Many academics are using academic related social platforms (silos) like Mendeley, Academia.edu, Research Gate and many others to collaborate, share data, and publish their work. (And should they really be trusting that data to those outside corporations?)
A few particular examples: I follow physicist John Carlos Baez and mathematician Terry Tao who both have one or more academic blogs for various topics which they POSSE work to several social silos including Google+ and Twitter. While they get some high quality response to posts natively, some of their conversations are forked/fragmented to those other silos. It would be far more useful if they were using webementions (and Brid.gy) so that all of that conversation was being aggregated to their original posts. If they supported webmentions directly, I suspect that some of their collaborators would post their responses on their own sites and send them after publication as comments. (This also helps to protect primacy and the integrity of the original responses as the receiving site could moderate them out of existence, delete them outright, or even modify them!)
While it’s pretty common for researchers to self-publish (sometimes known as academic samizdat) their work on their own site and then cross-publish to a pre-print server (like arXiv.org), prior to publishing in a (preferrably) major journal. There’s really no reason they shouldn’t just use their own personal websites, or online research journals like yours, to publish their work and then use that to collect direct comments, responses, and replies to it. Except possibly where research requires hosting uber-massive data sets which may be bandwidth limiting (or highly expensive) at the moment, there’s no reason why researchers shouldn’t self-host (and thereby own) all of their work.
Instead of publishing to major journals, which are all generally moving to an online subscription/readership model anyway, they might publish to topic specific hubs (akin to pre-print servers or major publishers’ websites). This could be done in much the same way many Indieweb users publish articles/links to IndieWeb News: they publish the piece on their own site and then syndicate it to the hub by webmention using the hub’s endpoint. The hub becomes a central repository of the link to the original as well as making it easier to subscribe to updates via email, RSS, or other means for hundreds or even thousands of researchers in the given area. Additional functionality could be built into these to support popularity measures as well to help filter some of the content on a weekly or monthly basis, which is essentially what many publishers are doing now.
In the end, citation metrics could be measured directly on the author’s original page by the number of incoming webmetions they’ve received on it as others referencing them would be linking to them and therefore sending webmentions. (PLOS|One does something kind of like this by showing related tweets which mention particular papers now: here’s an example.)
Naturally there is some fragility in some of this and protective archive measures should be taken to preserve sites beyond the authors lives, but much of this could be done by institutional repositories like University libraries which do much of this type of work already.
I’ve been meaning to write up a much longer post about how to use some of these types of technologies to completely revamp academic publishing, perhaps I should finish doing that soon? Hopefully the above will give you a little bit of an idea of what could be done.
Thanks for the thoughts here Liz. Somehow I hadn’t heard of ReadCube, but it looks very interesting and incredibly similar to Mendeley‘s set up and functionality. I’ve been using Mendeley for quite a while now and am reasonably happy with it, particularly being able to use their bookmarklet to save things for later and then do reading and annotations within the material. If researchers in your area are using Mendeley’s social features, this is also a potential added benefit, though platforms like Academia and ResearchGate should be explored as well.
Given their disparate functionalities, you may be better off choosing one of Evernote and OneNote and separately Mendeley or ReadCube. Personally I don’t think the four are broadly interchangeable though they may be easier to work with in pairs for their separate functionalities. While I loved Evernote, I have generally gone “all in” on OneNote because it’s much better integrated with the other MS Office tools like email, calendar, and my customized to do lists there.
Another interesting option you may find for sorting/organizing thousands of documents is Calibre e-book management. It works like an iTunes but for e-books, pdfs, etc. If you use it primarily for pdfs, you can save your notes/highlights/marginalia in them directly. Calibre also allows for adding your own meta-data fields and is very extensible. The one thing I haven’t gotten it to do well (yet) is export for citation management, though it does keep and maintain all the meta data for doing so. One of the ways that Mendeley and ReadCube seem to monetize is by selling a subscription for storage so if this is an issue for you, you might consider Calibre as a free alternative.
I’ve been ever working on a better research workflow, but generally prefer to try to use platforms on which I own all the data or it’s easily exportable and then own-able. I use my own website on WordPress as a commonplace book of sorts to capture all of what I’m reading, writing, and thinking about–though much of it is published privately or saved as drafts/pending on the back end of the platform. This seems to work relatively well and makes everything pretty easily searchable for later reference.
Here are some additional posts I’ve written relatively recently which may help your thinking about how to organize things on/within your website if you use it as a research tool:
I’ve also recently done some significant research and come across what I think is the most interesting and forward-thinking WordPress plugin for academic citations on my blog: Academic Blogger’s Toolkit. It’s easily the best thing currently on the market for its skillset.
Another research tool I can’t seem to live without, though it may be more specific to some of the highly technical nature of the math, physics, and engineering I do as well as the conferences/workshops I attend, is my Livescribe.com Pulse pen which I use to take not only copious notes, but to simultaneously record the audio portion of those lectures. The pen and technology link the writing to the audio portion directly so that I can more easily relisten/review over portions which may have been no so clear the first time around. The system also has an optional and inexpensive optical character recognition plugin which can be used for converting handwritten notes into typed text which can be very handy. For just about $200 the system has been one of the best investments I’ve made in the last decade.
If you haven’t come across it yet, I also highly recommend regularly reading the ProfHacker blog of the Chronicle of Higher Education which often has useful tips and tools for academic research use. They also do a very good job of covering some of the though in the digital humanities which you might find appealing.
Oddly, I had seen the VERY same post/repo a few weeks back and meant to add a readme too! (You’ll notice I got too wrapped up in reading through the code and creating some usability issues after installing the plugin instead.)
