Математик из нации чероки выпустил учебник по многомерному исчислению на основе исторических методов

JACKSON, Tenn. – Getting back to roots of calculus and how it was meant to be studied has been a mission for Cherokee Nation citizen and mathematician, Dr. C Bryan Dawson. Dawson, a professor at Union University in Jackson, Tennessee, has released his second calculus textbook, “Multivariable Calculus Set Free: Infinitesimals Ride Again” as a follow-up to his first textbook, “Calculus Set Free: Infinitesimals to the Rescue” that was published in 2022.  “The first book is for the first two semesters of college calculus – Calculus I and II. The ‘multivariable calculus’ book is for Calculus III in college curriculums,” Dawson said. “Prior to this, the work wasn’t complete because for the vast majority of colleges when they adopt a textbook, they adopt it for all three semesters of calculus.” Dawson explained that when calculus was first developed in the late 1600s and early 1700s, infinitely small numbers were used called infinitesimals, which is a non-zero quantity so small that it approaches zero without being zero.  “If you divide by them, you get infinitely large numbers,” he said. “But at the time, mathematicians didn’t know how to prove that there really is a number system with these infinitesimals.” He said mathematicians were getting results, but there were a lot of criticisms of calculus because it was not built on a rigourous foundation like geometry. “In the 1800s, mathematicians found kind of a workaround, a way to make calculus rigorous, but it was less intuitive and harder to compute,” he said. It was around 1960 that mathematician Abraham Robinson was able to prove the existence of a number system that included infinitesimals and infinite numbers. “Then that made it legitimate for authors to try to return calculus to its roots,” he said. “I was able to about 14 years ago … develop a system within this system that had numbers that had been developed by Abraham Robinson. I was able to develop some new notation and new procedures that helped students do the calculus in the way they were doing it when it was first developed using infinitesimals, and it made it easier for the students.” He said that gave him the push to develop his textbooks, which have been used across some college classrooms but also individually. “There are many individuals that have used it for self-learning. I’ve been contacted by people all over the world that have purchased the book and enjoy learning from it,” he said.  While the books help students studying calculus, Dawson has also used it to share his Cherokee heritage. For example, on the cover, his name is printed in both English and Cherokee. And within the text of the book, there are references to a chunky game spear and blow darts when referring to projectile motion, and marginal notes where these activities can be found.  “It’s great to be able to plant that seed of representation in the minds of students for whom you know they might not ever have really thought about Cherokees having a writing system or still being around. You can dispel misconceptions among young people, even just by having a name there on the cover,” he said.  Dawson said it’s satisfying to see his second book become available. “It’s a mission, in a way, and I have enjoyed that. It’s been a very satisfying career. But then this has been satisfying because I know that when the time comes that I retire, I have something that I’ve given to the mathematical community that can still continue to help students,” he said. “Multivariable Calculus Set Free: Infinitesimals Ride Again” is available as a hardcover and e-book in the UK at  global.oup.com, and will be available in October in the U.S.