MTH 505A Real Analysis - Reading and Conference

Course Objective:

This course is for prospective AP-calculus high school teachers who are required to add a sufficient knowledge of the real analysis to their teaching background. The real analysis is the most fundamental mathematical subject of the real and the vector-valued functions. It is the backbone of the calculus theories and focuses on the construction of calculus theories rather than focusing on the skill-building of calculus.  In this course, we study the construction of the real number system, the limits of the sequences and real-value functions, continuity, differentiation, and Riemann integration. 

Course Format: This course is geared primarily as an online course. However, a short weekly or bi-weekly meeting can be established to meet in Zoom, as necessary.

Textbook: Introduction to Real Analysis, 3rd/4th edition, Bartle and Sherbert, Wiley. 

 Course Outline:   

  • Chapter 2: The Real Numbers
  • Chapter 3: Sequences (and Series)
  • Chapter 5: Limits of Continuous Functions
  • Chapter 6: The Derivatives
  • Chapter 7 The Riemann Integration
Prerequisites: Students are assumed to have some knowledge of lower division differentiation, integration, sequences, infinite series, Taylor series, and some experiences of proofs.

 

Homework: There will be about seven weekly homework assignments. These will mainly base on your reading and proofs. There may be some skill-building problems. To help the progress of this course, each homework is expected to be submitted weekly in timely manner. Some details can be further discussed on our first Zoom meeting.

 Grade Policy: As this course is completed, a grade will be given. The exact format of the grade option can be further discussed.