# Spring 2018

## Course Materials

Syllabus
Mathematics Professors and Mathematics Majors' Expectations of Lectures in Advanced Mathematics [Keith Weber, AMS Blog]

## Lecture Notes

1A. Course Overview (Part A)
1B. Course Overview (Part B)
2. The Riemann Integral and Conditions for Integrability
3A. Lower and Upper Darboux Integrals (Part A)
3A. Lower and Upper Darboux Integrals (Part B)
4. Integrability Results
5. Properties of the Riemann Integral
6. Main Integration Theorems
7. Improper Integrals
8. The Gamma Function
9A. Functions of Bounded Variation (Part A)
9B. Functions of Bounded Variation (Part B)
9C. Functions of Bounded Variation (Part C)
10A. Riemann Stieltjes Integration (Part A)
10B. Riemann Stieltjes Integration (Part B)
10C. Riemann Stieltjes Integration (Part C)
10D. Riemann Stieltjes Integration (Part D)
11. Summary of Results on BV and RSI
12. Topology of Euclidean Space
13A. Lebesgue Measure on Euclidean Space (Part A)
13B. Lebesgue Measure on Euclidean Space (Part B)
14. Lebesgue Measure on Euclidean Space (Cont'd)
15. Inner and Outer Measure; Measurable Sets
16. Sigma-Algebras and Measurable Functions
17. Introduction to the Lebesgue Integral

## Homework Assignments

Homework 1 [Due Mon Jan 29]
Homework 2 [Due Mon Feb 5]
Homework 3 [Due Wed Feb 14]
Homework 4 [Due Wed Feb 21]
Homework 5 [Due Wed Mar 21]
Homework 6 [Due Mon Apr 2]
Homework 7 [Due Wed Apr 11]
Homework 8 [Due Wed Apr 18]
Homework 9 [Due Wed Apr 25]

## Practice Problems for Exams

The midterm exam will cover up to functions of bounded variation.

Practice Problems for Midterm Exam