College of the Holy Cross, Spring 2017

Math 242 (Principles of Analysis)

Professor Hwang (rhymes with song).

Teaching schedule and office hours.

Last modified: April 21, 2017

---

Course Information

The course text is Principles of Analysis, available only at the College Bookstore.

• Lecture Schedule
• Problem Sets
• Course Outline

Extra Resources

• Godfrey Harold Hardy's free 1921 text A Course of Pure Mathematics (third edition) is a more calculus-flavored account of introductory analysis.

Interactive Software

• Riemann integration.
• Images of complex mappings.
• Images and preimages game.
• Guess the supremum.
• Spirograph.
• The Lorenz Attractor
• Interactive wind map

Miscellaneous Images and Animations

• Zooming in on:
  $y = \sum\limits_{k=1}^{\infty} \frac{1}{100^{k}} \cos(100^{k} x)$ ,
  $y = x^{2} \sin(\frac{1}{x})$,
  A nowhere-differentiable function.
  
• Möbius transformations revealed, a short, award-winning movie by Douglas Arnold and Jonathan Rogness.
• Deterministic chaos (wikipedia).
• Bounded sequences that diverge:
  $a_{k} = k\gamma \pmod{1}$, $\gamma = \frac{1}{2}(1 + \sqrt{5})$ the golden ratio.
  $a_{k} = k\alpha \pmod{1}$, $\alpha$ a number close to $0.1$.
  $a_{k} = \sin(k)$.
• Greek alphabet