An online textbook priced at almost $1,000 has infuriated students trying to navigate an already confusing textbook marketplace, but Louisiana-Lafayette officials insist they had "good intentions."
Here publishers are marketing to professors who assign particular textbooks and subverting students which are the actual market and consumers of those textbooks. This causes an inflated market and has allowed textbook prices to spiral out of control.
The American Health Care Market
In this example, the health care providers (doctors, hospitals, etc.) have been segmented away from their consumers (patients) by intermediary insurance companies which are driving the market to their own good rather than a free-er set of smaller (and importantly local) markets that would be composed of just the sellers and the buyers. As a result, the consumer of health care has no ability to put a particular price on what they’re receiving (and typically they rarely ever ask, even more so when they have insurance). This type of economic anomie is causing terrific havoc within the area.
(Aside: while the majority of health care markets is very small in size (by distance), I will submit that the advent of medical tourism does a bit to widen potential markets, but this segment of the market is tiny and very privileged in comparison.)
In a non-economic setting it also seems to be highly applicable to social media silos like Facebook, Twitter, et al as they break social norms. I’ll have to circle back to write a longer essay about this with regard to the IndieWeb movement.
Hundreds of colleges are signing on to publishers’ programs, with apparent savings to students. Some applaud the movement, while others are skeptical.
Highlights, Quotes, Annotations, & Marginalia
The “inclusive” aspect of the model means that every student has the same materials on the first day of class, with the charge included as part of their tuition. ❧
It almost sounds to me like they know they’re not getting a cut of the money from poorer students who are finding the material for free online anyway, so they’re trying to up the stakes of the piece of pie that they’re getting from a different angle.
This other model of subscription at the level of the college or university is also one that they’re well aware of based on involvement with subscription fees for journal access.
August 21, 2018 at 10:17PM
She said that her institution, which has inclusive-access agreements with more than 25 publishers, had saved students more than $2 million this semester alone. Morrone said this figure was calculated by taking the retail price of a textbook, subtracting the cost that students paid for the equivalent etextbook and then dividing the cost saving in half to account for the fact that many students would not have bought the book new. ❧
$ 2million compared to what? To everyone having purchased the textbooks at going rates before? This is a false comparison because not everyone bought new in the first place. Many bought used, and many more still probably either pirated, borrowed from a friend, from the library, or simply went without.
August 21, 2018 at 10:21PM
Students like the convenience of the system, said Anderson, and all have access to the most up-to-date content, instead of some students having different editions of the same textbook. ❧
They’re also touting the most up-to-date content here, when it’s an open secret that for the majority of textbooks don’t really change that much from edition to edition.
August 21, 2018 at 10:24PM
A key difference between inclusive access and buying print textbooks is that students effectively lease the content for the duration of their course, rather than owning the material. If students want to download the content to access it beyond the duration of their course, there is often an additional fee. ❧
So now we need to revisit the calculation above and put this new piece of data into the model.
Seriously?! It’s now a “rental price”?
August 21, 2018 at 10:26PM
Campus stores are often the ones driving inclusive-access initiatives, as they receive a cut of the sales. While the profit margins are smaller than for print, inclusive access means that the stores receive revenue from a larger number of customers. Donovan Garcia, course materials manager at the University of Mary Washington, said that lower margins were also mitigated by lower overheads. “We’re not purchasing books, we’re not paying shipping, we’re not having to put any time or effort into returning unused books or paying restocking fees,” said Garcia. ❧
I suspect the publisher is also saving on sales commissions to their sales staff as well.
August 21, 2018 at 10:27PM
Access our free college textbooks and low-cost learning materials.
Friday, I made a visit to my campus bookstore, and I bought my books. The guy who runs Tusculum’s bookstore, Cliff Hoy, is a great guy, and the work that Tusculum’s bookstore does is fi…
I’ve spent some time talking about open pedagogy at several universities this Spring, and in each of those presentations and workshops, I have usually mentioned The Open Anthology of Earlier American Literature, an OER anthology that my students and I produced last year for an American literature survey course I taught. When I talk about the anthology, it’s usually to make a point about open pedagogy. I began the project with the simple desire to save my students about $85 US, which is how much they were (ostensibly) paying for the Heath Anthology of American Literature Volume A. Most of the actual texts in the Heath were public domain texts, freely available and not under any copyright restrictions. As the Heath produced new editions (of literature from roughly 1400-1800!), forcing students to buy new textbooks or be irritatingly out of sync with page numbers, and as students turned to rental markets that necessitated them giving their books back at the end of the semester, I began to look in earnest for an alternative.
Highlights, Quotes, Annotations, & Marginalia
Most of the actual texts in the Heath were public domain texts, freely available and not under any copyright restrictions. As the Heath produced new editions (of literature from roughly 1400-1800!), forcing students to buy new textbooks or be irritatingly out of sync with page numbers, and as students turned to rental markets that necessitated them giving their books back at the end of the semester, I began to look in earnest for an alternative. ❧
Repackaging public domain texts and charging a steep markup too much above and beyond the cost of the paper is just highway robbery. Unless a publisher is adding some actual annotative or analytical value, they shouldn’t be charging outrageous prices for textbooks of this nature.
