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Full-Text Articles in Other Mathematics
Teaching Introductory Statistics With Datacamp, Benjamin Baumer, Andrew P. Bray, Mine Çetinkaya-Rundel, Johanna S. Hardin
Teaching Introductory Statistics With Datacamp, Benjamin Baumer, Andrew P. Bray, Mine Çetinkaya-Rundel, Johanna S. Hardin
Statistical and Data Sciences: Faculty Publications
We designed a sequence of courses for the DataCamp online learning platform that approximates the content of a typical introductory statistics course. We discuss the design and implementation of these courses and illustrate how they can be successfully integrated into a brick-and-mortar class. We reflect on the process of creating content for online consumers, ruminate on the pedagogical considerations we faced, and describe an R package for statistical inference that became a by-product of this development process. We discuss the pros and cons of creating the course sequence and express our view that some aspects were particularly problematic. The issues …
Approaching Cauchy’S Theorem, Stephan Ramon Garcia, William T. Ross
Approaching Cauchy’S Theorem, Stephan Ramon Garcia, William T. Ross
Department of Math & Statistics Faculty Publications
We hope to initiate a discussion about various methods for introducing Cauchy’s Theorem. Although Cauchy’s Theorem is the fundamental theorem upon which complex analysis is based, there is no “standard approach.” The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include Green’s Theorem, Goursat’s Lemma, Leibniz’ Rule, and homotopy theory, each of which has its positives and negatives.
Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin
Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin
All HMC Faculty Publications and Research
I still recall my thrill and disappointment when I read Mathematical Carnival, by Martin Gardner. I was thrilled because, as my high school teacher had recommended, mathematics was presented in a playful way that I had never seen before. I was disappointed because it contained a formula that I thought I had "invented" a few years earlier. I have always had a passion for mental calculation, and the following formula appears in Gardner's chapter on "Lightning Calculators." It was used by the mathematician A. C. Aitken to mentally square large numbers.