical and complete conversion of consonant sounds for most languages. The links between the letters and numbers in the major system are also much easier to remember and don’t require as much work to remember them.  I also appreciate the major system for its deeper historical roots as well as for its precise overlap with the Gregg Shorthand method. The poorer structure of the Dominic system is the only evidence I can find to indicate that he seems to have separately re-discovered some of his memory methods.

I appreciated that most of his focus was on practical tasks like to do lists, personal appointments, names and faces, but wish he’d spent some additional time walking through general knowledge examples like he did for the list of the world’s oceans and seas.

While I appreciated his outlining the ability to calculate what day of the week any particular date falls on (something that most memory books don’t touch upon), he failed to completely specify the entire method. He also used a somewhat non-standard method for coding both the days of the week and the months of the year, though mathematically all of these systems are equivalent.  I did appreciate his trying to encode a set up for individual years, which will certainly help many cut down on the mental mathematics, particularly as it relates to the dread many have for long division.  Unfortunately, he didn’t go far enough and  this is where he also failed to finish supplying the full details for all of the special cases for the years.  He also failed to mention the discontinuities with the Gregorian versus the Julian calendar making his method more historically universal. For those interested, Wikipedia outlines some of the more familiar mathematical methods for determining the day of the week that a particular date would fall on.

Instead of having spent the time outlining the calendar, which is inherently difficult to do in audio format compared to printed format, he may have been better off having spent the time going into more depth memorizing poetry or prose as an extension of his small aside on memorizing quotes and presenting speeches.

I could have done without the bulk of the final disk which comprised mostly of tests for the material previously presented. The complete beginner may get more out of these exercises however.  The final portion of the disk was more interesting as he did provide some philosophy on how memory systems engage both lobes of the brain within the right-brained/left-brained conceptualizations from neuropsychology.

While O’Brien doesn’t completely draw out his entire system, to many this may be a strong benefit as it forces individuals to create their own system within his framework. This is bound to help many to create stronger personalized links between their numbers and their images. The drawback the beginner may find for this is that they may find themselves ever tinkering with their own customized system, or even more likely rebuilding things from scratch when they discover the list of online resources from others that rely on people having a more standardized system.

O’Brien also provides more emphasis on creativity and visualization than some books, which will be very beneficial to many beginners.

Overall, while I’d generally recommend this to the average mnemonist, I’d recommend they approach it after having delved in a bit and learned the major system from somewhere else.

NIMBioS Workshop: Information Theory and Entropy in Biological Systems

Over the next few days, I’ll be maintaining a Storify story covering information related to and coming out of the Information Theory and Entropy Workshop being sponsored by NIMBios at the Unviersity of Tennessee, Knoxville.

For those in attendance or participating by watching the live streaming video (or even watching the video after-the-fact), please feel free to use the official hashtag #entropyWS, and I’ll do my best to include your tweets, posts, and material into the story stream for future reference.

For journal articles and papers mentioned in/at the workshop, I encourage everyone to join the Mendeley.com group ITBio: Information Theory, Microbiology, Evolution, and Complexity and add them to the group’s list of papers. Think of it as a collaborative online journal club of sorts.

Those participating in the workshop are also encouraged to take a look at a growing collection of researchers and materials I maintain here. If you have materials or resources you’d like to contribute to the list, please send me an email or include them via the suggestions/submission form or include them in the comments section below.

Resources for Information Theory and Biology

RSS Icon  #ITBio" href="http://boffosocko.com/tag/ITBio/feed/" target="_blank">RSS Feed for BoffoSocko posts tagged with

 

Machiavelli in Hollywood | Gavin Polone’s ‘Textbook’ on the Entertainment Industry

Dearth of (Great) Textbooks on The Entertainment Business

In having previously taught several classes on the business of the entertainment industry, I was never quite able to pick out even a mediocre textbook for such a class. There are a handful that will give one an overview of the nuts and bolts and one or two that will provide some generally useful numbers (see the syllabi from those classes), but none comes close to providing the philosophy of how the business works in a short period of time.

A Short Term Solution

To remedy this problem, I was always a fan of producer and ex-agent Gavin Polone, who had a series of articles in New York Magazine/Vulture.  I’ve recently gone through and linked to all of the forty-four articles, in chronological order, he produced in that series from 9/21/11 to 5/7/14.

I’ve aggregated the series via Readlists.com, so one can click on each of the articles individually.  Better yet, for students and teachers alike, one can click on the “export” link and very easily download them all in most ebook formats (including Kindle, iPad, etc.) for your reading/studying convenience.

My hope is that for others, they may create an excellent starter textbook on how the entertainment business works and, more importantly: how successful people in the business think. For those who need more, Gavin is also an occasional contributor to the Hollywood Reporter.  (And, as a note for those not trained in the classics and prone to modern-day stereotypes, I’ll make the caveat that I use the title “Machiavelli” above with the utmost reverence and honor.)

I’m still slowly, but surely making progress on my own all-encompassing textbook, but, until then, I hope others find this series of articles as interesting and useful as I have.

 

Gavin Polone is an agent turned manager turned producer. His production company, Pariah, has brought you such movies and TV shows as Panic Room, Zombieland, Gilmore Girls, and Curb Your Enthusiasm. Follow him on Twitter @gavinpolone

Nothing Would be More Devastating than Reduced Access to a Technical Library

Nassim Nicholas Taleb, flâneur
in the Financial Times in response to the question:
“If you lost everything tomorrow, what would you do?”

 


 

Why Aren’t Math Textbooks More Straightforward?

Some General Advice for Math Students of All Ages

I recently saw the question “Why aren’t math textbooks more straightforward?” on Quora.

In fact, I would argue that most math textbooks are very straightforward!

The real issue most students are experiencing is one of relativity and experience.  Mathematics is an increasingly sophisticated, cumulative, and more complicated topic the longer you study it. Fortunately, over time, it also becomes easier, more interesting, and intriguingly more beautiful.

As an example of what we’re looking at and what most students are up against, let’s take the topic of algebra. Typically in the United States one might take introductory algebra in eighth grade before taking algebra II in ninth or tenth grade. (For our immediate purposes, here I’m discounting the potential existence of a common pre-algebra course that some middle schools, high schools, and even colleges offer.)  Later on in college, one will exercise one’s algebra muscles in calculus and may eventually get to a course called abstract algebra as an upper-level undergraduate (in their junior or senior years).  Most standard undergraduate abstract algebra textbooks will cover ALL of the material that was in your basic algebra I and algebra II texts in about four pages and simply assume you just know the rest! Naturally, if you started out with the abstract algebra textbook in eighth grade, you’d very likely be COMPLETELY lost. This is because the abstract algebra textbook is assuming that you’ve got some significant prior background in mathematics (what is often referred to in the introduction to far more than one mathematics textbook as “mathematical sophistication”, though this phrase also implicitly assumes knowledge of what a proof is, what it entails, how it works, and how to actually write one).

Following the undergraduate abstract algebra textbook there’s even an additional graduate level course (or four) on abstract algebra (or advanced subtopics like group theory, ring theory, field theory, and Galois theory) that goes into even more depth and subtlety than the undergraduate course; the book for this presumes you’ve mastered the undergraduate text and goes on faster and further.

A Weightlifting Analogy

To analogize things to something more common, suppose you wanted to become an Olympic level weightlifter.  You’re not going to go into the gym on day one and snatch and then clean & jerk 473kg! You’re going to start out with a tiny fraction of that weight and practice repeatedly for years slowly building up your ability to lift bigger and bigger weights. More likely than not, you’ll also very likely do some cross-training by running, swimming, and even lifting other weights to strengthen your legs, shoulder, stomach, and back.  All of this work may eventually lead you to to win the gold medal in the Olympics, but sooner or later someone will come along and break your world record.

Mathematics is certainly no different: one starts out small and with lots of work and practice over time, one slowly but surely ascends the rigors of problems put before them to become better mathematicians. Often one takes other courses like physics, biology, and even engineering courses that provide “cross-training.”  Usually when one is having issues in a math class it’s because they’re either somehow missing something that should have come before or because they didn’t practice enough in their prior classwork to really understand all the concepts and their subtleties.  As an example, the new material in common calculus textbooks is actually very minimal – the first step in most problems is the only actual calculus and the following 10 steps are just practicing one’s algebra skills. It’s usually in carrying out the algebra that one makes more mistakes than in the actual calculus.

Often at the lower levels of grade-school mathematics, some students can manage to just read a few examples and just seem to “get” the answers without really doing a real “work out.” Eventually they’ll come to a point at which they hit a wall or begin having trouble, and usually it comes as the result of not actually practicing their craft.  One couldn’t become an Olympic weightlifter by reading books about weightlifting, they need to actually get in the gym and workout/practice. (Of course, one of the places this analogy breaks down is that weightlifting training is very linear and doesn’t allow one to “skip around” the way one could potentially in a mathematics curriculum.)

