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Expanding Your Horizons in Science and Mathematics™ conferences nurture girls' interest in science and math courses to encourage them to consider careers in science, technology, engineering, and math
"Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematics. These may be the legacy of a dominant individual (e.g. the Newtonianism of 18th century British mathematics). Or, there may be social or economic reasons (such as the practical bent of early modern Dutch mathematics). Sometimes, a local style results from deliberate policy. For example, in the 1920s and 1930s, Polish officials identified ‘foundations of mathematics’ in the style of topology and real analysis as something that Polish mathematicians should excel in. Local mathematical cultures can reflect the uneven geographical spread of a methodological division. For example, in theoretical computer science, there are two main directions: ‘Algorithms and Complexity’, and ‘Logic in Computer Science’ . In many countries, the split between those areas is heavily uneven. "
We present a foundation for inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying finite lattices of logical statements in a way that satisfies general lattice symmetries. With other applications in mind, our derivations assume minimal symmetries, relying on neither complementarity nor continuity or differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of rules governing quantification of the lattice. These rules form the familiar probability calculus. We also derive a unique quantification of divergence and information. Taken together these results form a simple and clear foundation for the quantification of inference.
"That means one way to figure out whether mainstream economics makes sense is to see what the assumptions are, and to try to decide whether those assumptions make sense. For example, what were Samuelson’s assumptions? What were Arrow and Debreu’s assumptions?
Samuelson had one big assumption, that economists call ergodicity.
[Teacher pauses to give kids time to stumble over the word.]
When they say ergodicity, they mean that no matter what happens in the world, in the end, everything will reach a point whether things stop changing. That point is called the “equilibrium.” At the equilibrium, everyone will end up with a certain amount of money. The amount of money that everybody gets at the equilibrium depends on how talented they are, and not on anything that happened before. So if you rob a bank, it won’t matter because when you get to the equilibrium, if you’re stupid, you will still have the same amount of money you would have had if you didn’t rob the bank."
"This paper examines a fundamental problem in applied mathematics. How can one model the behavior of materials that display radically different, dominant behaviors at different length scales. Although we have good models for material behaviors at small and large scales, it is often hard to relate these scale-based models to one another."
"I’ve posted to YouTube a series of 22 short videos giving an introduction to quantum computing. Here’s the first video:
Below I list the remaining 21 videos, which cover subjects including the basic model of quantum computing, entanglement, superdense coding, and quantum teleportation.
To work through the videos you need to be comfortable with basic linear algebra, and with assimilating new mathematical terminology. If you’re not, working through the videos will be arduous at best! Apart from that background, the main prerequisite is determination, and the willingness to work more than once over material you don’t fully understand."
If one ‘goes Platonic’ with math, one has to face several important philosophical consequences, perhaps the major one being that the notion of physicalism goes out the window.
"A new book, Loving and Hating Mathematics: Challenging the Myths of Mathematical Life (Princeton University Press) takes a look at some of the most common (mis)conceptions about mathematics and mathematicians, addressing their origins and assessing their truth value in a somewhat unexpected fashion. Rather than amassing data on PISA and SAT scores, analyzing the race and gender breakdowns of degrees awarded or tenure and promotion rates, or perhaps administering Enneagram tests to math majors, authors Reuben Hersh and Vera John-Steiner focus on the lives and experiences of mathematicians, past and present."
"But this isn’t about natural aptitude, it’s about practice. That other student has more practice. You can catch-up, but you have to put in the hours, which brings me back to my original advice: keep working even after you get stuck.
That’s where you make up ground."
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