1
$\begingroup$

I have taught College Algebra several times and will teach it again in the next semester. College Algebra, according to the catalogue of my college, is described as follows:

This course provides students an opportunity to gain algebraic knowledge needed in many different fields such as engineering, business, education, science, computer technology, and mathematics. Graphical, numerical, symbolic, and verbal methods support the study of functions and their corresponding equations and inequalities. Students will study linear, quadratic, rational, exponential, logarithmic, inverse, composite, radical, and absolute value functions; systems of equations and inequalities modeling applied problems; and curve fitting techniques. There will be extensive use of graphing calculators.

I have asked a related question a few years ago and here I would like to ask this question:

Is there a College Algebra book that was written by a world-class mathematician?

I am not sure if there is a universally accepted definition of "world-class mathematician" but let me give two examples here.

  1. I have used Israel Moiseevich Gelfand's Trigonometry for my trigonometry class. The author was the first laureate of the Wolf Prize in Mathematics.
  2. I have also used Frederick Mosteller's Beginning Statistics with Data Analysis for my Elementary Statistics class. The author was the founding chair of Harvard's statistics department.

I enjoyed these two books greatly and now I am hoping to find a College Algebra book that the author (or one of the authors) is a world-class mathematician. Of course, this book must be available for purchasing.

Improve this question
$\endgroup$
9
  • 13
    $\begingroup$ Just out of curiosity, what did you enjoy about the two books you mentioned? Was it the credentials of the authors, or how they write? I do hope you get some good answers to this question, I'm just wondering about the motivation. Why does it matter so much that the author is "world-class"? $\endgroup$
    – Brendan W. Sullivan
    Feb 25, 2022 at 6:16
  • 11
    $\begingroup$ @Zuriel: I suspect that (indeed, I feel almost certainly that) there are very many "non-titled coaches" who would be better for beginner level players (even for players with rankings 1700 or 1800) than any of the World Champions from the past few decades. $\endgroup$
    – Dave L Renfro
    Feb 25, 2022 at 18:28
  • 6
    $\begingroup$ @Zuriel no, absolutely not. Plenty of advanced experts in their fields are terrible teachers. Nobel laureate in physics Isidor Rabi, basically the (grand)father of MRI machines, was a notoriously terrible lecturer. As a terrible amateur chess player myself, I bet that I would benefit more from being coached by someone used to coaching amateurs than someone like Magnus, whose gulf of knowledge and ability is so vast he probably wouldn't even be able to comprehend what I'm missing. $\endgroup$
    – llama
    Feb 25, 2022 at 18:28
  • 5
    $\begingroup$ I think for something as low level as college algebra, most any moderately good upper level undergraduate math student has plenty of content knowledge for this, and what's more important (and definitely needed) beyond this is teaching experience and the ability to write well -- engagingly, at the appropriate level, anticipating standard student misunderstandings, non-ambiguously which also means an awareness of unintended interpretations of what's written, etc. $\endgroup$
    – Dave L Renfro
    Feb 25, 2022 at 18:33
  • 2
    $\begingroup$ @Zuriel There was another recent question on academia which had several good answers discussing the different requirements for pedagogy and content knowledge at different levels of education, I liked this answer: academia.stackexchange.com/a/182678/24304 For textbooks, I imagine the graph tilts even more heavily towards pedagogy, since the textbook author can always stop and look things up while writing. $\endgroup$
    – user3067860
    Feb 25, 2022 at 18:53

2 Answers 2

Reset to default
14
$\begingroup$

This question is close to one you've already asked, a subset of it practically. Should I append a cute Venn diagram, showing the relation?

Which textbooks on College Algebra, Trigonometry, Pre-calculus, Calculus, Linear Algebra, ODE are written by world-class mathematicians?

The answers to that previous one (rarity of research mathematicians writing lower level books, the noncongruence of good pedagogy and great research breakthroughs) apply still.

