| MTH436: Mathematical Analysis and Topology II |
Instructor: Tom Sharland
Course description: This course is a continuation of MTH435. This semester we will study continuity of functions of one real variable and in metric spaces. We will then look at derivatives of real valued functions, followed by studying the Darboux Integral. For the integral, I will prepare worksheets to replace Chapter 7 in the book. If there is time, we will choose from a collection of optional topics; these include looking at properties like compactness and connectivity in metric and topological spaces, functions of several real variables or something else. Which topics we cover will be a decision made as a class.
This course will be relatively fast-paced, so in order to keep up with the material, you should be prepared to spend sufficient time outside of class attempting practice problems and reading and understanding your notes and textbook. You should certainly make sure you are comfortable with the material from MTH435 - we will be making use of much of it throughout this semester. There is insufficient class time to teach everything you need to know from this class, and so a fair amount of learning will have to take place away from the class room. You are more than welcome to come to office hours to discuss any issues you have with concepts, theorems and so on. The earlier you sort these problems out, the better.
Textbook: Introduction to Real Analysis by Bartle and Sherbet (4th Ed.).
Homework: The homework will be as in MTH435. Homework will be assigned weekly. Each assignment will be split into (up to) 3 parts. Part A will be simpler questions, which you may find useful with solving the later questions and may also appear on the weekly quiz (more later). Part B will consist of the questions to be submitted for credit. Part C are harder questions and may go beyond the scope of the course. Tackle these if you want a challenge or are interested in learning more.
Quizzes: These will take place weekly and will be based on the homework.
Grade breakdown: The grading scheme will be as follows: