| 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 Riemann Integral. 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 and the generalised Riemann Integral. 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.
Textbook: Introduction to Real Analysis by Bartle and Sherbert (4th Ed.).
Homework: The homework will be as in MTH435, unless stated otherwise. 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.
Knowledge Check: This may or may not be continued in MTH436. Each week there will be a reading assignment. To check this is being done, a weekly knowledge check will take place. This will be a quick check that you know a definition or statement from this (or previous) weeks reading. For example, you may be asked to give the definition of a convergent sequence or the statement of the monotonic sequence theorem.
Grade breakdown: The grading scheme will be as follows: