Tue and Thu, 10:450am - 12:20pm, Room 417 Math
May 27 - August 15
2. Schedule of Lectures and Homeworks
Instructor: Donovan McFeron (408 Mathematics, dmcferon@math.columbia.edu)
Office Hours: By appointment.
Teaching Assistant: James McIvor
Text: Rudin, Walter. Principles of Mathematical Analysis.
Course description: We'll cover the following (mostly, but not exclusively, from Chapters 1-8 Rudin):
Policies: Here are some suggested policies:
1. Active participation is strongly encouraged.
2. Reading the book is helpful. Please try to read the material we are going to cover before class.
3. Please go to class.
4. Do the homework. Collaboration is encouraged, as long as the work you hand in is your own. Also, staple your homework.
5. For all written work, solve the problems in organized fashion, with clear explanations.
6. Ask questions if something is not clear, both in class and outside of class. Help is always available from the Help Room (Mathematics 406, 10am-5pm Mon-Thur), me, or the TA.
Homework: Homework will be assigned daily and will be due on Tuesdays by 5pm. Turn homework into the drop box outside of room 406 labeled "12 week Analysis". Late homework will not be accepted.
Exams: There will be two midterms, and a final.
There will be no make-up exams without a note from a doctor or a dean.
Grading: The tentative grading scheme is as follows:
1. Final: 35%
2. Midterms: 20% and 25%
3. Homeworks: 20%
This schedule is tentative and WILL change. Please check regularly for current homework information.
|
Date |
Topics/Sections covered |
Remarks |
Homework |
Date Due |
Suggested Probelms |
|
May 27 |
Sets and Fields |
Ch 1 |
1-5, 8, 9, 11, 15, 18 |
June 3 |
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May 29 |
The Real Field, Complex Field, and Euclidean Space |
Ch 1 |
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June 3 |
Finite, Countable, and Uncountable Sets Metric Spaces |
Ch 2 |
2, 5, 6, 8, 11, 13, 17, 18, 22, 23 |
June 10 |
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June 5 |
Compact, Perfect, and Connected Sets |
Ch 2 |
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June 10 |
Sequences and Series |
Ch 3 |
4, 7-13, 20, 23 |
July 01 |
19 |
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June 12 |
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Ch 3 |
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June 17 |
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Ch 3 |
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June 19 |
Review |
Ch's 1-3 |
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June 24 |
Midterm 1 |
Ch's 1-3 |
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June 26 |
Power Series Absolute Convergence Rearrangements |
Ch 3 |
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July 1 |
Limits, Continuity, and Compactness |
Ch 4 |
1-13, 18, 23, 24 |
July 08 |
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July 3 |
Connectedness, Discontinuities, and Monotonic Functions |
Ch 4 |
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July 8 |
Derivatives |
Ch 5 |
4,6,9,10,15 |
July 22 |
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July 10 |
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Ch 5 |
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July 15 |
Riemann-Stieltjes Integral |
Ch 6 |
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July 17 |
Properties of Stieltjes Integral Review |
Ch 6 Ch's 3-5 |
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July 22 |
Midterm 2 |
Ch's 3-5 |
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July 24 |
Integrals and Differentiation |
Ch 6 |
1-6, 11, 15, 16, 18 |
Aug 5 |
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July 29 |
Sequences and Series of Functions |
Ch 7 |
3, 4, 8, 11, 12, 23 |
Aug 12 |
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July 31 |
Uniform Convergence and Continuity, Differentiation, and Integration |
Ch 7 |
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Aug 5 |
Stone-Weierstrass Theorem |
Ch 7 |
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Aug 7 |
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Aug 12 |
Review |
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Aug 14 |
Final Exam |
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