forall x: Calgary Remix

Aaron is teaching our intro logic course (“Logic I”) this term, and as part of a pilot project to redesign that course (which also includes partially “flipping” it), we’ve also adapted P. D. Magnus’s open textbook forall x. To be more precise, we’ve remixed a remix by Tim Button of P.D. Magnus’ textbook with some material from J. Rob Loftis’s remix plus some material from Tim Button’s Metatheory and then added our own material and revisions.  (Aaron previously wrote about how we decided on these changes.) Thanks to Creative Common open licensing, we can do this: just shamelessly take other people’s work and make it work for us, without paying them. In this case, the license is CC BY-SA, which requires only that we give credit (the “BY” part) and that we make the end product available under the same terms (the “SA”) part.

In order to keep track of our changes, I’ve put our remix as well as PDM’s original and TB’s remix on GitHub. (JRB maintains his own GitHub repository of the Lorain County remix/expanded “Open Introduction to Logic”.) is  So if you want to start your own remix and also want to use Git, you can start from any of the four version by forking the respective repository.

Here’s a rundown of the most important changes, with links to the corresponding Git commits where you can see what’s changed.

  • We put some material from PDM’s original version back into TB’s version (b3b6f97).
  • We added some material from JRL’s remix, mainly a discussion of soundness and completeness and many exercises (09b6d3a) and glossary entries (3f1276c).
  • We added a chapter on normal forms and truth-functional completeness from TB’s Metatheory (f49b6b3) and make it independent of the rest of that book (0721158)
  • We moved the chapter on natural deduction for TFL to before the FOL part.
  • We made a whole bunch of smaller stylistic changes, e.g., change all I’s to we’s, shall’s to will’s, change some examples to make them less reliant on a US or British background, etc. (fd9b99e, f091b03, 2a95058), added a preface (afd969d), glossary entries for the part on FOL (367d614), as well as some changes to terminology (ffa6567).
  • Changed the typography and layout to match the Sets, Logic, Computation layout and to fit on Crown Quarto paper for printing at lulu.com.

You can see a complete line-by-line comparison on GitHub.

You can download the final product if you don’t want to compile it yourself, and you can even buy a printed copy if you want!

Warning: We have not done anything with the solutions yet, so those do not match the numbering in the book and in fact might not match the exercises themselves!

Four New Photos

Fresh from the Archives of American Mathematics at UT Austin, the photos repository now includes Henkin, Huntington, Rosser, and von Neumann.

Revisions to enumerability and size of sets sections

As per issues 107 and 109, the material in sets-relations-functions/sizes-of-sets needs to be cleaned up. It was inconsistent in its assumption about whether functions are always total (they are, according to the definition in the preceding chapter), it gave an incorrect formal definition of enumerability (leaving out the empty set), and whenever it mentions \mathbb{N} it inconsistently assumes that \mathbb{N} begins at 1. Issue 109 deals with the problem that the section size-of-sets uses the cardinality notation \left|X\right| which leads students to assume that they can manipulate cardinalities as they can in the finite case; the proposal is to replace \left|X\right| \le \left|Y\right| with X \preceq Y to avoid this.

Commit a6a70a4 fixes issue 109; commit 370cb02 fixes issue 107. The latter also reformulates the diagonal proofs to make them direct instead of reductio proofs.

If you teach these sections, these changes may affect you. Please comment on the issues in GitHub if you have concerns. They will be merged into the master branch in a week otherwise.

For Ada Lovelace Day: Julia Bowman Robinson

Julia Bowman Robinson was an American mathematician. She is known mainly for her work on decision problems, and most famously for her contributions to the solution of Hilbert’s tenth problem. Robinson was born in St. Louis, Missouri on December 8, 1919. At a young age Robinson recalls being intrigued by numbers. At age nine she contracted scarlet fever and suffered from several recurrent bouts of rheumatic fever. This forced her to spend much of her time in bed, putting her behind in her education. Although she was able to catch up with the help of private tutors, the physical effects of her illness had a lasting impact on her life.

Despite her childhood struggles, Robinson graduated high school with several awards in mathematics and the sciences. She started her university career at San Diego State College, and transferred to the University of California, Berkeley as a senior. There she was highly influenced by the mathematician Raphael Robinson. They quickly became good friends, and married in 1941. As a spouse of a faculty member, Robinson was barred from teaching in the mathematics department at Berkeley. Although she continued to audit mathematics classes, she hoped to leave university and start a family. Not long after her wedding, however, Robinson contracted pneumonia. She was told that there was substantial scar tissue build up on her heart due to the rheumatic fever she suffered as a child. Due to the severity of the scar tissue, the doctor predicted that she would not live past forty and she was advised not to have children .

