MATH 421

Institutional Syllabus ___ New Course ___ Substantive Change in Existing Course

I.

Course Title: Advanced Analysis II

II.

Course Prefix/Number: MATH 421

Date of Last Review Date of Most Recent Approval

Fall 2007 Fall 2007

III. Credit Hours: 3 IV. Prerequisites: MATH 420 minimum grade: C V.

Catalog Description This course is a continuation of Math 420 with an emphasis on integration, sequences and series of functions, uniform convergence, infinite series, and additional topics of the instructor's choosing.

VI. Curricular Relationships This course is an elective in the mathematics curriculum. VII. Student Learning Outcomes 

Students will be able to demonstrate a deep understanding of and proficiency in the fundamental concepts of integration, including the Riemann integral, and the Generalized Riemann integral or the Lebesgue integral..



Students will be able to prove theorems and solve problems in an abstract setting.

VIII. Content Outline 

Riemann integral.



Sequences and Series of functions, including uniform convergence properties.

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Generalized Riemann integral or the Lebesgue integral.

IX. Course Procedures/Policies/Grading Scale:  Homework assignments will comprise some portion of the course grade. Assignments are designed to develop a student's reading, writing, synthesis, and critical thinking skills.  At least three examinations are given each term.  A comprehensive final examination is given during finals week.  Computer software may be used to solve realistic problems. X.

Required/Recommended Readings A standard undergraduate book in Real Analysis. Examples: 

Bartle, Robert G., and Donald R. Sherbert. Introduction to real Analysis. 3rd Ed. New York, NY: John Wiley and Sons, 2000.



Lay, Steven R. Analysis with an Introduction to Proof. Fourth Edition. Upper Saddle River, NJ: Pearson/ Prentics Hall 2005.

XI. Issues Unique to this Course: None XII. Additional Departmental Issues: None