I’m reminded of a quote by mathematician Pierre Anton Grillet: “…algebra is like French pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” It is one of the most beautiful expressions of the recurring sentiment written by almost every author into the preface of nearly every mathematics text at or above the level of calculus. They all exhort their students to actually put pencil to paper and work through the logic of their arguments and the exercises to learn the material and gain some valuable experience.  I’m sure that most mathematics professors will assure you that in the end, only a tiny fraction of their students actually do so. Some of the issue is that these exhortations only come in textbooks traditionally read at the advanced undergraduate level, when they should begin in the second grade.

Patissiere puts their hands to a pie crust in a rustic kitchen
“Algebra is like French Pastry: wonderful, but cannot be learned without putting one’s hands to the dough.” -Pierre Anton Grillet

“It’s Easy to See”

A common phrase in almost every advanced math textbook on the planet is the justification, “It’s easy to see.” The phrase, and those like it, should be a watchword for students to immediately be on their guard!  The phrase is commonly used in proofs, discussions, conversations, and lectures in which an author or teacher may skip one or more steps which she feels should be obvious to her audience, but which, in fact, are far more commonly not obvious.

It’s become so cliche that some authors actually mention specifically in their prefaces that they vow not to use the phrase, but if they do so, they usually let slip some other euphemism that is its equivalent.

The problem with the phrase is that everyone, by force of their own circumstances and history, will view it completely differently.  A step that is easy for someone with a Ph.D. who specialized in field theory to “see” may be totally incomprehensible for a beginning student of algebra I in the same way that steps that were easy for Girgory Perelman to see in his proof of the Poincaré conjecture were likewise completely incomprehensible for teams of multiple tenured research professors of mathematics to see. (cross reference: The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O’Shea (Walker & Co., 2007))

How to Actively Read a Math Text

The Problem

So how are students to proceed? It will certainly help to see a broader road map of what lies ahead and what the expected changes in terrain will look like. It will also help greatly if students have a better idea how to approach mathematics for themselves and even by themselves in many cases.

In my opinion, the most common disconnect occurs somewhere between high school mathematics and early college mathematics (usually a calculus sequence, linear algebra) and then again between linear algebra/differential equations (areas which usually have discussion followed by examples and then crank-out problems) and higher abstract mathematical areas like analysis, abstract algebra, topology (areas in which the definition-theorem-proof cycle of writing is more common and seemingly more incomprehensible to many).

The first big issue in early college mathematics is the increased speed at which college courses move. Students used to a slower high school pace where the teachers are usually teaching to the middle or lower end of the class get caught unaware as their college professors teach to the higher ability students and aren’t as afraid to leave the lower end of the spectrum behind. Just like high school athletes are expected to step up their game when they make the transition to college and similarly college athletes who go pro, mathematics students should realize they’re expected to step up their game at the appropriate times.

Often math students (and really any student of any subject) relies on the teacher assigning readings or problems from their book rather than excersizing their curiosity to more avidly and broadly explore the material on their own.  If they can take the guidance of their teacher as well as that of the individual authors of books, they may make it much further on their own.  High school teachers often skip sections of textbooks for time, but students should realize that there is profitable and interesting material that they’re skipping.  Why not go and read it on their own?

Earlier I mentioned that an average undergraduate abstract algebra textbook might cover the totality of a high school algebra textbook in about three pages.  What does this mean for upper level mathematics students?  It almost always means that the density of material in these books is far greater than that of their earlier textbooks.  How is this density arrived at?  Authors of advanced textbooks leave out far more than they’re able to put in, otherwise their 300 page textbooks, if written at the same basic level as those that came before would be much more ponderous 1000+ page textbooks.  What are they leaving out?  Often they’re leaving out lots of what might be useful discussion, but more often, they’re leaving out lots of worked out examples. For example, a high school text will present a definition or concept and then give three or more illustrations or examples of problems relating to the concept.  The exercises will then give dozens of additional drill problems to beat the concept to death.  This type of presentation usually continues up to the level of calculus where one often sees massive tomes in the 800+ page length. Math texts after this point generally don’t go much over 300 pages as a rule, and it’s primarily because they’re leaving the examples out of the proverbial equation.

