Five Free Calculus Textbooks

Ben Crowell writes: "The economics of college textbooks is goofy, because the person who picks the book isn't the person who has to pay for it. Combined with the increasing consolidation of the publishing industry, this has blown the lid off of textbook prices over the last decade. But remember what the World-Wide Web was basically about before the Dot-Com Detour? It wasn't about marketing dog food, it was about democratizing publishing. Many textbook authors these days are using the internet to bypass the traditional publishing system, making their books available for free downloading. Although MIT's Open Courseware project gets most of the press, the movement started before that, and is going strong. In this article, I've reviewed five calculus textbooks that are either free as in speech or free as in beer." Read on for Crowell's take on each of the five books he's selected -- and pass the review on to any math teachers you know.

(See each)
author	(See each)
pages	(See each)
publisher	(See each)
rating	(See each)
reviewer	Ben Crowell
ISBN	(n/a)
summary	(See each)

First-Year Calculus Notes
author	Paul Garrett
pages	70
URL	http://www.math.umn.edu/~garrett/calculus/
rating	7/10
summary	Would make a good concise refresher.

The author provides this book in PDF format. As far as I can tell from the somewhat ambiguous notice on his web page, the book is intended to be licensed under the GPL copyleft license. That warms my heart as an open-source enthusiast, but it's slightly strange, for a couple of reasons. First, the GPL is a software license, and is less suitable as a copyleft license for books than the GFDL or a CC license. Also, the source code of the book isn't available (it appears to have been done in LaTeX), which I think makes it legally impossible under the GPL to redistribute the book, whereas the author's intent in GPL-ing it was presumably to make it freely distributable. Just as I was in the process of submitting this review to Slashdot, the author replied to an e-mail I'd sent him about this, and it sounds like he's interested in clearing up this issue, and really does want his book to be free as in speech.

This is a lively and very readable treatment of basic calculus. At 70 pages, it's a welcome antidote to the usual bloated textbooks, and the topics that are included match up pretty well with my own opinions of what it's really vital for a student to know after taking a calculus course. The tone is conversational without being condescending or cutesy, and the author almost always explains why he's introducing something, rather than just throwing it at the reader. (An unfortunate exception is the opening section on inequalities.) There is no attempt at rigor whatsoever, which I consider to be a feature, not a bug. Applications are discussed, although not enough for my taste (and I have to suppress my gag reflex every time I see a calculus book that insists on presenting the acceleration of gravity in non-metric units).

Although the book comes with some of the paraphernalia of a complete college textbook, such as homework problems, it's probably not the kind of book that another professor could just adopt as a stand-alone text, nor would I recommend it for someone learning calculus on her own for the first time. The title suggests that the author had in mind more of a memory aid, or a way to keep students from having to scribble madly in their notebooks for an hour and a half at a stretch. It lacks an index and illustrations, and there are some misfeatures in terms of organization: the chapters aren't numbered, and the homework problems are scattered around where they're hard to find. In some cases it sounds as though the first time a word or concept is used, he's assuming the reader has already heard it defined. I would, however, recommend this book to someone who needs to refresh her memory of calculus, and doesn't want to spend hours wading through epsilons and deltas to get to the highlights. It might also be a good option for the student who is completely broke, and needs a reference to use in place of an officially required text that carries an exploitative price tag. Although there are other calculus textbooks that can be downloaded without paying, this is the only one I'm aware of that follows the typical order of topics, and is also (AFAICT) copylefted, so that we can be assured it needn't evaporate if the author signs a publishing contract, or loses interest in maintaining his web site.

Difference Equations to Differential Equations: An Introduction to Calculus
author	Dan Sloughter
pages	600
URL	http://math.furman.edu/~dcs/book/
rating	6/10
summary	Takes too long to get there.

Like Garrett's text, this one appears to have been done in LaTeX, is licensed under the GPL, and appears to suffer from the same legal problems, because it's not available in source form.

The book is well written, and seems to have been well designed for practical classroom use. The approach is visual and intuitive, and there are lots and lots of graphs and numerical calculations. I felt, however, that it took a long time to get going, and the idiosyncratic selection of topics might make it difficult to use at many schools. Although the very first page gives a nice clear explanation of what calculus is about, we then have to wait until about page 136 to learn any calculus. I say "about" because of the inconvenient way in which the book is split up into 54 separate PDF files, each of which has page numbers starting from 1. I had to estimate page number 136 by weighing part of the book on a postal scale. Related to this problem is the fact that the book has no index or table of contents.

The book uses many numerical examples, which gives it a modern feeling . After all, calculus was invented by Newton and Leibniz because they needed to do calculations in closed form, but nowadays it's more natural to solve many problems on a computer, using a spreadsheet or a programming language. The book has a problem, however, in integrating the computer stuff with the didactic parts and the homework problems. No indication is given of how the numerical examples were actually computed. The author may consider it a trivial task to set up a spreadsheet or write a ten-line program in Python or Mathematica, but it's not so trivial for many students, and they will need extensive guidance from elsewhere to be able to carry out such computations for themselves. This makes the text incomplete in practical terms: any instructor wanting to use it would have to come up with extensive support materials to go with it. It also contributes to my sense that the book lacks focus. Students have a hard enough time learning the basic concepts and techniques of integration and differentiation, but to use this book, they would also have to learn about computer programming and difference equations. Adding to the bloat is the author's tendency to discuss every possible pathological case before moving on to the main event. It's a little like a parent trying to explain sex to his child, but feeling obliged to explain foot fetishes before getting on with where babies come from.

The examples that students are expected to do numerically also presuppose quite a bit of resourcefulness and insight. For instance, one of the homework problems asks the student to sum the series 4(1-1/3+1/5-1/7+...) numerically, adding up "...a sufficient number of terms to enable you to guess the value of the sum," which turns out to be pi. The trouble is that over 600 terms are required to get the sum to settle down in the second decimal place, which is about the minimum I'd want to see to convince me it was pi. Pity the poor student who first tries 10 terms on a calculator, then 50 terms on a spreadsheet, and then finally realizes he's going to need to write a Python program to get the job done. Of course, some students might enjoy the process, but my experience (teaching college science majors taking introductory physics) is that the majority don't consider computers to be fun.

