Asking questions in conversation has become problematic. For example, try saying this out loud: “I wonder when Martin Luther King was born?” If you ask that online, a likely response is: “Just Google it!” Maybe with a snarky link: http://lmgtfy.com/?q=when was martin luther king born?
I love the idea of this… It’s very similar to helping to teach young children how to attack and solve problems in mathematics rather than simply saying follow this algorithm.
When you’re back and settled, I’d love to get together for coffee to discuss Domains 2019 and math. I couldn’t make it but caught big chunks remotely. I’m nearby in the Pasadena area and happy to come to you if necessary.
Preface This is a first draft of a free (as in speech, not as in beer) (although it is free as in beer as well) undergraduate number theory textbook. It was used for Math 319 at Colorado State University – Pueblo in the spring semester of 2014. Thanks are hereby offered to the students in that class — Megan Bissell, Tennille Candelaria, Ariana Carlyle, Michael Degraw, Daniel Fisher, Aaron Griffin, Lindsay Harder, Graham Harper, Helen Huang, Daniel Nichols, and Arika Waldrep — who offered many useful suggestions and found numerous typos. I am also grateful to the students in my Math 242 Introduction to Mathematical Programming class in that same spring semester of 2014 — Stephen Ciruli, Jamen Cox, Graham Harper, Joel Kienitz, Matthew Klamm, Christopher Martin, Corey Sullinger, James Todd, and Shelby Whalen — whose various programming projects produced code that I adapted to make some of the figures and examples in the text.
The author gratefully acknowledges the work An Introductory Course in Elementary Number Theory by Wissam Raji [see www.saylor.org/books/] from which this was initially adapted. Raji's text was released under the Creative Commons CC BY 3.0 license, see creativecommons.org/licenses/by/3.0. This work is instead released under a CC BY-SA 4.0 license, see creativecommons.org/licenses/by-sa/4.0. (The difference is that if you build future works off of this one, you must also release your derivative works with a license that allows further remixes over which you have no control.)
You can buy a physical copy, if that's your thing, from the on-demand printing service Lulu at this link for $6 (plus shipping and handling). [I make 61¢ profit for each such sale: I'm happy to reimburse you that amount if you will personally contact me.]
Alan Alda wanted to get off the island quickly. Steven Strogatz explains how an 18th century British clergyman could have helped. In this short bonus episode, Steven helps Alan understand something that he’s wondered about for years.
Quadrilateral equation?? Did he mean the Pythagorean theorem?
There’s a reasonable basic discussion of Bayesian statistics here.
Steven Strogatz possesses a special ability to see into the unseen. How does he do it? Steve is a world class mathematician, who sees through the window of math. But, lucky for us, he’s also a world class communicator. An award-winning professor, researcher, author, and creative thinker, Steve can help anyone (even Alan Alda) understand some of the unseen world of numbers. In this episode, Alan and Steven start from zero, not the number, but from a place of not knowing anything. He emerges from the darkness for a moment as Steve actually gets Alan to understand something that’s always mystified him. Steven's latest book, "Infinite Powers: How Calculus Reveals the Secrets of the Universe," is now available online and at all major book sellers.
While doing a good job of warming people up to math there was still a little bit too much “math is hard” or “math is impenetrable” discussion in the opening here. We need to get away from continuing the myth that math is “hard”. The stories we tell are crucially important here. I do like the fact that Alan Alda talks about how he’s been fascinated with it and has never given up. I’m also intrigued at Strogatz’ discussion of puzzling things out as a means of teaching math–a viewpoint I’ve always felt was important. It’s this sense of exploration that has driven math discovery for centuries and not the theorem-proof, theorem-proof structure of math text books that moves us forward.
I’ve always thought that Euler and Cauchy have their names on so many theorems simply because they did a lot of simple, basic exploration at a time when there was a lot of low hanging mathematical fruit to be gathered. Too many math books and teachers mythologize these men for what seems like magic, yet when taught to explore the same way even young children can figure out many of these same theorems for themselves.
If we could only teach the “how to do math” while children are young and then only move to the theorem-proof business later on as a means of quickly advancing through a lot of history and background so that students can get to the frontiers of math to begin doing their own explorations on their own again we would be far better off. Though along that path we should always have at least some emphasis on the doing of math and discovery to keep it at the fore.
QUINCY, MA—Confirming that they have no intention of modifying the traditional uniform of their profession at any point in the foreseeable future, mathematics professors from across the country joined their voices Monday to reaffirm their commitment to wearing chinos with running shoes. “We believe that this singular look has really been working for us for the past few decades, allowing as always for slight variations such as the presence or absence of pleats and the availability of slightly different varieties of white Reebok footwear, and we have decided to formally recommit to this outfit for as long as our profession continues to exist,” said Boston University vector analysis professor Paul Slavish, explaining that the pairing of khakis with cross trainers had become the symbol of his profession, as it offered a perfect combination of professionalism, approachability, and the comfort vital for on-campus life. “We acknowledge that our sneakers, while technically advanced, will never be used for actual running; our pants, while relatively clean, will never actually be ironed; and that this lower ensemble will always be paired with either a dress shirt two sizes too large or a sweat-wicking polo shirt that has never—and will never—wick away the sweat of exercise. Never shall we stray from this sacred combination, which proclaims at a glance that we are casual, unfussy people who happen to be very serious about mathematics. Plus, check out all these side pockets!” Slavish also confirmed that certain professors would occasionally wear a wacky necktie printed with mathematical symbols, but that this would occur at a maximum of three days per semester.
As it happens, he’d already done some work on coding theory—in the area of biology. The digital nature of DNA had been discovered by Jim Watson and Francis Crick in 1953, but it wasn’t yet clear just how sequences of the four possible base pairs encoded the 20 amino acids. In 1956, Max Delbrück—Jim Watson’s former postdoc advisor at Caltech—asked around at JPL if anyone could figure it out. Sol and two colleagues analyzed an idea of Francis Crick’s and came up with “comma-free codes” in which overlapping triples of base pairs could encode amino acids. The analysis showed that exactly 20 amino acids could be encoded this way. It seemed like an amazing explanation of what was seen—but unfortunately it isn’t how biology actually works (biology uses a more straightforward encoding, where some of the 64 possible triples just don’t represent anything). ❧
I recall talking to Sol about this very thing when I sat in on a course he taught at USC on combinatorics. He gave me his paper on it and a few related issues as I was very interested at the time about the applications of information theory and biology.
I’m glad I managed to sit in on the class and still have the audio recordings and notes. While I can’t say that Newton taught me calculus, I can say I learned combinatorics from Golomb.
Hagoromo Fulltouch Chalk is highly coveted around the world by mathematicians, who say it's superior to other kinds of chalk because it has an almost buttery texture and erases easily. When Hagoromo announced it was ceasing production, many mathematicians bought lifetime supplies, like one professor who has a four-stick-a-day habit. But a Korean company bought Hagoromo and has faithfully reproduced the original recipe so there is no longer a need to stockpile it. It's sometimes available on Amazon from third-party resellers.