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Analysis I >> Content Detail



Calendar / Schedule



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 #TopicsKEY DATES
L1Real Numbers
R1We will discuss some samples of writing.
L2Complex Numbers

Euclidean Spaces
L3Countable, Uncountable SetsProblem set 1 due
R2The first writing assignment (see problem set 1) is due.
L4Metric Spaces
R3Hand in a second draft of the previous assignment (see problem set 2).
L5Compact SetsProblem set 2 due
L6Heine-Borel Theorem

Connected Sets
Problem set 2b due
R4A short expository paper on compact sets is due (see problem set 2b).
L7Convergent Sequences
L8Cauchy Sequences, Completeness
R5Student Presentations
L9SeriesProblem set 3 due
E1Quiz 1 (Ses #L1-L9)
R6Student Presentations (cont.)
L10Limits of Functions, ContinuityA short paper (see problem set 3) is due
L11Continuity, Compactness, ConnectednessProblem set 4 due
R7Student Presentations (cont.)

Discussion about the completion of a metric space.
L12Discontinuities, Monotonic Functions
L13Differentiation

Mean Values Theorem
Problem set 5 due
R8Discussion about fixed point problems and the algorithms for finding square roots.
L14l'Hopital

Taylor's Theorem
L15Riemann-Stieltjes IntegralProblem set 6 due
R9Homework Discussion

Students present solutions to exercises from homework.
L16Riemann-Stieltjes Integral (cont.)
R10First 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.
L17Properties of the IntegralProblem set 7 due
E2Quiz 2 (Ses #L10-L17)
R11Student Presentations (cont.)
L18The Fundamental Theorem of Calculus
L19Sequences of Functions

Uniform Convergence
R12Second draft of the paper is due.

Student Presentations (cont.)
L20Uniform Convergence, EquicontinuityProblem set 8 due
L21Stone-Weierstrass Theorem
R13A critique for one paper is due (each student will receive by email a file with the paper to review).

Student Presentations (cont.)
L22Analytic Functions

Algebraic Completeness
Problem set 9 due
L23Fourier Series
R14The final version of the paper is due.
L24Review
E3Final Exam

 








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