### Daily Syllabus - Math 301 Real Analysis - Fall 2011

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

• You should read the section listed for each day and check onCourse for the summary of definitions and theorems. On a few days, there are supplemental sections listed in italics that you should read as well.
• All numbers indicate sections from Understanding Analysis by Abbott

 Monday Wednesday Friday 8/31 No power on campus due to Irene. Bummer. 9/2 Welcome to Real Analysis 9/5 Labor DayNo Classes 9/7 1.2 Some preliminaries 1.3 The Axiom of Completeness Sections 1.1 & 1.6 Honor Code onCourse assignment due 9/9 1.4 Consequences of Completeness Homework due 9/12 1.4 Consequences of Completeness (cont) 9/14 1.5 Cantor's Theorem 9/16 1.5 Cantor's Theorem (cont) Homework due 9/19 2.2 The Limit of a Sequence Sections 2.1 & 2.9 9/21 2.2 The Limit of a Sequence (cont) 9/23 2.3 The Algebraic and Order Limit Theorems Homework due 926 2.4 The Monotone Convergence Theorem 9/28 2.5 Subsequences and the Bolzano-Weierstrass Theorem 9/30 2.6 The Cauchy Criterion Homework due 10/3 2.7 Properties of Infinite Series 10/5 3.1 The Cantor Set Section 3.6 Title for Book Review due 10/7 3.2 Open and Closed Sets Takehome Exam 1 due 10/10 Fall Break No Classes 10/12 3.3 Compact Sets 10/14 4.1 Examples of Dirichlet & Thomae 10/17 4.2 Functional Limits 10/19 4.3 Combinations of Continuous Functions 10/21 4.4 Continuous Functions on Compact Sets Homework due 10/24 Flex Day 10/26 4.5 The Intermediate Value Theorem 10/28 5.2 Derivatives and the Intermediate Value Property Section 5.1 Homework due 10/31 5.2 Derivatives and the Intermediate Value Property (cont) 11/2 5.3 The Mean Value Theorem Progress Report on Book Review due 11/4 5.3 The Mean Value Theorem (cont) Homework due 11/7 5.4 A Continous Nowhere-Differentiable Function 11/9 6.2 Uniform Convergence of a Sequence of Functions 11/11 6.2 Uniform Convergence of a Sequence of Functions (cont) Homework due 11/14 6.3 Uniform Convergence and Differentiation 11/16 6.4 Series of Functions 11/28 6.5 Power Series Takehome Exam 2 due 11/21 6.5 Power Series (cont) 11/23 Thanksgiving Break No Classes 11/25 Thanksgiving Break No Classes 11/28 6.6 Taylor Series 11/30 7.2 The Definition of the Riemann Integral 12/2 7.3 Integrating Functions with Discontinuities Homework due 12/5 7.4 Properties of the Integral Book Review due 12/7 7.5 The Fundamental Theorem of Calculus 12/9 The BIG Picture Homework due Final Exam DueSaturday 12/17, 11:00 am

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