1 day agoWhat is “Mathematical Alchemy?”So what exactly is mathematical alchemy? I designed it as a term to capture something that seems to happen a lot in mathematics (both in elementary and research contexts), but doesn’t have a name attached to it. Mathematical alchemy refers to a rephrasing or other transformation of a problem that…Mathematics3 min read
Jun 23Backtracking in Mathematics ResearchOne of the greatest misconceptions of mathematical research to the untrained eye is that all of the work done on a project appears in the final paper that makes its way to a journal. From my personal experience, this couldn’t be further from the truth. …Mathematics5 min read
May 16Pythagorean Triples and Similar TrianglesWhat is a Pythagorean triple? To best understand Pythagorean triples, we had best talk briefly about the Pythagorean Theorem first. The Pythagorean Theorem says that if a right triangle has a hypotenuse of side length c, and legs of lengths a and b, then the following formula must be true: …Mathematics4 min read
Apr 1Teaching isn’t just standing in front of a classroom and talking about formulasTeaching isn’t just standing in front of a classroom and talking about formulas After spending close to three years teaching at the University of Tennessee, I’m inclined to reflect on my time as a GTA. I immediately remember that my teaching experience reaches much farther back than this. Well before…Education3 min read
Mar 13How to turn non-recursive formulas into recursive formulasIntroduction A sequence of numbers (often, but not always integers) can sometimes be described by a formula, if said numbers have a special pattern. These types of formulas can take one of two shapes: A formula is said to be recursive if you must explicitly use previous value(s) in the…Mathematics4 min read
Published in Ed-Tech Talks·Mar 6Teaching pedagogy tool: inverse magic-8 ballOk…so who’s heard of a magic 8-ball? I see lots of hands going up in the audience. For those whose hands didn’t go up, you ask a magic-8 ball a question, and it spits out an answer. The “O.G.” …Teaching4 min read
Feb 12Mathematical Reasoning: Problem Solving TipsWell, I’m at it again teaching the entry-level Mathematical Reasoning course at the University of Tennessee. So far this semester I’ve had some of my students tell me that they don’t know where to start when solving problems. Knowing the definitions is only enough for the most straightforward of problems…Mathematics3 min read
Feb 9Some tips on math talks: seminar vs. colloquiumOne of the requirements for my graduation from the University of Tennessee’s math Ph.D. program is the completion of the presentations seminar. This is a 1-unit course offered by the department designed to train students in the art of giving mathematical talks, and I am taking the course this semester…Math4 min read
Jan 30Is Less Really More? Developing a Mathematical IdentityIt’s not uncommon for me to talk with other students in my math department about their advisors’ mentoring styles, and what type of advice they give. This certainly includes discussion of what courses we’re all taking, and why. At least at the University of Tennessee, it seems a lot of…Mathematics2 min read
Jan 16Course selection as a math Ph.D. studentIn a few days I’ll be starting my sixth semester as a mathematics Ph.D. student at the University of Tennessee, roughly marking the halfway point until I’m out with a degree in hand and [hopefully] with a job. I’ve been giving some thought to the background I’ve developed through my…Mathematics10 min read
