Balance As A Student

As a student, there’s no shortage of things I could be doing to help my academic career. I could do some side research, I could read more about my field, I could network with other researchers, I could study more for my upcoming exams, I could work through another textbook, I could volunteer for any number of academic events, and the list goes on. There are so many things I could be doing to advance…

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Models as maps and maps as interfaces

One of my favorite conceptual metaphors from David Basanta is of mathematical models as maps. From this perspective, we as scientists are exploring an unknown realm of our particular domain of study. And we want to share with others what we’ve learned, maybe so that they can follow us, so we build a model. We draw a map. At first, we might not know how to identify prominent landmarks, or orient ourselves in our fields.…

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The Grit to Push Through

If you ask someone what the point of a mathematics or science degree is, chances are they will tell you a tale about becoming a great problem-solver and seeing the world through new eyes. This has become a sort of battle cry for many who want to encourage people to learn about science and mathematics. The problem-solving skills you develop during these degrees allows you to be valuable in a wide range of careers later…

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Bourbaki vs the Russian method as a lens on heuristic models

There are many approaches to teaching higher maths, but two popular ones, that are often held in contrast to each other, are the Bourbaki and Russian methods. The Bourbaki method is named after a fictional mathematician — a nom-de-plume used by a group of mostly French mathematicians in the middle of the 20th century — Nicholas Bourbaki, who is responsible for an extremely abstract and axiomatic treatment of much of modern mathematics in his encyclopedic…

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Behind the Equations

In secondary school, students in physics learn about the kinematics equations. These equations describe the motion of objects under a constant acceleration (often gravity). There are several equations, which describe the relationships between acceleration, speed, position, and time. In particular, here is one of the equations: x(t) = x0 + v0t + at2/2. This equation lets us find the position at any time t, since the other parameters are known. You might even recognize this…

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The Noble Eightfold Path to Mathematical Biology

Twitter is not a place for nuance. It is a place for short, pithy statements. But if you follow the right people, those short statements can be very insightful. In these rare case, a tweet can be like a kōan: a starting place for thought and meditation. Today I want to reflect on such a thoughtful tweet from Rob Noble outlining his template for doing good work in mathematical biology. This reflection is inspired by…

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Emmy Noether arrives in the 22nd century

ICYMI: one of my short stories that appeared in The Mathematical Intelligencer. Enjoy! -AB ** My short story featuring a time travelling Emmy Noether has appeared in The Mathematical Intelligencer. You can also read the story here. Emmy Noether is one of my mathematical heroes and the story is my homage to her. I don’t… Read More Emmy Noether arrives in the 22nd century

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Quantities in Context

One of the differences between physics and mathematics is that mathematicians don’t tend to care about the units they are working with. In fact, they will usually consider all quantities as unitless1. This makes it easy to compare quantities, because one only has to look at the number itself. If you have two numbers, 5 and 9, you know that 9 is the larger quantity. In physics, however, the situation isn’t quite the same. That’s…

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