Questions, etc, from students, grouped by upcoming Class number when received.
Additional suggestions for reading and watching: Maths in Pop Culture.
Most recent first, here are things you have expressed interest in talking about.
Student input received before Class #8
I didn't expect a math course. I expected a history of math (with focus on the life of P. Erdos). When the 2 of you shared math problems (which have been interesting to mathematicians throughout history) I sometimes understood, until it went "over my head" and some I didn't understood at all. Same with the math in the bio of Erdos.
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Course fit - and exceeded - my expectations, from OLLI's catalog, esp. the quality & openness to learning from the students by Steve & Gale. I found some of the unexpected data about mathematics really fascinating. I'm now reading a novel called: "The Mathematician's Shiva." author: Stuart Rojstaczer. It's about the narrator's mother. Within the 30 pages, he writes about Euler's problem of crossing bridges while growing up in Konigsberg.
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I found these books at the Ptld. Public Library (about math & mathematicians). I'm dipping into them, but don't know if I recommend them or not, but FYI: "A Strange Wilderness, The Lives of the Great Mathematicians" by Amir D. Aczel; "The Mathematician's Shiva" by Stuart Rojstaczer (novel); "S.M. Ulam, Adventures of a Mathematician." (note this entry from Maths in Pop Culture: NEW Movie [October 2021]: "Adventures of a Mathematician", based on the book by Stan Ulam (find him in the index of our textbook). Available now to rent ($6.99) at Prime Video, or see it in November at 2021 Virtual Maine Jewish Film Festival. Deals mainly with the period of his work on nuclear weapons.
Student input received before Class #7
In the BBC documentary the name of Sophie Germain was fleetingly mentioned. She lived 1776-1831 and, according to Wikipedia, her work on Fermat’s Last Theorem provided a foundation for mathematics exploring the subject for hundreds of years after.
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Since we were speaking about spirals this week in class, I thought I'd share a picture of my father, Ben Seltzman (the inventor) with one of the mechanical sculptures of which he was most proud. Ben entitled it On a Treadmill to Oblivion. Ben was fascinated with spirals and triangles, usually incorporating one or the other into his art.
Treadmill had a motor inside which caused the spiral to turn. A metal ball would appear, roll down the spiral and disappear at the back. Then the ball would pop up again at the bottom and repeat.
Amy
Student input received before Class #6
Do not understand the method to get GCD by Euclidean division.
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I found another amusing book about math: "Here's looking at Euclid; from counting ants to games of chance - on awe-inspiring journey through the world of numbers" by Alex Bellos (Simon & Schuster, 2010).
I just heard a program on Wisconsin Public Radio called "To the Best of Our Knowledge" which contained a fascinating segment called "The Price of Genius," which is an eleven-minute long interview with Jim Holt, the author of When Einstein Walked with Gödel. The section about Gödel starts about 4 minutes in, but the entire interview includes a discussion of Alan Turing, Georg Cantor, and Evariste Galois as well. https://www.ttbook.org/interview/price-genius
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A fun book I'd recommend (if you like math) is The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes by David Darling (Hoboken, NJ: John Wiley & Sons, 2004), a one-volume encyclopedia with more than 1,800 entries covering math concepts, theorems, and mathematicians and also includes some puzzles and games.
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When I looked up the traveling salesman problem there was a see also reference to the Hamilton circuit of minimum weight in a weighted complete graph, which led me to a brief mention of the Hamilton path and then to the knight's tour, which is "a classic chess puzzle: to find a sequence of moves by which a knight can visit each square of a chessboard exactly once." (It can be done and Euler found a tour that visits two halves of the board in turn.)
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Another book you might want to take a look at is Simon: The Genius in My Basement by Alexander Masters (New York: Delacorte Press, 2012), a biography of sorts about Simon Norton, a mathematical prodigy. (https://www.amazon.com/Simon-Genius-Basement-Alexander-Masters/dp/0385341083) Hia obituary appeared in The Guardian and was written by the author of the book: https://www.theguardian.com/education/2019/feb/22/simon-norton-obituary
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On a lighter note, I suggest the following:https://youtu.be/ReOQ300AcSU
Homer Simpson vs. Pierre de Fermat--Numberphile
Student input received before Class #5
Student input received before Class #4
About Class #3: Interesting discussion of possible uses of the Pythagorean Theorem "back in the day" and the "proof" that all triangles are isosceles. Steve mentioned in passing that Euclidean geometry dealt with flat surfaces and that there were other approaches when surfaces aren't flat. This reminded me of the story of how Erastothenes figured out the approximate circumference of Earth more than two thousand years ago.
Here's a link to a simple six-minute explanation for young people: https://youtu.be/J_elgAu-Hgk
and this is a link to a two-minute segment from Cosmos, in which Carl Sagan gives a similar explanation: https://youtu.be/f-ppBtuc_wQ
Thanks again to both of you for all the work you're putting into this class and to all my fellow students for their participation and contributions; e.g., Mary, when she pointed out that the line that bisects the top angle of an isosceles triangle would be the same line as the perpendicular bisector of the base (and therefore would intersect the base at the midpoint of the base and not the perpendicular bisector below the base and outside the triangle).
Student input received before Class #3
John Keats' definition of truth: "... what the imagination seizes as beauty must be truth --- whether it existed before or not"
From "The Heart of Mathematics: An Invitation to Effective Thinking" by Edward B. Burger and Michael Starbird. This is my go-to book when I need to understand something mathematical!
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Two numberphile videos about prime numbers, both of which show mathematicians having fun with numbers..
James Grimes "Infinite Primes" https://www.youtube.com/watch?v=ctC33JAV4FI provides another look at the proof that there are an infinite number of primes and about halfway through this seven minute video mentions Euclid’s different definition of a prime number.
Matt Parker's "Squaring Primes" https://www.youtube.com/watch?v=ZMkIiFs35HQ presents an entertaining look at the “fact that all prime numbers, when you square them, are one more than a multiple of 24.” He comes up with his own proof and then shows another, easier way.
The Errol Morris book about what is true: Believing is Seeing: Observations on the Mysteries of Photography
Another Tom Lehrer math song: “ Lobachevsky” https://www.youtube.com/watch?v=gXlfXirQF3A
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Student input received before Class #2
Received Sept. 16, 9:26 PM
Based on the class #1 problem, is it true that the sum of the first n even numbers (excluding 0) can be calculated as n^2 + n?
Steve replies: Yes, nicely spotted.
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Student input received before Class #1
Received Sept. 14, 7:09 PM
I thought it was interesting for a book like this to say in the acknowledgements to Ron " . . . who made the last 39.76 percent of Paul's life. . . " etc. Pretty precise and unusual !
Received Sept. 14, 8:54 PM
Chapter 0-Erdos Number
When I learned about the Erdos number, it reminded me of the “connections” 1st, 2nd, 3rd on LinkedIn. Wondering how they tracked that back in the day and do they work the same way?
Received Sept. 12, 10:39 AM
Do either of you have an Erdos number and, if so, what is it?
Received Sept. 11, 9:13 PM
Have any of Erdös's proofs had significant practical consequences affecting the general population or business?