The Solution

How does one combat this issue?  Students need to more actively think back to the math they’ve taken previously and come up with their own simple examples of problems, and work though them on their own.  Just because the book doesn’t give lots of examples doesn’t mean that they don’t exist.

In fact, many textbooks are actually presenting examples, they’re just hiding them with very subtle textual hints. Often in the presentation of a concept, the author will leave out one or more steps in a proof or example and hint to the student that they should work through the steps themselves. (Phrases like: “we leave it to the reader to verify” or “see example 2.”) Sometimes this hint comes in the form of that dreaded phrase, “It’s easy to see.” When presented with these hints, it is incumbent (or some students may prefer the word encumbering) on the student to think through the missing steps or provide the missing material themselves.

While reading mathematics, students should not only be reading the words and following the steps, but they should actively be working their way through all of the steps (missing or not) in each of the examples or proofs provided. They must read their math books with pencil and paper in hand instead of the usual format of reading their math book and then picking up paper and pencil to work out problems afterwards.  Most advanced math texts suggest half a dozen or more problems to work out within the text itself before presenting a dozen or more additional problems usually in a formal section entitled “Exercises”. Students have to train themselves to be thinking about and working out the “hidden” problems within the actual textual discussion sections.

Additionally, students need to consider themselves “researchers” or think of their work as discovery or play.  Can they come up with their own questions or exercises that relate the concepts they’ve read about to things they’ve done in the past? Often asking the open ended question, “What happens if I…” can be very useful.  One has to imagine that this is the type of “play” that early mathematicians like Euclid, Gauss, and Euler did, and I have to say, this is also the reason that they discovered so many interesting properties within mathematics.  (I always like to think that they were the beneficiaries of “picking the lowest hanging fruit” within mathematics – though certainly they discovered some things that took some time to puzzle out; we take some of our knowledge for granted as sitting on the shoulders of giants does allow us to see much further than we could before.)

As a result of this newly discovered rule, students will readily find that while they could read a dozen pages of their high school textbooks in just a few minutes, it may take them between a half an hour to two hours to properly read even a single page of an advanced math text. Without putting in this extra time and effort they’re going to quickly find themselves within the tall grass (or, more appropriately weeds).

Another trick of advanced textbooks is that, because they don’t have enough time or space within the primary text itself, authors often “hide” important concepts, definitions, and theorems within the “exercises” sections of their books.  Just because a concept doesn’t appear in the primary text doesn’t mean it isn’t generally important.  As a result, students should always go out of their way to at least read through all of the exercises in the text even if they don’t spend the time to work through them all.

One of the difficult things about advanced abstract mathematics is that it is most often very cumulative and even intertwined, so when one doesn’t understand the initial or early portions of a textbook, it doesn’t bode well for the later sections which require one to have mastered the previous work.  This is even worse when some courses build upon the work of earlier courses, so for example, doing well in calculus III requires that one completely mastered calculus I. At some of the highest levels like courses in Lie groups and Lie algebras requires that one mastered the material in multiple other prior courses like analysis, linear algebra, topology, and abstract algebra. Authors of textbooks like these will often state at the outset what material they expect students to have mastered to do well, and even then, they’ll often spend some time giving overviews of relevant material and even notation of these areas in appendices of their books.

As a result of this, we can take it as a general rule: “Don’t ever skip anything in a math textbook that you don’t understand.” Keep working on the concepts and examples until they become second nature to you.

Finally, more students should think of mathematics as a new language.  I’ve referenced the following Galileo quote before, but it bears repeating (emphasis is mine):

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Though mathematical notation has changed drastically (for the better, in my opinion) since Galileo’s time, it certainly has its own jargon, definitions, and special notations.  Students should be sure to spend some time familiarizing themselves with current modern notation, and especially the notation in the book that they choose.  Often math textbooks will have a list of symbols and their meanings somewhere in the end-papers or the appendices. Authors usually go out of their way to introduce notation somewhere in either the introduction, preface, appendices, or often even in an introductory review chapter in which they assume most of their students are very familiar with, but they write it anyway to acclimate students to the particular notation they use in their text.  This notation can often seem excessive or even obtuse, but generally it’s very consistent across disciplines within mathematics, but it’s incredibly useful and necessary in making often complex concepts simple to think about and communicate to others. For those who are lost, or who want help delving into areas of math seemingly above their heads, I highly recommend the text Mathematical Notation: A Guide for Engineers and Scientists by my friend Edward R. Scheinerman as a useful guide.

