Biomedical and Electrical Engineer with interests in information theory, evolution, genetics, abstract mathematics, microbiology, big history, IndieWeb, mnemonics, and the entertainment industry including: finance, distribution, representation
Ben, some great food for thought here. I like the idea of a framework with the ability to adapt. I'm definitely going to borrow this.
If your example mentioning accounting coursework is more than an example, you could probably (quickly) get a lot out of a standard textbook on "Financial Accounting" which is typically a cornerstone course in any MBA program. The basics don't change much, so almost any used text in the past twenty years will give you what you're looking for. There are also many free/inexpensive online courses (coursera, edX, etc.) if you search for MOOC and financial accounting.
@dsifford My case will not likely be seen frequently in the first place, so I suspect that your fix should handle the largest number of cases. I don't think one would ever(?) face the issue with respect to journal articles and it's probably only books where it may crop up. In most modern book titles it's relatively infrequent that books will have the same title (usually for marketing purposes) but it may happen in cases like mine here, where some of the texts are older.
The only other potential issue I might see is if someone were doing an analysis of multiple editions of the same book by the same authors and they wanted to cite them all separately. In this case, possibly saving the ISBN field as the unique identifier for the book may be more useful, though it might not differentiate between slightly different "updates" (or corrected versions) of some text editions. (Off hand I know that Springer will often release moderate updates--usually with corrected typos--of a particular edition of a textbook without changing the edition number or the ISBN and some might want to potentially cite slightly different corrections of the same edition of a book.
There may also be edge cases in which one might want to separately cite a pre-print of a journal article (an early draft, on arXiv.org as an example) and then separately cite the final published article with potential updates. You'll then also likely run into this type of matching issue where you'll have the same title and authors but different publications with different dates.
If you want to get into super-edge-cases, there are some areas of scholarship in which one may also be studying time-varying versions of texts as in the Roman De La Rose Project [http:/
I highly suspect that your proposed fix will handle the largest majority of cases as I can't think of an actual real-world example of any of the edge cases I mention in the preceding three paragraphs other than the Roman de la Rose project.
@Jacob_Biamonte @manlius84 Diagram is from the Cover/Thomas textbook Elements of Information Theory, see also http:/
reference request - Relation between Group theory and Information theory - Theoretical Computer Science Stack Exchange
http:/
Sadly, group structure is nearly so limited that there isn't much one can do with it to be of use in information theory, thus the literature is prone to be fairly sparse. Even Abelian groups aren't enough structure.
Even basic abstract algebra texts which have some basic coding theory applications generally provide examples using field theory or linear algebra. If there were useful examples for groups, they'd most likely be introduced there.
- [Hungerford, Thomas; Abstract Algebra: An Introduction][1]
- [Rotman,J.J.; A First Course in Abstract Algebra, Third Edition][2]
As most of Rotman's work was in group theory, if anyone would have had examples there, certainly he would. Steven Roman at UCI also did a good bit of textbook writing (separately) on coding theory and field theory and has a text [Fundamentals of Group Theory: An Advanced Approach (Birkhauser)][3], but not having read it, I suspect you'll find it barren of the group theoretical work you're looking for.
In the late 90's I seem to recall some work on binary codes defined by using codes over the alphabet $ \mathbb {Z}_4$. For some background (and possible references) see [J.H. van Lint's Introduction to Coding Theory, Third Edition (Springer, 1999)][4].
Once you take the algebraic step up to even finite fields, you're far more likely to find overlap with more coding theory. For this, try taking a look at [Error-Correcting Linear Codes: Classification by Isometry and Applications (Springer) by Betten, Braun, et al.][5] which may have some scant material on applications to groups as I recall.
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Shoniqua: This is a poor conspiracy theory at best.
Given the tight margins in publishing math texts, it's my experience that any but the top .01% actually make any real profit for the authors. Given my experience the vast majority of math textbook authors actually want to give away the answers and actually help students. in the past several years, I've directly emailed math professors who've written textbooks for help and advice and most of them have actually replied, not only promptly, but typically with more information that I requested about particular problems and often with full solutions, and in many cases they've sent met full sets of solutions for their entire texts and in a few other cases, they've sent me full electronic copies of their texts for free!
I'll also note, there's also been a growing trend for mathematicians to reserve the right to publish electronic copies of their books on their personal websites where they make them freely available to students.
