Math 601
Rational & Irrational Numbers:
The Foundation of Real Analysis
Summer 2008
June 16- July 4
M-F 9am-12pm
 

Instructor: Dr. Mike Coco
Office: Hobbs 322
Telephone: 544-8366
Email: coco@lynchburg.edu
Homepage: http://coco_m.web.lynchburg.edu
Office Hours: by appointment
Textbook: none
 
COURSE DESCRIPTION
This course explores the basic structure of the Real Number system, with a focus on the properties of rational and irrational numbers. Topics will include basic properties of numbers, rational and irrational approximation, and transcendental number theory.

COURSE OBJECTIVES
Upon completion of this course the student will:

  1. Understand defining characteristics of rational and irrational numbers.
  2. Understand defining characteristics of algebraic and transcendental numbers.
  3. Be familiar with important results concerning number approximation.
  4. Be able to use properties of the Real Number system to prove basic results in Real Analysis.

HOMEWORK
Homework will be assigned almost every day.  These assignments will consist of 1-3 questions to be turned in the following day. Your solutions should be written up as neatly and as detailed as possible. Your homework average will make up 25% of your course grade. I encourage you to work together as much as possible on all homework assignments. Each person should hand in his/her own separate homework assignment and this should not be an exact copy of someone else's.

TESTS
There will be two semester tests. Each test will be worth 25% of your final grade. Their dates are:

Test 1 Friday June 20
Test 2 Friday June 27
Test make-ups will not be given. If you miss a test for a legitimate reason that test will be dropped and the final exam will be counted twice in its place.

FINAL EXAM
The final exam will be comprehensive, covering the entire content of the course, and will make up 25% of your final grade. Under no circumstances will the final exam be given early.  Make travel plans accordingly.  The scheduled date, time and place of the final are:   Friday July 4, 2008 Hobbs 312

GRADING
Course grades will be assigned using a 10-point scale. That is,

A 90-100
B 80-90
C 70-80
D 60-70
F 0-60
Your grade will be calculated by a straight average of your test grades, homework and your final exam.

TEACHER LICENSURE OBJECTIVES

  1. Understanding of the core knowledge base of concepts and procedures within the discipline of mathematics, including the following strands: number systems and number theory; geometry and measurement; analytic geometry; statistics and probability; functions and algebra; calculus; and discrete mathematics;
  2. Understanding of the sequential nature of mathematics and the mathematical structures inherent in the content strands;
  3.  Understanding of the connections among mathematical concepts and procedures and their practical applications;
  4. Understanding of and the ability to use the four processes -- becoming mathematical problem solvers, reasoning mathematically, and making mathematical connections -- at different levels of complexity; 
  5. Understanding of the history of mathematics, including the contributions of different individuals and cultures toward the development of mathematics and the role of mathematics in culture and society; 
  6. Understanding of major current curriculum studies and trends in mathematics; 
  7. Understanding of the role of technology and the ability to use graphing utilities and computers in the teaching and learning of mathematics;