MTH 311 Real Analysis (Fall 2022):
- What is Real Analysis?
Real analysis is an examination of the theory of calculus of a single variable. Topics include properties of the real numbers, topology of the real line, and a rigorous treatment of sequences, functions, series of functions, limits, continuity, differentiation and integration. Find more information about the course in the syllabus and introduction. - Instructor: Dr. Sofya Chepushtanova, office SLC 408, email: sofya.chepushtanova@wilkes.edu.
- Class meetings: MWF 11:00-11:50 am and T 02:00-02:50 pm in SLC 405.
- Office Hours: MTR 10:00-10:50 am and MW 12:00-12:50 pm or by appointment.
- Textbook: Understanding Analysis by Stephen Abbott, 2nd ed. (Springer).
- Reading:
- LaTeX: a markup language to typeset documents. It excels at making math and the overall layout beautiful.
You can use it to type your homework solutions. Read the tutorial here. You may find the following LaTeX cheat-sheet useful.
Schedule (updated as the semester progresses):
Week of |
| Topics to Read | | Remarks, Materials, Assignments |
8/29 | Introduction. Chapter 1: §1.1 The Irrationality of √2. §1.2 Preliminaries. §1.3 The Axiom of Completeness. |
Notes for §1.1 Notes for §1.2 Notes for §1.3 Homework Guidelines |
9/5 | No class on Monday (Labor Day) §1.4 More on Completeness. §1.5 Cardinality. |
Notes for §1.4 Notes for §1.5 Homework 1 due 9/7: Read Sections 1.2, 1.3 and do exer. 1.2.1, 1.2.5, 1.2.7 (a,b), 1.2.8, 1.2.11 (a,b), 1.2.12, 1.3.1 Latex template for homework: here Homework 1 Solutions |
9/12 | §1.6 Cantor's Theorem. Chapter 2: §2.1 Rearrangements of Infinite Series. §2.2 The Limit of a Sequence. |
Notes for §1.6 Notes for §2.1 Notes for §2.2 Homework 2 due 9/14: Read Sections 1.3, 1.4 and do exer. 1.3.2, 1.3.4 (a), 1.3.5 (a), 1.3.8, 1.4.1, 1.4.4, Bonus: 1.4.5 Homework 2 Solutions |
9/19 | §2.3 Limit Theorems. §2.4 The Monotone Convergence Theorem and Infinite Series. §2.5 Subsequences. |
Notes for §2.3 Notes for §2.4 Notes for §2.5 Homework 3 due 9/21: Read Sections 1.5, 1.6, 2.1, 2.2 and do exer. 1.5.5 (c), 1.6.6, 2.2.2, 2.2.6, 2.2.7 (a,b), Bonus: 1.5.4 (a) Homework 3 Solutions |
9/26 | §2.6 The Cauchy Criterion. §2.7 Properties of Infinite Series. |
Notes for §2.6 Notes for §2.7 Homework 4 due 9/30: Read Sections 2.3, 2.4 and do exer. 2.3.1, 2.3.3, 2.3.4 (b,c), 2.3.7 (a,b,c), Bonus: 2.3.7 (d,e) Homework 4 Solutions |
10/3 | More on Infinite Series. Chapter 3: §3.1 The Cantor Set. §3.2 Open and Closed Sets. |
Notes for §3.1 Notes for §3.2 Exam I is on Friday, 10/7: study guide (Exam I solutions ) |
10/10 | No class on Friday (Fall Recess) §3.2 Open and Closed Sets Continued. |
Homework 5 due 10/11: Read Sections 2.5, 2.6, 2.7 and do exer. 2.5.1, 2.6.2, 2.7.2, 2.7.4, Bonus: 2.7.5. Homework 5 Solutions |
10/17 | §3.3 Compact Sets. §3.4 Perfect Sets and Connected Sets. Chapter 4: §4.1 Discussion. §4.2 Functional Limits. |
Notes for §3.3, 3.4 Notes for §4.1, 4.2 Homework 6 due 10/21: Read Sections 3.2, 3.3, 3.4 and do exer. 3.2.2, 3.2.3, 3.3.1, 3.3.2, 3.3.5 (a, b) Bonus: 3.2.7 (b) and 3.3.5 (c) Homework 6 Solutions |
10/24 | §4.3 Continuous Functions. §4.4 Continuous Functions on Compact Sets. |
Notes for §4.3 Notes for §4.4 Homework 7 due 10/31: Read Sections 4.1, 4.2 and do exer. 4.2.1 (a,b), 4.2.5 (c,d), 4.2.7, 4.2.10 Bonus: 3.4.2 (from Section 3.4) Homework 7 Solutions |
10/31 | §4.5 The Intermediate Value Theorem. Chapter 5: §5.1 Discussion §5.2 Derivatives |
Notes for §4.5 Notes for §5.2 Homework 8 due 11/9: Read Sections 4.3, 4.4 and do exer. 4.3.1, 4.3.6 (a,b,c), 4.4.1, 4.4.3, 4.4.7 Bonus: 4.3.6 (d,e) Homework 8 Solutions |
11/7 | §5.3 The Mean Value Theorem Chapter 6: §6.1 Discussion |
Notes for §5.3 Notes for §6.1 |
11/14 | §6.2 Uniform Convergence Review for Exam II |
Exam II is on Wednesday, 11/16: study guide (Exam II solutions ) Homework 9 due 11/18: Read Sections 5.1, 5.2, 5.3 and do exer. 5.2.1, 5.2.2, 5.2.5, 5.3.3 Bonus: 5.3.7 Homework 9 Solutions |
11/21 | §6.2 Uniform Convergence Continued No class on Tuesday (Thursday schedule) Thanksgiving Recess 11/23 - 11/27 |
Notes for §6.2 |
11/28 | §6.3 Uniform Convergence and Differentiation §6.4 Series of Functions §6.5 Power Series |
Notes for §6.3 Notes for §6.4 Notes for §6.5 Homework 10 due 12/2: Read Sections 6.1, 6.2, 6.3 and do exer. 6.2.1, 6.2.3 (a,b), 6.2.9 (a), 6.3.1, 6.3.5 (a,b) Bonus: 6.3.4 Homework 10 Solutions |
12/5 | §6.6 Taylor Series Chapter 7: The Riemann Integral |
Notes for §6.6 Homework 11 due 12/9: Read Sections 6.4 - 6.6 and do exer. 6.4.6, 6.4.8, 6.5.1, 6.5.4, 6.6.2, 6.6.5 Bonus: 6.5.3 Homework 11 Solutions |
12/12 | Chapter 8: Constructing R from Q Final Exam: 12/14 (Wednesday) 10:30 - 12:30 (SLC 405) |
Final exam study guide |