Grad Real Analysis, Fall 2015

Math 211, Fall 2015
Course Graduate Real Analysis
Meetings E+ (see Announcements), BP 5
Professor Moon Duchin -- ( moon.duchin @ tufts.edu )

Materials, resources, links

Here are the (rather minimalist) syllabus and the slides from the first lecture.

The whole textbook is available free online. However, I really recommend that you purchase a physical copy.

Here's my sheet of course highlights to help you while you're consolidating the material for the midterm.

Background/Prerequisites:

Here is a colleague's list of prerequisites for working with our text. I'll go over some of this, but you should get very quickly up to speed on this material.
  • Point-set topology Notes by Hatcher
  • Topology Crash Course written for new Chicago grads
  • Lecture notes containing basic properties of the reals (least upper bound/monotone convergence, Bolzano-Weierstrass, Heine-Borel, nested interval property, etc) and other greatest hits of undergraduate real analysis (Riemann integration, uniform convergence)

    (Links are offered with no warranty! Let me know about errors.)

    • Announcements

    Our default meeting time is E+MW (Mon,Wed 10:30-11:45) with some use of Fridays (advertised in advance).

    Final Exam: Weds Dec 16, 3:30-5:30pm, usual classroom.

    Homework

    Due Wednesdays at the beginning of class.

  • HW1 (Sept 16): Ch 1 Ex 1,2,3,4,14,24.
  • HW2 (Sept 23): Ch 1 Ex 6,10,11,16. Extra credit: Prob 1 (p46)
  • HW3 (Sept 30): Ch1 Ex 13,18,22,26,27,32,33
  • HW4 (Oct 7): Ch2 Ex 1,3,5,6,7
  • HW5 (Oct 21): Ch2 Ex 7 (again), Napkin Ring problem. Extra credit: Prob 5 (p96)
  • HW6 (Nov 4): Understand one of the major proofs from Ch3.
  • HW7 (Nov 11): Ch 3 Ex 3,10,13,18,19,31
  • HW8 (Nov 18): Ch 4 Ex 1,2,3,4,5
  • HW9 (Nov 30) Ch 4 Ex 7,8,10,11,12
  • HW10 (Dec 2): Ch 4 Ex 19,20,22,24,32
  • HW11 (Dec 11): Ch 6 Ex 2,3,5,10,12,14,15 Extra credit: Ex 16,17
    Note for #5: the gamma function is \(\Gamma(s)=\int_0^\infty e^{-t} t^{s-1}\, dt\).