MTH 311/411 Real Analysis (Fall 2020):
 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 410, email: sofya.chepushtanova@wilkes.edu.
 Class meetings: MWF 09:0009:50 am and R 01:0001:50 pm in SLC 405.
 Office Hours: MWF 10:0011:00 am and TR 12:0001:00 pm or by appointment. Note that office hours will be held virtually via Google Meet. The following link will allow you to sign up for a 20minute slot (within office hour times listed above): signup calendar.
 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 cheatsheet useful.
Consider the following LaTeX template to start: download (it is the template of document On Proofs).
Schedule (updated as the semester progresses):
Week of 
 Topics   Remarks, Materials, Assignments 
8/23  Introduction. Chapter 1: §1.1 The Irrationality of √2. §1.2 Preliminaries. §1.3 The Axiom of Completeness. 
Notes §1.1 Notes §1.2 Notes §1.3 
8/30  §1.4 More on Completeness. §1.5 Cardinality. §1.6 Cantor's Theorem. 
Notes §1.4 Notes §1.5 Notes §1.6 Homework 1 due 9/2: All students: 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 Graduate (MTH 411) student: in addition, do exer. 1.2.7 (c,d) and 1.2.11 (c) (MTH 311 students are welcome to do these problems for extra credit.) Latex template for homework: here. Make sure to read homework guidelines. Homework 1 Solutions Quiz 1 
9/6  Chapter 2: §2.1 Rearrangements of Infinite Series. §2.2 The Limit of a Sequence. §2.3 Limit Theorems. 
Notes §2.1 Notes §2.2 Notes §2.3 Homework 2 due 9/9: All students: 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, 1.4.3, 1.4.4, 1.4.5 Graduate (MTH 411) student: in addition, do exer. 1.3.4 (b), 1.3.5 (b), 1.3.10 (a) (MTH 311 students are welcome to do these problems for extra credit.) Homework 2 Solutions 
9/13  §2.4 The Monotone Convergence Theorem and Infinite Series. §2.5 Subsequences. 
Notes §2.4 Notes §2.5 Homework 3 due 9/16: All students: read Sections 1.5, 1.6, 2.1, 2.2 and do exer. 1.5.4 (a), 1.5.5, 1.5.6 (a), 1.6.6, 2.2.2, 2.2.6, 2.2.7 Graduate (MTH 411) student: in addition, do exer. 1.5.6 (b), 1.5.8, 2.2.4 (MTH 311 students are welcome to do these problems for extra credit.) Quiz 2 
9/20 
Homework 4 due 9/23: All students: 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) Graduate (MTH 411) student: in addition, do exer. 2.3.6, 2.3.7 (d,c) (MTH 311 students are welcome to do these problems for extra credit.) 