August 13, 2018 at 12:14PM
If OER is free, what hidden costs exist in its production? Making these textbooks is taking me a chunk of time in the off-season. Thanks to my salaried position, I feel ok about putting in the overtime, but it’s a privilege my colleagues who teach under year-to-year part-time non-contracts can’t afford. Who should be funding OER creation? Institutions? Students? For-profit start-ups? How will you invest time in this project without obscuring the true costs of academic labor? Right now, we pass the corruptly high cost of academic publishing onto the backs of academia’s most vulnerable members: students. But as OER gains steam, we need to come up with funding models that don’t land us back in the same quagmire of exploitation that we were trying to get out of. ❧
This is a nearly perfect question and something to watch in the coming years.
August 13, 2018 at 12:35PM
working in public, and asking students to work in public, is fraught with dangers and challenges. ❧
August 13, 2018 at 12:36PM
What David told me was his energy, enthusiasm in the class was at a much higher level with the OER approach. Sure we choose the polished “professional” textbook because of its assumed high standards, quality etc, but then its a more passive relationship a teacher has with it. I make the comparison to growing and/or making your own food versus having it prepared or taking it out of a package. Having produced our own food means we know everything about it from top to bottom, and the pride in doing that has to make the whole experience much more energized. ❧
As I read both this post and this comment from Alan, I can’t help but think again about scholars in the 14th century who taught students. It was more typical of the time that students were “forced” to chose their own textbooks–typically there were fewer, and at the advent of the printing press they were significantly higher in price. As a result students had to spend more time and attention, as Robin indicates here, to come up with useful things.
Even in this period students often annotated their books, which often got passed on to other students and even professors which helped future generations. So really, we’re not reinventing the wheel here, we’re just doing it anew with new technology that makes doing it all the easier.
As a reference, I’ll suggest folks interested in this area read Owen Gingerich’s The Book Nobody Read which I recall as being one of the texts I’ve read that references early teaching and textbook practices during that time period.
August 13, 2018 at 12:44PM
Teachers need to do a better job of providing options, flexibility, and guidance in the panoply of choices available to students of all income levels and abilities. Increased choice at the student level will drastically improve both the literal and proverbial marketplace of ideas.
Here’s some additional detail I wrote on this day a few years back:
A great new book has me thinking about ed tech.
In ed tech, schools are the customers, but students are the users.
This also reminds me of the market disconnect between students and their textbooks. Professors are the ones targeted for the “sale” or adoption when the actual purchasers are the students. This causes all kinds of problems in the way the textbook market works and tends to drive prices up–compared to a market in which the student directly chooses their textbook. (And the set up is not too dissimilar to how the healthcare industry works in which the patient (customer) is making a purchase of health care coverage and not actually the health care itself.
Education and publishing giant Pearson is drawing criticism after using its software to experiment on over 9,000 math and computer science students across the country. In a paper presented Wednesday at the American Association of Educational Research, Pearson researchers revealed that they tested the effects of encouraging messages on students that used the MyLab Programming educational software during 2017's spring semester.
I do know, however, that there were a few who couldn’t make part of the Fall course, but who had some foundation in the subject and wanted to join us for the more advanced portion in the second half. Toward that end, below are the details for the course:
Introduction to Complex Analysis: Part II | MATH X 451.41 – 350370
Complex analysis is one of the most beautiful and practical disciplines of mathematics, with applications in engineering, physics, and astronomy, to say nothing of other branches of mathematics. This course, the second in a two-part sequence, builds on last quarter’s development of the differentiation and integration of complex functions to extend the principles to more sophisticated and elegant applications of the theory. Topics to be discussed include conformal mappings, Laurent series and meromorphic functions, Riemann surfaces, Riemann Mapping Theorem, analytical continuation, and Picard’s Theorem. The course should appeal to those whose work involves the application of mathematics to engineering problems, and to those interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.
Time: 7:00PM to 10:00PM
Dates: Jan 10, 2017 to Mar 28, 2017
Contact Hours: 33.00
Location: UCLA, Math Sciences Building
Course Fee(s): $453.00
Available for Credit: 3 units
Instructors: Michael Miller
No refund after January 24, 2017.
Class will not meet on one Tuesday to be announced.
For many who will register, this certainly won’t be their first course with Dr. Miller–yes, he’s that good! But for the newcomers, I’ve written some thoughts and tips to help them more easily and quickly settle in and adjust: Dr. Michael Miller Math Class Hints and Tips | UCLA Extension
If you’d like additional details as well as lots of alternate textbooks, see the announcement for the first course in the series.
If you missed the first quarter and are interested in the second quarter but want a bit of review or some of the notes, let me know in the comments below.
I look forward to seeing everyone in the Winter quarter!