A high school student may pick up a textbook on Lie Groups and be astounded at the incomprehensibility of the subject, but most of the disconnect is in knowing and understanding the actual language in which the text is written.  A neophyte student of Latin would no sooner pick up a copy of Cicero and expect to be able to revel in the beauty and joy of the words or their meaning without first spending some time studying the vocabulary, grammar, and syntax of the language.  Fortunately, like Latin, once one has learned a good bit of math, the notations and definitions are all very similar, so once you can read one text, you’ll be able to appreciate a broad variety of others.

Actively Reading a Mathematics Text Review:

  • Work through the steps of everything within the text
  • Come up with your own examples
  • Work through the exercises
  • Read through all the exercises, especially the ones that you don’t do
  • Don’t ever skip anything you don’t fully understand
  • Math is a language: spend some time learning (memorizing) notation

Exceptions

Naturally there are exceptions to the rule. Not all mathematics textbooks are great, good, or even passable.  There is certainly a spectrum of textbooks out there, and there are even more options at the simpler (more elementary) end, in part because of there is more demand.  For the most part, however, most textbooks are at least functional.  Still one can occasionally come across a very bad apple of a textbook.

Because of the economics of textbook publishing, it is often very difficult for a textbook to even get published if it doesn’t at least meet a minimum threshold of quality. The track record of a publisher can be a good indicator of reasonable texts. Authors of well-vetted texts will often thank professors who have taught their books at other universities or even provide a list of universities and colleges that have adopted their texts. Naturally, just because 50 colleges have adopted a particular text doesn’t necessarily mean that that it is necessarily of high quality.

One of the major issues to watch out for is using the textbook written by one’s own professor.  While this may not be an issue if your professor is someone like Serge Lang, Gilbert Strang, James Munkres, Michael Spivak, or the late Walter Rudin, if your particular professor isn’t supremely well known in his or her field, is an adjunct or associate faculty member, or is a professor at a community college, then: caveat emptor.

Since mathematics is a subject about clear thinking, analysis, and application of knowledge, I recommend that students who feel they’re being sold a bill of goods in their required/recommended textbook(s), take the time to look at alternate textbooks and choose one that is right for themselves.  For those interested in more on this particular sub-topic I’ve written about it before: On Choosing Your own Textbooks.

Parting Advice

Often, even with the best intentions, some authors can get ahead of themselves or the area at hand is so advanced that it is difficult to find a way into it. As an example, we might consider Lie groups and algebras, which is a fascinating area to delve into. Unfortunately it can take several years of advanced work to get to a sufficient level to even make a small dent into any of the textbooks in the area, though some research will uncover a handful of four textbooks that will get one quite a way into the subject with a reasonable background in just analysis and linear algebra.

When one feels like they’ve hit a wall, but still want to struggle to succeed, I’m reminded of the advice of revered mathematical communicator Paul Halmos, whose book Measure Theory needed so much additional background material, that instead of beginning with the traditional Chapter 1, he felt it necessary to include a Chapter 0 (he actually called his chapters “sections” in the book) and even then it had enough issueshewas cornered into writing the statement:

…[the reader] should not be discouraged, if on first reading of section 0, he finds that he does not have the prerequisites for reading the prerequisites.

Paul Halmos in Measure Theory(1950)

This is essentially the mathematician’s equivalent of the colloquialism “Fake it ’til you make it.”

When all else fails, use this adage, and don’t become discouraged. You’ll get there eventually!

 

Algebra is Like Pastry: Wonderful!

Pierre Anton Grillet (1941 – ), algebraist
in preface to Abstract Algebra, Second Edition (Springer, 2007)

 

2015 Viterbi Lecture: H. Vincent Poor on “Fundamental Limits on Information Security and Privacy”

USC’s Ming Hsieh Department of Electrical Engineeing has announced that H. Vincent Poor will deliver the 2015 Viterbi Lecture

“Fundamental Limits on Information Security and Privacy”

H. Vincent Poor
H. Vincent Poor

H. Vincent Poor, Ph.D.  
Dean of the School of Engineering and Applied Science
Michael Henry Strater University Professor
Princeton University

Education

  • Ph.D., Princeton University, 1977
  • M.A., in Electrical Engineering, Princeton University, 1976
  • M.S., in Electrical Engineering, Auburn University, 1974
  • B.E.E., with Highest Honor, Auburn University, 1972

