Course Syllabus
Course Overview
Careful development of elementary real analysis for those who intend to take graduate courses in Mathematics. We begin with a construction of the real number system and then move on to properties of real-valued functions. Topics include completeness property of the real number system; basic topological properties of n-dimensional space and general metric spaces; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration. Credit is not given for both MAΤH 447 and either MATH 424 or MATH 444.
General Information
This is a 3 credit hour course. The course is 16 weeks long and consists of 16 Units. You should dedicate approximately 10 hours per week to work on the course itself, but actual time commitments will vary depending on your input, needs, and personal study habits. It is recommended that you log on to the course website and check your email frequently for updates, news and announcements.
Required and Recommended Texts
Required:
• Kenneth Ross. (2013). Elementary Analysis: The Theory of Calculus (2nd Edition). Springer.
Recommended
• R. Creighton Buck. Advanced Calculus (3rd Edition)
o A very good book at roughly the same level as our course with different areas of focus. This is a good source of examples and exercises and contains explanations that are not in our textbook or the lectures.
• Walter Rudin. Principles of Mathematical Analysis.
o A more advanced book that covers the same material. It is a (the) classic textbook on this subject.
Course Components
This course will consist of the following components:
Pre-Assignment
The pre-assignment should be completed first. It is used to ensure that you understand the policies, expectations and resources provided in the course. The pre-assignment is worth the same value as each of the other homework assignments.
Units
Each unit begins with an overview and the learning goals you are expected to achieve. These goals should guide your study through the unit. Every unit consists of a homework assignment, lectures, readings and additional exercises to support these goals. They are designed with the same structure and components unless otherwise specified. The module activities are explained in greater detail below.
Homework Assignments
Each unit contains a homework assignment consisting of several exercises. After clicking the assignment you will see assignment instructions and a link to a PDF file containing these exercises. View the PDF file and complete the exercises. When you are finished, scan or take a picture of your work and submit the file via the assignment link in Canvas.