The calendar below provides information on the course's lecture (L), recitation (R) and exam (E) sessions.
The recitations are interactive, therefore attendance is required.
Course calendar.
| SES # |
Topics |
KEY DATES |
| L1 |
Real Numbers |
|
| R1 |
We will discuss some samples of writing. |
|
| L2 |
Complex Numbers
Euclidean Spaces |
|
| L3 |
Countable, Uncountable Sets |
Problem set 1 due |
| R2 |
The first writing assignment (see problem set 1) is due. |
|
| L4 |
Metric Spaces |
|
| R3 |
Hand in a second draft of the previous assignment (see problem set 2). |
|
| L5 |
Compact Sets |
Problem set 2 due |
| L6 |
Heine-Borel Theorem
Connected Sets |
Problem set 2b due |
| R4 |
A short expository paper on compact sets is due (see problem set 2b). |
|
| L7 |
Convergent Sequences |
|
| L8 |
Cauchy Sequences, Completeness |
|
| R5 |
Student Presentations |
|
| L9 |
Series |
Problem set 3 due |
| E1 |
Quiz 1 (Ses #L1-L9) |
|
| R6 |
Student Presentations (cont.) |
|
| L10 |
Limits of Functions, Continuity |
A short paper (see problem set 3) is due |
| L11 |
Continuity, Compactness, Connectedness |
Problem set 4 due |
| R7 |
Student Presentations (cont.)
Discussion about the completion of a metric space. |
|
| L12 |
Discontinuities, Monotonic Functions |
|
| L13 |
Differentiation
Mean Values Theorem |
Problem set 5 due |
| R8 |
Discussion about fixed point problems and the algorithms for finding square roots. |
|
| L14 |
l'Hopital
Taylor's Theorem |
|
| L15 |
Riemann-Stieltjes Integral |
Problem set 6 due |
| R9 |
Homework Discussion
Students present solutions to exercises from homework. |
|
| L16 |
Riemann-Stieltjes Integral (cont.) |
|
| R10 |
First draft of the paper is due. We will also start the presentations based on the final papers. The talks should be about 10-15 minutes long. |
|
| L17 |
Properties of the Integral |
Problem set 7 due |
| E2 |
Quiz 2 (Ses #L10-L17) |
|
| R11 |
Student Presentations (cont.) |
|
| L18 |
The Fundamental Theorem of Calculus |
|
| L19 |
Sequences of Functions
Uniform Convergence |
|
| R12 |
Second draft of the paper is due.
Student Presentations (cont.) |
|
| L20 |
Uniform Convergence, Equicontinuity |
Problem set 8 due |
| L21 |
Stone-Weierstrass Theorem |
|
| R13 |
A critique for one paper is due (each student will receive by email a file with the paper to review).
Student Presentations (cont.) |
|
| L22 |
Analytic Functions
Algebraic Completeness |
Problem set 9 due |
| L23 |
Fourier Series |
|
| R14 |
The final version of the paper is due. |
|
| L24 |
Review |
|
| E3 |
Final Exam |
|