Introduction to Analysis I

Internet Based

MATH 310

Section ALL

Term:Fall, 2008 (August - December)
Revision:14 My 08
Credits:3
Class Time:Two or three lectures weekly.
You should set aside several definite times each week to work homework.
Instructor:Frank Daniels
Instructor e-mail address: fdaniels@gbcnv.eduYou need to know this!
Office:
Frank Daniels
Great Basin College
Ely Branch Campus
2115 Bobcat Drive
Ely, NV 89301
Phone:
(775) 289-3589 (office)
(775) 289-3599 (college fax)

Textbook: Real Analysis and Foundations, Second Edition, by Steven G. Krantz
ISBN: 1-58488-483-5


This book may be ordered through your outlet of choice (e.g., Amazon.com).



Class Conditions:

  1. You must be using a Windows-based system.
  2. You must have Microsoft Word 97 or higher on your system and know how to use it.
  3. You should have your own access to the Internet through a commercial provider.
  4. You must have the access software installed and working. This class does not teach how to set up the access software.
  5. You must have an Internet user (or login) name if you are going to use the GBC Computer labs.
  6. You must have a Web browser. The class assumes you are using Netscape version 7 or higher or Explorer version 6 or higher.
  7. You must have an e-mail account somewhere to send and receive feedback. The class assumes that you know how to properly use e-mail and your browser.

Class Description:

Prerequisite: MATH 283, recently.
A re-examination of the calculus of functions of one-variable: real numbers, convergence, continuity, differentiation and integration.

This course is NOT "self-paced". The pace is established by the course Calendar, which is attached to the course Syllabus. It is considerably difficult, but if you succeed in keeping up and ask questions about material that you do not understand, you will succeed. Remember that you have a "live" instructor who will answer your questions.

Withdrawal Policy:

If you determine that you wish to drop the course prior to its conclusion, it is necessary for you to officially drop, either online through the college's website, or by visiting one of our college campuses and submitting a drop form. Any student who does not officially drop will receive a grade at the conclusion of the course. These grades will be based on the number of points that you have accumulated (see below).
If you do not officially drop the course as described above, by taking this class you agree that your "last date of attendance" for official purposes will be the last day of this course. Since this may affect your financial aid, it behooves you to drop officially or to complete the entire course.

Course Objectives:

The successful student will be able to:
  • Explain the development of the Rational Numbers, Real Numbers, and Complex Numbers distinguishing Countability from Uncountable Sets.
  • Discuss the convergence and divergence of sequences, including Cauchy sequences
  • Apply the series convergence tests, providing proofs of some of them
  • Discuss topological properties of sets such as the Cantor Set
  • Define compactness, connectedness, and open and closed sets, proving which subsets of the real line have these properties
  • Competently discuss continuity from the viewpoints of Limits and Topology
  • Classify discontinuities
  • Define derivatives rigorously
  • Uncover points where a continuous function is not differentiable
  • Relate continuity and differentiability
  • Prove the major results, including the Mean Value Theorem
  • Express knowledge of key examples and counterexamples (such as a function that is continuous on the real line but nowhere differentiable)
In order to provide accurate assessment of the learning outcomes, students will be tested regularly on the items documented above, as they are covered in the course. This testing includes homework, tests, and a final exam.

Instructional Methods:

Each week, there will be assigned readings from the book, which will be contained on each course lecture. You will work the homework from each lesson, and will hand in homework periodically -- as identified below.

Feel free to ask questions on the phone, via e-mail, by fax, or by attaching MS Word files to e-mail. I plan to answer all questions within 24 hours.

Homework Policy:

If you don't do homework, it is unlikely that you will pass the course. However, homework will not normally be collected for a grade. The student is expected to do half of the problems from each section that we cover. Test problems will be similar but not identical to those in the book. Occasionally (see below), I will ask that you turn in your homework to be graded. When I do this, you should submit your homework as MS Word files, attached to an e-mail message.

Withdrawal Policy:

If you determine that you wish to drop the course prior to its conclusion, it is necessary for you to officially drop, either online through the college's website, or by visiting one of our college campuses and submitting a drop form. Any student who does not officially drop will receive a grade at the conclusion of the course. These grades will be based on the number of points that you have accumulated (see below).

If you do not officially drop the course as described above, by taking this class you agree that your "last date of attendance" for official purposes will be the last day of this course. Since this may affect your financial aid, it behooves you to drop officially or to complete the entire course.

Grading:

The class is graded on four tests and various assignments, as follows:
4 tests, each worth 35 points. These will be sent by me via e-mail and must be completed without assistance in one weekend's time, typically due the Monday after they are assigned in the lessons. Most test problems will be difficult enough that you cannot simply copy something from the book, although you should remember that the methods are generally the same. These tests normally occur at the end of each chapter. Consequently, each test will be no longer than 14 questions. You will mail your completed tests back to me as attached files or may fax them. After they have been graded (usually by the following Thursday), you may e-mail me for your results.

5 homework assignments, each worth 20 points. These will be assigned at various times during the semester and will include a subset of your normal homework assignment. As with the other material, you will write the homework in MS Word and attach the file to an e-mail message. Homework must be completed on time.

1 Final Exam, worth 60 points. The test will be cumulative, covering all of the course material. It will be mailed out to you as an attached MS Word file, and you will complete it within 2 days. It will contain no more than 26 questions. Special: If you have an "A" average (216 points or better) going into the final, you do not have to take the final exam, but you must still hand in the final homework.

Therefore, the total number of points available for the semester is 300 points. The number of points required to obtain each grade is as follows:

A 270 B+ 255 C+ 225 D+ 195
B 240 C 210 D 180 F 0

Academic Integrity:

The Nevada System of Higher Education expressly forbids all forms of academic dishonesty, including (but not limited to) all forms of cheating, copying, and plagiarism. Students who are discovered cheating will be assigned zero points for the current assignment. If the cheating is believed to be widespread -- to involve other students and/or to cover more than one assignment or test -- then all students involved will receive "F" grades for the course and will be brought to the GBC academic officers for prosecution. I will normally recommend that students found guilty in that instance be placed on one year disciplinary probation.

Starting from scratch:

This class is accessed from the Internet. Therefore, there has to be some pre-knowledge. I need to have you send me an e-mail message telling me you are ready to begin, and you need to do this by September 1st, 2008. If you need to find some help to get started, you can always e-mail or phone me at the college building.

Getting started:

  1. Purchase the book ahead of time.
  2. Have your Internet software installed, and know how to use it.
  3. The course schedule, including test dates, appears on the course Calendar.
  4. Familiarize yourself with MS Word and the Equation Editor.
  5. If you are having problems (e.g., you do not have the book), e-mail me by September 1st.
  6. Read the book and lecture material for lesson 1, and notice that Lesson 2 is assigned for Wednesday.
  7. PLEASE ask questions about any material that you find difficult to understand!
You must not take this course if you have not had MATH 283, or higher, (or the equivalent) within two years

Good luck!

All lessons are © 2005, 2008 Frank Daniels
and are licensed to Great Basin College