MAT 513 Syllabus Analysis for Teachers I Spring 2016

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 26
  Section 3.1, Natural Numbers and Induction.
  
• January 28
  Section 3.2, Ordered Fields.
  
• February 2
  Section 3.3, The Completeness Axiom.
  
• February 4
  Section 3.4, Topology of the Reals.
  Problem Set 1 due in lecture. Practice for Exam 1.
  
• February 9
  Section 3.4, Topology of the Reals.
  
• February 11
  EXAM 1
  No Problem Set Due This Week.
• February 16
  Discussion of Exam 1. More about topology of the reals.
  
• February 18
  Section 3.5, Compact Sets.
  Problem Set 2 due in lecture.
  
• February 23
  Section 4.1, Convergence.
  
• February 25
  Section 4.2, Limit Theorems.
  Problem Set 3 due in lecture.
  
• March 1
  Section 4.3, Monotone Sequences and Cauchy Sequences.
  Section 4.4, Subsequences.
  
• March 3
  Section 5.1, Limits of Functions.
  Problem Set 4 due in lecture. Practice for Exam 2.
  
• March 8
  Section 5.2, Continuous Functions.
  Section 5.3, Properties of Continuous Functions.
  
• March 10
  EXAM 2
  No Problem Set Due This Week.
• March 22
  Section 5.4, Uniform Continuity.
  
• March 24
  Section 6.1, The Derivative.
  Problem Set 5 due in lecture.
  
• March 29
  Review of Calculus
  
• March 31
  Review of Calculus
  Problem Set 6 due in lecture.
  
• April 5
  Section 6.2, The Mean Value Theorem.
  
• April 7
  Section 6.3, L'Hospital's Rule.
  Problem Set 7 due in lecture.
  
• April 12
  Section 6.4, Taylor's Theorem.
  TERM PAPER TOPICS DUE
• April 14
  Section 7.1, The Riemann Integral.
  Problem Set 8 due in lecture. Practice for Exam 3.
  
• April 19
  Section 7.3, The Fundamental Theorem of Calculus.
  
• April 21
  EXAM 3
  No Problem Set Due This Week.
• April 26
  Section 8.1, Convergence of Infinite Series.
  
• April 28
  Section 8.2 and 8.3, Convergence Tests and Power Series.
  Problem Set 9 due in lecture.
  
• May 3
  FINAL REVIEW
  
• May 5
  FINAL REVIEW
  Problem Set 10 due in lecture.
  TERM PAPERS DUE.

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