Lecture Information

Tuesday, March 24, 2015
Hughes Electrical Engineering Center (EEB) 132
Reception 3:00pm
Lecture 4:00pm

Abstract

As has become quite clear from recent headlines, the ubiquity of technologies such as wireless communications and on-line data repositories has created new challenges in information security and privacy. Information theory provides fundamental limits that can guide the development of methods for addressing these challenges. After a brief historical account of the use of information theory to characterize secrecy, this talk will review two areas to which these ideas have been applied successfully: wireless physical layer security, which examines the ability of the physical properties of the radio channel to provide confidentiality in data transmission; and utility-privacy tradeoffs of data sources, which quantify the balance between the protection of private information contained in such sources and the provision of measurable benefits to legitimate users of them. Several potential applications of these ideas will also be discussed.

Biography

H. Vincent Poor (Ph.D., Princeton 1977) is Dean of the School of Engineering and Applied Science at Princeton University, where he is also the Michael Henry Strater University Professor. From 1977 until he joined the Princeton faculty in 1990, he was a faculty member at the University of Illinois at Urbana-Champaign. He has also held visiting appointments at a number of other universities, including most recently at Stanford and Imperial College. His research interests are primarily in the areas of information theory and signal processing, with applications in wireless networks and related fields. Among his publications in these areas is the recent book Principles of Cognitive Radio (Cambridge University Press, 2013). At Princeton he has developed and taught several courses designed to bring technological subject matter to general audiences, including “The Wireless Revolution” (in which Andrew Viterbi was one of the first guest speakers) and “Six Degrees of Separation: Small World Networks in Science, Technology and Society.”

Dr. Poor is a member of the National Academy of Engineering and the National Academy of Sciences, and is a foreign member of the Royal Society. He is a former President of the IEEE Information Theory Society, and a former Editor-in-Chief of the IEEE Transactions on Information Theory. He currently serves as a director of the Corporation for National Research Initiatives and of the IEEE Foundation, and as a member of the Council of the National Academy of Engineering. Recent recognition of his work includes the 2014 URSI Booker Gold Medal, and honorary doctorates from several universities in Asia and Europe.

Texts

  

Introduction to Lie Groups and Lie Algebras (Part 2) | UCLA Extension

Dr. Mike Miller, who had previously announced a two quarter sequence of classes on Lie Groups at UCLA, has just opened up registration for the second course in the series. His courses are always clear, entertaining, and invigorating, and I highly recommend them to anyone who is interested in math, science, or engineering.

Philosophy is written in this grand book, the universe which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.

Galileo Galilee (1564–1642) in Il saggiatore (The assayer)

Prior to the first part of the course, I’d written some thoughts about the timbre and tempo of his lecture style and philosophy and commend those interested to take a peek. I also mentioned some additional resources for the course there as well.  For those who missed the first portion, I’m happy to help fill you in and share some of my notes if necessary. The recommended minimum prerequisites for this class are linear algebra and some calculus.


Introduction to Lie Groups and Lie Algebras (Part 2)

Math X 450.7 / 3.00 units / Reg. # 251580W
Professor: Michael Miller, Ph.D.
Start Date: January 13, 2015
Location: UCLA, 5137 Math Sciences Building
Tuesday, 7-10pm
January 13 – March 24
11 meetings total
Class will not meet on one Tuesday to be annouced.

Register here: https://www.uclaextension.edu/Pages/Course.aspx?reg=251580

Course Description

A Lie group is a differentiable manifold that is also a group for which the product and inverse maps are differentiable. A Lie algebra is a vector space endowed with a binary operation that is bilinear, alternating, and satisfies the so-called Jacobi identity. This course is the second in a 2-quarter sequence that offers an introductory survey of Lie groups, their associated Lie algebras, and their representations. Its focus is split between continuing last quarter’s study of matrix Lie groups and their representations and reconciling this theory with that for the more general manifold setting. Topics to be discussed include the Weyl group, complete reducibility, semisimple Lie algebras, root systems, and Cartan subalgebras. This is an advanced course, requiring a solid understanding of linear algebra, basic analysis, and, ideally, the material from the previous quarter.Internet access required to retrieve course materials.

Recommended Textbook

Hall, Brian. Lie Groups, Lie Algebras, & Representations (Springer, 2004) ISBN: 9781441923134

 

A photograph of Sophus Lie's very full and bushy beard.
“I wouldn’t lie to you. This is Sophus’s beard.”

