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
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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 
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.