This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked.
Week #1:
Aug 30  Sep. 3 Homework 
Metric Spaces
Compact Sets 
Finite, countable infinite and uncountable sets.
NxN and Q are countable, binary operations. Groups, Examples, identity and inverse elements. 
Week #2:
Sep. 6  10 Homework  Compact Sets
Connected Sets  Rings, Examples
Fields, Examples, the Real numbers 
Administrative Note: Monday 6 September is Labor Day. Class will not meet.  
Week #3:
Sep 13  17 Homework Problem Session 1 
Convergent Sequences
Subsequences Cauchy Sequences 
Homomorphisms of groups, normal subgroups.

Week #4:
Sep. 20  24 Homework Problem Session 2 
Series
Series of Nonnegative terms The Root and Ratio Tests Power Series Summation by Parts 
Quotient groups, the First Isomorphism Theorem.

Week #5:
Sep. 27  Oct. 1 Homework Problem Session 3 
Absolute Convergence
Addition and Multiplication of Series Rearrangements Limits of Functions Continuous Functions 

Week #6:
Oct. 4  8 Homework Problem Session 4 
Continuity and Compactness
Continuity and Connectedness Discontinuities Monotonic Functions Infinite Limits and Linits at Infinity Connected, Path Connected and Simply Connected. Homotopies and the Fundamental Group. 

Week #7:
Oct 11  15 Midterm Problem Session 5 
The Derivative of a Real Function
Mean Value Theorems The Continuity of Derivatives L'Hospital's Rule Derivatives of Higher Order 

Week #8:
Oct 18  22 Homework Problem Session 6 
Taylor's Theorem
Differentiation of Vectorvalued Functions Sequences and Series of Functions: Discussion of Main Problem 

Administrative note: Friday 22 October is the MidSemester Break. Class will not meet.  
Week #9:
Oct 25  29 Homework 
Uniform Convergence
Uniform Convergence and Contuinity Uniform Convergence and Differentiation 

Week #10:
Nov 1  5 Homework Problem Session 8 
Equicontinuous Families of Functions
Definition and Existence of the (Riemann) Integral Properties of the Integral 

Week #11:
Nov 8  12 Homework 
Integration and Differentiation
Integration of Vector Valued Functions Rectifiable Curves 

Week #12:
Nov 15  19 Homework Problem Session 10 
Set Functions
Construction of the Lebesgue Measure 

Week #13:
Nov 22  26 Homework 
Measure Spaces


Week #14:
Nov 29  Dec 3 Homework 
Measurable Functions
Simple Functions Integration 

Week #15:
Dec 6  10 Homework 
Comparison with the Riemann Integral
Integration of Complex Functions Functions of Class L^{2} 

Administrative note: Friday 10 December is the last day of class.  
Final Exam
Dec 10  21 
The Final Exam will be a take some exam. 