Lectures on Calculus
author	Evgeny Shchepin
pages	143
URL	http://www.math.uu.se/~oleg/ShchepinCalc.html
rating	2/10
summary	Not for consumption by mere students.

This book is from a set of lectures on calculus given by visiting professor Evgeny Shchepin at Uppsala University in 2001. The first obstacle potential readers will encounter is that the book is provided in PostScript format, with hideous bitmapped type 3 fonts embedded. This makes it virtually impossible to view the book on a monitor in any legible representation, although it looks fine when you print it out. The typical Windows or MacOS user will give up long before that point. This is a shame, because it's not at all difficult these days to get LaTeX to output Adobe Acrobat files that are viewable on virtually any computer, and are legible on the screen. There is no index, and virtually no graphs or other figures.

The main question in my mind is for whom this book was written. This deep, dark forest of mathematical symbols, interspersed with ungrammatical English, is meant to follow the historical development of the subject, but it never makes it clear why the historical route is the right one to follow. There are many seemingly pointless digressions.

Is it possible that this book was meant for young people taking their first calculus course? The presence of end-of-chapter homework problems would seem to imply that it was. If so, I feel sorry for them. Although it's cute that the author manages to develop integrals before limits, and derivatives only at the very end, I somehow doubt that real, live students would read this book and exclaim, "We sure are lucky to be learning calculus using this novel order of topics!" Most of the problems begin with the words "Prove that...," and neither the text nor the problems give any of the standard applications to biology, economics, physics, etc.

Elementary Calculus: An Approach Using Infinitesimals
author	Jerome H. Keisler
pages	992
URL	http://www.math.wisc.edu/~keisler/calc.html
rating	10/10
summary	I wish I'd learned calculus from it!

Textbooks are usually unoriginal, because most teachers are conservative in their choices. They get used to teaching a subject a certain way, and don't want to change. This is a calculus textbook with a very unusual approach. It was published in 1976, and evidently was successful enough, despite its idiosyncracy, to justify a second edition a decade later. Its publisher, however, eventually allowed it to go out of print. The copyright has reverted to the author, and he has made it available in digital form on his web site. The digital book consists of pages scanned in from a printed copy and assembled into an Acrobat file, so it's a big download, and you can't do some things with it, such as searching the text for a particular word.

The title leaves no doubt that the book is different. Whereas most textbooks these days define derivatives and integrals in terms of limits, this one uses infinitesimals. The real numbers are generalized to make a number system called the hyperreal numbers, which include infinitesimally small numbers as well as infinitely large ones. Essentially, this represents a return to the way Newton and Leibniz originally conceptualized the calculus, but with more rigor.

I don't know about other people, but when I learned calculus, I got very uneasy when we got to the Leibniz notation. My teacher said that dy/dx wasn't really one number divided by another, but rather an abbreviation for the limit of the quantity y/x. That wasn't so bad, but what really made me queasy was when he then suggested that you could usually get the right answer by treating these dx and dy thingies as if they were numbers. The scary part was that word "usually." What was legal and what wasn't? How many sizes of infinitesimals were there? Was it legal to say that 1/dx was infinite? What operations would lead to paradoxes? What about proofs that used infinite numbers to show that 1=2? The wonderful thing about this book is that you end up knowing exactly what you can and can't do with infinities and infinitesimals, and you get to use the Leibniz notation in all its intuitively appealing glory. For instance, the chain rule really can be proved simply by writing (dz/dy)(dy/dx)=dz/dx, simply canceling the dy's.

It would be interesting to see how students reacted to this book when learning calculus from scratch. I suspect that they'd have an easier time with many of the concepts like implicit differentiation, which seems so awkward in the traditional approach, but they might be scared a little by the initial development of the hyperreal number system. The book develops the hypperreal system axiomatically, which left me yearning for more of a constructive method. Then again, we develop the rational and real numbers axiomatically in high school, so maybe it's not such a big issue. My initial unease was cleared up by a few crucial examples:

• If H and K are infinite, then H-K may be infinite or finite -- it depends on which infinite numbers H and K are.
• If H is infinite, then (2H+1)/(H+1) isn't equal to 2, but it differs infinitesimally from 2.
• (H+1)^1/2-(H-1)^1/2 is infinitesimal.

After that, I began to see the hyperreal numbers as simply another tool for calculating things.

I confess, however, to a little residual indigestion at the way the author develops the integral. He introduces finite Reimann sums first, and gives several numerical examples. But next, instead of taking the limit of sums with more and more terms, he takes the finite sum with n terms, and replaces n with an infinite integer. Instant vertigo!

This is a wonderful, original textbook, and I hope it remains free on the web forever -- it's not copylefted, so unfortunately it may disappear if the author stops maintaining his web site.

The Calculus Bible
author	G.S. Gill
pages	370
URL	http://www.math.byu.edu/Math/CalculusBible/
rating	3/10
summary	Incomplete, and badly written.

I'm reviewing this book in February of 2004. It's clearly not a finished product, and I'm not sure whether or not the author is still actively working on it. The book is available from the Brigham Young University math department's server, but the author isn't on the department's list of faculty, which makes me think he may have moved on to another job and abandoned the book. It's provided as a PDF file. There is no copyright page and no licensing agreement, so it's hard to know the book's real legal status.

The path through the topics is pretty standard for an introductory calculus course: a review of functions and trigonometry, followed by limits, differentiation, and integration. There is a good selection of problems, although to my taste as a physicist far too few are applied to anything useful. There is a table of contents, but no index. There are no illustrations; sprinkled throughout the text are little placeholders for graphs that just say "graph."

Although the problems I've referred to so far are ones that could be fixed if the author continued to work on the book, I feel that there are some more fundamental problems with this text that will not go away unless it is extensively rewritten. The style is extremely dry, and moreover the author has a habit of introducing concepts without any explanation or preparation. A symptom of this is that the student is expected to grind through the first hundred pages without any clear statement about what calculus is, what it's good for, or even whether the initial chapters are calculus (they're not). Equal prominence is given to topics that I would consider vital (the fundamental theorem of calculus) and others that I would label as trivial (tabulations of facts) or esoteric (the Dedekind cut property).