Robinson was depressed for a long time, but eventually decided to continue studying mathematics. She returned to Berkeley and completed her PhD in 1948 under the supervision of Alfred Tarski. The first-order theory of the real numbers had been shown to be decidable by Tarski, and from Gödel’s work it followed that the first-order theory of the natural numbers is undecidable. It was a major open problem whether the first-order theory of the rationals is decidable or not. In her thesis , Robinson proved that it was not.

Interested in decision problems, Robinson next attempted to find a solution Hilbert’s tenth problem. This problem was one of a famous list of 23 mathematical problems posed by David Hilbert in 1900. The tenth problem asks whether there is an algorithm that will answer, in a finite amount of time, whether or not a polynomial equation with integer coefficients, such as 3x2 − 2y + 3 = 0, has a solution in the integers. Such questions are known as Diophantine problems. After some initial successes, Robinson joined forces with Martin Davis and Hilary Putnam, who were also working on the problem. They succeeded in showing that exponential Diophantine problems (where the unknowns may also appear as exponents) are undecidable, and showed that a certain conjecture (later called “J.R.”) implies that Hilbert’s tenth problem is undecidable. Robinson continued to work on the problem for the next decade. In 1970, the young Russian mathematician Yuri Matijasevich finally proved the J.R. hypothesis. The combined result is now called the Matijasevich-Robinson-Davis-Putnam theorem, or MRDP theorem for short. Matijasevich and Robinson became friends and collaborated on several papers. In a letter to Matijasevich, Robinson once wrote that “actually I am very pleased that working together (thousands of miles apart) we are obviously making more progress than either one of us could alone” .

Robinson was the first female president of the American Mathematical Society, and the first woman to be elected to the National Academy of Science. She died on July 30, 1985 at the age of 65 after being diagnosed with leukemia.

(This short biography is part of the Open Logic Project; PDF here).

Have You Taught Using the Open Logic Project?

Have you used material from the Open Logic Project in your courses? We’d like to hear from you; please fill out this form:

How to Get (Printed) Open Textbooks to Your Students

One problem open textbooks (and instructors adopting open textbooks) face is how to make the texts available to their students. Of course, it’s easy to distribute electronic OERs. But if you want to provide your students a nice, printed version they can take to the coffee shop, you’re in a bind. First, you have to have it printed.  This is a bit of work, but with online print-on-demand services like lulu.com it’s possible.  But students would have to order the text themselves, and tax and shipping can almost double the (low) cost of a print-on-demand paperback, especially if you want it fast.

So big props to our campus bookstore, especially its manager Brent Beatty, who agreed to order 30 copies for my class and sell them at cost. Brent has been a member of UCalgary’s OER Working Group, so he’s attuned to the issues and challenges of open textbooks. All I had to do was send him the lulu.com order link; with volume discount, low volume shipping cost, and lulu.com’s frequent (constant?) promotional discount (25%) the shelf price is just a few cents above the list price on lulu (C$11).

Now I just hope enough students buy it so they’re not making a loss!

Fall 2016 edition of Sets, Logic, Computation

The Fall 2016 edition of the OLP remix Sets, Logic, Computation is ready. As before, it includes the OLP part on sets, relations, and functions; the part on first-order logic (with natural deduction chosen as the proof system); and the part on Turing computability including the unsolvability of the halting and decision problems. The methods chapter on induction and biographies of Cantor, Church, Gentzen, Gödel, Noether, Russell, Tarski, Turing, and Zermelo appear as appendices.

At students’ request, problems are now listed at the end of each chapter. Many typos and errors have been corrected, a number of examples and problems have been added, and several proofs rewritten for clarity. I’ve also added chapter summaries and a glossary. There are also a few added sections, notably introduction sections to Chapters 5 and 7, as well as discussion of Russell’s Paradox in both Chapter 1 and 6.

You can order a printed copy on Lulu, or download the PDF from the builds page. Read about what last term’s students thought of it here.

SLC F16

Line Art Portraits of Logicians

You’ve probably seen some of the line art portraits of logicians we’ve commissioned. They were done by Calgary illustrator and graphic designer Matthew Leadbeater. We’re pleased to release them all now under a Creative Commons BY-NC license: anyone is free to use them in their own work, to create derivative works from them, and to share them, provided (a) credit to Matt Leadbeater is properly given and (see license terms!) (b) they are not used for any commercial purposes.

They each come in two versions, one with a line below, and one with the portrait in a circle.

You can download the original Adobe Illustrator files. For PNG and PDF formats, we have set up a GitHub repository.

Commissioning these illustrations was made possible by a grant from the Alberta OER initiative. We gratefully acknowledge the support.

[Bonus: an image file with all of them that tiles nicely, for your desktop background.]

