MATH 431

MATH 431
Real Analysis II

Catalog Entry

MATH 431. Real Analysis II
Three hours lecture (3).

Prerequisites: MATH 430.

A systematic modern approach to higher-level topics in Real Analysis. 

 

Detailed Description of Content of Course

The course will cover the following topics:

1. Integration
2. Pointwise convergence vs Uniform Convergence
3. Normed Linear Spaces and Banach Spaces
4. Lebesgue Measure
5. Lebesgue Integration
6. Functions of Bounded Variation (time permitting)

 

Detailed Description of Conduct of Course

This course can be taught traditionally or flipped or via other Inquiry-Based Learning methods. Some professors may require students to work together in small groups. 

 

Goals and Objectives of the Course

The student learning outcomes are as follows:

1. to continue to develop an understanding of the analytic properties of functions
2. to develop and understanding of similarities and differences between uniform convergence and pointwise convergence
3. to develop an understanding of higher-level concepts including Banach spaces and measure theory. 
4. to continue to develop their proof-writing skills

 

Assessment Measures

Graded tasks may include homework, exams, final exams, quizzes, class participation, attendance, and final projects and presentations. 

 

Other Course Information

None

 

Review and Approval

DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair

March 30, 2026