# (very approximate) Schedule for MAT513, Spring 2017

Week Monday Wednesday Reading and Assignments
1.1 Discussion: the irrationality of √2
1.2 Preliminaries
Discussion of natural numbers, rationals, and reals.
Discussion of rationals-- why is every rational an (eventually) repeating decimal and vice versa?
8.6 Ordered fields
1.3 the Axiom of Completeness
Read all of chapter 1 in Abbott.
Background: Alcock, ch.1-4
Suggested: Alcock, ch.10
1/30 1.4 Consequences of Completeness
1.5, 1.6, 1.7 Cardinality and Cantor's theorem
2.1 Intro: Rearranging series
2.2 Limits of sequences
Start reading Chapter 2 of Abbott
HW 1 Due Wed, 2/8
2/6 2.3 Limit theorems
2.4 monotone convergence theorem
2.4 continued : the Harmonic series, Cauchy condensation, p-series
2.5 Subsequences, Bolzano-Weierstrauss
Read the rest of Abbott ch.2
Suggested: Alcock, ch.5
HW 2 Due Wed, 2/15
2/13 2.6 Cauchy sequences
2.7 Properties of infinite series
2.8 Double summation, Products of series
2.9 Epilogue
3.1 The Cantor set
Suggested: Alcock, 6.1-6.8
HW 3 Due Wed, 2/22
2/20 Proof party
3.2 Open and Closed sets
3.3 Compactness Finish reading Abbot ch.3
HW 4 Due Wed, 3/1
2/27 3.3 Heine-Borel Theorem 4.1, 4.2 Limits of functions
4.3 Continuity
Suggested: Alcock, ch.7
3/6 review for midterm. Midterm 1 covers chapters 1-3
Here is a copy of the midterm, and here are the solutions.
HW 5 Due Wed, 3/22(after break)
3/13 Spring Break
(probably not like this)
Spring Break
3/20 4.3 A bit more on continuity
4.4 Continuous functions on compact sets
4.4 Extreme Value Theorem
4.5 Intermediate Value Theorem
4.6 Discontinuities
HW 6 Due Wed, 3/29
3/27 5.1 Continuity of Derivatives
5.2 Derivatives and Intermediate Value Property
5.3 Mean Value Theorem
5.4 A continuous, nowhere differentiable function
HW 7 Due Wed, 4/3
4/3 6.1, 6.2 Uniform Convergence of a sequence of functions
6.3 Uniform convergence and differentiation
6.4 Series of functions
6.5 Power series
HW 8 Due Wed, 4/10
Suggested: Alcock, ch.8
4/10 6.6 Taylor series 6.7 Weierstrauss approximation theorem HW 9 Due Wed, 4/26(1 week after midterm)
Suggested: Alcock, ch.9
4/17 review for midterm. Midterm 2 covers chapters 4, 5, 6.1-6.3
Here is a copy of the midterm, and here are the solutions.
4/24 7.1, 7.2 The Riemann integral
7.3 discontinuities
7.4 Properties of integrals
7.5 Fundamental theorem of Calculus
HW 10 Due Wed, 5/3
finish Abbot Ch.7
5/1 7.6 a non-integrable derivative review? Paper due on Friday, May 5
5/8 Final Cumulative
Thursday, May 11, 5:30pm, Physics P-128.
If you want to relive the magic, here is the exam, and here are the solutions.