Math 432 - Syllabus

 THE UNIVERSITY OF HAWAI'I AT HILO - MATHEMATICS DEPARTMENT

Course Description:

Real Analysis I and II focus on an analytic study of the real line R and its higher dimensional analogue R^n.  To many students, Analysis is simply a more detailed look at the various concepts and theorems from Calculus.  While this may be a major motivation, it is not until one looks deeply into the Topology of the Real line that one sees that this seemingly ordinary object is remarkably deep and complicated.  Even answering the question of "What is a real number?" will be difficult to answer at first.  The purpose of this course is to take an axiomatic approach at studying the real line and continuous/differentiable functions on it.

Learning Outcomes:

The successful student will be able to:
- write a rigorous analytic proof, complete with full syntax and proper mathematical notation
- prove that a number is or not rational
- prove various properties about integer, rational, irrational, and complex numbers
- understand the basic concepts of the Complex plane
- use basic properties of sets and functions on sets
- utilize the basic concepts in point-set topology (open/closed sets, compactness)
- prove that a sequence converges or diverges
- prove that a function is or is not continuous
- understand the basic properties of derivatives

Homework:

This course will have frequent homework assignments.  In fact, homework will be the primary pedagogical tool in this course.  Since mathematics is a highly communal activity, you are encouraged to work in groups.  That being said, copying will be severely punished.  If you write something down on your HW and can't explain it to me later on in person, then I'll consider this to be copying.

All homework is required to be typeset in LaTeX.  Homework must be printed out prior to class and turned in at the beginning of lecture on the due date.

LaTeX:

The use of AMS LaTeX is not only encouraged but will be required.   LaTeX is the universally accepted scientific typesetting program that allows mathematicians to write well-formatted mathematical papers.  This open-source compiler and associated interfaces can be found as freeware.  Please see the below links for how to download the appropriate software.

All HW assignments can be found on our HW site in .pdf form.  If you change the ".pdf" to ".tex", your browser will download the LaTeX source code.

The final grade will be based largely on homework, midterms, and final.
Furthermore, class participation (e.g., asking questions in class, going to the Math Lab, going to
office hours, asking Bob email questions, consistent attendeance in class, etc) will also be used in this computation.  The class participation grade is computed at the discretion of the instructor.