 

BIRS Workshop on Biological and Bio-Inspired Information Theory | Storify Stream

Over the span of the coming week, I’ll be updating (and archiving) the stream of information coming out of the BIRS Workshop on Biological and Bio-Inspired Information Theory.

Editor’s note: On 12/12/17 Storify announced they would be shutting down. As a result, I’m changing the embedded version of the original data served by Storify for an HTML copy which can be found below:

BIRS: Biological and Bio-Inspired Information Theory

A 5 Day workshop on Biology and Information Theory hosted by the Banff International Research Station

  1. Wishing I was at the Gene Regulation and Information Theory meeting starting tomorrow  http://bit.ly/XnHRZs  #ITBio
  2. Mathematical and Statistical Models for Genetic Coding starts today.  http://www.am.hs-mannheim.de/genetic_code_2013.php?id=1  @andreweckford might borrow attendees for BIRS
  3. Mathematical Foundations for Information Theory in Diffusion-Based Molecular Communications  http://bit.ly/1aTVR2c  #ITBio
  4. Bill Bialek giving plenary talk “Information flow & order in real biological networks” at Feb 2014 workshop  http://mnd.ly/19LQH8f  #ITBio
  5. #ITBio http://t.co/Ty8dEIXQUT"/>

    CECAM Workshop: “Entropy in Biomolecular Systems” starts May 14 in Vienna.  http://jhu.md/1faLR8t  #ITBio pic.twitter.com/Ty8dEIXQUT
  6. Last RT: wonder what the weather is going to be like at the end of October for my @BIRS_Math workshop
  7. @JoVanEvery I’m organizing a workshop in Banff in October … hopefully this isn’t a sign of weather to come!
  8. Banff takes its name from the town of Banff, Scotland, not to be confused with Bamff, also Scotland.
  9. Good morning from beautiful Banff. How can you not love the mountains? http://t.co/mxYBNz7yzl

    Good morning from beautiful Banff. How can you not love the mountains? pic.twitter.com/mxYBNz7yzl
  10. “Not an obvious connection between utility and information, just as there is no obvious connection between energy and entropy” @BIRS_Math
  11. Last RT: a lot of discussion of my signal transduction work with Peter Thomas.
  12. Live now: Nicolo Michelusi of @USCViterbi on Stochastic Model for Electron Transfer in Bacterial Cables  http://www.birs.ca/live  #ITBio
  13. Nicolo Michelusi (University of Southern California), A Stochastic Model for Electron Transfer in Bacterial Cables  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271450-Michelusi.mp4 
  14. Listening to the always awesome @cnmirose talk about the ultimate limits of molecular communication.
  15. “Timing is fundamental … subsumes time-varying concentration channel” @cnmirose @BIRS_Math
  16. Standard opening quote of these talks: “I’m not a biologist, but …” @BIRS_Math
  17. Stefan Moser (ETH Zurich), Capacity Bounds of the Memoryless AIGN Channel – a Toy-Model for Molecular Communicat…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271610-Moser.mp4 
  18. Weisi Guo (University of Warwick), Communication Envelopes for Molecular Diffusion and Electromagnetic Wave Propag…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410271643-Guo.mp4 
  19. .@ChrisAldrich @andreweckford @Storify @BIRS_Math Sounds like a fascinating workshop on bioinformation theory in Banff.
  20. Toby Berger, winner of the 2002 Shannon award, speaking right now. @BIRS_Math
  21. Naftali Tishby (Hebrew University of Jerusalem), Sensing and acting under information constraints – a principled a…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281032-Tishby.mp4 
  22. “…places such as BIRS and the Banff Centre exist to facilitate the exchange and pursuit of knowledge.” S. Sundaram  http://www.birs.ca/testimonials/#testimonial-1454 
  23. We’re going for a hike tomorrow. Many thanks to Lukas at the @ParksCanada info centre in Banff for helpful advice! @BIRS_Math
  24. Alexander Dimitrov (Washington State University), Invariant signal processing in auditory biological systems  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281416-Dimitrov.mp4 
  25. Joel Zylberberg (University of Washington), Communicating with noisy signals: lessons learned from the mammalian v…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281450-Zylberberg.mp4 
  26. Robert Schober (Universitat Erlangen-Nurnberg), Intersymbol interference mitigation in diffusive molecular communi…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281549-Schober.mp4 
  27. Rudolf Rabenstein (Friedrich-Alexander-Universitat Erlangen-Nurnberg (FAU)), Modelling Molecular Communication Cha…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281627-Rabenstein.mp4 
  28. THis week @BIRS_Math ” Biological and Bio-Inspired Information Theory ” @thebanffcentre #biology #math @NSF
  29. “Your theory might match the data, but the data might be wrong” – Crick @BIRS_Math
  30. So information theory seems to be a big deal in ecology. @BIRS_Math
  31. Tom Schneider (National Institutes of Health), Three Principles of Biological States: Ecology and Cancer  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410290904-Schneider.mp4 
  32. “In biodiversity, the entropy of an ecosystem is the expected … information we gain about an organism by learning its species” @BIRS_Math
  33. Seriously, I’m blown away by this work in information theory in ecology. Huge body of work; I had no idea. @BIRS_Math
  34. I encourage @BIRS_Math attendees at Biological & Bio-Inspired Information Theory to contribute references here:  http://bit.ly/1jQwObk 
  35. Christoph Adami (Michigan State University), Some Information-Theoretic Musings Concerning the Origin and Evolutio…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410291114-Adami.mp4 
  36. #ITBio http://t.co/VA8komuuSW"/>