Given that you’ve got your own domain and website (and playing in ed/tech like many of us are), and you’re syndicating your blog posts out to Medium for additional reach, I feel compelled to mention some interesting web tech and philosophy in the #IndieWeb movement. You can find some great resources and tools at their website.
In particular, you might take a look at their WordPress pages which includes some plugins and resources you’ll be sure to appreciate. One of their sets of resources is allowing you to not only syndicate your WP posts (what they call POSSE), but by using the new W3C webmention spec, you can connect many of your social media resources to brid.gy and have services like twitter, facebook, G+, instagram and others send the comments and likes on your posts there back to your blog directly, thereby allowing you to own all of your data (as well as the commentary that occurs elsewhere). I can see a lot of use for education in some of the infrastructure they’re building and aggregating there. (If you’re familiar with Known, they bake a lot of Indieweb goodness into their system from the start, but there’s no reason you shouldn’t have it for your WordPress site as well.)
If you need any help/guidance in following/installing anything there, I’m happy to help.
An exclusive look at data from the controversial web site Sci-Hub reveals that the whole world, both poor and rich, is reading pirated research papers.
Sci Hub has been in the news quite a bit over the past half a year and the bookmarked article here gives some interesting statistics. I’ll preface some of the following editorial critique with the fact that I love John Bohannon’s work; I’m glad he’s spent the time to do the research he has. Most of the rest of the critique is aimed at the publishing industry itself.
From a journalistic standpoint, I find it disingenuous that the article didn’t actually hyperlink to Sci Hub. Neither did it link out (or provide a full quote) to Alicia Wise’s Twitter post(s) nor link to her rebuttal list of 20 ways to access their content freely or inexpensively. Of course both of these are editorial related, and perhaps the rebuttal was so flimsy as to be unworthy of a link from such an esteemed publication anyway.
Sadly, Elsevier’s list of 20 ways of free/inexpensive access doesn’t really provide any simple coverage for graduate students or researchers in poorer countries which are the likeliest group of people using Sci Hub, unless they’re going to fraudulently claim they’re part of a class which they’re not, and is this morally any better than the original theft method? It’s almost assuredly never used by patients, which seem to be covered under one of the options, as the option to do so is painfully undiscoverable past their typical $30/paper firewalls. Their patchwork hodgepodge of free access is so difficult to not only discern, but one must keep in mind that this is just one of dozens of publishers a researcher must navigate to find the one thing they’re looking for right now (not to mention the thousands of times they need to do this throughout a year, much less a career).
Consider this experiment, which could be a good follow up to the article: is it easier to find and download a paper by title/author/DOI via Sci Hub (a minute) versus through any of the other publishers’ platforms with a university subscription (several minutes) or without a subscription (an hour or more to days)? Just consider the time it would take to dig up every one of 30 references in an average journal article: maybe just a half an hour via Sci Hub versus the days and/or weeks it would take to jump through the multiple hoops to first discover, read about, and then gain access and then download them from the over 14 providers (and this presumes the others provide some type of “access” like Elsevier).
Those who lived through the Napster revolution in music will realize that the dead simplicity of their system is primarily what helped kill the music business compared to the ecosystem that exists now with easy access through the multiple streaming sites (Spotify, Pandora, etc.) or inexpensive paid options like (iTunes). If the publishing business doesn’t want to get completely killed, they’re going to need to create the iTunes of academia. I suspect they’ll have internal bean-counters watching the percentage of the total (now apparently 5%) and will probably only do something before it passes a much larger threshold, though I imagine that they’re really hoping that the number stays stable which signals that they’re not really concerned. They’re far more likely to continue to maintain their status quo practices.
Some of this ease-of-access argument is truly borne out by the statistics of open access papers which are downloaded by Sci Hub–it’s simply easier to both find and download them that way compared to traditional methods; there’s one simple pathway for both discovery and download. Surely the publishers, without colluding, could come up with a standardized method or protocol for finding and accessing their material cheaply and easily?
“Hart-Davidson obtained more than 100 years of biology papers the hard way—legally with the help of the publishers. ‘It took an entire year just to get permission,’ says Thomas Padilla, the MSU librarian who did the negotiating.” John Bohannon in Who’s downloading pirated papers? Everyone
Personally, I use use relatively advanced tools like LibX, which happens to be offered by my institution and which I feel isn’t very well known, and it still takes me longer to find and download a paper than it would via Sci Hub. God forbid if some enterprising hacker were to create a LibX community version for Sci Hub. Come to think of it, why haven’t any of the dozens of publishers built and supported simple tools like LibX which make their content easy to access? If we consider the analogy of academic papers to the introduction of machine guns in World War I, why should modern researchers still be using single-load rifles against an enemy that has access to nuclear weaponry?
My last thought here comes on the heels of the two tweets from Alicia Wise mentioned, but not shown in the article:
She mentions that the New York Times charges more than Elsevier does for a full subscription. This is tremendously disingenuous as Elsevier is but one of dozens of publishers for which one would have to subscribe to have access to the full panoply of material researchers are typically looking for. Further, Elsevier nor their competitors are making their material as easy to find and access as the New York Times does. Neither do they discount access to the point that they attempt to find the subscription point that their users find financially acceptable. Case in point: while I often read the New York Times, I rarely go over their monthly limit of articles to need any type of paid subscription. Solely because they made me an interesting offer to subscribe for 8 weeks for 99 cents, I took them up on it and renewed that deal for another subsequent 8 weeks. Not finding it worth the full $35/month price point I attempted to cancel. I had to cancel the subscription via phone, but why? The NYT customer rep made me no less than 5 different offers at ever decreasing price points–including the 99 cents for 8 weeks which I had been getting!!–to try to keep my subscription. Elsevier, nor any of their competitors has ever tried (much less so hard) to earn my business. (I’ll further posit that it’s because it’s easier to fleece at the institutional level with bulk negotiation, a model not too dissimilar to the textbook business pressuring professors on textbook adoption rather than trying to sell directly the end consumer–the student, which I’ve written about before.)
