Mathematics and Statistics

Applied Mathematics, Geometry and Topology, Analysis, Mathematical Modeling, Statistical Modeling, Game Theory, Operations, Biostatistics, Epidemiology, GIS, Image Processing

The Right Touch Of Novelty

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
We all like new things. It’s exciting to try a new activity, to do something we’ve never done before. It breaks us out from the usual rhythm of our lives. A novel activity ends up looking much more enticing than the regular activities you usually do. We are wired to respond to novelty. This is a double-edged sword. On the one hand, it means we don’t get trapped doing the same things all the time.…

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Abstracting evolutionary games in cancer

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
As you can tell from browsing the mathematical oncology posts on TheEGG, somatic evolution is now recognized as a central force in the initiation, progression, treatment, and management of cancer. This has opened a new front in the proverbial war on cancer: focusing on the ecology and evolutionary biology of cancer. On this new front, we are starting to deploy new kinds of mathematical machinery like fitness landscapes and evolutionary games. Recently, together with Peter…

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Safe Questions

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
The process of learning with another person is a tricky thing. When you’re on your own, it’s fine to ask as many dumb questions as you can come up with. After all, nobody is going to judge you, since you can simply look up the answer in a book or online. As such, learning by yourself is safe (though it can be slow). On the other hand, I’ve come to realize how vulnerable you can…

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The Right Time

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
Do you hate mathematics? Have you found that the rules you have to follow seem to make no sense? No matter what you do, it never feels obvious, like the teacher says it should. Perhaps you can follow your teacher through a problem, but you know that if you ever had to do the problem on your own, there’s no way you could do it. For someone that identifies with the above paragraph, I want…

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Supply and demand as driving forces behind biological evolution

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
Recently I was revisiting Xue et al. (2016) and Julian Xue’s thought on supply-driven evolution more generally. I’ve been fascinated by this work since Julian first told me about it. But only now did I realize the economic analogy that Julian is making. So I want to go through this Mutants as Economic Goods metaphor in a bit of detail. A sort of long-delayed follow up to my post on evolution as a risk-averse investor…

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How Deliberate Are Your Explanations?

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
As a student and someone who tutors others in science and mathematics, I’ve been able to get a lot of experience on both the teaching and the learning side of education. It has given me a better appreciation of the difficulty of our job as teachers trying to get students to understand. In particular, I’ve learned that being deliberate in my explanations is important if I want students to get what I’m explaining. Sure, I…

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The Whole Ride

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
With a few taps, we can compare ourselves with thousands of other people. The comparisons can be anything we can think of. If there’s some kind of performance metric associated with your activity, you can bet there are places to compare results. It’s the nature of things. Humans like competition and comparison, so we build places where these comparisons are easy to find. Due to this, whenever we find an activity we like, there will…

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Quick introduction: Problems and algorithms

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
For this week, I want to try a new type of post. A quick introduction to a standard topic that might not be familiar to all readers and that could be useful later on. The goal is to write a shorter post than usual and provide an launching point for future more details discussion on a topic. Let’s see if I can stick to 500 words — although this post is 933, so — in…

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One-Sentence Summary

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
As a student, I’m used to diving right into the technical details of a topic. I don’t mind working through a wall of algebra, because that’s what I’m used to. If I wanted to describe how I learn in my classes, it would be: mathematics first, “high-level” understanding second. This isn’t a bad thing. I don’t mind going through the details first. Sure, I might not know how the concept relates to other ideas immediately,…

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Familiar Forms

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
When you first start solving a problem in mathematics, the goal is often to find a way to express the problem as some sort of differential equation. During this initial search, you don’t care how the equation looks. It’s more important to get it written down so that you can proceed. However, once you do have an equation, the first step is not to try and solve it. That’s a rookie mistake. Instead, the question…

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