<i>Manny wrote: "I see Jacobson was an expert on Lie algebras... yes, that might certainly be useful! Thanks..."</i>
Many/most graduate math texts on Lie Groups/Algebras utilize manifold theory as their basis, which can make the field more daunting for physicists. As a result, I recommend looking at books that take a more linear algebraic bent to the subject, which can make some of the quantum mechanics related areas more transparent. I've used [book:Lie Groups, Lie Algebras, and Representations: An Elementary Introduction|1051566], [book:Matrix Groups for Undergraduates.|1162374], and [book:Lie Groups, Lie Algebras, and Some of Their Applications|424103] for these types of applications and viewpoints.
About a year ago, I took a two quarter sequence at UCLA on Lie Groups from an ("easier") matrix group perspective which I imagine you may find somewhat useful in your reading on quantum mechanics. Several engineers, programmers, amateur mathematicians, physicists, and quantum mechanics enthusiasts had spent several years coaxing the professor into teaching it from this perspective. It was geared toward the advanced undergraduate level, and based on your comments here and your reading of Shankar, should be relatively easily followable.
We loosely followed Hall's textbook and portions of [book:Matrix Analysis|647523], which will give you some of the advanced linear algebra you could possibly be missing depending on your background. If it helps, here's a link to a downloadable pdf copy of the notes for the first class with the audio of the lecture embedded (using Livescribe.com digital pen technology which should let you click on the notes and jump to the audio portion related to where you've clicked): http:/
Having this background may make Weyl and Woit's developing textbook more easily manageable. My guess is that Woit is doing a more thorough job of developing the math than typical physics-oriented texts like [book:Geometry, Topology and Physics|439357] which do a lot of hand-waving at the math in an effort to get to the physics more quickly, but at the detriment of understanding what is happening mathematically.
I've dipped into some of Weyl's work in the past, but also keep in mind that some of his notation and definitions can be dated in relation to more modern presentations.
A general foothold into the overlap of maximum entropy methods and biology:
John Harte's work on applying the mathematical theory of maximum entropy to ecology is certainly one of the better known examples of the application of this area of mathematics to science, in part because he literally wrote the textbook: [Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Series in Ecology and Evolution)][1]
To be clear, maximum entropy (also known as MaxEnt in some of the literature, though most/all researchers use the longer form in publications) is a mathematical tool stemming from the fields of probability theory, statistics, and information theory. It's use is classically most often seen in thermodynamics, statistical thermodynamics, physics, and information theory, primarily because these were the areas in which E.T. Jaynes was working when he posited the idea. [Wikipedia has links to his two seminal papers.][2]But because of it's mathematical form, it can be applied in a multitude of areas, typically where one can utilize probabilistic methods.
If you're looking for additional areas of application, simply google the phrase "applied maximum entropy" and you'll find a [wealth of areas][3] including: econometrics, natural language processing, nuclear medicine, queuing systems, mass spectrometry, image processing, machine learning, and many others.
For ecology related work, a cross search on maximum entropy and "genetics", "evolution", "species", and similar words will provide a wealth of papers like ["A maximum entropy approach to species distribution modeling"][4].
Given the generic nature of your question, I might suggest that you'll find E.T. Jaynes' paper ["On the Rationale of Maximum-Entropy Methods" (IEEE, 1982)][5] useful.
Those generally interested in the broader applications of information theoretic methods to biology will likely appreciate some of the work that came out of last year's [NIMBioS Workshop on Information and Entropy in Biological Systems][6] (which Harte both attended and presented at), the [BIRS Workshop Biological and Bio-Inspired Information Theory][7], and the 2014 [CECAM Entropy in Biomolecular Systems][8]. The NIMBios Workshop was organized by John Baez, a physicist, who has worked with MaxEnt methods and explored them on his blog "[Azimuth][9]".
Those with a more sophisticated mathematical background (including measure theory, functional analysis, etc.) may appreciate Henryk Gzyl's text [The Method of Maximum Entropy (World Scientific: Series on Advances in Mathematics for Applied Sciences, Vol 29, 1995)][10].
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It actually looks like you're missing one of the biggest -- and now, according to the Supreme Court, legal -- new loopholes for cheap textbooks.
One of the most important changes in the textbook market that every buyer should be aware of: last year in Kirtsaeng v. John Wiley & Sons, Inc. [http:/
To stick with your math example: I recently bought an international edition of Walter Rudin's Principles of Mathematical Analysis (Amazon $121 http:/
Hint: Abe Books (a subsidiary of Amazon http:/
The same Calculus textbook you mentioned as a Sixth Edition can be easily found in paperback for $55.44 (I only did one search to find it, but I'm sure a little elbow grease might cut the price further) and ships within the US for less than $10. And because many students are apt to take the multi-variable calculus course as a follow up, this textbook also includes that material as an added bonus as well. http:/
The other option you leave out is purchasing the fifth edition, which isn't substantially different from the 6th edition and which can be easily found for less than $6 in good condition and including shipping.