The Leibniz notation, dy/dx, is given with only this explanation "To emphasize the fact that the derivatives are taken with respect to the independent variable x, we use the following notation, as is customary..." Huh? So are these dx and dy things numbers? Is dy/dx the quotient of them?

Even if the missing graphs were included, the approach would still be relentlessly symbolic, rather than visual. For instance, integration by parts is introduced without ever giving its geometric interpretation.

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Yeah... it's an f'en review of five calc books. The author should be committed and never allowed to enter society again.

Re:See any serious problems with this story?

So, you're saying there's a limit as reviewed_calc_books --> infinity such that in the relation

author_insanity
----------------
reviewedd_cal c_books

author_insanity approaches infinity?

Re:See any serious problems with this story?

This is a tad off-topic, but I couldn't resist tossing in another calculus goodie I saw on a LiveJournal post [livejournal.com] a while back. For those not familiar with it, MIT hosts an Integration Bee [mit.edu] every January -- kinda like a spelling bee, but with (obviously) integrating.

evelio (evelio) wrote, @ 2004-01-23 15:24:00

I love MIT

>Geek thing #1
A friend of mine won the Integration Bee at MIT. He got $50 of Certificates to Toscis (Ice cream place) and a baseball cap.

>Geek thing #2:
Another friend wrote him this poem:

I love you;
You are my hero.
My love for you is 1/x
as x approaches 0.

>Geek thing #3:
To which another friend of mine replied: Wait Wait! As x approaches zero from which direction?

Yes we are geeks. And damn proud of it too.

More useful than you think

I would have killed for a slashdot story like this 3 or 4 years ago when I was making my calc requirements. One of the best things about using the web for study is the diversity of material out there. You aren't just limited to the dead tree on your desk to help you understand the material.

BTW, Anyone studying math who hasn't been turned on to http://mathworld.wolfram.com [wolfram.com] should definitely check it out.

Re:More useful than you think

I would have killed for a slashdot story like this 3 or 4 years ago when I was making my calc requirements.

This story couldn't have been any better timing for me. I just sold my calc book back to my school because I was short on cash. It wasn't a very good calc book in the first place, but I was dissapointed to get rid of it anyways. Now, I not only know of some free ones, but I've got some reviews to help me know where to start. :)

Re:More useful than you think

I just sold my calc book back to my school because I was short on cash.

Selling your books is very short sighted. You need to be thinking more of a long term stategy like giving blood and eating Raman noodles. ;)

Re:More useful than you think

it's absolutely useful. the reviewer fails to mention, however, how limited the open courseware program is.

sad as it is (and slightly off-topic), the open courseware program is essentially a publicity stunt for MIT. most of the online courses lack complete references, let along complete lecture notes or useful guidance. nor is this a priority for MIT. OCW has gotten nothing but positive publicity, so MIT feels no need to better the program. sure, it's better than nothing, but it's a major stretch to call it courseware.

thank heavens someone is putting up useful online resources. and thank goodness someone is giving us an idea of what the are!

Re:See any serious problems with this story?

Yeah... it's an f'en review of five calc books. The author should be committed and never allowed to enter society again.

Me too ! I agree! Me too!

God forbid that anyone -- much less the readers of a site "for nerds [about] stuff that matters' should deviate from a steady diet of Star Wars, Tentacle Anime, and MMORGS.

Because it's more important to know the exact blue-prints of the X-Wing, Y-Wing and Z-Wing fighters than to understand physics -- and that the laws of physics don't actually allow the aerobatic maneuvers these fictional starships are depicted as making.

God forbid that we should know the calculus! Better we should be techno-peasants, with metaphorical manure between our toes, unable to comprehend the technical wizardry we gawp at in the movie houses.

The only reason we all have comparatively cheap PCs on our desks -- or the special effects that makes movies like Star Wars so absorbing (if inaccurate), or the ability to download Anime film or play MMORGS -- is because someone, lots of someones, took the time to learn the calculus -- and metallurgy, and materials engineering, and chemical engineering, and electrical engineering, and even computer science.

So before you "ban" the reviewer from society, please understand that the reason your sole amusement isn't getting chased by a wild boar as each of you tries to make the other lunch, is because of "dweebs" like the reviewer who care about the science and technology that created the society that allows you to have it so good and so easy.

Democratizing publishing?

"But remember what the World-Wide Web was basically about before the Dot-Com Detour? It wasn't about marketing dog food, it was about democratizing publishing."

It was about porn and you know it. Then again, perhaps that IS democratizing publishing. Never mind.

wow

fell asleep after the third paragraph....pretty much what I did in calc and analytical statistics classes in college.

Price != Quality

A calculus textbook that costs $100 to buy doesn't mean it's worth a dime. My college used one of the more popular textbooks last year, and it was one of the worst textbooks I've ever encountered.

Re:Price != Quality

I agree. Many textbooks are used because of ties to the faculty of the deptartment. For instance, if a professor at a given university writes a textbook, and has a lot of say in what goes on in the deptartment, you can be sure that soon enough most other professors in the deptartment will be using their book. It's just the way university politics go.

Re:Price != Quality

The publishers send loads of books out for free to lecturers in the hopes that the lecturer will recommend this text to the students that year.
This ends in the ludicrous situation of some lecturers having 3 different editions of the same text, and the competing/equivalent books from other publishers.
Some of the lecturers handle this well by giving surplus books away to those who ask.

Re:Price != Quality

I took an investment class a couple of semesters ago and the textbook cost $120 brand new. With a resale value of about half that, the book itself was a terrible investment.

Re:Price != Quality

Yeah, but it was the textbook they required, so you had to buy it. None of these five alternatives would do you a damn bit of good when the Prof said, "Read pages 128-154 and do problems 3.15 through 3.24 by tomorrow."

Re:Price != Quality

That's a very good point. Some years ago (when I was still in school), I found out (thanks to the strong dollar and subsidies or something), you could buy textbooks from amazon.co.uk for 25% to 50% of what you could buy in the US. So I figured, well and good, and bought all my books online. I saved several hundred dollars -- but had to buy a chemistry text book here in the US again, because I was shipped the international edition -- and the problem sets were completely different. <sighs />

Textbooks online

To second this, one of my roommates does all his textbook shopping online. I believe he uses half.com, and he reportedly *makes* money on his textbook transactions by selling them back slightly higher than he bought them for. Not much money, like $14 USD, but still, it beats losing $400 each semester...

Re:Price != Quality

Do all your lecturers do that, or are some good enough at the subject they lecture to write their own problems?

All my lecturers do that. It's not an issue of being good or bad, it's an issue of time and efficiency. You need to have a textbook anyway: not all students learn best by listening to you talk, and even those students are going to miss class every once in a while. So, since you have a textbook, why not use all it has to offer?

The other thing about writing your own problems is that, in subjects such as calculus, it's pretty easy to write problems which range from ridiculously hard to literally impossible, just by adding one little term to an otherwise simple equation. Much better to use the textbook, which has been (exhaustively, one would hope) checked for such things, and which has answers (although usually not solutions, which most teachers require) in the back of the book, which IS helpful to students.

The difference between a good teacher and a bad teacher, then, is how they respond when you ask for help on a certain problem. My highly excellent physics teacher (Leonid Minkin) reads the problem from the book, writes it on the board, and then solves it. My crappy math teacher looks up the problem in his notes, and then copies his notes onto the board, and still manages to get confused in the process. They both assign problems from the book, but one is much better than the other.

Re:Price != Quality

For relatively static topics like elementary mathematics, physics, chemistry, history, English, etc. there really is no reason to change a textbook more often than say, every 10 years (and really only so that the application sections remain relevant). I think that one of the big issues with going to a free web-based, static course text is the homework problems. See if you follow my logic: Profs are basically lazy (when it comes to teaching undergrad courses that is), and love to assign questions from the textbook - if the textbook itself is static, they have to make up their own questions, and solve them (otherwise the answers to all questions would become common knowledge after a semester or two). I took a discrete mathematics course a few years ago where I literally was able to search the web using the exact question to get answers to questions I wasn't sure of - the prof was so lazy that he was plagiarizing other assignments! Don't discount the fact that a lot of book publishers bribe profs with expensive lunches, publishing offers, etc. It wouldn't surpise me to know that less ethical profs are also taking kickbacks based on volume (which decrases significantly when used books come into play). The solution? Some profs are sympathetic to the plight of the poor student. I've e-mailed this article to two of my college professors, maybe it will cause someone to at least think about it, but I'm not hopeful. Surely a community developped, open, free (as in beer!), free (as in freedom!) textbook is superior to something written by one or two authors and reviewed by only a handful of others.

Re:Price != Quality

That's classic. Prof uses the internet to copy questions, and then the students use the internet to copy the answers. That reminds me of the story about the prof who decides that lecturing is too much work, so he records all of his lectures to tape and just lets the machine play in the classroom. Pretty soon the students get the same idea, and not long after the room is filled with tape recorders, no student or professor in sight.

Re:Statistics Textbooks?

This book [amazon.com] is worth every dollar I spent.

The author is nice too. When I couldn't figure out a problem instead of helping me, he pointed me to the pages I missed in his book (a round about way of making sure I actually bought the book no doubt, but helpful none the less).

Re:Statistics Textbooks?

I don't know about statistics, but I found this site [gatech.edu] helpful.

Then again, I'm more interested in theoretical mathematics (abstract alebra, topology, etc) than statistics. You'll find a basic probability text that may or may not help, depending on your ability.

A major missing niche in online publishing...

I am a statistician of sorts (my training isn't in statistics per se, but that's what I do research on), and I'm sorry to say that I'm not aware of any good online statistics references.

There are some sites that come close.

Mathworld [wolfram.com], for example, has some excellent reference material on statistics, but beyond some very basic or introductory material, it tends to become sparse quickly. It's typical of much of what's out there: lots of material on mathematics, but not statistics in particular. I also have ethical objections to Wolfram, and so feel uncomfortable supporting any site hosted by his company.

PlanetMath [planetmath.org]: is a good alternative to Mathworld, filling in some material that Mathworld lacks. It has the benefit of being open. However, PlanetMath suffers from the problem of being extremely disorganized. Many of the entries seem incomplete or lacking in depth. Finally, like Mathworld, it doesn't treat statistics as much as other branches of math.

HyperStat [davidmlane.com] is a good online resource for introductory statistics. I've actually referred to it a couple of times in my research when I can't remember exactly what some formula is, and don't trust my memory of it. It covers introductory material in depth, but doesn't go into fundamentals or intermediate or advanced material. It's also sort of commercial, disorganized, and poorly designed.

Statsoft Electronic Textbook [statsoft.com] covers more advanced material, but doesn't seem to provide much explanation or background. It's really more a guide to doing analyses in STATISTICA than anything else.

Finally, I've noticed the Statistics Glossary [lancs.ac.uk] more and more, but it really is a glossary more than an explanatory reference. It also doesn't get further than very introductory topics.

In short, there is a huge niche for a comprehensive, open, in depth statistics resource ala Mathworld or PlanetMath. Perhaps PlanetMath will become more organized and complete. I've thought about contributing to PlanetMath, but I don't feel completely comfortable with it.

My deepest sympathies for you sacrifice

This is the greatest act sacrifice by a reviewer since that Washington Post guy compared and contrasted the 5 latest colonoscopy devices.

All I ask of a first year calculus book:

- Lots of clear, thorough examples
- Minimize use of crazy symbols high school kids have never seen before. Or at least have a reference where you can look up what they mean.

That's all.

Re:All I ask of a first year calculus book:

- That the problems actually reflect what was "taught" in the examples.

I loved being "taught" what the examples showed and given a graded homework assignment only to find that 90% of the problems could not be solved with the given examples.

Re:Exactly.

If you need 15 examples in order to solve 15 problems on some general topic, I might suggest that you haven't learned anything.

If solving a problem becomes a monkey-see, monkey-do type of excersize where you've been trained to use specific techniques on certain homework problems, then the student is practicing a technique but not understanding the subject. If the homework problems make the student think a bit and extend those "examples" in new ways, then they might be learning. Hopefully calc students expect that at the end of the course they can solve real-world problems that haven't been solved before, and apply the tools of calculus in ways that they haven't been explicitly taught. If they can't, then the entire course was a waste of time.