(Trigger alert: Apophasis to come) And none of this is to mention the quality control that is (or isn’t) put into the journals or papers themselves. Fortunately one need’t even go further than Bohannon’s other writings like Who’s Afraid of Peer Review? Then there are the hordes of articles on poor research design and misuse of statistical analysis and inability to repeat experiments. Not to give them any ideas, but lately it seems like Elsevier buying the Enquirer and charging $30 per article might not be a bad business decision. Maybe they just don’t want to play second-banana to TMZ?
Interestingly there’s a survey at the end of the article which indicates some additional sources of academic copyright infringement. I do have to wonder how the data for the survey will be used? There’s always the possibility that logged in users will be indicating they’re circumventing copyright and opening themselves up to litigation.
I also found the concept of using the massive data store as a means of applied corpus linguistics for science an entertaining proposition. This type of research could mean great things for science communication in general. I have heard of people attempting to do such meta-analysis to guide the purchase of potential intellectual property for patent trolling as well.
Finally, for those who haven’t done it (ever or recently), I’ll recommend that it’s certainly well worth their time and energy to attend one or more of the many 30-60 minute sessions most academic libraries offer at the beginning of their academic terms to train library users on research tools and methods. You’ll save yourself a huge amount of time.
His response was probably innocuous enough, but I thought the article should be put to task a bit more.
“35 million academics, independent scholars and graduate students as users, who collectively have uploaded some eight million texts”
35 million users is an okay number, but their engagement must be spectacularly bad if only 8 million texts are available. How many researchers do you know who’ve published only a quarter of an article anywhere, much less gotten tenure?
“the platform essentially bans access for academics who, for whatever reason, don’t have an Academia.edu account. It also shuts out non-academics.”
They must have changed this, as pretty much anyone with an email address (including non-academics) can create a free account and use the system. I’m fairly certain that the platform was always open to the public from the start, but the article doesn’t seem to question the statement at all. If we want to argue about shutting out non-academics or even academics in poorer countries, let’s instead take a look at “big publishing” and their $30+/paper paywalls and publishing models, shall we?
“I don’t trust academia.edu”
Given his following discussion, I can only imagine what he thinks of big publishers in academia and that debate.
“McGill’s Dr. Sterne calls it “the gamification of research,”
Most research is too expensive to really gamify in such a simple manner. Many researchers are publishing to either get or keep their jobs and don’t have much time, information, or knowledge to try to game their reach in these ways. And if anything, the institutionalization of “publish or perish” has already accomplished far more “gamification”, Academia.edu is just helping to increase the reach of the publication. Given that research shows that most published research isn’t even read, much less cited, how bad can Academia.edu really be? [Cross reference: Reframing What Academic Freedom Means in the Digital Age]
If we look at Twitter and the blogging world as an analogy with Academia.edu and researchers, Twitter had a huge ramp up starting in 2008 and helped bloggers obtain eyeballs/readers, but where is it now? Twitter, even with a reasonable business plan is stagnant with growing grumblings that it may be failing. I suspect that without significant changes that Academia.edu (which is a much smaller niche audience than Twitter) will also eventually fall by the wayside.
The article rails against not knowing what the business model is or what’s happening with the data. I suspect that the platform itself doesn’t have a very solid business plan and they don’t know what to do with the data themselves except tout the numbers. I’d suspect they’re trying to build “critical mass” so that they can cash out by selling to one of the big publishers like Elsevier, who might actually be able to use such data. But this presupposes that they’re generating enough data; my guess is that they’re not. And on that subject, from a journalistic viewpoint, where’s the comparison to the rest of the competition including ResearchGate.net or Mendeley.com, which in fact was purchased by Elsevier? As it stands, this simply looks like a “hit piece” on Academia.edu, and sadly not a very well researched or reasoned one.
In sum, the article sounds to me like a bunch of Luddites running around yelling “fire”, particularly when I’d imagine that most referred to in the piece feed into the more corporate side of publishing in major journals rather than publishing it themselves on their own websites. I’d further suspect they’re probably not even practicing academic samizdat. It feels to me like the author and some of those quoted aren’t actively participating in the social media space to be able to comment on it intelligently. If the paper wants to pick at the academy in this manner, why don’t they write an exposé on the fact that most academics still have websites that look like they’re from 1995 (if, in fact, they have anything beyond their University’s mandated business card placeholder) when there are a wealth of free and simple tools they could use? Let’s at least build a cart before we start whipping the horse.
For academics who really want to spend some time and thought on a potential solution to all of this, I’ll suggest that they start out by owning their own domain and own their own data and work. The #IndieWeb movement certainly has an interesting philosophy that’s a great start in fixing the problem; it can be found at http://www.indiewebcamp.com.
You can now highlight and annotate most of the pages here on Boffo Socko as well as other web pages.
I’d played around with many of them in the past, but a recent conversation with Matt Gross about News Genius and their issues in the last week reminded me about internet annotation platforms. Since some of what I write here is academic in nature, I thought I would add native Hypothes.is Annotation support to the site.
If you haven’t heard about it before, you might find the ability to highlight and annotate web pages very useful. Hypothesis allows for public or private highlights and notes and it can be a very useful extension of one’s commonplace book.
