Control of the Future

It’s tempting as a student to think that nothing is in your control. We often feel like our whole lives revolve around the whims of professors and their decisions for assignments and tests. It can be easy to retreat into “reactive” mode, making sure that everything which is thrown at you gets done. When we operate like this, we tend to be exhausted, since we can never look further than a week. The issue with…

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Introduction to Algorithmic Biology: Evolution as Algorithm

As Aaron Roth wrote on Twitter — and as I bet with my career: “Rigorously understanding evolution as a computational process will be one of the most important problems in theoretical biology in the next century. The basics of evolution are many students’ first exposure to “computational thinking” — but we need to finish the thought!” Last week, I tried to continue this thought for Oxford students at a joint meeting of the Computational Society…

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Slick Versus Pedagogical Proofs

In mathematics, there’s almost always an opportunity to make proofs more concise. For example, when you first learn a concept, it might take a while to prove a result using the definitions that were developed. The reason it’s longer to do is because the definitions require you to spell out ideas explicitly. As a result, you might get to the end of the proof, but it takes a bunch of little intermediate steps to do…

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Levelling Up

We enjoy doing comfortable things. We don’t want to stretch ourselves too much, because when you stretch, there’s a possibility of overstretching. We fear this potential negative, so we buck the other way, contenting ourselves with doing activities and pursuing projects that aren’t too risky. It’s not that we don’t want to do better work and overcome new challenges. Ask anybody around you if they want to overcome challenges, and their answer will be “yes”.…

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British agricultural revolution gave us evolution by natural selection

This Wednesday, I gave a talk on algorithmic biology to the Oxford Computing Society. One of my goals was to show how seemingly technology oriented disciplines (such as computer science) can produce foundational theoretical, philosophical and scientific insights. So I started the talk with the relationship between domestication and natural selection. Something that I’ve briefly discussed on TheEGG in the past. Today we might discuss artificial selection or domestication (or even evolutionary oncology) as applying…

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The Rational Roots Theorem

One of the skills students learn in secondary school is to factor quadratic expressions. In particular, they learn how to solve equations like x2+2x+1=0. There are a slew of techniques one can use to deal with quadratics, and they mostly rely on the fact that questions asked in assignments and tests have “nice” factorizations. Most expressions have integer solutions, or at worst rational ones. This makes it straightforward to factor. Of course, this might take…

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Mathematics Isn’t Just Numbers

We often equate mathematics with numbers, as if mathematics doesn’t extend further than doing arithmetic. Each time this happens, I have to restrain myself from going on a rant. I want to grab the person by the collar and exclaim, “There’s so much more to mathematics than just numbers! It’s like saying that running is just a bunch of one-legged hops. While that might be technically true, it’s not the way most people would describe…

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Space-time maps & tracking colony size with OpenCV in Python

One of the things that the Department of Integrated Mathematical Oncology at the Moffitt Cancer Center is doing very well, is creating an atmosphere that combines mathematics and experiment in cancer. Fellow TheEGG blogger, Robert Vander Velde is one of the new generation of cancer researchers who are combining mathematics and experiment. Since I left Tampa, I’ve had less opportunity to keep up with the work at the IMO, but occasionally I catch up on…

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Degeneracy of the Quantum Harmonic Oscillator

Note: This post uses MathJax for rendering, so I would recommend going to the site for the best experience. I just love being able to find neat ways to solve problems. In particular, there’s something about a combinatorial problem that is so satisfying when solved. The problem may initially look difficult, but a slight shift in perspective can bring the solution right into focus. This is the case with this problem, which is why I’m…

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Being Happy With Being Repetitive

One of the most difficult things to do in life is to focus. Maybe you’re different than me, but I have a lot of trouble sitting down and focusing on one task or idea. Instead, my mind buzzes with activity while my hands do another. I’m always switching between ideas, and it takes a lot of energy to focus on just one. On a more macro level, my trouble with focus manifests in the types…

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