Math 401 Introduction to Real Analysis

REVISED SYLLABUS: in-class portion of final exam removed (its all take-home now)

Fall 2013, UAF

Instructor: Ed Bueler
Office: Chapman 301C.  Office hours online.
Phone: 474-7693
eMail: elbueler@alaska.edu 		Class Time:  MWF 9:15--10:15 Brooks 104A
CRN:  76579
Text: K. Ross, Elementary Analysis: The Theory of Calculus,
   2nd ed., Springer 2013

Course Web Site: www.dms.uaf.edu/~bueler/Math401F13.htm

Course Content and Goals:   The content of the course is cleanly summarized in the UAF Catalog: "Completeness of the real numbers and its consequences: convergence of sequences and series, limits and continuity, differentiation, and the Riemann integral."

Real analysis is a major milestone in the development of mathematics.  It was built in the 19th century as the rigorous underpinning of the 17th century calculus, which was useful but suspect when examined closely.

Real analysis is a core discipline in modern mathematics, and central to a student's maturing understanding of mathematics.  It is essential for much of applied mathematics including differential equations, approximation theory, fluid dynamics, and quantum physics.  It is a major part of 20th century pure mathematics including functional analysis, differential geometry, and stochastic processes.

Outcomes:  From my point of view this course is key preparation for teaching calculus.  Many math majors do that job, whether in high schools, community colleges, or universities.  Regardless of the level, teaching calculus requires you have a coherent thread to follow, and that thread is the clear understanding of the limit process(es) in calculus.  Just being able to work problems in calculus, which is a skill you should have already, does not suffice.  On the other hand, all further work in mathematics, whether the goal is to understand 20th century mathematics or to create new 21st century mathematics, assumes a rigorous basis in things like convergent sequences and precise definitions of derivatives and integrals.

Assigned Work and Evaluation and Grade:  Weekly homework will mostly be proofs.  There will be two in-class midterm exam, each one hour long, emphasizing definitions and shorter proofs.  The final exam will include both an in-class and take-home component.  The final exam will be take-home.

Exams/Homework
Homework
Midterm Exam I
Midterm Exam II
Final Exam: in-class
                    take-home
 Percent of Grade
45% 50%
15%
15%
15%
10% 20%
 Dates
weekly
in-class Wednesday 9 October
in-class Wednesday 13 November
Wednesday 18 December, 8--10 am
due in my box 5:00 p.m., Thursday 19 December

Based on your raw homework and exam scores, I guarantee grades according to the following schedule: 90 - 100 % = A, 79 - 89 % = B, 68 - 78 % = C, 57 - 67 % = D, 0 - 56 % = F.  I reserve the right to increase your grade above this schedule based on the actual difficulty of the work and on average class performance.

The "W" designator, draft/re-draft of some homework, and LaTeX too:  This will indeed be a writing-intensive course.  Almost every problem will be a proof, and I'll grade the quality of the writing on every problem.  This includes complete sentences, correct grammar, and appropriate writing style for the mathematical discipline.

On each homework assignment I will also circle one problem which will involve even more focus on both writing and mathematical quality.  Each student will have a different problem circled.  For that circled problem you will be required to write a LaTeX solution and submit it electronically.  You may LaTeX all your homework, but I want all problems submitted on paper, with your circled problem also submitted electronically.  I will grade your LaTeXed solution and return it with comments, both on the mathematical correctness and the writing.  You'll resubmit the corrected version on paper.  (The first assignment will be an exception.  On A#1 everyone will LaTeX the same problem based on a known proof, just for practice.)

Policies:   The Dept of Mathematics and Statistics has reasonable policies on incompletes, late withdrawals, early final examinations, etc.; see www.uaf.edu/dms/policies/.  You are covered by the UAF Student Code of Conduct.  I will work with the Office of Disabilities Services (208 WHIT, 474-5655) to provide reasonable accommodation to student with disabilities.

Prerequisites:    ENGL 111 Intro Academic Writing and (ENGL 211 Academic Writing about Literature or ENGL 213 Academic Writing about the Social and Natural Sciences or permission of instructor) and MATH 202 Calculus III and MATH 215 Intro Mathematical Proofs.