At the moment, I’m not sure where it all fits into the IndieWeb infrastructure I’m building here, but, at least for the moment, I’d hope that those making public annotations and notes will also enter their commentary into the comments either here on the blog or by way of syndicated versions on Facebook or Twitter so that they’re archived here for posterity. (Keep in mind site-deaths are prevalent and even Hypothes.is acknowledges in a video on their homepage that there have been many incarnations of web annotations that have come and gone in the life of the internet.) Perhaps one day there will be a federated and cross-linked version of highlights and annotations in the IndieWeb universe with webmentions included?!
Educators and researchers interested in using web annotation are encouraged to visit the wealth of information provided by providers like Hypothes.is and Genius.com. In particular, the Hypothes.is blog has some great material and examples over the past year, and they have a special section for educators as well.
As it’s similar in functionality to highlighting on the web, I’ll remind users that we also still support Kevin Marks’sfragmentions as well.
If anyone is aware of people or groups working on the potential integration of the IndieWeb movement (webmentions) and web annotation/highlighting, please include them in the comments below–I’d really appreciate it.
It’s almost like they write some of this stuff just for me. Though I was already aware of most of the movies they mentioned, they did miss a few:
Washington Square (1997) directed by Agnieszka Holland in Hollywood Pictures/Caravan Pictures production has a stunning cameo of the interior of the Peabody Library – this cameo is the only reason I vaguely remember the film at all.
The Johns Hopkins Science Review (1948-1955) This production is also particularly notable as being the television debut (October 8, 1951) of actor and alum John Astin who now heads the JHU Drama program and for whom the eponymous theater in the Merrick Barn is named.
Fratricide (1966) – A very independent short black and white film (with no credits) starring professor Richard Macksey that was produced by a group of students which included later Hollywood luminaries Walter Murch (who just a few years later co-wrote THX 1138 with George Lucas), Caleb Deschanel, and Matthew Robbins, who coincidentally co-wrote Crimson Peak with Guillermo del Torro which comes out in theaters today.
I have a nagging feeling there are a few more, but they’re just not coming to me at the moment…
By the way, for those suffering through Head of State, you should know in advance that the Shriver Hall scene doesn’t appear until the very end of the movie and then plays through the credits.
An informal orientation for those taking math classes from Dr. Michael Miller through UCLA Extension.
Congratulations on your new math class, and welcome to the “family”!
Invariably the handful of new students every year eventually figure the logistics of campus out, but it’s easier and more fun to know some of the options available before you’re comfortable halfway through the class. To help get you over the initial hump, I’ll share a few of the common questions and tips to help get you oriented. Others are welcome to add comments and suggestions below. If you have any questions, feel free to ask anyone in the class, we’re all happy to help.
First things first, for those who’ve never visited UCLA before, here’s a map of campus to help you orient yourself. Using the Waze app on your smartphone can also be incredibly helpful in getting to campus more quickly through the tail end of rush hour traffic.
Whether you’re a professional mathematician, engineer, physicist, physician, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of Dr. Miller’s math courses, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (from actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years (and yes, he’s THAT good — we’re sure you’ll be addicted too.) Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past Calculus or Linear Algebra, this is bound to be the most entertaining thing you can do with your Tuesday nights in the Autumn and Winter. 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. 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.
Don’t be intimidated if you feel like everyone in the class knows each other fairly well — most of us do. Dr. Miller and mathematics can be addictive so many of us have been taking classes from him for 5-20+ years, and over time we’ve come to know each other.
Tone of Class
If you’ve never been to one of Dr. Miller’s classes before, they’re fairly informal and he’s very open to questions from those who don’t understand any of the concepts or follow his reasoning. He’s a retired mathematician from RAND and long-time math professor at UCLA. Students run the gamut from the very serious who read multiple textbooks and do every homework problem to hobbyists who enjoy listening to the lectures and don’t take the class for a grade of any sort (and nearly every stripe in between). He’ll often recommend a textbook that he intends to follow, but it’s never been a “requirement” and more often that not, the bookstore doesn’t list or carry his textbook until the week before class. (Class insiders will usually find out about the book months before class and post it to the Google Group – see below).
His class notes are more than sufficient for making it through the class and doing the assigned (optional) homework. He typically hands out homework in handout form, so the textbook is rarely, if ever, required to make it through the class. Many students will often be seen reading various other texts relating to the topic at hand as they desire. Usually he’ll spend an 45-60 minutes at the opening of each class after the first to go over homework problems or questions that anyone has.
For those taking the class for a grade or pass/fail, his usual policy is to assign a take home problem set around week 9 or 10 to be handed in at the penultimate class. [As a caveat, make sure you check his current policy on grading as things may change, but the preceding has been the usual policy for a decade or more.]
Lot 9 – Located at the northern terminus of Westwood Boulevard, one can purchase a parking pass for about $12 a day at the kiosk in the middle of the street just before Westwood Blvd. ends. The kiosk is also conveniently located right next to the parking structure. If there’s a basketball game or some other major event, Lot 8 is just across the street as well, though it’s just a tad further away from the Math Sciences Building. Since more of the class uses this as their parking structure of choice, there is always a fairly large group walking back there after class for the more security conscious.
Lot 2 – Located off of Hilgard Avenue, this is another common option for easy parking as well. While fairly close to class, not as many use it as it’s on the quieter/darker side of campus and can be a bit more of a security issue for the reticent.
Tip: For those opting for on-campus parking, one can usually purchase a quarter-long parking pass for a small discount at the beginning of the term.
