I recently added two new pages to the blog: a bibliography for listing references I cite on multiple occasions, and a suggestions and requests page. The bibliography is likely to soon contain citations for at least some of the following books which have recently come into my possession: Introduction to the Theory of Computation, Sipser [...]
Posts Tagged ‘pedagogy’
Textbooks
Posted in remarks, tagged pedagogy on December 18, 2009 | 10 Comments »
Halmos on writing and education
Posted in remarks, tagged pedagogy, philosophy of mathematics on August 5, 2009 | 8 Comments »
John Ewing wrote up a nice collection of quotes from Paul Halmos for the Notices of the AMS; let’s meditate on his words. For example: The best notation is no notation; whenever possible to avoid the use of a complicated alphabetic apparatus, avoid it. A good attitude to the preparation of written mathematical exposition is [...]
IMO 2009 and proof systems
Posted in abstract algebra, number theory, Putnam / competitions, remarks, tagged Chebyshev polynomials, equivalence relations, Galois theory, Grobner bases, pedagogy, philosophy of mathematics, trigonometry on July 17, 2009 | 3 Comments »
The problems from IMO 2009 are now available. I haven’t had much time to work on them, though. There are two classical geometry problems, which I already know I won’t attempt. While I am well aware that classical geometry often requires a great deal of ingenuity, I am also aware of the existence of the [...]
Mathematical historical fiction
Posted in remarks, tagged pedagogy, philosophy of mathematics on July 3, 2009 | 7 Comments »
Bill Gasarch is right – writing technical posts is tiring! (I’ve been trying to finish the next GILA post for days.) So I’ll share some more thoughts instead. Today’s thought was triggered by David Corfield: In the first of the above posts I mention Leo Corry’s idea that professional historians of mathematics now write a [...]
Going beyond your comfort zone
Posted in remarks, tagged pedagogy on June 30, 2009 | 7 Comments »
When someone linked me to Ravi Vakil’s advice for potential graduate students, I was struck by the following passage: …[M]athematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you’ll never get anywhere. Instead, you’ll have tendrils [...]
I hate axioms
Posted in remarks, tagged pedagogy, philosophy of mathematics on June 27, 2009 | 4 Comments »
(A more appropriate title for this post would probably be “I hate Bourbaki,” but I like it as is.) I spend a lot of my free time reading research papers, usually in combinatorics; those tend to require the least background. Today I decided to read everything I could find written by one of the great [...]
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