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Career opportunities for PhDs in the mathematical sciences have never been better. Traditional faculty positions in mathematics departments in colleges and universities range from all teaching to combined teaching and research responsibilities. Beyond those, a wide array of careers has now opened up to freshly minted graduates, in academics, industry, business, and government. It is well-understood that these all require somewhat different preparations for PhDs to be competitive. This commentary compares and contrasts mathematics graduate programs with Ph.D. programs in the life and biomedical sciences, which are structured in a way that allows considerable customization around each students career goals. While these programs may not be appropriate templates for the mathematical sciences, they have some features that might be informative. This commentary is intended to add perspective to the ongoing discussion around PhD training in the mathematical sciences. It also provides some concrete proposals for changes.
Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching of mathema
I am an industrial mathematician. When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement is commonly greeted by a blank stare or an uncomfortab
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
This is an expanded version of my review of Nina Engelhardts book Modernism, Fiction and Mathematics, Edinburgh University Press 2018. A considerably shortened version will appear in the Notices of the AMS.
We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and several t