| 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 |