Prof Timothy Gowers is the Cambridge Professor who won the 1998 Fields Medal. Surprisingly he teaches such “low level” undergrad course (Analysis I), but he takes a higher-level approach to tackle the subject with much deeper and broader view.
A master can teach the same subject with a ‘helicopter’ view than an ordinary prof who only confuses the students with over-detailed views of ‘trees’ without letting them see the ‘forest’. (见树不见林).
For example, Prof Gowers brilliantly points out that Analysis is all about Real Number Structure with ONLY 1 AXIOM : Least Upper Bound.
I really enjoy Prof Gowers’s blog. He is the man whom David Hilbert was looking for : “The Pied Piper”, able to bring complicated Math down approachable to the ordinary men on the streets.
Abel also advised us, “Read Direct from the Masters“. Prof Gowers is the Master. 行家一出手, 便知有没有.
Note: I have a ‘lay-man’ analogy of the “Least Upper Bound” of Real Number (or the scary name: Complete Ordered Field). Example: The Bible said God gave the descendants of Noah (i.e. include all mankind now) after The Flood a life span of maximum 120 years. This week the Hong Kong Movie tycoon, billionaire and philanthropist, Sir Run Run Shaw, died at 107 years-old. His Life Span = (0,120), but his extraordinary Least Upper Bound is 107 🙂 Prof Gowers, do you agree with my analogy for non-mathematicians ?
This term I shall be giving Cambridge’s course Analysis I, a standard first course in analysis, covering convergence, infinite sums, continuity, differentiation and integration. This post is aimed at people attending that course. I plan to write a few posts as I go along, in which I will attempt to provide further explanations of the new concepts that will be covered, as well as giving advice about how to solve routine problems in the area. (This advice will be heavily influenced by my experience in attempting to teach a computer, about which I have reported elsewhere on this blog.)
I cannot promise to follow the amazing example of Vicky Neale, my predecessor on this course, who posted after every single lecture. However, her posts are still available online, so in some ways you are better off than the people who took Analysis I last year, since you will have…
View original post 3,819 more words