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Calendar

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.

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