# Summer Mini-Courses 2018

Summer 2018 will feature two mini-courses:

**Mini-Course #1****Math 8910 - Analysis and Number Theory**

CRN#62067

Instructor: Neil Lyall

Ten Lectures on June 18-22 (MTWRF) and 25-29 (MTWRF), 10:00-11:00 AM, Boyd 410

Lecture 1: Basic Prime Number Estimates

Lecture 2: The Riemann-Zeta Function

Lecture 3: Newman's Short Proof of the Prime Number Theorem

Lecture 4: Dirichlet Convolution, Dirichlet's Hyperbola Method, and Landau's Theorem on the Mean Value of the Mobius Function

Lecture 5: Borel's Law of Large Numbers and Hausdorff's improvement, Random Series, and a second proof of Hausdorff's improvement

Lecture 6: Maximal Functions and the Lebesgue Differentiation Theorem

Lecture 7: Ergodic Theory I - Examples, Weyl's equidistribution theorem and V.I. Arnold’s "first digits of the powers of 2" problem

Lecture 8: Ergodic Theory II - Poincare Recurrence, Ergodicity, and von-Neumann's Mean Ergodic Theorem

Lecture 9: Ergodic Theory III - Birkhoff's Pointwise Ergodic Theorem

Lecture 10: Ergodic Theory IV - Applications to Normal Numbers and Continued Fractions (Khintchine’s constant)

**Mini-Course #2**__Math 8920 - A crash course on homotopy theory__

CRN#61994

Instructor: Weiwei Wu

Seven Lectures on June 11-14 (MTWR) and 20-22 (WRF), 1:30-3:00 PM, Boyd 410

Course Description: The course is to cover basic notions of homotopy groups, homotopy fibrations and cofibrations, Puppe sequences, Hurewicz and Whitehead theorems. Time allowing I will explain how this fits into the framework of model categories, or in a different direction, I could go towards generalized homology and spectra, depending on student interests. The main reference will be Chapters 6 and 8 of "Lecture Notes in Algebraic Topology" by Davis and Kirk.