| Lecture | Date | Topic
|
| 1 | Tue 8/26 | Introductory remarks, elementary logic
|
| 2 | Thu 8/28 | Methods of proof, mathematical induction
|
| 3 | Tue 9/2 | Sets and relations
|
| 4 Q | Thu 9/4 | Functions, cardinality
|
| 5 | Tue 9/9 | Ordered fields, the completeness axiom
|
| 6 | Thu 9/11 | Topology of the real line
|
| 7 | Tue 9/16 | More on topology
|
| 8 Q | Thu 9/18 | Compactness
|
| --- | Tue 9/23 | No class
|
9 | Thu 9/25 | Sequences and their limits
|
| 10 | Tue 9/30 | Limit theorems
|
--- | Thu 10/2 | No class
|
| 11 | Tue 10/7 | Review I
|
| 12 | Thu 10/9 | Midterm I
|
| --- | Tue 10/14 | No class
|
| 13 | Thu 10/16 | Monotone sequences and Cauchy sequences
|
| 14 | Tue 10/21 | Subsequences, limsup and liminf
|
| 15 Q | Thu 10/23 | Limits of functions
|
| 16 | Tue 10/28 | Continuity and its equivalent formulations
|
| 17 | Thu 10/30 | Continuous functions
|
| 18 | Tue 11/4 | More on continuous functions
|
| 19 Q | Thu 11/6 | The derivative
|
| 20 | Tue 11/11 | Review II
|
| 21 | Thu 11/13 | Midterm II
|
| 22 | Tue 11/18 | The mean value theorem and its consequences
|
| 23 Q | Thu 11/20 | L'Hospital's rule
|
| 24 | Tue 11/25 | Taylor's theorem
|
| --- | Thu 11/27 | No class
|
| 25 | Tue 12/2 | The Riemann integral
|
| 26 Q | Thu 12/4 | Basic properties of the Riemann integral
|
| 27 | Tue 12/9 | The fundamental theorem of calculus and applications
|
| 28 | Thu 12/11 | Review III
|