Monday

Wednesday

Friday

1

Read §2.5: Subsequences and the BolzanoWeierstrass
Theorem
Exercises: 2.5.1, 2.5.3
531: Prove that the Monotone
Convergence Theorem implies the Least Upper Bound Property.


3

Reread §2.5: Subsequences and the BolzanoWeierstrass
Theorem
Exercises: 2.5.4, 2.5.6 

5

Read §2.6: The Cauchy Criterion
Exercises: 2.6.1, 2.6.2, 2.6.3


8

Reread §2.6: The Cauchy Criterion
Exercises: 2.6.5, 2.6.6
531: Prove that the
BolzanoWeierstrass Theorem implies the Least Upper Bound Property.


10 
Reread §2.1§2.6
Study for the Chapter 2 Exam 


15 
Read §3.1: The Cantor Set
531: Does R(x) have the Cauchy Criterion? Prove your
answer.
Prove that the Cauchy
Criterion and the Archimedean Property together imply the Least Upper Bound Property.


17 
Read §3.2: Open and Closed Sets
Exercises: 3.2.1, 3.2.3, 3.2.4


19

Reread §3.2: Open and Closed Sets
Exercises: 3.2.5, 3.2.12, 3.2.13 

22 
Read §3.3: Compact Sets
Exercises: 3.3.1, 3.3.2, 3.3.4, 3.3.5
531: Look up the
definition of a connected set on p. 91. Use the Least Upper Bound
property to prove that R is connected.


24 
Reread §3.3: Compact Sets
Exercises: 3.3.8, 3.3.9, 3.3.10 

26

Read §4.1: Examples of Dirichlet and Thomae



31

Read §4.2: Functional Limits
Exercises: 4.2.1, 4.2.2, 4.2.4, 4.2.6 