A good professor should be able to help any student gain this kind of working understanding of their subject, provided the student is also willing to work as hard as necessary. But there are a lot of professors out there that aren't that good. Since students don't often have much choice in the matter, they might have to look for help elsewhere.

Another problem is that students who have spent more time rehearsing techniques (recipies) and less time actually learning math tend to do better on timed, standardized tests. So to some extent the system punishes good students and teachers.

Re:All I ask of a first year calculus book:

I loved being "taught" what the examples showed and given a graded homework assignment only to find that 90% of the problems could not be solved with the given examples.

Sorry. As a calculus teacher, my job isn't to teach you a step-by-step program for, say, maximizing a smooth function of two variables with a unique maximum on an open interval. You don't have to understand a darned thing to do that.

My job is to teach you some underlying concepts, and to give you practice using those concepts as tools to solve a variety of problems.

This means that while I will give students lots of examples, explain concepts as clearly as I possibly can, and do everything to help, I will *always* assign problems that require fundamentally different solutions from the solutions given in any of the examples.

I've seen a lot of frustrated freshman who've learned over the years to do homework by skimming a chapter quickly (if at all) before looking for the example that gives them a template to solve the particular problem. You have to get past that.

--Bruce Fields

You can contribute too.

The Wikipedia group has started a wiki textbook site [wikibooks.org], though the ones I've looked at are not very far along yet.

However, if you've got expertise you'd like to contribute to the public, that might be an easy place for you to do it.

Re:Books

>At least some people in the educational system have finally realized that open source is the future. If all educators were like this the classes would be much better.

Student: "I have a question about..."
Teacher: "RTFM!!!"
Student: "I did and I still don't understand ..."
Teacher: "Google IS YOUR FRIEND!"
Student: "I came up with 31, 208 results, most of them trying to sell me ..."
Teacher: "N3WBI3!!!"

Applied Math

Sean Mauch [caltech.edu] has a free online book covering several areas of applied mathematics. It's not complete, but I've found it useful. The page for the book is here [caltech.edu].

If you like free calculus books...

www.lightandmatter.com has some free introductory physics texts that are pretty interesting.

Re:If you like free calculus books...

Note that the author of the review is also the author of the Light and Matter [lightandmatter.com] books. Very cool guy. Erm, okay. I have a rather odd definition of "cool," but what he's doing could become very important.

Free as in Beer?

Free beer and calculus books leads to a dangerous combination:

Drinking and Deriving.

Clickable Links

First-Year Calculus Notes [umn.edu]
Difference Equations to Differential Equations: An Introduction to Calculus [furman.edu]
Lectures on Calculus [math.uu.se]
Elementary Calculus: An Approach Using Infinitesimals [wisc.edu]
The Calculus Bible [byu.edu]

Somehow...

I can't picture Homer saying "Mmmmmmm... free math. *drool*

Great, except...

...for many professors, writing textbooks provides a serious boost to their salary. I had several courses in which the professor not only wrote the text, but made serious revisions every year in order to keep his revenue stream up. So not only could you not shop around to find a better price on a new text nor buy a used copy to keep your costs down, the resale value at the end of the semester was zip.

Bookmark Story

The college bookstore near me used to give out free bookmarks for every book they sold.

They later stopped the trend because students complained about how on average you read 10 pages out of every book you purchased for each class.

The bookstore figured if people are just buying the books cause the professor said so... and the students never intend on really reading it. They mind as well maximize profit by a few cents.

Slashdot Posting of the same subject

http://slashdot.org/article.pl?sid=04/01/30/204622 6&mode=thread [slashdot.org]

This thread was about on the ridiculous pricing of college textbooks posted some time back, which can be supplementary to a book review like this

Hell hath no place in American primary

and high school textbooks.

But then again you can't find anyone riding on a yacht or playing polo in the pages of an American textbook either. The texts also can't say someone has a boyish figure, or is a busboy, or is blind, or suffers a birth defect, or is a biddy, or the best man for the job, a babe, a bookworm, or even a barbarian.

All these words are banned from U.S. textbooks on the grounds that they either elitist (polo, yacht) sexist (babe, boyish figure), offensive (blind, bookworm) ageist (biddy) or just too strong (hell which is replaced with darn or heck). God is also a banned word in the textbooks because he or she is too religious.

To get the full 500-word list of what is banned and why, consult "The Language Police," a new book by New York University professor of education Dianne Ravitch, a former education official in President George H.W. Bush's administration and a consultant to the Clinton administration.

She says she stumbled on her discovery of what's allowed and not allowed by accident because publishers insist that they do not impose censorship on their history and English textbook authors but merely apply rules of sensitivity -- which have expanded mightily since first introduced in the 1970s to weed out gender and racial bias.

Re:Hell hath no place in American primary

Honestly, I do not have a problem with this. The purpose of a textbook is to instruct a wide range of readers on a particular topic, not to provide an outlet for the author's free expression. I would certainly not be in favor of this type of standard for literary works, or for that matter in an English text which features reprints of actual stories, but for something that is strictly technical, the author's intentional and unintentional personal biases need to be removed. Textbooks are published to instruct, not for the author to make a statement.

reviewer

Who is the reviewer and what is his math background? what made it possible for him to draw these conclusions for each book? Just curious. The conclusions I can draw from his reviews would vary depending on if I were receiving the insight of a university math professor, a grad student, a practicing engineer, a regular student, and so on...

Re:reviewer

is it this Ben Cowell, from http://commoncontent.org/user/14


Name: Ben Crowell
Bio: I teach physics and astronomy at Fullerton College, a community college in southern California. I come fully equipped with a PhD in physics from Yale, but I more fondly remember my undergraduate years at UC Berkeley. On the rare occasions when I'm away from my Linux box, I like to play jazz saxophone.

Re:reviewer

I strongly suspect it is. I have corresponded with Dr. Crowell on the subject of open source/free textbooks before, and I must say that he is the most visible proponent of free textbooks around today. He has written his own free physics textbook, so he walks the walk as well as talking the talk.

