Colloquium Title: The Axiom of Completeness: Grounding Calculus and Resolving Paradoxes
Abstract: While calculus powered technological revolutions, its rigorous foundation came later through mathematical analysis. At its core is the Axiom of Completeness—the idea that the real line has no “gaps”. We will examine how calculus fails without this axiom, resolve a classic paradox, and discuss key applications.
Connect to Department of Mathematics and Statistics at Bucknell University on LinkedIn.
Current job: Assistant Professor of Mathematics at Bucknell University
Tell us about your journey to your current job.
I have wanted to be a professor since being an undergraduate at Cal Poly – San Luis Obispo. I attended graduate school at The University of Alabama and, afterwards, was fortunate to be hired at Bucknell.
Shout out a teacher or mentor that helped you along the way.
Professor Kabe Moen (Univ of Alabama) was my advisor and has been instrumental in my success as a teacher and a scholar.
What first got you into the particular topic you will talk about in your talk?
Professor Hamilton (Cal Poly – SLO) and her amazing Analysis class is where I became passionate about Calculus.
If students want to learn more about the topic in your talk, what resources do you recommend checking out?
Understanding Analysis by Stephen Abbott is a great undergraduate level analysis textbook that covers completeness well.
Where and when do you get your best work done? What does your working environment have to look/feel like to be productive?
I have three kids so precisely zero work gets done at home! I work most effectively in my office before lunch. It’s all downhill form there! I prefer a calm and quiet environment.
What general advice do you have for students?
College is a great opportunity to learn how to commit. Many classes you take will not be easy, and may not even be what you’re passionate about. Buy into the concept of working hard the whole semester. The gratification of success that comes later is amazing!
What do you like to do for fun?
I love running and watching sports! Roll Tide Roll!
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