Introduction to Complex Analysis
Complex analysis is one of the most beautiful and useful disciplines of mathematics, with applications in engineering, physics, and astronomy, as well as other branches of mathematics. This introductory course reviews the basic algebra and geometry of complex numbers; develops the theory of complex differential and integral calculus; and concludes by discussing a number of elegant theorems, including many–the fundamental theorem of algebra is one example–that are consequences of Cauchy’s integral formula. Other topics include De Moivre’s theorem, Euler’s formula, Riemann surfaces, Cauchy-Riemann equations, harmonic functions, residues, and meromorphic functions. The course should appeal to those whose work involves the application of mathematics to engineering problems as well as individuals who are interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.
Basic calculus or familiarity with differentiation and integration of real-valued functions.
MATH X 451.37 – 268651 Introduction to Complex Analysis
Time 7:00PM to 10:00PM
Dates Tuesdays, Sep 20, 2016 to Dec 06, 2016
Contact Hours 33.00
Location: UCLA, Math Sciences Building
Standard credit (3.9 units) $453.00
Instructor: Michael Miller
Register Now at UCLA
For many who will register, this certainly won’t be their first course with Dr. Miller — yes, he’s that good! But for the newcomers, I’ve written some thoughts and tips to help them more easily and quickly settle in and adjust:
Dr. Michael Miller Math Class Hints and Tips | UCLA Extension
I often recommend people to join in Mike’s classes and more often hear the refrain: “I’ve been away from math too long”, or “I don’t have the prerequisites to even begin to think about taking that course.” For people in those categories, you’re in luck! If you’ve even had a soupcon of calculus, you’ll be able to keep up here. In fact, it was a similar class exactly a decade ago by Mike Miller that got me back into mathematics. (Happy 10th math anniversary to me!)
I look forward to seeing everyone in the Fall!
Dr. Miller is back from summer vacation and emailed me this morning to say that he’s chosen the textbook for the class. We’ll be using Complex Analysis with Applications by Richard A. Silverman. 
(Note that there’s another introductory complex analysis textbook from Silverman that’s offered through Dover, so be sure to choose the correct one.)
As always in Dr. Miller’s classes, the text is just recommended (read: not required) and in-class notes are more than adequate. To quote him directly, “We will be using as a basic guide, but, as always, supplemented by additional material and alternate ways of looking at things.”
The bonus surprise of his email: He’s doing two quarters of Complex Analysis! So we’ll be doing both the Fall and Winter Quarters to really get some depth in the subject!
If you’re like me, you’ll probably take a look at some of the other common (and some more advanced) textbooks in the area. Since I’ve already compiled a list, I’ll share it:
- Complex Analysis by Joseph Bak and Donald J. Newman 
- Complex Analysis by Theodore Gamelin 
- Complex Variables and Applications by James Brown and Ruel Churchill 
- Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics by Edward Saff and Arthur D. Snider (Pearson, 2014, 3rd edition) 
- Complex Analysis by Lars Ahlfors 
- Complex Analysis by Serge Lang 
- Functions of One Complex Variable (Graduate Texts in Mathematics by John B. Conway (Springer, 1978) 
- Complex Analysis (Princeton Lectures in Analysis, No. 2) by Elias M. Stein and Rami Shakarchi (Princeton University Press, 2003) 
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:
— Alicia Wise (@wisealic) March 14, 2016
— Alicia Wise (@wisealic) March 14, 2016
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.
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.)
Most public libraries use systems like Overdrive, Axis 360 (Baker & Taylor), Adobe Digital Editions, 3M Cloud Library, etc. to allow students to check out a broad array of fiction and non-fiction for free for loan terms from as short as a week up to a month or more. Additionally well-known websites like the Project Gutenberg and Archive.org have lots of commonly used texts available for free download in a broad variety of formats. This includes a lot of classic fiction, philosophy, and other texts used in the humanities. Essentially most works published in the United States prior to 1923 and many additional texts published after this as well can be found in the public domain. Additional information on what is in the public domain can be found here: Copyright Term and Public Domain in the United States.
Why pay $10-20 for a classic book like Thomas Hobbes’ Leviathan when you can find copies for free online, unless of course you’re getting a huge amount of additional scholarship and additional notes along with it.
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.
Hint: Abe Books (a subsidiary of Amazon) is better than most at finding/sourcing international editions of textbooks.
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.)
- Students Get Savvier About Textbook Buying | The Chronicle of Higher Education (1/27/13)
- Study Indicates College Textbook Piracy is on the Rise, But Fails to Call Out Publishers for Skyrocketing Prices | TechDirt.com (9/23/14)
- How Slugbooks Subverts the Dirty Tricks of the College Textbook Market | Fast Company (4/14/14)
- More students are illegally downloading college textbooks for free | Washington Post (9/17/14)
- Why digital natives prefer reading in print. Yes, you read that right. | Washington Post (2/22/15)
- A Smarter Approach to College Textbooks | Inside HigherEd (8/18/15)
- (Update 8/26/15): Great article via Attn: Here’s Exactly Why College Textbooks are So Expensive | Attn: (3/12/15)
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.
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!