Dedekind Cuts Notes  Chapter 2  Chapter 3  Chapter 4  Chapter 6, A brief overview

Week 1

Lecture 1: Introduction. Algebraic Systems.             text    video (17 min, 38 sec)    
Lecture 2: Chapter 1, Section 2, Dedekind Cuts.         text    video (42 min, 48 sec)
Lecture 3: Chapter 1, Section 2, Dedekind Cuts.         same    video (42 min,  2 sec)

Week 2

Lecture 4: Chapter 2, Section 1, Metric Spaces.         text    video (17 min, 24 sec)
Lecture 5: Chapter 2, Section 2, Continuity.            text    video (11 min,  9 sec)
Lecture 6: Chapter 2, Section 3, Topology.              text    video (18 min, 16 sec)
Lecture 7: Chapter 2, Section 3, More Continuity.       text    video ( 7 min, 38 sec)

Week 3

Lecture 8: Chapter 2, Section 3, Closure, etc.          text    video (10 min, 18 sec)
Lecture 9: Chapter 2, Section 3, Subspaces.             text    video ( 9 min, 10 sec)
Lecture 10: Chapter 2, Section 3, Prod's & complete     text    video ( 9 min, 55 sec)
Lecture 11: Supplement, The Open Subsets of R.          text    video (16 min, 42 sec)
 
Week 4

Lecture 12: Chapter 2, Section 4: Compactness.          text    video (24 min, 45 sec)  correction!!! 
Lecture 13: Chapter 2, Section 4: Compactness.          same    video (17 min,  7 sec)
Lecture 14: Chapter 2, Section 5: Connectedness.        text    video (36 min, 35 sec)
Lecture 15: Chapter 2, Section 6: Other stuff.          text    video (16 min, 39 sec)

Week 5

Lecture 16: Chapter 2, Section 6: Other stuff.          same    video ( 1 min, 17 sec)
Lecture 17: Chapter 2, Section 7: Coverings.            text    video (29 min,  7 sec)
Lecture 18: Chapter 2, Section 8: Cantor Sets.          text    video (41 min,  6 sec)
Lecture 19: Chapter 2, Section 9: Cantor Sets.          same    video (10 min, 15 sec)

Week 6

Lecture 20: Supplement, Fractals.                       text    video (10 min, 26 sec)
Lecture 21: Chapter 2, Section 10: Completion.          text    video ( min, sec)
Lecture 22: Chapter 2, Section 10: Completion.          text    video ( min, sec)
Lecture 23: Chapter 3, Section 1: Differentiation.      text    video ( min, sec)

Week 7

Lecture 24: Chapter 3, Section 1: Differentiation.      same    video ( min, sec)
Lecture 15: Supplement, e is irrational.                text    video ( 5 min, 45 sec)
Lecture 16: Chapter 3, Section 2: Riemann Integration.  text    video ( min, sec)
Lecture 17: Chapter 3, Section 2: Riemann Integration.  same    video ( min, sec)

Week 8

Lecture 18: Chapter 3, Section 2: Riemann Integration.  same    video ( min, sec)
Lecture 19: Chapter 3, Section 2: Riemann Integration.  same    video ( min, sec)
Lecture 20: Supplement, Riemann-Stieltjes integration.  text    video (10 min, 42 sec)

Week 9

Lecture 21: Chapter 3, Section 3: Series.               text    video (11 min, 44 sec)
Midterm
Lecture 22: Chapter 3, Section 3: Series.               same    video (12 min, 42 sec)

Week 10

Lecture 23: Chapter 4, Section 1: Uniform Convergence   text    video ( min, sec)
Lecture 24: Chapter 4, Section 1: Uniform Convergence   same    video ( min, sec)
Lecture 25: Chapter 4, Section 1: Uniform Convergence   same    video ( min, sec) 
Lecture 26: Chapter 4, Section 1: Uniform Convergence   same    video ( min, sec) 

Week 11

Lecture ##: Chapter 4, Section 2: Power Series          text    video ( min, sec)
Lecture ##: Chapter 4, Section 3: Equicontinuity        text    video ( min, sec) 
Lecture ##: Chapter 4, Section 3: Equicontinuity        same    video ( min, sec) 

Week 12

Lecture ##: Chapter 4, Section 4: Uniform Approximation text    video ( min, sec) 
Lecture ##: Chapter 4, Section 4: Uniform Approximation same    video ( min, sec) 
Lecture ##: Chapter 4, Section 4: Uniform Approximation same    video ( min, sec) 

Week 13

Lecture ##: Chapter 4, Section 5: Contractions &        text    video ( min, sec) 
Lecture ##: Chapter 4, Section 5: Diff Eqs              same    video ( min, sec) 
Lecture ##: Chapter 4, Section 6: Analytic Functions    text    video ( min, sec) 

Week 14

Lecture ##: Chapter 4, Section 6: Analytic Functions    text    video ( min, sec) 
Lecture ##: Chapter 4, Section 7: Continuous nowhere    text    video ( min, sec) 
Lecture ##: Chapter 4, Section 7: diff'able functions   same    video ( min, sec) 
Lecture ##: Chapter 4, Section 7: are everywhere!       same    video ( min, sec) 

Week 15

Lecture ##: Chapter 6, Section 1:                       text    video ( min, sec) 
Lecture ##: Chapter 6, Section 1:                       text    video ( min, sec) 
Lecture ##: Chapter 6, Section 1:                       text    video ( min, sec) 

Week 15

Final Exam