Wk  Lectures  Topics  Remarks 
1  9/12 
Review of the Riemann Integral
 
 9/14 
$\sigma$algebras and Borel sets
 
 9/15  Problem session  
 9/16 
Measurable functions
 
2  9/19 
Simple functions
 
 9/21 
Measures
 Lecture by Prof. Williams 
 9/23 
Integral of positive functions
 Lecture by Prof. van Erp 
3  9/26 
Integration of complex functions
 
 9/28 
Dominated Convergence, null sets
 
 9/30 
Outer measures
 Not in text 
4  10/03 
Lebesgue measure on the real line
 Not in text 
 10/05 
Extension of premeasures
 Folland 
 10/06  Problem session  
 10/07 
Product measures
 Folland 
5  10/10 
Integration on products
 Folland 
 10/12 
$L^1$spaces
 
 10/13  Problem session  Comparison of the Riemann and Lebesgue integrals 
 10/14 
Complex and signed measures
 
6  10/17 
Modes of convergence
 
 10/19 
The RadonNikodym Theorem
 
 10/20  Midterm examination  Elements of solution 
 10/21 
Holomorphic functions
 
7  10/24 
Curves and paths
 
 10/26 
Integrals on paths
 
 10/27 
Cauchy's Theorem for convex sets
 
 10/28 
Analyticity
 
8  10/31 
Zeroes and singularities
 
 11/02 
Cauchy estimates
 
 11/03  Problem session  
 11/04 
Local behavior of holomorphic functions
 
9  11/07 
Chains, cycles, homology
 
 11/09 
Cauchy's Theorem, homotopy invariance
 
 11/10 
Meromorphic functions, the Residue Theorem
 
 11/11 
Laurent series expansions
 
10  11/14  Wrapup  
 11/15  Problem session  from 2:30pm in Kemeny 120 
 11/18  Final examination
 Elements of solution
