The Sliding Scale of Academia

When I start thinking about where I am going in the future – or when someone asks me the age-old question, “What do you want to do when you graduate?” – I hesitate to answer. My hesitation is well-warranted. It has been my experience that professors and adults alike enjoy providing you a label and tossing you into a predetermined box. It’s quite funny how quickly they change the way they interact with you. Honestly, I am not about that life. This could potentially close off some really important doors that I am still investigating. And, as it turns out, I am a growing human being with extreme amounts of passion; wild and wonderful amounts of passion. So I don’t need constraints. Thanks, but no thanks.

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Communicating Mathematics to a Broader Audience

How we communicate mathematics is an essential part of making mathematics accessible. You’ve probably experienced communicating with peers and faculty in your area of specialization, taught a few math courses, or even been involved in outreach activities with younger students.  All these types of audiences shape how we communicate mathematical ideas and require different types of skills.  While I consider all of them an important part of our growth as mathematicians, there is still one more type of  audience I want you to consider, the general audience.

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Reflections on Time and Space in Mathematics Classrooms

During this semester of teaching, I have decided to focus on the ways in which I engage with time and space in the classroom.  To frame this consideration, I have been looking at a book chapter entitled Landscaping Classrooms Towards Queer Utopias, by Kai Rands, Jess McDonald, and Lauren Clapp (2013).  Their chapter title is inspired by the work of Jill Casid who proposes that we should consider landscape as a verb.  Using an analogy between performative models of queerness, in which queerness is about doing rather than being, Casid proposes opening up spaces for non-normative landscaping. Continue reading “Reflections on Time and Space in Mathematics Classrooms” »

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A Eulogy Of Lipschitz Maps

A Lipschitz map (/function) is one that does not extend distances by more than a pre-assigned factor: $f: X \longrightarrow Y$ is Lipschitz if there exists an $L \in \mathbb{R}$ such that

$$ \forall x, \ \  \forall y \ \ \ d(f(x),f(y)) \leq L d(x,y) \ .$$

The definition makes sense as long as a distance is defined on the spaces. This makes Lipschitz maps highly versatile. Almost every space you deal with daily is either a priori a metric space (a set plus a distance function) or can be made one by endowing it with a distance. (Check for instance the word metric on a group that builds metric spaces out of groups, opening the doors to the beautiful topic of Geometric Group Theory.)

We will, nonetheless, limit ourselves to studying (some of) the properties of Lipschitz maps between Euclidean spaces. Properties?! Look at the definition again, what else could we expect of a Lipschitz map? What else could that condition possibly impose on $f$? Continue reading “A Eulogy Of Lipschitz Maps” »

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Introduction to Ideal Class Groups

Algebraic number theory is a really interesting subject, but unlike some other subjects, it’s not 100% clear what objects people study. This post provides an introduction to the class group of a finite dimensional field extension of $\mathbb{Q}$, an object often used in modern number theory.

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