Of course all this belies the true discussion of the how's and why's for why the textbook market is overpriced in the first place. For some of those ideas and suggestions of how we can fix them, I've written a short essay: "To Purchase, Rent, or Pirate? The Broken Economics of Textbooks in the Digital Age" http:/
This is a great article pinpointing the primary issue along with some more helpful advice on fixing the larger textbook problem than most of the traditional ever-green articles that hit the wire just prior to the start of a new term! However, if Congress is going to take steps, they may be better off trying to regulate the industry back into a more competitive shape, but this as unlikely to happen as the current Congressional plan. Instead, I'd recommend that students, professors, and universities fix the problem for the publishers by changing the word "Required" to "Recommended" in every syllabus in the country. Doing this would help allow students to pay as much for textbooks as they do for the average bestseller, which average about $15 and generally doesn't go over $40, even in hardback.
I've written some more specific details and thoughts on the roots of the issue here: "To Purchase, Rent, or Pirate? The Broken Economics of Textbooks in the Digital Age" http:/
Thanks BI, for helping to not only highlight the problem, but to push solutions. Given the thesis of Cesar Hidalgo's recent text "Why Information Grows", one of the greatest business issues America faces is making it easier for information to disseminate within our culture, and the excessive cost of textbooks and education is going to have drastic effects on our culture and country in the coming century.
I'm presuming they won't let him bring the book home? I'll bet that if you can wait a few weeks into the school year you'll find a handful of used copies begin to hit the market, but I HIGHLY doubt that the 6th edition is substantively different from the 4th or 5th edition which you can probably get for pennies on the dollar. (Outside of David Christian's Big History concept (https:/
For an AP class, you may be better off buying some supplementary popular non-fiction books (eg. Genghis Khan and the Making of the Modern World; Cleopatra: A Life; Guns, Germs & Steel; The Landmark Thucydides, anything written by Simon Winchester) which are likely to be more interesting, entertaining, and informative than the "assigned" textbook. They'll help reinforce not only material, but reading skills, and critical thinking. You could also check to see if international editions exist yet and buy one of those at a steep discount (see the link in the article).
Digging around in free online MOOC's can also reveal some excellent non-textbooks and references (like Jeremy Edelman's History of the World Since 1300 https:/
You can also find some additional ideas via: http:/
Category Theory certainly isn't useless, and has some really beautiful and interesting things going on. One of the bigger issues it has is that it is relatively so young as a discipline within math. (Imagine what people said about set theory in 1910.) Your toughest hurdle as an undergraduate is finding a university that is offering it as an accessible class depending on your level of mathematical background. I haven't noticed a lot of universities even offering it at the graduate level yet either.
That being said, David Spivak's new book Category Theory for the Sciences which came out of MIT Press last year is the closest textbook I've seen to attempt making Category Theory easily accessible to not only an undergraduate audience, but also to a broader range of scientists who are not necessarily steeped in mathematics. For your particular purposes, it actually has a nice handful of biology related examples in the early chapters.
Because it expounds on some of the beauty of category theory and it's application to science, I'll draw your attention to an essay that Ilyas Khan wrote recently: https:/
I'd recommend category theory more highly, if you plan on pursuing a Ph.D. and research work, but in the meanwhile you might also find some interesting material in John Carlos Baez's Azimuth blog or on the n-Category Cafe.
My @Quora answer to Where do you prefer to order textbooks from? http:/
First I make sure that it's a good textbook and compare it to others: On Choosing Your Own Textbooks [http:/
However, when making the final purchase, I'll often redirect/reset the affiliate code so that the purchase supports one of several specific charities.
Free textbook: Abstract and Concrete Categories: The Joy of Cats
Abstract and Concrete Categories was published by John Wiley and Sons, Inc, in 1990, and after several reprints, the book has been sold out and unavailable for several years. We now present an improved and corrected version as an open access file. This was made possible due to the return of copyright to the authors, and due to many hours of hard work and the exceptional skill of Christoph Schubert, to whom we wish to express our profound gratitude. The illustrations of Edward Gorey are unfortunately missing in the current version (for copyright reasons), but fortunately additional original illustrations by Marcel Erné, to whom additional special thanks of the authors belong, counterbalance the loss.
Open access includes the right of any reader to copy, store or distribute the book or parts of it freely. (See the GNU Free Documentation License at the end of the text.)
#categorytheory #mathematics #textbook
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