To which I would add "college algebra" is a bit of a funny topic, maybe even more so than finding a HS geometry book or calc intro. This is because "college algebra" in the US is something MOST students are expected to have done in high school. It's often called "algebra 2". The standard STEM freshman course at the Naval Academy, Virginia Tech, Cal etc. starts with calculus. Since at least the 80s (probably much earlier).

The term college algebra has a bit of a 1940s flair to it, like from my father, when many US high schools stopped after first year algebra (mostly lines, culminating in the quadratic equation, but not logs/exponents/synth division) and geometry. But probably since the 60s, most schools expect you to start at calculus, In fact, most US students will have been exposed to a calculus in high school and a substantial portion will place out of the first year...but still, the nominal start of college is calculus. If you start higher, you're ahead of pace. If you take college algebra, you are taking REMEDIAL MATH. This is even more extreme in places with better school systems (Germany, UK, Russia, Japan), where calculus is a standard HS senior class. But in any case, "college algebra" is politically correct phrasing, using that 1940s flair (think bobby sox and sweaters) to cover for college kids that are taking REMEDIAL CLASSES.

Given the kids are taking remedial math. Are not on pace, not ahead of pace, not the best and the brightest, why would you even THINK about torturing them with some flashy name, bad pedagogy book? No. Just no. You need to train them effectively and efficiently. Heck, I don't like it when the crap pedagogy is used on the advanced kids. But at least you have an excuse there. "Enriching them" with such torture.

Now of course, we are not talking about mathematic concepts, but fuzzy topics, when we say "what is a course". And things may differ in other countries or...uh...cantons. And even within one (unless France), it's difficult to be axiomatic. But, all those caveats aside, college algebra is advanced (second course) high school algebra. You might as well look for an algebra 2 book (or "pre-calc", whatever the HECK that means!) by Andrew Wiles--you won't find it either, but at least it wouldn't be remedial.

Improve this answer
$\endgroup$
4
  • 4
    $\begingroup$ I think this makes a better comment than answer, as you have not suggested an college algebra textbook at all $\endgroup$
    – David Steinberg
    Feb 25, 2022 at 18:43
  • 3
    $\begingroup$ @DavidSteinberg: "Don't do it"-type answers. $\endgroup$
    – Nat
    Feb 26, 2022 at 0:07
  • $\begingroup$ @Nat I agree with that policy, but I don't think this is a "don't do it"-answer, or at least, not one that justifies its position. $\endgroup$
    – David Steinberg
    Feb 26, 2022 at 0:19
  • 2
    $\begingroup$ @DavidSteinberg: It would be neat if someone could find a way to elaborate a bit more on the basic issue. Seems hard to explain.. like, naively, it might seem like experts would be like beginners, only far more polished. But experts do tend to develop more complex perspectives that might be a bit much for beginners, perhaps losing touch with the difficulties a beginner might encounter. $\endgroup$
    – Nat
    Feb 26, 2022 at 0:33
5
$\begingroup$

Yes, Gelfand also has an algebra book:

https://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/algebra_gelfand.pdf

Improve this answer
$\endgroup$
6
  • 1
    $\begingroup$ This is a good book, but I find some topics missing such as logarithms and exponential functions. $\endgroup$
    – Zuriel
    Feb 25, 2022 at 15:57
  • 4
    $\begingroup$ @Zuriel To be fair, despite being treated in many college algebra classes, logarithms and exponentials aren't algebraic. $\endgroup$
    – Adam
    Feb 25, 2022 at 18:50
  • $\begingroup$ @Adam, thanks! I have not even thought about this. $\endgroup$
    – Zuriel
    Feb 26, 2022 at 1:32
  • $\begingroup$ @Adam : So much the worse for definitions of "algebraic". Choices of topics in books of this kind should not be guided by that sort of definition. $\endgroup$
    – Michael Hardy
    Feb 26, 2022 at 4:30
  • 1
    $\begingroup$ @Adam : I won't go so far as to say that Gelfand should include those topics, but I have seen the book and I think they would not feel out of place there. $\endgroup$
    – Michael Hardy
    Feb 26, 2022 at 22:30

Not the answer you're looking for? Browse other questions tagged or ask your own question.