10 years from now we might be looking at Dr. Crowell as the 'Linus of textbooks'.

Please check out the Wikibooks site (cited above in another post) if you are interested in contributing to the movement.

*** SPOILER WARNING ***

f(x)=x

Wheelock's Latin Grammar

I took Latin in college, which was a mistake, but that's not what this post is about.

It's about the fact that every single year, Wheelock comes out with a new and improved Latin textbook, making the old ones obsolete, so that I couldn't sell mine back to the school store and recoup a small portion of my investment.

Now, when was the last time Latin grammar changed? About 1900 years ago? They could use Latin grammar texts from 50 years ago, and they'd be as good today as they were then. It seems to me that professors are complicit in this little scam.

The same goes for calculus. My calculus text was obsolete by the time I finished the course. Did calculus change? Did they put in some brand new groundbreaking stuff about measuring curves? No, they just wanted to make sure I couldn't sell back my book for others to buy more cheaply than the "new" one.

At the University of Texas, the cost of my books made up at least 30% of my total tuition costs. How insane is that? It's a racket, plain and simple.

progress in calculus

What, you have not heard about the recent groundbreaking discoveries in calculus?

It is amazing how these textbooks manage to keep up.

Re:What is Calculus for?

I would tend to disagree. It is rather a fault of the professors who taught Calc to fail to point out the practical uses of it, or at least the possible uses of it.

I never liked math much. I could figure it out, but physics, chemistry, comp. sci were more related to the world we live in. It was later in college when I had the painful realization that without math all those disciplines (and most others) are meaningless. I regret I had not put more effort into it then, that would have made my life much easier now. For example I took a Linear Algebra course in soph. year and after the exam week I had forgotten what an eigenvector was. It would have been nice for the prof. to point out the importance and the uses of it. Now I take a Quantum Computing course and I had to go back to the 4 year old dusty Linear Algebra notes for a review.

EE students

If you're taking introductionary electric circuit classes, or classes with advanced semiconductor stuff such as transistors (devices here at OSU), a really good EE reference/textbook is "Lessons in Electric Circuits" [allaboutcircuits.com]
The original is at ibiblio.org [ibiblio.org] though.

My Free Calc Book Is Better!

My undergraduate universtiy Computer Science department had a small lobby with tables and chairs. Professors used to put their old books on the tables for students to take and keep if they found the book useful.

One day I was browsing the free books when I saw a box of brand new calculus books. It seemed odd, but I thought, "Well these books must be free". It was a nice calc book so I took one.

As I was walking out the building it occured to me that maybe sombody just put the box down for a minute to use the restroom or something. I better return the book. By the time I got back to the lobby the box was gone.

I still have the book.

Democratize publishing

Publishing already is democratic, I think what the author was railing against was capitalism, which is another matter entirely. Granted, publishing companies have taken liberties with their content and their pricing structure. But what a good publisher brings to content delivery is filtering of garbage (which is what most of these free books are), quality editing, and a vehicle to reach a wide audience. Publishing books is expensive, the average profit margin for a text books is about %35, a lot less than the margin for jeans, sneakers or routers. If publishers learn to apply their knowlege to web delivery, which few have yet to do, then we may see quality content delivered on-line for a good price.

DO NOT SLASHDOT AARON

But he has links to some free math books at his home page [endernet.org] including a link to a calculus book in progress. He also had the CRC Encyclopedia of Mathematics there back when Mathworld was offline.

Calculus textbooks should not be free!

Think of it as a confirmation dialog. When you get to the counter and the pimple faced clerk says, "Three hundred and eighteen dollars." you should hear:

"You are about to install Calculus 251. This courseware has been certified by (INSERT_NAME) University. Installing some courseware could be hazardous to your brain. Your parents deny all responsibility for the consequences should you install third party courseware. Continue with the installation of Calculus 251?"

Removing the cost for treeware is poor courseware design, as it introduces the danger of making poor choices without warning of the potential ramifications.

Of course, there is that significant portion of humanity which clicks yes, and then spends countless hours sorting out the damage from higgledy-piggledy courseware installation. The poster certainly falls into this category...

what is source? when is it open?

Also, the source code of the book isn't available (it appears to have been done in LaTeX), which I think makes it legally impossible under the GPL to redistribute the book

THis is totally a side issue, but the source thing really interests me. i don't know a lot about what format actual source code comes in, but a lot of the software I download has its souce basically in a textfile...so here's my question: is having to format the book (for presentation, headings, etc.) any different than having to put source code through a compiler, and possibly having to port? Is the source in this case really unavailable,, since the text of the document is right there to be had?
Just curious... ;)

Great review

Thanks for an interesting review! The economics of college textbooks are indeed a bit nuts, and the development of free (and especially libre) courseware is exciting. I gotta say though, if there's any course for which I think it's worth plunking down cash for a nice, well-bound, colour-printed book, it'd have to be first-year calculus. In particular I'm thinking of Stewart.

Another comment - most of these books seem to cover single-variable only - if you're going to need it eventually (as i did, being a physicist), i really think it's helpful to have vector analysis/differentiation/integration covered in the same book in a unified presentation. Again I'm thinking Stewart here.

I have read a dead-tree "calculus in order of historcal development" book before and it was a bit sticky but it was intended for more advanced maths or history-of-maths students... maybe that was the intended audience of the Shchepin book?

CHEAPER AT AMAZON.COM!

...uhhh...wait...forget it.

CBV

GPL Abuse

This article brings up an interesting issue with the GPL - many people think GPL=="Open Source" or GPL=='No Cost" and automatically use the license even in things for which it makes no sense.

I have talked to a number of authors who applied the GPL to their products thinking that it simply made the binaries "free as in beer" and were shocked that I would ask for their source code.

It appears the authors' intents were to make these texts open and freely available, but the software-oriented GPL doesn't seem to be the appropriate license for what they are trying to do.

There are even some situations in software, such as image-based systems like Smalltalk (Squeak as an example), where the GPL's orientation around classical library linkage ends up inadvertently reducing the "free as in speech"-ness.

