Probability and Statistics (Science 3150):
Statistics is the heart of the scientific method, and the part of mathematics least separable from experience. It is founded upon probability theory developed 400 years ago by French gamblers, began to be an independent discipline 200 years ago, and in the past century, became a regular course on offer in schools. During that time, statistics has appeared elusive to many people: a bag of miscellaneous tricks, dogma, and jargon. That needs to change since, in our era, statistical reasoning drives constant social-technological revolutions. Its worldview is so potent that the world has become incomprehensible without it. This course covers standard introductory topics: description and depiction of data; design of useful experiments; the structure of possible outcomes; evaluating the quality of results as evidence; what generalities are implied by limited observations; incremental revision of belief in response to changing data; formulating predictive rules based on experience. In addition to mathematical problem-solving, more reading will be assigned than in a typical math course. There will be an independent data analysis project. The course includes an introduction to computer programming, for statistical calculations and visualizations.
Physical Means of Mathematics (Course Proposal):
The purpose of this course is to build the things that have built mathematics. It's obvious that things are made from ideas. Conversely, ideas come from things. Mathematics develops in such a feedback loop. It surely relies on abstraction, but the common prejudice---among people inclined toward mathematics---that exaggerates its unrelatedness to real things is often harmful. The "things of mathematics" are its tools. They are interesting, subtle, and ... nowadays, mostly unknown. Abacus, astrolabe, sextant, sector, slide rule, planimeter, and others were ancestors of the earliest computers, such as the difference engine and the differential analyzer, which were special-purpose and mechanical. This course sets electronics aside to rediscover how mathematics was, so to speak, "handled" by earlier people in a much more literal way. To make tools (not merely use them) expertise is indispensable. That is why, rigorously to revisit fundamental mathematics, we will examine, understand, and actually build devices such as these. The course content extends across traditional divisions in mathematics (arithmetic, algebra, geometry, trigonometry, calculus) and, in the context of ancient calculation methods, incorporates perspectives on mathematical cognition from psychology and anthropology.
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