Westwood Village and Neighborhood – Those looking for less expensive options street parking is available in the surrounding community, but use care to check signs and parking meters as you assuredly will get a ticket. Most meters in the surrounding neighborhoods end at either 6pm or 8pm making parking virtually free (assuming you’re willing to circle the neighborhood to find one of the few open spots.)
Broxton Avenue Public Parking at 1036 Broxton Avenue just across from the Fox Village and Bruin Theaters – $3 for entering after 6pm / $9 max for the day
Geffen Playhouse Parking at 10928 Le Conte Ave. between Broxton and Westwood – price varies based on the time of day and potential events (screenings/plays in Westwood Village) but is usually $5 in the afternoon and throughout the evening
More often than not a group of between 4 and 15 students will get together every evening before class for a quick bit to eat and to catch up and chat. This has always been an informal group and anyone from class is more than welcome to join. Typically we’ll all meet in the main dining hall of Ackerman Union (Terrace Foodcourt, Ackerman Level 1) between 6 and 6:30 (some with longer commutes will arrive as early as 3-4pm, but this can vary) and dine until about 6:55pm at which time we walk over to class.
The food options on Ackerman Level 1 include Panda Express, Rubio’s Tacos, Sbarro, Wolfgang Puck, and Greenhouse along with some snack options including Wetzel’s Pretzels and a candy store. One level down on Ackerman A-level is a Taco Bell, Carl’s Jr., Jamba Juice, Kikka, Buzz, and Curbside, though one could get takeout and meet the rest of the “gang” upstairs.
There are also a number of other on-campus options as well though many are a reasonable hike from the class location. The second-closest to class is the Court of Sciences Student Center with a Subway, Yoshinoya, Bombshelter Bistro, and Fusion.
Naturally, for those walking up from Westwood Village, there are additional fast food options like In-N-Out, Chick-fil-A, Subway, and many others.
For those who’ve already eaten or aren’t hungry, you’ll often find one or more of us browsing the math and science sections of the campus bookstore on the ground level of Ackerman Union to kill time before class. Otherwise there are usually a handful of us who arrive a half an hour early and camp out in the classroom itself (though this can often be dauntingly quiet as most use the chance to catch up on reading here.) If you arrive really early, there are a number of libraries and study places on campus. Boelter Hall has a nice math/science library on the 8th Floor.
Mid-class Break Options
Usually about halfway through class we’ll take a 10-12 minute coffee break. For those with a caffeine habit or snacking urges, there are a few options:
Kerckhoff Hall Coffee Shop is just a building or two over and is open late as snack stop and study location. They offer coffee and various beverages as well as snacks, bagels, pastries, and ice cream. Usually 5-10 people will wander over as a group to pick up something quick.
The Math Sciences Breezeway, just outside of class, has a variety of soda, coffee, and vending machines with a range of beverages and snacks. Just a short walk around the corner will reveal another bank of vending machines if your vice isn’t covered. The majority of class will congregate in the breezeway to chat informally during the break.
The Court of Sciences Student Center, a four minute walk South, with the restaurant options noted above if you need something quick and more substantial, though few students use this option at the break.
Bathrooms – The closest bathrooms to class are typically on the 5th floor of the Math Sciences Building. The women’s is just inside the breezeway doors and slightly to the left. The men’s rooms are a bit further and are either upstairs on the 6th floor (above the women’s), or a hike down the hall to the left and into Boelter hall. I’m sure the adventurous may find others, but take care not to get lost.
Informal Class Resources
Over the years, as an informal resource, members of the class have created and joined a private Google Group (essentially an email list-serv) to share thoughts, ideas, events, and ask questions of each other. There are over 50 people in the group, most of whom are past Miller students, though there are a few other various mathematicians, physicists, engineers, and even professors. You can request to join the private group to see the resources available there. We only ask that you keep things professional and civil and remember that replying to all reaches a fairly large group of friends. Browsing through past messages will give you an idea of the types of posts you can expect. The interface allows you to set your receipt preferences to one email per message posted, daily digest, weekly digest, or no email (you’re responsible for checking the web yourself), so be sure you have the setting you require as some messages are more timely than others. There are usually only 1-2 posts per week, so don’t expect to be inundated.
Depending on students’ moods, time requirements, and interests, we’ve arranged informal study groups for class through the Google Group above. Additionally, since Dr. Miller only teaches during the Fall and Winter quarters, some of us also take the opportunity to set up informal courses during the Spring/Summer depending on interests. In the past, we’ve informally studied Lie Groups, Quantum Mechanics, Algebraic Geometry, and Category Theory in smaller groups on the side.
As a class resource, some of us share a document repository via Dropbox. If you’d like access, please make a post to the Google Group.
Many people within the class use Livescribe.com digital pens to capture not only the written notes but the audio discussion that occurred in class as well (the technology also links the two together to make it easier to jump around within a particular lecture). If it helps to have a copy of these notes, please let one of the users know you’d like them – we’re usually pretty happy to share. If you miss a class (sick, traveling, etc.) please let one of us know as the notes are so unique that it will be almost like you didn’t miss anything at all.
You can typically receive a link to the downloadable version of the notes in Livescribe’s Pencast .pdf format. This is a special .pdf file but it’s a bit larger in size because it has an embedded audio file in it that is playable with the more recent version of Adobe Reader X (or above) installed. (This means to get the most out of the file you have to download the file and open it in Reader X to get the audio portion. You can view the written portion in most clients, you’ll just be missing out on all the real fun and value of the full file.) With the notes, you should be able to toggle the settings in the file to read and listen to the notes almost as if you were attending the class live.
Viewing and Playing a Pencast PDF
Pencast PDF is a new format of notes and audio that can play in Adobe Reader X or above.
