MAT 513 Syllabus Analysis for Teachers I Spring 2018

The revised schedule for topics covered in lecture is as follows. You must do the assigned reading prior to lecture. This will make the lectures more effective for you.

• January 22
  Section 1.1. Irrationality of the Square Root of 2.
  Section 1.2. Some Preliminaries.
  Required Reading: Abbott Chapter 1.
  Recommended Reading: Alcock Chapters 1-4 and 10.
  
  
• January 24
  Section 8.6.
  Section 1.3. The Axiom of Completeness.
  
  
• January 29
  Section 1.4. Consequences of Completeness.
  Section 1.5. Cardinality.
  Section 1.6. Cantor's Theorem.
  Section 1.7. Epilogue.
  Required Reading: Abbott Chapter 2.
  
  
• January 31
  Section 2.1. Discussion: Rearrangements of Infinite Series.
  Section 2.2. The Limit of a Sequence.
  
  Problem Set 0 due in lecture.
  
  
• February 5
  Section 2.3. The Algebraic and Order Limit Theorems.
  Section 2.4. The Monotone Convergence Theorem.
  Required Reading: Abbott Chapter 2.
  Recommended Reading: Alcock Chapter 5.
  
  
• February 7
  Section 2.4. The Monotone Convergence Theorem.
  Section 2.5. Subsequences and the Bolzano-Weierstrass Theorem.
  
  Problem Set 1 due in lecture.
  
  
• February 12
  Section 2.6. The Cauchy Criterion.
  Section 2.7. Properties of Infinite Series.
  Required Reading: Abbott Chapter 3.
  Recommended Reading: Alcock Chapter 6.1-6.8..
  
  
• February 14
  Section 2.8. Double Summations and Products of Infinite Series.
  Section 2.9. Epilogue.
  Section 3.1. Discussion: The Cantor Set.
  
  Problem Set 2 due in lecture.
  
  
• February 19
  Section 3.2. Open and Closed Sets.
  Required Reading: Abbott Chapter 3.
  
  
• February 21
  Section 3.3. Compact Sets.
  
  Problem Set 3 due in lecture.
  
  
• February 26
  Section 3.3. Compact Sets.
  Required Reading: Abbott Chapter 4.
  Recommended Reading: Alcock Chapter 7.
  
  
• February 28
  Section 4.1. Discussion: Examples of Dirichlet and Thomae.
  Section 4.2. Functional Limits.
  Section 4.3. Continuous Functions.
  
  Problem Set 4 due in lecture.
  
  
• March 5
  Practice for Exam 1.
  
  
• March 7
  EXAM 1
  No Problem Set Due This Week.
  
  
• March 19
  Section 4.3. Continuous Functions.
  Section 4.4. Continuous Functions on Compact Sets.
  Required Reading: Abbott Chapter 4.
  
  
• March 21
  Section 4.4. Continuous Functions on Compact Sets.
  Section 4.5. The Intermediate Value Theorem.
  Section 4.6. Sets of Discontinuity.
  
  Problem Set 5 due in lecture.
  
  
• March 26
  Section 5.1. Discussion: Are Derivatives Continuous?
  Section 5.2. Derivatives and the Intermediate Value Property.
  Required Reading: Abbott Chapter 5.
  
  
• March 28
  Section 5.3. The Mean Value Theorems.
  Section 5.4. A Continuous Nowhere-Differentiable Function.
  
  Problem Set 6 due in lecture.
  
  
• April 2
  Section 6.1. Discussion: The Power of Power Series.
  Section 6.2. Uniform Convergence of a Sequence of Functions.
  Section 6.3. Uniform Convergence and Differentiation.
  Required Reading: Abbott Chapter 6.
  Recommended Reading: Alcock Chapter 8.
  
  
• April 4
  Section 6.4. Series of Functions.
  Section 6.5. Power Series.
  
  Problem Set 7 due in lecture.
  
  
• April 9
  Section 6.6. Taylor Series.
  Required Reading: Abbott Chapter 7.
  Recommended Reading: Alcock Chapter 9.
  
  
• April 11
  Section 6.7. The Weierstrass Approximation Theorem.
  
  Problem Set 8 due in lecture.
  
  
• April 16
  Practice for Exam 2.
  TERM PAPER TOPICS DUE
  
  
• April 18
  EXAM 2
  No Problem Set Due This Week.
  
  
• April 23
  Section 7.1. Discussion: How Should Integration be Defined?
  Section 7.2. The Definition of the Riemann Integral.
  Section 7.3. Integrating Functions with Discontinuities.
  Required Reading: Abbott Chapter 7.
  
  
• April 25
  Section 7.4. Properties of the Integral.
  Section 7.5. The Fundamental Theorem of Calculus.
  
  Problem Set 9 due in lecture.
  
  
• April 30
  Section 7.6. Lebesgue's Criterion for Riemann Integrability.
  
  
• May 5
  FINAL REVIEW
  Problem Set 10 due in lecture.
  
  

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