    .@ChristophAdami talk Some Information-Theoretic Musings Concerning the Origin of Life @BIRS_Math this morning #ITBio pic.twitter.com/VA8komuuSW
  37. ICYMI @ChristophAdami had great paper: Information-theoretic Considerations on Origin of Life on arXiv  http://bit.ly/1yIhK2Q  @BIRS_Math
  38. Baez has a post on Tishby's talk "Sensing &  Acting Under Information Constraints" http://t.co/t1nPVI1pxa @BIRS_Math http://t.co/dFuiVLFSGC

    Baez has a post on Tishby’s talk “Sensing & Acting Under Information Constraints”  http://bit.ly/1yIDonR  @BIRS_Math pic.twitter.com/dFuiVLFSGC
  39. INFORMATION THEORY is the new central ...

    INFORMATION THEORY is the new central …
  40. I’m listening to a talk on the origin of life at a workshop on Biological and Bio-Inspired Information Theory. …  https://plus.google.com/117562920675666983007/posts/gqFL7XY3quF 
  41. Now accepting applications for the #Research Collaboration Workshop for Women in #MathBio at NIMBioS  http://ow.ly/DzeZ7 
  42. We removed a faulty microphone from our lecture room this morning. We’re now fixing the audio buzz in this week’s videos, and reposting.
  43. Didn’t get enough information theory & biology this week @BIRS_Math? Apply for NIMBioS workshop in April 2015  http://bit.ly/1yIeiWe  #ITBio
  44. Amin Emad (University of Illinois at Urbana-Champaign), Applications of Discrete Mathematics in Bioinformatics  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301329-Emad.mp4 
  45. Paul Bogdan (University of Southern California), Multiscale Analysis Reveals Complex Behavior in Bacteria Populati…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301401-Bogdan.mp4 
  46. Lubomir Kostal (Institute of Physiology, Academy of Sciences of the Czech Republic), Efficient information transmi…  http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410301534-Kostal.mp4 
  47. Banff ☀️❄️🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲🌲❤️
  48. @conservativelez I’m a big fan of your dad’s research & was reminded of much of it via a workshop on Biological Information Theory
  49. @conservativelez Though he may not have been able to attend, he can catch most of the talks online if he’d like  https://www.birs.ca/events/2014/5-day-workshops/14w5170 
  50. Depressed that @BIRS_Math Workshop on Biological & Bio-Inspired Information Theory is over? Relive it here:  http://bit.ly/1rF3G4B  #ITBio
  51. A few thoughts about that workshop while I wait for my flight back to Toronto.
  52. 1/ Everyone I talked to said it was the best workshop they’d ever been to, and they’d like to do a follow-up workshop @BIRS_Math
  53. 2/ There is an amazing diversity of work under the umbrella of “information theory”. @BIRS_Math
  54. 3/ Much of this work is outside the IT mainstream, and an issue is that people use different terms for related concepts. @BIRS_Math
  55. 4/ Some community building is in order. I think this workshop was a good first step. @BIRS_Math
  56. 5/ Many many thanks to @BIRS_Math and huge kudos to @NGhoussoub for excellent service to the Canadian scientific community. BIRS is a gem.
  57. 6/ Also many thanks to the participants for their excellent talks, and to @ChrisAldrich for maintaining a Storify.