You can open a Pencast PDF as you would other PDF files in Adobe Reader X. The main difference is that a Pencast PDF can contain ink that has associated audio—called “active ink”. Click active ink to play its audio. This is just like playing a Pencast from Livescribe Online or in Livescribe Desktop. When you first view a notebook page, active ink appears in green type. When you click active ink, it turns gray and the audio starts playing. As audio playback continues, the gray ink turns green in synchronization with the audio. Non-active ink (ink without audio) is black and does not change appearance.
Audio Control Bar
Pencast PDFs have an audio control bar for playing, pausing, and stopping audio playback. The control bar also has jump controls, bookmarks (stars), and an audio timeline control.
Active Ink View Button
There is also an active ink view button. Click this button to toggle the “unwritten” color of active ink from gray to invisible. In the default (gray) setting, the gray words turn green as the audio plays. In the invisible setting, green words seem to write themselves on blank paper as the audio plays.
For those interested in past years’ topics, here’s the list I’ve been able to put together thus far:
What's wrong with the economics of the textbook industry, and what students, parents, professors, and universities can do to mitigate the ever-rising price of textbooks.
t’s the beginning of yet another quarter/semester (or ovester, if you prefer) and a new crop of inquiries have come up around selling back used textbooks and purchasing new textbooks for upcoming classes. I’m not talking about the philosophical discussion about choosing your own textbooks that I’ve mentioned before. I’m considering, in the digital era,
What are the best options for purchasing, renting, or utilizing textbook products in what is a relatively quickly shifting market?
The popular press has a variety of evergreen stories that hit the wire at the beginning of each semester that scratch just the surface of the broader textbook issue or focus on one tiny upstart company that promises to drastically disrupt the market (yet somehow never does), but these articles never delve just a bit deeper into the market to give a broader array of ideas and, more importantly, solutions for the students/parents who are spending the bulk of the money to support the inequalities the market has built.
I aim to facilitate some of this digging and revealing based on years of personal book buying experience as well as having specified textbooks as an instructor in the past.
Most current students won’t have been born late enough that electronic files for books and texts will have been common enough to prefer them over physical texts, but with practice and time, many will prefer electronic texts in the long term, particularly as one can highlight, mark up, and more easily search, store, and even carry electronic texts.
Before taking a look at the pure economics of the market for the various forms of purchase, resale, or even renting, one should first figure out one’s preference for reading format. There are obviously many different means of learning (visual, auditory, experiential, etc.) which some will prefer over others, so try to tailor your “texts” to your preferred learning style as much as possible. For those who prefer auditory learning modes, be sure to check out alternatives like Audible or the wealth of online video/audio materials that have proliferated in the MOOC revolution. For those who are visual learners or who learn best by reading, do you prefer ebook formats over physical books? There are many studies showing the benefit of one over the other, but some of this comes down to personal preference and how comfortable one is with particular formats. Most current students won’t have been born late enough that electronic files for books and texts will have been common enough to prefer them over physical texts, but with practice and time, many will prefer electronic texts in the long term, particularly as one can highlight, mark up, and more easily search, store, and even carry electronic texts. It’s taken me (an avowed paper native) several years, but I now vastly prefer to have books in electronic format for some of the reasons indicated above in addition to the fact that I can carry a library of 2,500+ books with me almost anywhere I go. I also love being able to almost instantly download anything that I don’t currently own but may need/want.
The one caveat I’ll mention, particularly for visual learners (or those with pseudo-photographic or eidetic memory), is that they attempt to keep a two-page reading format on their e-reading devices as their long-term memory for reading will increase with the ability to place the knowledge on the part of the page(s) where they originally encountered it (that is, I remember seeing that particular item on the top left, or middle right portion of a particular page.) Sometimes this isn’t always possible due to an e-reader’s formatting capabilities or the readability of the size of the text (for example, a .pdf file on a Kindle DX would be preferable to the same file on a much smaller smartphone) , but for many it can be quite helpful. Personally, I can remember where particular words and grammatical constructs appeared in my 10th grade Latin text many years later while I would be very unlikely to be able to do this with the presentation of some modern-day e-readers or alternate technologies like rapid serial visual presentation (RSVP).
Purchasing to Keep
Personally, as a student and a bibliophile (read: bibliomaniac), I would typically purchase all of the physical texts for all of my classes. I know this isn’t a realizable reality for everyone, so, for the rest, I would recommend purchasing all of the texts (physical or electronic, depending on one’s preference for personal use) in one’s main area of study, which one could then keep for the long term and not sell back. This allows one to build a library that will serve as a long term reference for one’s primary area(s) of study.
Renting vs Short-term Ownership
In general, I’m opposed to renting books or purchasing them for a semester or year and then returning them for a partial refund. It’s rarely a great solution for the end consumer who ends up losing the greater value of the textbook. Even books returned and sold later as used, often go for many multiples of their turn in price the following term, so if it’s a newer or recent edition, it’s probably better to hold on to it for a few months and then sell it for a used price, slightly lower than the college bookstore’s going rate.
For tangential texts in classes I know I don’t want to keep for the long term, I’d usually find online versions or borrow (for free) from the local college or public library (many books are available electronically through the library or are borrow-able through the library reserve room.)
Often college students forget that they’re not just stuck with their local institutional library, so I’ll remind everyone to check out their local public library(s) as well as other nearby institutional libraries and inter-library loan options which may give them longer term loan terms.
General Economics in the Textbook Market
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.the US Supreme Court upheld the ability for US-based students to buy copies of textbooks printed in foreign countries (often at huge cut-rate prices) [see also Ars Technica]. This means that searching online bookstores in India, Indonesia, Pakistan, etc. will often find the EXACT same textbooks (usually with slightly different ISBNs, and slightly cheaper paper) for HUGE discounts in the 60-95% range.
Example: I recently bought an international edition of Walter Rudin’s Principles of Mathematical Analysis (Amazon $121) for $5 (and it even happened to ship from within the US for $3). Not only was this 96% off of the cover price, but it was 78% off of Amazon’s rental price! How amazing is it to spend almost as much to purchase a book as it is to ship it to yourself!? I’ll also note here that the first edition of this book appeared in 1964 and this very popular third edition is from 1976, so it isn’t an example of “edition creep”, but it’s still got a tremendous mark up in relation to other common analysis texts which list on Amazon for $35-50.
For some of the most expensive math/science/engineering texts one can buy an edition one or two earlier than the current one. In these cases, the main text changes very little, if any, and the primary difference is usually additional problems in the homework sections (which causes small discrepancies in page number counts). If necessary, the problem sets can be easily obtained via the reserve room in the library or by briefly borrowing/photocopying problems from classmates who have the current edition. The constant “edition-churning” by publishers is mean to help prop up high textbook prices.
Definition: “Edition Churning” or “Edition Creep“: a common practice of textbook publishers of adding scant new material, if any, to textbooks on a yearly or every-other-yearly basis thereby making older editions seem prematurely obsolete and thereby propping up the prices of their textbooks. Professors who blithely utilize the newest edition of a texbook are often unknowingly complicit in propping up prices in these situations.
One may find some usefulness or convenience in traditional bookstores, particularly Barnes & Noble, the last of the freestanding big box retailers. If you’re a member of their affinity program and get an additional discount for ordering books directly through them, then it may not be a horrible idea to do so. Still, they’re paying for a relatively large overhead and it’s likely that you’ll find cheaper prices elsewhere.
These are becoming increasingly lean and many may begin disappearing over the next decade or so, much the way many traditional bookstores have disappeared in the last decade with the increasing competition online. Because many students aren’t the best at price comparison, however, and because of their position in the economic chain, many are managing to hang on quite well. Keep in mind that many campus bookstores have fine print deals in which they’ll match or beat pricing you find online, so be sure to take advantage of this fact, particularly when shipping from many services will make an equivalent online purchase a few dollars more expensive.
There are fewer and fewer of these around these days and even fewer textbook-specific stores that traditionally sprouted up next to major campuses. This last type may not be a horrible place to shop, but they’re likely to specialize in used texts of only official texts. Otherwise, general used bookstores are more likely to specialize in paperbacks and popular used fiction and have very lean textbook selection, if any.
Naturally when shopping for textbooks there are a veritable wealth of websites to shop around online including: Amazon, Alibris, Barnes & Noble, AbeBooks, Google Play, Half/EBay. Chegg, Valore, CampusBookRentals, TextBooks.com, and ECampus. But in the Web2.0 world, we can now uses websites with even larger volumes of data and meta-data as a clearing-house for our shopping. So instead of shopping and doing price comparison at the dozens of competing sites, why not use a meta-site to do the comparison for us algorithmically and much more quickly.
There are a variety of meta-retailer shopping methods including several browser plugins and comparison sites (Chrome, Firefox, InvisibleHand, PriceBlink, PriceGong, etc.) that one can install to provide pricing comparisons, so that, for example, while shopping on Amazon, one will see lower priced offerings from their competitors. However, possibly the best website I’ve come across for cross-site book comparisons is GetTextbooks.com. One can easily search for textbooks (by author, title, ISBN, etc.) and get back a list of retailers with copies that is sortable by price (including shipping) as well as by new/used and even by rental availability. They even highlight one entry algorithmicly to indicate their recommended “best value”.
Similar to GetTextbooks is the webservice SlugBooks, though it doesn’t appear to search as many sites or present as much data.
When searching for potential textbooks, don’t forget that one can “showroom” the book in one’s local bookstore or even at one’s local library(s). This is particularly useful if one is debating whether or not to take a particular class, or if one is kicking tires to see if it’s really the best book for them, or if they should be looking at other textbooks.
From an economic standpoint, keep in mind there is usually more availability and selection on editions bought a month or so before the start of classes, as often-used texts are used by thousands of students over the world, thus creating a spot market for used texts at semester and quarter starts. Professors often list their textbooks when class listings for future semesters are released, so students surfing for the best deals for used textbooks can very often find them in mid-semester (or mid-quarter) well before the purchasing rush begins for any/most titles.
And finally, there is also the black market (also known as outright theft), which is usually spoken of in back-channels either online or in person. Most mainstream articles which reference this portion of the market usually refer tangentially to a grey market in which one student passes along a .pdf or other pirated file to fellow students rather than individual students being enterprising enough to go out hunting for their own files.
Most will know of or have heard about websites like PirateBay, but there are a variety of lesser-known torrent sites which are typically hosted in foreign countries which extend beyond the reach of the United States Copyright law enforcement. Increasingly, mega-pirate websites in the vein of the now-defunct Library.nu (or previously Gigapedia) or the slowly dying empire of Library Genesis are hiding all over the web and become quick and easy clearing houses for pirated copies of ebooks, typically in .pdf or .djvu formats, though many are in .epub, .mobi, .azw, or alternate e-book formats. The typical set up for these sites is one or more illegal file repositories for allowing downloads with one (or more) primary hubs that don’t necessarily store the pirated materials, but instead serve as a searchable hub which points to the files.
Creative advanced searches for book authors, titles, ISBNs along with the words .pdf, .djvu, torrent, etc. can often reveal portions of this dark web. Naturally, caveat emptor applies heavily to these types of sites as often files can be corrupted or contain viruses to unwary or unwitting thieves. Many of these sites may attempt to extract a small token monthly fee as a subscription or will rely heavily on serving banner advertising to help to offset large web hosting and traffic fees associated with their maintenance, though it is posited that many of them make in the millions of dollars in profit annually due to advertising arrangements, though this is incredibly hard to validate given the nature of these types of markets and how they operate.
Rather than stoop as low as finding textbooks on the black market this way, students should place pressure on their professors, the faculty of their departments, and their colleges or universities to help assist in smoothing out some of the pricing inequities in the system (see below). In the long run, this will not only tend to help them, but many future generations of students who will be left adrift in the market otherwise.
Long Term Solution(s) to Improving the Textbook Market
The biggest primary issue facing the overpriced textbook market is that the end consumers of the textbooks aren’t really firmly in charge of the decision of which textbook to purchase. This is why I advocate that students research and decide by themselves which textbook they’re going to use and whether or not they really need to make that purchase. Instead, individual professors or the departments for which they work are dictating the textbooks that will be purchased. The game theory dynamics behind this small decision are the massive fulcrum which allows the publishing industry to dictate their own terms. Students (and parents) should, in a sense, unionize and make their voices heard not only to the professors, but to the departments and even the colleges/universities which they’re attending. If universities took a strong stance on how the markets worked, either for or against them and their students, they could create strong market-moving forces to drastically decrease the cost of textbooks.
The other larger issue is that market forces aren’t allowed to play out naturally in the college textbook market. Publishers lean on professors and departments to “adopt” overpriced textbooks. These departments in turn “require” these texts and students aren’t questioning enough to use other texts for fear of not succeeding in courses. If the system were questioned, they’d realize that instead of their $200-300 textbook, they could easily purchase alternate, equivalent, and often even better textbooks for $20-50. To put things into perspective, the time, effort, energy, and production cost for the typical book isn’t drastically different than the average textbook, yet we’re not paying $250 for a copy of the average new hardcover on the best seller list. I wouldn’t go so far as to say that universities, departments, and professors are colluding with publishers, but they’re certainly not helping to make the system better.
I’ve always taken the view that the ‘required’ textbook was really just a ‘suggestion’. (Have you ever known a professor to fail a student for not purchasing the ‘required’ textbook?!)
In past generations, one of the first jobs of a student was to select their own textbook. Reverting back to this paradigm may help to drastically change the economics of the situation. For the interested students, I’ve written a bit about the philosophy and mechanics here: On Choosing Your Own Textbooks.
Basic economics 101 theory of supply and demand would typically indicate to us that basic textbooks for subjects like calculus, intro physics, or chemistry that are used by very large numbers of students should be not only numerous, but also very cheap, while more specialized books like Lie Groups and Lie Algebras or Electromagnetic Theory should be less numerous and also more expensive. Unfortunately and remarkably, the most popular calculus textbooks are 2-5 times more expensive than their advanced abstract mathematical brethren and similarly for introductory physics texts versus EM theory books.
To drastically cut down on these market inequities, when possible, Colleges and Universities should:
Heavily discourage “edition creep” or “edition churning” when there really aren’t major changes to textbooks. In an online and connected society, it’s easy enough to add supplemental errata or small amounts of supplemental material by means of the web.
Quit making institution-specific readers and sub-editions of books for a specific department
If they’re going to make departmental level textbook choices, they should shoulder the burden of purchasing all the textbooks in quantity (and taking quantity discounts). I’ll note here, that students shouldn’t encourage institutions to bundle the price of textbooks into their tuition as then there is a “dark curtain,” which allows institutions to take the drastic mark-ups for themselves instead of allowing the publishers to take it or passing it along to their students. Cross-reference Benjamin Ginsberg’s article Administrators Ate My Tuition or his much longer text The Fall of the Faculty (Oxford University Press, 2013).
Discourage the use of unpopularly used textbooks written by their own faculty. Perhaps a market share of 5-10% or more should be required for a common textbook to be usable by a department, and, until that point, the professor should compete aggressively to build market share? This may help encourage professors to write new original texts instead of producing yet-another-introductory-calculus-textbook that no one needs.
Discourage packaged electronic supplemental materials, which
are rarely used by students,
could be supplied online for free as a supplement,
and often double or triple the price of a textbook package.
Strongly encourage professors to supply larger lists of relatively equivalent books and encourage their students to make their purchase choices individually.
Consider barring textbook sales on campus and relying on the larger competitive market to supply textbooks to students.
Calibre: E-book and Document Management Made Simple
As an added bonus, for those with rather large (or rapidly growing) e-book collections, I highly recommend downloading and using the free Calibre Library software. For my 2000+ e-books and documents, this is an indispensable program that is to books as iTunes is to music. I also use it to download dozens of magazines and newspapers on a daily basis for reading on my Kindle. I love that it’s under constant development with weekly updates for improved functionality. It works on all major OSes and is compatible with almost every e-reader on the planet. Additionally, plug-ins and a myriad of settings allow for additional extensibility for integration with other e-book software and web services (for example: integration with GoodReads or the ability to add additional data and meta-data to one’s books.)
Be sure to read through the commentary on some of these posts for some additional great information.
What other textbook purchasing services and advice can you offer the market?
I invite everyone to include their comments and advice below as I’m sure I haven’t covered the topic completely or there are bound to be new players in the space increasing competition as time goes by.
Math textbooks often seem difficult, obtuse, and often incomprehensible. Here are some hints and tips for making the situation better for all students.
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.
“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
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.
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):
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
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.
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:
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!