Lecturer: Kiril Datchev, room 2-173, firstname.lastname@example.org.
Class meetings: Tuesdays and Thursdays 9:30-11:00 in room 4-163.
Textbook: Walter Rudin, Principles of Mathematical Analysis.
Recommended reading: G. H. Hardy, A Course of Pure Mathematics. Edmund Landau, Foundations of Analysis. Tom M. Apostol, Mathematical Analysis. See also these notes on the text by George Bergman. For inspirational reading, consult The Study of Mathematics by Bertrand Russell.
Grading is based on:
Problem sets are due Thursdays at 4:00 in room 2-285. Late problem sets are not accepted.
Problem set 1 due September 13th. Solutions.
Problem set 2 due September 20th. Solutions.
Problem set 3 due September 27th. Solutions.
Review sheet for Midterm 1. Solutions to the midterm.
Problem set 4 due October 11th. Solutions.
Problem set 5 due October 18th. Solutions.
Problem set 6 due October 25th. Solutions.
Problem set 7 due November 1st. Solutions.
Review sheet for Midterm 2. Solutions to the midterm.
Problem set 8 due November 15th. Solutions.
Problem set 9 due November 29th. Solutions.
Problem set 10 due December 6th. Solutions.
Review sheet for the final.
Office hours for the final:
|9/6||1 – 12||ordered sets, fields, real numbers|
|9/11||12 – 26||complex numbers, Euclidean spaces, functions, finite and infinite sets|
|9/13||26 – 34||countable and uncountable sets, metric spaces|
|9/18||34 – 36||open and closed sets|
|9/20||36 – 38||compact sets|
|9/25||38 – 40||the Heine-Borel theorem, the Bolzano-Weierstrass theorem|
|9/27||40 – 43||perfect sets, the Cantor set, connected sets|
|10/2||1 – 46||Midterm on Chapters 1 and 2|
|10/4||47 – 54||sequences, convergence, Cauchy sequences|
|10/11||54 – 60||completeness, monotonic sequences, upper and lower limits, series, comparison test|
|10/16||60 – 65||series of nonnegative terms, the number e|
|10/18||65 – 72||root and ratio tests, power series, conditional and absolute convergence|
|10/23||83 – 90||continuous functions, continuity and compactness|
|10/25||90 – 97||uniform continuity, continuity and connectedness, monotonic functions|
|10/30||103 – 109||differentiation, mean value theorems|
|11/1||109 – 113||l'Hospital's rule, Taylor's theorem|
|11/6||47 – 119||Midterm on Chapters 3, 4 and 5|
|11/8||120 – 127||the Riemann-Stieltjes integral|
|11/13||128 – 137||properties of the integral, fundamental theorem of calculus, rectifiable curves|
|11/15||140 – 148||sequences and series of functions, pointwise and uniform convergence|
|11/20||148 – 154||uniform convergence, continuity and differentiation|
|11/27||154 – 158||equicontinuous families of functions, the Arzelà-Ascoli theorem|
|11/29||159 – 165||the Stone-Weierstrass theorem|
|12/4||172 – 178||functions given by power series|
|12/6||178 – 184||exponential, logarithmic and trigonometric functions|
|12/11||185 – 192||Fourier series|
|12/20||1 – 192||Final Exam on Chapters 1 – 8