Carmichael’s Totient Conjecture

Photo Credit: Avery Carr

Photo Credit: Avery Carr

In the wake of mathematical enlightenment a profound understanding of basic notions bridges the gap between the conceptual and concrete.   In many cases, problems that have an exterior of simplicity exploit the boundaries of comprehension and provide insight into extensive associations.  From the mind-stretching inclinations of geometry and algebra emerges the intricate framework from which these connections form.  Piece by piece, generalizations are built from the material of empirical understanding fabricated by the process of asking intrinsic questions.

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Reflections on Teaching

I was recently asked to be part of an advice panel for newly minted teaching assistants. Oh, how time flies! After assisting with numerous classes and teaching vector calculus twice, I’d like to think I have some advice to offer. Since I took the time to put my thoughts onto paper, I may as well share them with the blog. (Consider this a “reply to all”, one of Matt Might’s tips for low cost academic blogging.)

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Everyday Sexism in STEM – A New Website

It is common knowledge that women are heavily under-represented in STEM disciplines (science, technology, engineering, and mathematics), despite efforts to recruit and retain more women in these fields. Though progress has been made, a recent paper from Yale University researchers delivered some sobering news – there is still a clear bias against female scientists.

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Tips for New Grad Students

Photo Credit: Stephanie Blanda

Photo Credit: Stephanie Blanda

It’s that time of year again – the summer is coming to an end, classes are getting started, and new grad students are arriving on campus.  Graduate school can be an intimidating and challenging experience, especially in the first year.  I asked some of my fellow grad students at Penn State what advice they would give to new grad students or what they wish they had known when they started grad school.  Here is a list of advice that we came up with.

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Fields Medal 2014

Congratulations to the 2014 Fields Medalists! Every four years, the International Mathematical Union (IMU) awards the Fields Medal to two, three, or four mathematicians under forty, recognizing them for their research and contributions to the discipline. The Fields Medal was established in 1936 and is often compared to the Nobel Prize. This year four mathematicians were honored: Artur Avila for his contributions to chaos theory and dynamical systems; Martin Hairer for his study of stochastic PDEs; Manjul Bhargava for his work in algebra and number theory; and Maryam Mirzakhani for her research on the dynamics and geometry of Riemannian surfaces. This year’s prize was particularly historic because Mirzakhani is the first woman to be awarded the Fields Medal. Continue reading “Fields Medal 2014” »

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