Math 351 - Principles of Analysis (Section 002 Winter 2006)
· Time and Location: MWF 12-1 East Hall 1068.
· Instructor: Richard Kollár, East Hall 1847, phone: (734) 936-2879.
· E-mail: kollar....umich.edu (a preferred way of communication).
· Office Hours: M 2-3, W 1-2, Thu 1-2 or by appointment.
Final Exam Office Hours: Mon 4/17 2-3, Tue 4/18 1-2, Thu 4/20 1-2, Fri 4/21 1-2, Wed 4/26 1-3
· Textbook: Elementary Analysis by Kenneth A. Ross (Springer).
· Syllabus: Rigorous foundations of mathematical analysis. Since the textbook is fairly terse we will not be able to cover the whole book. The emphasis will be on material in Chapters 1, 2, 3, 4 and 5.
· Grading Policy: Grades will be based on individual homework, team homework, a midterm exam, and a final exam, with the following weights:
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Individual homework: |
Approx. 11 assignments |
(20%) |
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Team homework: |
Approx. 10 assignments |
(20%) |
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Midterm exam: |
Wednesday February 22 (in class) |
(25%) |
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Final exam: |
Thursday April 27, 10:30am-12:30pm (B844 East Hall) |
(35%) |
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· Individual Homework Assignments: Individual homework assignments will be regularly posted on the individual homework page.
· Team Homework Assignments: These can be done either individually or in a group. The assignments will be regularly posted on the team homework page.
· Lesson plan: The topics covered will be regularly updated:
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Jan 6 |
F |
Introduction, §1 Natural Numbers, Mathematical Induction |
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Jan 9 |
M |
More Mathematical Induction, §2 Rational Numbers |
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Jan 11 |
W |
More Rational Numbers, §3 Real Numbers |
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Jan 13 |
F |
More Real Numbers, Absolute Value |
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Jan 16 |
M |
MLK Day – No class |
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Jan 18 |
W |
§4 Infimum, Supremum, Completeness, Denseness |
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Jan 20 |
F |
Boundedness, §5 Infinity, Finite, Countable and Uncountable Sets (Notes) |
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Jan 23 |
M |
§7 Limits of Sequences |
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Jan 25 |
W |
§8 More Limits of Sequences, Proofs |
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Jan 27 |
F |
More Proofs |
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Jan 30 |
M |
§9 Limit Theorems for Sequences |
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Feb 1 |
W |
More Limit Theorems |
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Feb 3 |
F |
§10 Monotone Sequences |
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Feb 6 |
M |
More Monotone Sequences |
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Feb 8 |
W |
Cauchy Sequences |
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Feb 10 |
F |
§11 Subsequences |
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Feb 13 |
M |
More Subsequences |
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Feb 15 |
W |
§14 Series, Ratio and Root Test for Series |
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Feb 17 |
F |
§15 Alternating Series and Integral Test |
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Feb 20 |
M |
Chapter 1 & 2 Review, Midterm (take home) |
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Feb 22 |
W |
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Feb 24 |
F |
Midterm Solutions |
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Feb 27 |
M |
Spring Break - No Class |
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Mar 1 |
W |
Spring Break - No Class |
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Mar 3 |
F |
Spring Break - No Class |
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Mar 6 |
M |
17 Continuous Functions |
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Mar 8 |
W |
More Continuous Functions |
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Mar 10 |
F |
§18 Properties of Continuous Functions |
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Mar 13 |
M |
More Properties of Continuous Functions |
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Mar 15 |
W |
§19 Uniform Continuity |
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Mar 17 |
F |
More Uniform Continuity |
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Mar 20 |
M |
§20 Limits of Functions – Hand-out |
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Mar 22 |
W |
More on Limits of Functions |
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Mar 24 |
F |
§23 Power Series |
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Mar 27 |
M |
More Power Series, §24 Uniform Convergence |
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Mar 29 |
W |
More Uniform Convergence |
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Mar 31 |
F |
§26 Differentiation and Integration of Power Series |
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Apr 3 |
M |
Abel’s Theorem, § 27 Weierstrass Theorem |
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Apr 5 |
W |
§ 28 Basic Properties of the Derivative |
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Apr 7 |
F |
§ 29 Rolle’s Theorem, The Mean Value Theorem |
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Apr 10 |
M |
§ 30 L’Hospital Rule |
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Apr 12 |
W |
§ 31 Taylor’s Series |
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Apr 14 |
F |
More on Taylor’s Series, Binomial Series |
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Aqr 17 |
M |
Chapter 3, 4 & 5 Review – Last Class |
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Apr 27 |
Thu |
Final Exam 10:30-12:30. List of Final Exam Topics (Proofs) Final Exam - Proofs, Final Exam – Multiple choice, Solutions More references: University of Michigan Math 451 webpage |
Page Updated: 4/17/2006