Posted by guest on 05. February 2013 · 1 comment · Categories: books · Tags: , ,
A Guest Post by Emily Shier

From Here to Infinity: A Guide to Today’s Mathematics
By Ian Stewart
1996 edition

“From Here to Infinity” is an enchanting read, which inspires both budding mathematicians, and curious outsiders alike. For mathematicians are mysterious beings to the general population; enshrouded in a cloak of cryptic symbols, they slip into another world, with an aura the ignorant classify as having a residue of chalky smoke, and mundane arithmetic.

Stewart bridges the gap between the uninformed individual and the world of mathematics with friendly, open approach. Several comprehensive chapters discuss intriguing topics, including chaos theory, knots, computer technology, algorithms, fractals, Fermat’s last theorem, and how to increase one’s odds of winning the lottery.

Never speaking down to the reader, Stewart provides many examples to illustrate a concept, which are punctuated with the occasional joke. For the reader with little exposure, the examples are fascinating, and show another side of thinking all together. However, as the examples develop, the level of math increases steeply. But, the initial feeling of frustration with a challenging idea gives way to a feeling of satisfied accomplishment with the completion of each chapter.
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Posted by Jason Polak on 29. January 2013 · 2 comments · Categories: math · Tags: ,

Early one morning in the halls of a typical mathematics department, Katie, a graduate student in the field of higher category theory, walks into her final exam for grad algebra 1. She had enough sleep the previous night, and feels confident about her abilities. The first question is a routine application of Nakayama’s lemma, and the next an exercise in computing a $ \mathrm{Tor}$ group. After half an hour of deftly dealing out solutions, she comes to the last item:

Explain the importance of module theory in ring theory using a few examples.

What kind of exam is this? Katie thinks. The question is not true, false, a computation, a proof, or undecidable in ZFC + V=L! Madness!

The Role that Essays Could Have in Math

I made this story up entirely. However, believe incorporating a small amount of such questions would be useful in emphasising intuition and the aesthetic side of mathematics, and this is something that could be used in upper undergraduate and all graduate courses.
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