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from the how-to-learn-mathematical-thinking dept.
Technology Review is running an unusual book review -- books about learning math, pure math, not applied math, https://www.technologyreview.com/2023/04/24/1071371/book-reviews-math-education/
The author admits to being adrift,
As a graduate student in physics, I have seen the work that goes into conducting delicate experiments, but the daily grind of mathematical discovery is a ritual altogether foreign to me. And this feeling is only reinforced by popular books on math, which often take the tone of a pastor dispensing sermons to the faithful.
An initial attempt led to a MasterClass by a "living legend of contemporary math", but the master is seated in a white armchair with no blackboards, pens or paper and does not enlighten.
A side story covers a writer for the New Yorker who plans a year to go back and learn the high school algebra/geometry/calculus that escaped him, but mostly fails. For backup he has a niece who is a math professor...but after months without getting it, he complains. Her answer?
"For a moment, think of it as a monastic discipline. You have to take on faith what I tell you." Where his niece and others see patterns and order, he perceives only "incoherence, obfuscation, and chaos"; he feels like a monk who sees lesser angels than everybody around him.
I won't spoil the end, but the author does make some progress with books by mathematician and concert pianist Eugenia Cheng, starting with "Cakes, Custard and Category Theory", where each chapter starts with an analogy to baking.
Unfortunately, for the SN audience, the article does not include any car analogies...
(Score: 3, Interesting) by looorg on Sunday June 11 2023, @05:10PM (3 children)
A good book is hard to replace. If nothing else you could get some rework or translation of Elements by Euclid. That should have expired copyright wise a while back since it's a bit over 2000 years old. The reworks might not tho. I wish they would have used that in elementary school instead, I didn't get to learn about it until university. It opened a lot of eyes on how things worked and why instead of just "use formula X, put in the numbers and compute the answer ... you don't need to know why!".
(Score: 1) by pTamok on Sunday June 11 2023, @08:21PM (1 child)
Translation?
One of the more interesting websites is one that aims to teach you how to read Euclid in the original Greek. There are times I wish I had more than one life so I could do all the things I think are interesting.
Reading Euclid: This course combines Greek and Geometry to show how to read Euclid's Elements in the original language. [du.edu]
(Score: 2) by looorg on Sunday June 11 2023, @08:31PM
Yes. It had to be a translation. It was a rework of his work. I can't tell if it explained things better then Euclid or not but it was a real eyeopener as far as geometry and axiomatic theory was concerned.
Right. If only I had the time to spare. That does appear to be quite interesting. Bookmarked for future reference and reading. If only the day had more hours ... There is always retirement, decades away if ever ...
(Score: 2) by VLM on Monday June 12 2023, @12:34PM
Yeah there's good books but there's no good new books, no textbook written by boomers or younger is worth buying, generally.
There's an entire business model around "I'm going to teach linear algebra as a new prof, so I'll write a new textbook, charge at least $200 for it, and require my students to buy it to make a stack of cash in a corrupt manner". On the other hand the best linear algebra book you could buy for undergrads, at least recently, was probably Strangs book. So just buy Strang's book for $75 and call it good. No need to make some lesser known professor writing a lower quality book an extra $125. His students have to suffer and pay an extra $125 but no one else has to suffer.
The main determinant (oh the bad puns) of success at learning linear algebra or anything else is the willingness to put in the time and sweat, not the name of the author on the book, anyway. So just get a cheap old book, ideally the best book of the last half of the previous century.