Meet the Colloquium Speaker: Prof. Adam Mair

Prof. Adam Mair stands in front of his opening talk slide. The slide features the department logo and QR codes to the blog, Instagram, and LinkedIn.

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.

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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!

A large group of students and faculty tune in to Prof. Mair's talk.

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A day in MATH 208: Mathematical Explorations

Math 208: Mathematical Explorations is a half credit class for intended Math/Statistics/Applied Math/Mathematical Economics majors. In this class, students:

  • Investigate a wide-range of math ideas beyond intro calculus and statistics
  • Build community and work closely with the other first-year majors 
  • Get involved with the math & stat department

This semester, Prof. Kelly Bickel is teaching the class. Most class days involve hands-on activities where students explore math-related ideas in groups. On Wednesday August 26th, the topic of class was Mathematical Games- games whose rules are governed by mathematical principles. If you have such a game, some natural questions are:

  1. If it’s a one-player game, when is it winnable?
  2. If it’s a two-player game, what’s the best strategy for each player?
  3. Does either player have a winning strategy?

During class, students played some mathematical games and tried to answer those questions. First they looked at grids of different sizes with two dots marking two grid cells. Is there a path between the two dots that goes through each grid cell exactly once? Once students played a few boards, they were then asked to come up with more general questions about these grid games. One question in particular was popular: is there a pattern to when boards are unsolvable?

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Next up, was a two-player game. Groups split into pairs to play a game and try to determine a way to win.

The group in the top middle photo is made up of Finley Wardrip (Mathematical Economics major, ’30), Joe Cavalcanti (Mathematical Economics major, ’30), Abigail Angler (Applied Mathematics Major, ’30) and Rose Wayland (Mathematics Major, ’30)

The group in the top right photo is made up of Zach Timms (Mathematics major, ’30), Cora Milner (Applied Mathematics Major, ’30), Emily Koplin (Mathematical Economics major, ’30), and Nathan Small (Statistics Major and Data Science Co-Major, ’30).

The group in the bottom left photo is made up of Izzy Van Dyke (Mathematics major, ’30), Cece Sonthonnax (Applied Mathematics Major, ’30), Nguyen Nguyen (Mathematical Economics major, ’30) and Ariah Vona (Mathematics Major + seeking teacher certification, ’30)

The group in the bottom right is made up of Ava Abrahamson (Mathematical Economics Major, ’30), Yosmairi Arias (Mathematics Major + seeking teacher certification, ’30), and Peter Caputa (Mathematical Economics major, ’30).

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Two players start with 10 beads and take turns taking beads until someone takes the last bead and is declared a winner.

Want to experience this game yourself? Grab a friend and put 10 beads/pennies/pick your object on a table. During each turn, a player can take between 1 and 4 beads. How do you win? Take the last bead. Can you come up with a winning strategy? What if you start with 11 beads? 24 beads? N beads?

Want a chance to be featured in a future blog post? Respond to our question of the week here, and your answer may be chosen for a future post.

Math Adventures in Budapest!

Thinking about studying abroad? Sam Berry (Applied Mathematics major, ’27), Skyler Le (Mathematics major, ’27), and Dante Mancino (Mathematics major, ’27) spent last fall semester, and Celine Chang (Applied Mathematics major, ’27) spent last spring semester learning math in Budapest, Hungary. They had a blast; see for yourself…

They saw the sights, tasted the food, heard the music!

Interested in studying math abroad in Budapest?

Find out more here.

They made some new friends!

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They learned some cool math! Check out this lecture hall where students gathered together for info sessions, colloquia, and research presentations.

They experienced new traditions!

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If all of these photos make you excited about studying abroad, but you aren’t quite sure about this particular program, learn more from the Bucknell Global Education team here.

Want a chance to be featured in a future blog post? Respond to our question of the week here, and your answer may be chosen for a future post.

Last year’s department highlights

Welcome back! We hope your summers were restful, and you feel recharged for another fun semester ahead.

This year we’re going to have more action on this blog, so stay tuned weekly for the latest update on what is going on in the Mathematics and Statistics Department. Want a chance to be featured in a future post? Respond to our question of the week here, and your answer may be chosen for a future post.

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But before we kick off the Fall 2026 semester, let’s throwback to Fall 2025 and Spring 2026.

Before we know it, there will be a chill in the air, and we’ll be sipping on fall-themed, cozy drinks. Last fall the MAA students hosted a pumpkin painting and carving night and Prof. Bickel’s MATH 208 hosted a math-art show.

In the spring we had four students complete honors theses!

Faculty and staff hit milestones last year too!

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And now we’re ready to do it all again!

Save the date for our first student colloquium with our very own Prof. Mair, and check out the new chalkboard by the student lounge in Olin to vote on a very important question… 😀

Student colloquium series poster for Prof. Adam Mair's upcoming talk on Thursday, September 3rd at noon in Olin 268. Pizza is provided, but please bring your own drink.