John McCarthy on Arithmetic

John McCarthy (), an American computer scientist and cognitive scientist who was one of the founders of the discipline of artificial intelligence
in Computer Scientist Coined ‘Artificial Intelligence’ in The Wall Street Journal

 

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The Response of the Schoolmaster

This must certainly be the quote of the week from English author Alan Bennett’s play Forty Years On:

Foster: I’m still a bit hazy about the Trinity, sir.
Schoolmaster: Three in one, one in three, perfectly straightforward.  Any doubts about that see your maths master.

 

Paul Halmos on Prerequisites

Definitely the quote of the day:

Paul Halmos (1916 – 2006, Hungarian-born American mathematician
in Measure Theory (1950)

 

This is essentially the mathematician’s equivalent of the adage “Fake it ’til you make it.”

Riemann’s On the Hypotheses Which Lie at the Foundations of Geometry

One must be truly enamored of the internet that it allows one to find and read a copy of Bernhard Riemann’s doctoral thesis Habilitation Lecture (in English translation) at the University of Göttingen from 1854!

His brief paper has created a tsunami of mathematical work and research in the ensuing 156 years. It has ultimately become one of the seminal works in the development of the algebra and calculus of n-dimensional manifolds.

Terence Tao Teaching Real Analysis at UCLA this Fall

Holy cow! I discovered on Friday that Terence Tao, a Fields Medal winner, will be teaching a graduate level Real Analysis class this fall at UCLA.

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Surprisingly, to me, it ony has 4 students currently enrolled!! Having won a Fields Medal in August 2006, this is a true shock, for who wouldn’t want to learn analysis from such a distinguished professor? Are there so few graduate students at UCLA who need a course in advanced analysis? I would imagine that there would be graduate students in engineering and even physics who might take such a course, but perhaps I’m wrong?

Most of his ratings on RateMyProfessors are actually fairly glowing; the one generally negative review was given for a topology class and generally seems to be an outlier.

On his own website in a section about the class and related announcements we seem to find the answer to the mystery about enrollment.  There he says:

 I intend this to be a serious course, focused on teaching the material in the course description.  As such, students who are taking or auditing the course out of idle curiosity or mathematical “sightseeing”, rather than to learn the basics of measure theory and integration theory, may be disappointed.  I would therefore prefer that frivolous enrollments in the class be kept to a minimum.

This is generally sound advice, but would even the most serious mathematical tourists really bother to make an attempt at such an advanced course? Why bother if you’re not going to do the work?!

Fans of the Mathematical Genealogy Project will be interested to notice that Dr. Tao is requiring his Ph.D. advisor’s text Real Analysis: Measure Theory, Integration, and Hilbert Spaces. He’s also recommending Folland‘s often used text as well, though if he really wanted to scare off the lookie-loos he could just say he’ll be using Rudin‘s text.

Baum’s Point Set Topology

You know it's a good start to the weekend when you've just acquired Baum's Point Set Topology for $2.72!
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Elements of Point-Set Topology (Dover Books on Advanced Mathematics) Elements of Point-Set Topology by John D. Baum

Commenting only after reading to page 11, but having skimmed some other parts/sections, it’s a nice and condensed volume with most of the standard material on point set topology. It reads somewhat breezily, is well laid out, and isn’t bogged down with all the technicalities which those who haven’t seen any of this material before might have interest in. It seems better for those with some experience in axiomatic mathematics (I’ve always enjoyed Robert Ash’s A Primer of Abstract Mathematics for much of this material), but in my mind isn’t as clear or as thorough as James Munkres’ Topology, which I find in general to be a much better book, particularly for the self-learning crowd. The early problems and exercises are quite easy.

Given it’s 1964 publication date, most of the notation is fairly standard from a modern perspective and it was probably a bit ahead of it’s time from a pedagogical viewpoint.

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