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What does it mean for a mathematical problem to be unsolvable? The very concept does not seem to have been much considered, until, in 1824, a young Norwegian named Niels Henrik Abel published a small pamphlet on an old problem. The pamphlet was one of the first markers of a sea change in mathematics, and by the time Abel died, six years later at the age of twenty-six,
In this experimental class, we will create space for you to pursue work within or near mathematics, statistics, data science, etc. This course is intended for students at a variety of levels of experience with a solid interest in following questions and curiosity to lead to a deeper understanding. You will lead your work, in collaboration and with the support of
This foundational class covers modes of reasoning used in quantitative sciences and mathematics. While learning the art of mathematical modeling, i.e. translating the physical systems/real-life situations into mathematics, we will apply problem solving and practice effective communication of mathematics. This process involves isolating the essential variables and
Carl Friedrich Gauss wrote: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it." The thesis of this class is that this is still true today. Leonhard Euler's (1707–1783) collected works run to 81 volumes and over 35,000 pages, the publication only having been (mostly) completed in 2022. Most of
Together with calculus, linear algebra is one of the foundations of higher-level mathematics and its applications. This is NOT just the algebra you know from high school. There are several perspectives one can take on linear algebra: it is a method for handling large systems of linear equations, it is a theory of linear geometry (including in dimensions larger than three),
