MATH 430

MATH 430:431: Real Analysis I

Prerequisites: MATH 301.

Credit Hours: (3)

A systematic modern approach to limits, continuity, and differentiation of functions of one variable, including standard topics of mathematical analysis.

Detailed Description of Content of Course

The course will cover the following topics: Some selected contents will be explored with appropriate technological tools.

1. General Metric Spaces and the Metric Topology
2. Standard Topology of the Real line 
3. Limits Superior and Inferior
4. Limits and Continuity of functions, Uniform Continuity, Lipschitz Continuity
5. Differentiation
6. The Mean-Value Theorem

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 learning outcomes for MATH 430 are as follows:

1. to develop an understanding of the metric topology for general metric spaces
2. to develop an understanding of the analytic behavior of functions
3. to further develop proof-writing skills of students, including the logical and orderly presentation of proofs. 

Students are expected to gain knowledge of Real Analysis, along with the theoretic underpinnings of single-variable Calculus. 

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

March 30, 2026
February 20, 2017
Sept. 2001 Review Stephen Corwin, Chair