Student Satisfaction Survey Results

In the Winter term 2016, I taught the University of Calgary’s second logic course from a textbook remixed from the Open Logic Project.  Traditionally, Logic II has used Boolos, Burgess & Jeffrey’s Computability and Logic, and it was taught in Fall 2015 using that book as the required text by my colleague Ali Kazmi, and before that by him, Nicole, and me twice a year from that same book.  One aim Nicole and I had specifically for the OLP was that it should provide a better text for Logic II, since neither we nor our students seemed to be very happy with “BBJ”.

In order to ascertain that the OLP-derived text fares better with students, we did something radical: we asked them what they thought of it.  Ali graciously gave permission to run the same textbook survey in his class, so we have something of a baseline.  A direct comparison of the two books as textbooks for the course is not easily made, since Ali and I used the books differently: I stuck closer to my text than he did to BBJ; I assigned homework problems from the text; and we assessed students differently, so it’s difficult to control for or compare teaching outcomes.  With small samples like ours the results are probably also not statistically significant. But the results are nevertheless interesting, I think, and also gratifying.

We obtained clearance from the Conjoint Faculties Research Ethics Board for the study.  All students in each section of Logic II in F15 and W16 were sent links to an electronic survey.  As an incentive to participate, one respondent from each group was selected to receive a $100 gift certificate to the University of Calgary bookstore. The surveys were started in the last week of classes and remained open for 3 weeks each.  Response rates were comparable (23/43 in F15, 23/42 in W16). The survey was anonymous and developed with the help of the Taylor Institute for Teaching and Learning, who also administered the survey; results were not given to us until past the grade appeal deadline in W16.

We asked 23 questions.  The first three regarded how students accessed and used the textbooks. In the F15 section, the textbook was not made available electronically, but students were expected to buy their own copy (about $40).  Most respondents did that, although almost a quarter apparently pirated electronic copies.  In W16, the OLP-derived text was available for free in PDF and students had the option to buy a print copy at $10. Over half the respondents still opted to buy a copy.  We asked students how they used the texts in hardcopy and electronic form.

When using the text in hardcopy, do you...

Those using the OLP-derived printed text underlined significantly less than those who used BBJ. I’m guessing the OLP text is better structured and so it’s not as necessary to provide structure & emphasis yourself by underlining. In fact, one student commented on BBJ as follows: “Very little in the way of highlighting, underlining, or separating the information. It was often just walls of text broken up by the occasional diagram.”

When using the text in electronic form, do you...

When using the electronic version (both PDF), students did not differ much in their habits between F15 and W16. More students took notes electronically in F15. I suspect it’s because the PDF provided in W16 was optimized for screen reading, with narrow margins, and so there was little space for PDF sticky notes as compared with a PDF of the print book in F15. Also notable: highlighting and bookmarking is not very common among users of the PDF.

The second set of questions concerned the frequency with which students consulted the textbook, generally and for specific purposes.  W16 students used the OLP-derived text significantly more often than F15 students did, and for all purposes.

How often do you consult the text?

The difference is especially striking for the questions about how often students consult the textbook for exams and homework assignments:

Do you read the text in preparation for exams?
Do you consult the text when working on homework problems?

We next asked a series of questions about the quality of the texts. These questions were derived from the “Textbook Assessment and Usage Scale” by Regan Gurung and Ryan Martin. On all but one of these questions, the OLP-derived text scored positive (4 or 5 on a 5-point Likert scale) from over half the respondents. The discrepancy to students’ opinions of BBJ is starkest in the overall evaluations:

How engaging/interesting is the writing?
How understandable/clear is the writing?

The one exception was the question “How well are examples used to explain the material?”:

How well are examples used to explain the material?

This agrees with what we’ve heard in individual feedback: more, better examples!

Lastly, we were interested in how students think of the prices of textbooks for Logic II. We asked them how much they’d be willing to spend, how much the price influenced their decision to buy it. Interestingly, students seemed more willing to spend money on a textbook in the section (W16) in which they liked the textbook better. They also thought a free/cheap textbook was better value for money than the commercial textbook.

Is the price of the textbook too high for the amount of learning support it provides?

We also asked demographic data. Respondents from both sections were similar: almost all men in each (the course is mainly taken by Computer Science and Philosophy majors), evenly divided among 2nd, 3rd, 4th year students plus a couple of grad students in each (Logic II is required for the Philosophy PhD program). Student in W16 expected higher grades than those in F15, but that may well be just an effect of differences in assessment and grading style rather than better student performance.

If you care, there’s an interactive dashboard with all the graphs, and the raw data.

A Few Photos More

I added a few more logician’s photos: Carnap, Herbrand, Kalmar, Lewis, Kleene, Montague, Quine, Wang.

See previous post on how to download/integrate them into your OLP directory.