$$\def\R{\mathbb{R}} \def\N{\mathbb{N}} \def\e{\epsilon} \def\dst{\displaystyle}$$

### Daily Syllabus - Math 301 Real Analysis - Fall 2017

Be sure to check back, because this will be updated during the semester.

All numbers indicate sections from Understanding Analysis, Second Edition by Abbott.

 Monday Wednesday Friday 8/30 Welcome to Real Analysis! 1.2 Some preliminaries 9/1 1.3 The Axiom of Completeness 9/4 Labor Day 9/6 1.4 Consequences of Completeness 9/8 1.4 Consequences of Completeness Prob Set 1 (Group) due @ 9:30 am 9/11 1.5 Cardinality 9/13 1.6 Cantor's Theorem 9/15 1.6 Cantor's Theorem Prob Set 2 (Indiv) due @ 9:30 am 9/18 2.2 The Limit of a Sequence 9/20 2.2 The Limit of a Sequence 9/22 2.3 The Algebraic and Order Limit Theorems Prob Set 3 (Group) due @ 9:30 am 9/25 2.4 The Monotone Convergence Theorem 9/27 2.5 Subsequences and the Bolzano-Weierstrass Theorem   Johnson Lecture @ 5:30 pm 9/29 2.6 The Cauchy Criterion Prob 4 (Indiv) due @ 9:30 am 10/2 2.7 Properties of Infinite Series 10/4 3.1 The Cantor Set   Exam 1 on 10/5 @ 6:00 pm 10/6 3.2 Open and Closed Sets 10/9 Fall Break 10/11 3.3 Compact Sets 10/13 4.1 Examples of Dirichlet & Thomae Title for Book Review due 10/16 4.2 Functional Limits 10/18 4.3 Combinations of Continuous Functions 10/20 4.4 Continuous Functions on Compact Sets Prob Set 5 (Group) due @ 9:30 am 10/23 4.4 Continuous Functions on Compact Sets 10/25 4.5 The Intermediate Value Theorem 10/27 5.2 Derivatives and the Intermediate Value Property Prob Set 6 (Indiv) due @ 9:30 am 10/30 5.2 Derivatives and the Intermediate Value Property 11/1 5.3 The Mean Value Theorem 11/3 5.3 The Mean Value Theorem Prob Set 7 (Group) due @ 9:30 am 11/6 5.4 A Continous Nowhere-Differentiable Function 11/8 6.2 Uniform Convergence of a Sequence of Functions 11/10 6.2 Uniform Convergence of a Sequence of Functions Prob Set 8 (Indiv) due @ 9:30 am Progress Report on Book Review due 11/13 6.3 Uniform Convergence and Differentiation 11/15 6.4 Series of Functions   Exam 2 on 11/16 @ 6:00 pm 11/17 6.5 Power Series 11/20 6.5 Power Series 11/22 Thanksgiving Break 11/24 Thanksgiving Break 11/27 6.6 Taylor Series 11/29 6.7 The Weierstrass Approximation Theorem 12/1 7.2 The Definition of the Riemann Integral Prob Set 9 (Group) due @ 9:30 am 12/4 7.3 Integrating Functions with Discontinuities Book Review due 12/6 7.4 Properties of the Integral 12/8 7.5 The Fundamental Theorem of Calculus Prob Set 10 (Indiv) due @ 9:30 am Final Exam Thursday, December 14, 9:00 - 12:00

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