Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 125A: Real Analysis
Approved: (revised 2007-04-24, Eric Rains)

ATTENTION:

Effective Winter 2010, the Department is in discussion about the use of a different textbook than what is noted on the suggested syllabus for this course. As always with any class, please consult with your instructor for more information.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Kenneth Ross, Elementary Analysis: The Theory of Calculus. Springer-Verlag ($34.70)
Search by ISBN on Amazon: 1441928111

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics


Chapter 3

Continuity

3

17

Continuous functions

2

18

Properties of continuous functions

3

19

Uniform continuity

2

20

Limits to functions


Chapter 4

Sequences and Series

2

23

Power series

2

24

Uniform convergence

2

26

Differentiation of power series


Chapter 5


2

28

Derivatives

2

29

Mean Value Theorem

2

31

Taylor’s Theorem


Metric Spaces


3

21

Metric Spaces and Continuity

2

22

Metric Spaces and connectedness

Additional Notes:

Total number of lectures = 25.

Optional if time allows:

- 2 lectures, Section 27, Weierstrass Approximation
- 2 lectures, Section 30, L’Hopital’s Rule

This syllabus recommends covering metric spaces at the end of the quarter, but they can be covered earlier if preferred.