### 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.

Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr