Math 301: Real Analysis
Daily Schedule
MW 11-12:15, F 11-11:50
Date Assignment
January 29
  • Reading: Read our syllabus online and read sections 1.1 and 1.3 of the text.
  • Problems for discussion 2/2: 1.5, 1.11, 3.1, 3.5. (Note: Cancel 3.7a and try both parts of 3.5 instead.)
  • Homework problems for 2/7 1.4, 1.8, 3.4, 3.6, 3.8, 4.8, 4.16.
January 31
  • Reading: Read sections 1.4 and 1.5.
  • Problems for discussion 2/5: 4.1, 4.2, 4.3, 4.4.
February 2
  • Finish reading section 1.5 and work on the discussion problems for Monday.
February 5
  • Read sections 7 and 8 of the text.
  • Be prepared to discuss problems 8.1 and 8.5 in class on Wednesday.
February 7
  • Homework 1 due.
  • Start reading section 9.
  • Note: Office hours 2/8 from 2-3 instead of from 3-4.
February 9
  • Finish reading through section 9
  • Think about 9.9 (a) and 9.11 (a) for discussion in class on 2/12.
February 12
  • Read section 10 through page 57.
  • We'll start class with a discussion of 8.9 (a).
February 14
  • Homework 2 due. (Please note the important instructions on the cover sheet. You need to hand in the assignment in two pieces.)
  • Read section 10, pages 58-62.
February 19
  • We'll start class with a short quiz. Be sure to know the definitions sup, inf, lim sup, lim inf, Cauchy sequence. I may ask you to state a definition or to apply a definition, but you won't have to prove anything.
  • Begin reading section 11 and answer the reading question on ella before class on 2/21.
February 21
  • Homework 3 due.
  • Finish reading section 11 and answer the reading question on ella before class on 2/23.
February 23
  • Read section 12.
February 26
  • TBA.
February 28
March 2
March 5
  • Continue working on your exams due Wednesday.
March 7
  • Read section 14.
  • Your exams are due in class today.
March 9
  • Read section 15.
  • We're going to discuss Exercises 14.5 and 14.7 in class today. Check ella for "warmup" questions to get you thinking about these problems. (I know the answers are in the back of the book, but try not to look.)
March 12
  • Read section 17.
March 14
March 16
  • Check out ella for a discussion assignment.
March 26
  • Warmup discussion: Prove that |x| is continuous.
  • Discusion of Exercise 17.14.
  • Proofs of Theorem 18.2 and Corollary 18.3.
March 28
  • Homework 6 due.
  • I'll start by asking for questions from the material in section 18.
  • I'll give the definition of uniform continuity.
  • Examples of uniform continuity (lecture and discussion).
  • Theorem 19.2.
March 30
  • We'll prove Theorems 19.4, 19.5, 19.6.
  • Be prepared to discuss Exercise 19.1 in class. (There is a preparatory discussion question to be submitted on ella.)
April 2
  • Proof of Theorem 19.6.
  • Discussion of Exercise 19.1 (d).
  • Proof of Theorem 23.1.
  • Discussion of Exercise 23.1.
April 4
  • More discussion of Exercise 23.1.
  • We'll discuss the meaning and implications of Definitions 24.1 and 24.2 and Theorems 24.3 and 25.7. Please read the definitions and theorem statements before class. Look for required reading questions on ella.
  • Proofs of Theorems 26.1, 26.3.
  • Homework 7 due.
April 6
  • We'll start by assuming Theorem 26.4 and using it to discuss Exercise 26.2.
  • Proof of Theorem 26.3 and 26.4.
  • Proof of case 1 of Theorem 26.5.
April 9
  • Finishing Abel's theorem + application to ln 2.
  • Definition of the limit of a function (Important note: We will be using a definition that differs from the nonstandard definition in the book. You can find our definition in the notes on ella.)
  • Explanation of why we won't be using Definition 20.1 in the text.
  • Discussion of Exercise 20.1.
  • Explanation of why we won't be using Theorem 20.6.
April 11
April 13
  • Part I of the in-class exam. The exam will cover sections 14, 15, 17, 18, 19, 23, 26.
  • Exam 2.
April 16
  • Discussion of limit points.
  • Two definitions of the limit of a function
  • How should we define one-sided limits?
April 18
  • Discussion of Exercise 20.1
  • Definition 28.1.
  • Discussion of exercise 28.1.
  • Proof of Theorem 28.2.
  • The product rule.
April 20
  • The chain rule.
  • Discussion of Exercises 28.5 and 28.7. See ella for required discussion questions.
April 23
  • Finish discussion of Exercises 28.5 and 28.7.
  • Proofs of Theorems 29.1, 29.2, 29.3.
  • Discussion of Exercise 29.1.
  • Please read through the rest of the chapter. I'll post reading questions on ella which will be due on the 25th.
April 25
  • Discussion of questions about Chapter 29.
  • We'll begin our discussion of integration with definition 32.1.
  • You are responsible for the material through Theorem 32.5 in section 32.
  • Homework 9 due.
  • In class exam redos due.
    		•
    April 27
    • We'll discuss the Fundamental Theorem of Calculus (Theorem 34.1). You are only responsible for the portion of section 34 through the proof of Theorem 34.1.
    April 30
    • Integration example. (11-11:15)
    • Theorems 32.4, 32.5, 34.1. (11:15-11:45)
    • Continuity review. (11:45-12)
    • Metrics. (12-12:15)
    May 2
    • Review of limit points.
    • Open and closed sets.
    • The Cantor set.
    • Homework 10 due.
    May 4
    May 7
    • Review: focus on power series.