Dates 
Lectures 
Topics 


Chapter 1. The Real and Complex Number Systems

1/7

Lecture 1

Introduction. Ordered Sets.

1/9

Lecture 2

Fields

1/11

Lecture 3

The Real Field

1/14

Lecture 4

The Complex Field

1/16

Lecture 5

Euclidean Spaces



Chapter 2. Basic Topology

1/18

Lecture 6

Finite, Countable, and Uncountable Sets

1/23

Lecture 7

Metric Spaces

1/25

Lecture 8

Metric Spaces (continued)

1/28

Lecture 9

Compact Sets

1/30

Lecture 10

Compact Sets (continued). Perfect Sets. Connected Sets.

2/1

Lecture 11

First midterm exam



Chapter 3. Numerical Sequences and Series

2/4

Lecture 12

Convergent Sequences

2/6

Lecture 13

Subsequnces.
Cauchy Sequences.

2/8

Lecture 14

Upper and Lower Limits.
Some Special Sequences.

2/11

Lecture 15

Series.
Series of Nonnegative Terms.

2/13

Lecture 16

Series of Nonnegative Terms
(continued)

2/15

Lecture 17

The Number e

2/20

Lecture 18

The Root and Ratio Tests

2/22

Lecture 19

Power Series.
Summation by Parts.

2/25

Lecture 20

Absolute Convergence.
Addition and Multiplication of Series.

2/27

Lecture 21

Rearrangements

3/1

Lecture 22

Second midterm exam



Chapter 4. Continuity

3/4

Lecture 23

Limits of Funtions.
Continuous Functions.

3/6

Lecture 24

Continuous Functions (continued).

3/8

Lecture 25

Continuity and Compactness

3/11

Lecture 26

Continuity and Connectness.
Discontinuity.

3/13

Lecture 27

Monotonic Functions.
Infinite Limits and Limits at Inifinite.

3/15

Lecture 28

Review
