Mathematics and Statistics

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

Local maxima and the fallacy of jumping to fixed-points

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
An economist and a computer scientist are walking through the University of Chicago campus discussing the efficient markets hypothesis. The computer scientist spots something on the pavement and exclaims: “look at that $20 on the ground — seems we’ll be getting a free lunch today!” The economist turns to her without looking down and replies: “Don’t be silly, that’s impossible. If there was a $20 bill there then it would have been picked up already.”…

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Clarity and Words

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
A cornerstone of physics and mathematics is the process of labeling. If you want to learn any subject, you need to get familiar with the jargon of the field. In physics, terms like “work”, “resistance”, “capacitance”, “energy”, “potential”, and many more have precise meanings. Likewise, the terms “function”, “continuous”, and “one-to-one” have precise meanings in mathematics. When you first start learning the subject, it’s easy to be overwhelmed by the sheer number of terms. By…

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No Final Exam

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
Here’s a thought: what if the class you were in had no final exam? I know, it seems preposterous. Whenever one thinks of a mathematics or science course, a final exam is a no-brainer. It’s never a surprise to the students that your class will have a final exam, because that’s the tradition. Mathematics classes have final exams as a rule. It’s the way that students show that they’ve understood the material throughout the semester.…

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Quick introduction: the algorithmic lens

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
Computers are a ubiquitous tool in modern research. We use them for everything from running simulation experiments and controlling physical experiments to analyzing and visualizing data. For almost any field ‘X’ there is probably a subfield of ‘computational X’ that uses and refines these computational tools to further research in X. This is very important work and I think it should be an integral part of all modern research. But this is not the algorithmic…

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Patting Yourself On The Back

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
As a student or an academic, chances are you have a lot of work to do. Whether that is homework, studying for exams, preparing a presentation, writing a paper, doing research, or teaching, there is a lot that is asked of you. Often, the weeks seem like undulating waves, with regular spikes in work followed by brief periods of respite. This can lead to an unhealthy lifestyle if you are not careful with how you…

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Nudging Along Versus Waiting

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
The eternal question as a teacher or tutor is what to do when a student is struggling. Should you give them a hint, re-explain a key concept to them, or let them sit there and struggle? It’s not always clear which approach should be taken. I’ve often felt the pull to take the first route. After all, they are struggling! Shouldn’t I help them out? This meant I would give them some sort of pointer…

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Danger of motivatiogenesis in interdisciplinary work

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
Randall Munroe has a nice old xkcd on citogenesis: the way factoids get created from bad checking of sources. You can see the comic at right. But let me summarize the process without direct reference to Wikipedia: 1. Somebody makes up a factoid and writes it somewhere without citation. 2. Another person then uses the factoid in passing in a more authoritative work, maybe sighting the point in 1 or not. 3. Further work inherits…

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Learning is Offloading

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
When I’m learning a new topic, all of the details matter. If I want to understand what is going on, I need to have a firm handle on each detail. If I cannot imagine how each part operates and connects with the others, “getting” the concept is difficult. I suspect this happens for others, too. After all, if you want to understand without needing to take a result on faith, you have to know the…

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A Survey Of Homework Strategies

jeremy Communication, Education and Outreach, Mathematics and Statistics, Physics and Astronomy
If you take a look at any given class, you find that there are a variety of strategies employed by the students. In a way, it’s the perfect Darwinian battlefield: those with the best homework strategies end up doing well and move on to the next course. Some strategies are better than others, and this really shows up in any class. Even if your class is small (say, about ten people), you will find that…

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From perpetual motion machines to the Entscheidungsproblem

Theory, Evolution, and Games Group bloggers Biology and Life Sciences, Mathematics and Statistics, Technology and Engineering
There seems to be a tendency to use the newest technology of the day as a metaphor for making sense of our hardest scientific questions. These metaphors are often vague and inprecise. They tend to overly simplify the scientific question and also misrepresent the technology. This isn’t useful. But the pull of this metaphor also tends to transform the technical disciplines that analyze our newest tech into fundamental disciplines that analyze our universe. This was…

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