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MATH 215
MATHEMATICAL ANALYSIS SYLLABUS |
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Semester: |
Spring 2014 |
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Instructor: |
Mefharet Kocatepe |
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Office: |
Faculty of Science, Block A, Room: 115 A |
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Phone: 1255 |
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e-mail: kocatepe@fen.bilkent.edu.tr |
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Exams, grading: |
Midterm 1 (25%) March 14, 10:30-12:20 |
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Midterm 2 (25%) April 25, 10:30-12:20 |
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Final (30%) to be announced later |
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Homework (20%) Ten homework assisgnments |
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Course Schedule: |
Wednesday 08:30-10:20 in EB-204 |
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Friday 10:30-12:20 in EB-204 |
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Office hours: |
By appointment |
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Textbooks |
M. Rosenlicht, Introduction to Analysis, 1986, Dover |
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W. Rudin, Principles of Mathematical Analysis, 3rd.
Ed., 2000, Wiley |
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60% attendance is
required |
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Date |
Subjects |
Feb.5, 7 |
Sets and functions |
Feb. 12, 14 |
The real number system. |
Feb. 19, 21 |
Metric spaces: definition
and examples |
Feb. 26, 28 |
Topology of metric spaces |
Mar. 5, 7 |
Sequences, Cauchy sequences
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Mar. 12, 14 |
Completeness, Midterm 1 |
Mar. 19, 21 |
Completeness, Compact sets |
Mar. 26, 28 |
Compact
sets |
Apr. 2, 4 |
Connected
sets |
Apr. 9, 11 |
Continuity |
Apr.16, 18 |
Uniform
continuity |
Apr. 25 |
Midterm 2 |
April 30 |
Preservation of compactness and connectedness under continuity |
May
7, 9 |
Contractions and Banach fixed point theorem |
May
14, 16 |
Review |