
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 14 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 BolzanoWeierstrass 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 6.16.8..
 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 NowhereDifferentiable 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.
Back to my home page.
Jason Starr
4108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 117943651
Phone: 6316328270
Fax: 6316327631
Jason Starr