You get what you pay for

When I was in college, our physics books were a "collaborative" book developed by Thomas Moore and "published" by McGraw-Hill. I dug one of the volumes out- it's bound with that cheesy plastic springy binder, because my college had to print it. So it's practically falling apart- whereas the textbooks from my father's classes are still looking good on his shelf in his office.

Doing your homework was fun- absolutely every problem set we did had at LEAST one mistake, to the point that our physics teacher was probably the most annoyed and frustrated of all of us as we went over our homework the next day. Every problem had to be worked out by the class together and double-checked, because the teacher's edition was wrong too! Great except when you're behind, everyone understood the problem, and you need to catch up on the curriculum schedule.

Graphs has wrong units, labels, variable names, or simply didn't exist but had problems referencing them. Equations were flat-out wrong or had typos. Page numbers and section numbers didn't match(Ie "see section 3-2 for more information on..."). Diagrams looked like they were drawn by a kid(you know, things like sailboats with triangle sails and trapezoid hulls? Flowers with smiley faces? Etc.)

The kicker? We were the second year to use the book, and the first year's class had turned in a HUGE list of corrections to Moore. The second edition sprouted even more errors, and some of the errors from the first year were never corrected. We weren't the only ones using it, either; plenty of other schools turned in corrections as well. I feel sorry for the kids at Pomona, must have been embarrassing to know other schools were using it.

OMG, I used Kiesler in 1976

I can't believe it, the Kiesler book on Infinitesimal Calculus is the text I learned from way back when I was a freshman in 1976. And it's the reason I can't do calculus AT ALL.
I was in the Honors Math program, and the program director, in a moment of insanity, decided to use Kiesler's new book with the Infinitesimals approach. But there was only one problem, the book wasn't actually IN PRINT yet. Every monday, we received a new chapter of the book's galley proofs, followed by a long session of corrections. The teacher would write the errata on the blackboard and we wrote them in our texts. This took almost the entire session. We met 3 times a week, so the errata effectively nuked 1/3 of our classroom time.
Of course, this isn't likely to be a problem in the revised 2nd edition. However, the problem with this text is that it uses a completely nonstandard approach to calculus. The Infinitesimals approach is weak on the standard methods you really study calculus FOR, like differential equations. My roommate took the regular calc course and I studied with him, learning a few standard differentiation methods. I used a few of those techniques in the midterm test, they were marked wrong (even though they were the correct answers) and got called into the teacher's office. He said, "you didn't learn that in MY COURSE, did you?" We had to do everything the hard way, with infinitesimals, which was supposed to make you a better mathematician. It didn't.
As an amusing side note, I had a scheduling conflict with another final and had to take a makeup test, I was assigned a room to take the test all by myself, the teacher said he'd come back at the end to collect the test and if I left the room, he'd assumed I cheated and he'd give me an F. During the test, the building caught on fire on an upper floor and smoke started to drift in through the ducts. A campus security cop came in the room and told me to leave. I said I wouldn't, I only had 10 more minutes left on the test and I could finish before the fire spread. The cop grabbed me and shoved me out the door. The teacher gave me an F on the final for leaving the room. I got a D+ for the course, a passing grade, and that was good enough for me.
Anyway, I suppose the main problem was that the teachers hadn't figured out how to teach Infinitesimal Calculus yet, and I suspect they still haven't. Grappling with the abstraction of hyperreal numbers is extremely impractical in a world where everyone else uses an entirely different methodology. Avoid this text if you don't want your math skills permanently damaged. I think I'll pick up one of these other freebie calc texts and learn it over from scratch.

Re:OMG, I used Kiesler in 1976

Wow, I'm really disappointed to see all the negative opinion's on Keisler's book, and the infinitesimal approach to calculus.

I happened to run across the book on Keisler's site a couple of months ago, and... I read the whole pdf through virtually non-stop. All 913 pages. This is by far the best introduction to calculus I've ever seen - very intuitive and clean.

Those of you arguing for the conventional, limits-based approach vs. the "nonstandard", infinitesimal-based approach are missing the point that the very notation in standard use for calculus (dy/dx etc.) really makes no sense without a notion of infinitesimal. Originally Newton developed calculus in terms of limits, while Leibniz used infinitesimals. Leibniz's notation won out over Newton's, because it accords with the way mathematicians intuitively think about calculus. Neither approach was on a sound mathematical footing until the limits-based approach was formalized in the 1870's. The infinitesimal-based approach was only formalized in 1960, by Robinson - the mathematical tools needed to do so were not available in the 19th century. Due to an historical accident Robinson's approach is called "nonstandard analysis", but the implication that there is anything deficient or deviant about it does not follow. (BTW, in addition to infinitesimals, the hyperreals (or "nonstandard numbers") also include infinite numbers.)

With this approach, developed in Keisler's book, not only is the notation in accord with the model, but many results are much more straightforward to understand and to prove. No more long, tedious epsilon-delta arguments. Really, the only thing complicated about using nonstandard numbers for calculus is the formal development of the hyperreals - and in this book that is relegated to a brief treatment in an appendix. It's easy enough to state and use the properties of the hyperreals without having to go through their formal mathematical construction.

I find it disheartening that the book was allowed to go out of print, and that there are now no (as far as I'm aware) current popular calculus texts using the infinitesimal-based approach. I, like the original poster, and like most students learning today, was always confused by what you could and couldn't do with dy and dx. How I wish I'd had this book 20 years ago.

The upside is that the book is now freely available on the author's site! Go get it!

Bob Hearn

This is a very heartening thing

I feel strongly about the universal access of inforamation (at least information of educational value). There will come a time when people in poor countries will have easy access to computers just as they have access to TV now. However, there may not be enough educational information available.

Open source books (where some others can create derived works too) will make the future good for all (in a statistical sense -- there will be a few that benefit from withholding information).

The main concerns are legal threats (e.g. someone like SCO saying, "All partial derivatives are derivative work of SCO"), public perception.
The perception that the free material is somehow inferior can be propagated (e.g. in societies that pride on conspicuous consumption, the people that influence decisions can make a statement against free books), and general bitterness when some contributors don't think they are given credit.

I envison a big movement of free educational books, where the educators/scientists provide information, techies volunteer effort to find effective means of publishing/presentation, and end users do QA and feedback.

A physicist will come up with a nice theory, a document designer will design a fancy document, a web kiddie will create fancy animations explaining the concept, and all will fit into a standard form of information exchange (provided a large set of people overcome egos, preconceptions and prejudices).

S

I've taken two courses with Paul Garrett

Paul Garrett, the author of the first textbook, is easily the best Math professor I encountered during my time at the University of Minnesota. I took two courses with him: Error Correcting Codes and Cryptology. Both courses used a course packet or textbook written by him. Both books were very good, and fit in with his course material very well. Last I checked, he had all of his course notes freely available, which cover much of what is in the text.

His style tends to be slightly curt, but as stated, this fits with his course. His material provides very good overviews, and strives to explain everything in 'layman's terms,' something that almost every one of his students have problems with at first. As an example, he wants factorial explained when you use it the first time (he's not so mundane to make you do this every time on every assignment, thankfully.) This means you [theoretically] could read the book start to finish without too much previous knowledge, and understand most of it.

Definitely worth a look, and if you're currently at, or going to attend, the University of Minnesota, I highly recommend you look up Garrett's courses and consider taking them.

Open Source K-12 texts can save billions

Textbooks are required by every public school, most private schools, and many home schools, and public universities in America. American public educational institutions spend several billion of tax dollars per year for textbooks. Added to this cost is the fact that K-12 textbooks have risen at three times the rate of inflation since 1992. In California alone, the annual cost for K-12 textbooks is more than $400M per year.

The textbook industry began its climb to prominence in the 1950's and 60's's, as Baby Boomers entered private and public educational institutions in unpecedented numbers. There was a real need for mass produced educational materials, and commercial textbook publishers filled the demand.

As enrollment in educational institutions continued to increase, commercial educational publishers gradually became default the suppliers of text-based educational materials.

Realizing that they had a near monopoly on the educational publishing market, commercial publishers began to raise prices and force "new editions" of classic textbooks into the market to compell new purchases, and defeat the used textbook market. Also, textbook prices began to rise precipitously; it's not unusual for a high school textbook to approach $100, or more.

Continued dependence on commercial publishers for basic textbooks has led to a "fox is living in the henhouse" situation. As a result, massive diseconomies and inefficiencies have been introduced to the academic textbook market.

We now live in a time where most consumers can walk into their neighborhood bookstore and purchase a 10th-grade level book on Euclidean Geometry for $10-15. Yet, the same curriculum material, embellished for a 10th-grade school district, can cast upwards of $100, often in addition to the purchase of required ancillary materials (teacher's guides, study guides, lab tapes, etc.).

Until recently, short of requiring every teacher (or school district) to write its own textbooks, nothing could be done about this costly situation.

With the advent of new Internet technology, and new intellectual property licensing innovations, it is now possible to create free high-quality, distributed banks of educational content. This content can published and distributed for far less than similar materials provided by commercial publishers.

Here is a listing of some well-known open source educational projects

Some new current open source content projects are as follows:

California Open Source Textbook Project (conducting pilot projects)
http://www.opensourcetext.org

Wikipedia World History Project (a beginning pilot)
http://wikibooks.org/wiki/World_History_Pr oject

MIT's OpenCourseWare project (a university =based open curriculum project)
http://ocw.mit.edu/index.html

There is a burgeoning movement to create "open source" educational content banks, from which insitutional (even individual) users can select - and publish - content about virtually *any* educational topic. These content resevoirs will be constructed to meet the most demanding curriculum frameworks, at all levels of curriculum instruction.

The open educational content movement makes sense because the bulk of formal educational content - i.e. the content that is delivered to student by educational institutions - doesn't change very much from year to year. For instance, there has been almost no change in the Calculus, or Euclidean Geometry for hundreds of years. Some basic curriculum areas do change, although slowly (with a very few exceptions). Thus, it's possible to imagine a scenario where free, open source access to educational content - based on sound curriculum frameworks put forward by our best public and private institutions - would benefit educational institutions, students, and taxpayers. More, bettwr quality, and less costly educational content will result.

Many foreign governments and international agencies are on the constant lookout for high quality inexpensive acce

U.S. Navy Calculus book

I once came across an official "U.S. Navy Calculus" textbook. This was written for use during WWII, when there was an urgent need for engineers. It was utterly practical. Integration methods included the "tables method", looking up the appropriate integral in a table of integrals.

After the war, the theory people took over again, of course.

Google

Now, I still buy books for my liberal arts classes for a number of reasons, but I haven't bought a single text for a class in my major (IT) in over three years. Quite frankly, for any technical question I could have, there's almost always an answer out there on the intarweb just waiting for me.

The text choices of my professors always seemed so arbitrary, and the same information appears in countless forums, web pages, and so forth. Instead of reading pages 110-115 in a $90 text, I google for "Microsoft Active Directory" or "Kernal Hacking," and spend $90 on a giant honking steak dinner ;^)

My favorite excerpts from "The Calculus Bible"

First, to be honest, I much prefer the King Isaac version.

"In the beginning, God created X, and X was without function. And God said, "Let there be f(X)!" and there was f(X). And God created Y to hold the f(X) and saw that it was good."

"And the serpent said unto Eve, 'has God told you that you may divide by any number in the garden?' And she replied unto him, 'By any number of the garden we may divide, but the by the zero in the center of the garden we must not divide, lest we die.' Then the serpent said unto her, 'You will not die. God knows that if you divide by the zero, you will become a Math professor and will become like God, or at least think you are.'

"And thus it is written that a Sine shall leave his mother, and a Cosine shall leave their home, and the two of them squared shall be as one."

Problem with math books(or me)

I remember one math book i was reading(calc or linear algebra). I had no idea what the author was talking about.
Completely lost I plodded through the remaining pages in the section.

I then looked at the questions and could answer every one correctly. I had already learned what the book was trying to teach and still couldn't understand the chapter.

Harrison's Laws of Math Textbooks

1. Anything entitled "Fundamental Theorem of X" will have no obvious connection to X.

2. Any section entitled "Applications of ..." is going to be a lot of work.