Week  Monday  Wednesday  Reading and Assignments 

1/23  Administrivia 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.14 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, pseries 2.5 Subsequences, BolzanoWeierstrauss 
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 
Start reading Abbot ch.3 Suggested: Alcock, 6.16.8 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 HeineBorel Theorem  4.1, 4.2 Limits of functions 4.3 Continuity 
Start reading Abbot Ch.4 Suggested: Alcock, ch.7 
3/6  review for midterm.  Midterm 1 covers chapters 13 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 Finish reading Abbot Ch.4 
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 read Abbot Ch.5 
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 read Abbot Ch.6 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) start reading Abbot Ch.7 Suggested: Alcock, ch.9 
4/17  review for midterm.  Midterm 2 covers chapters 4, 5, 6.16.3 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 nonintegrable derivative  review?  Paper due on Friday, May 5 
5/8  Final Cumulative Thursday, May 11, 5:30pm, Physics P128. 
If you want to relive the magic, here is the exam, and here are the solutions. 