---Spring 2016---

Math 615, Elementary Number Theory SEC#:21286
4:00-5:15 MW 372 JB

Some basic information follows.

I will be using my own notes for the textbook in this course. The notes are available in two forms: a free PDF file that you can download from the Content folder on Blackboard,   or a coil bound copy  can purchased from lulu.com. The link to the coil bound copy is posted below.

www.lulu.com/shop/bill-richardson/spiral-bound-number-theory/paperback/product-22514064.html 

 (the cost for the coil bound copy is $12.49, $8.50 plus $3.99 shipping and handling.)

NOTE: If you are going to purchase a coil bound copy from lulu.com, go to the page lulu.com before you go to the link for the actual book.  At times lulu makes available discounts which are listed on their Homepage. 
 
Since the book I once used sold for $148.49 on Amazon, you may feel you just got  a $150 scholarship for this semester.

The PDF file that you can download from Blackboard is formatted to the 6" x 9" form that I used for the coil bound book, so you can use it as an ebook if you wish.

First we should understand what is meant by "elementary number theory." Number theory is divided into four branches: elementary (or classical) number theory; algebraic number theory; analytic number theory; and computational number theory. "Elementary" number theory means that the mathematical tools needed are elementary (non-calculus based). The major attraction of elementary number theory that has made it so popular among non-professional mathematicians is that the problems can be stated so that anyone can understand them. That does not mean that everyone can solve the problems. The most famous example is that of "Fermat's Last Theorem" which states that there are non-trivial solutions to the equation xⁿ + yⁿ = zⁿ only for positive integers n less than or equal to 2. This theorem was conjectured by Fermat in the early 17^th century. He claimed to have a beautiful proof that would not fit in the margin of his book. Many mathematicians, including some of the greatest in the history of mathematics, tried to find a proof for this result. The theorem was finally proved in 1997 by Andrew Wiles and the proof was not an elementary one.

Through the centuries number theory has been, by far, the favorite area of study for non-professional mathematicians. But even the greatest of the professional mathematicians have had a love and appreciation of this field. One of the greatest mathematician of all time, Carl Friedrich Gauss (1777 - 1855), proclaimed: "Mathematics is the queen of the sciences and number theory is the queen of mathematics."

Many people, and I am among them, find number theory quite fascinating. At times, from my desire to share with you as much information as I can about this material, I may talk too fast and write too fast. If I go into this mode please request that I slow down. I am well aware of this problem and would appreciate your help in overcoming it. If, during a lecture, you have trouble understanding a concept, don't hesitate to ask a question at that time. You may forget it if you wait. I do not mind being interrupted to answer questions. This is how learning takes place.

We will try to cover Chapters 1, 2, 3, 4, 5, 6, and 7 of the text, with some additions and omissions.

Math 615 may be quite different from any other mathematics course you have taken. The major goal of the course is to have some fun and learn some interesting properties of the integers, as well as learning some problem solving techniques. Some very interesting and seemingly complex problems can be solved using very basic mathematics and strong logic. On the other hand, some very simple looking problems may require a considerable amount of thought.

A tentative daily schedule is not provided. Since no course depends on this course as a prerequisite, we may, on occasion, go off on tangents to examine topics of interest to the class. We will probably have three exams during the semester plus the final exam. A tentative examination schedule is as follows: Exam 1 will be given after we finish the material through Chapter 3, Exam 2 will be given after we finish the material through Chapter 5, and Exam 3 will be given over the remainder of the material covered.

Spring Break is March 14 - March 20 <

April 1 is the last day to drop without penalty.

There will be no individual make up exams given. Exams will be either in-class exams or take-home exams. The Final Exam, which will be a comprehensive examination, will serve as a make up for any and all missed exams.

If you are planning to leave Wichita at the end of the Spring Semester, make your travel plans early. "I have plane reservations." is not an acceptable reason for missing the final examination.

To be successful in a mathematics course one must work problems and attend class. We consider mathematics to be a participation course, not a spectator course. You cannot learn by just watching someone else do mathematics. You should do all problems assigned whether they carry point value or not. If you have difficulties with any concept or problem ask questions in class or come to my office for help. Don't be bashful!

Not all assigned problems will be graded. The reward for doing homework will be higher quiz and test scores. This is a fact!

Attendance will be taken but it is not graded; however, students who attend their mathematics classes do better than those who don't!

Don't hesitate to ask questions in class. This is part of the learning process.

Cell phones and pagers must be turned off during class. If there is an emergency situation that requires you be reachable, let me know and be sure that your phone, or pager, is immediately available so that its ringing will not disturb the class. Also sit in the back of the class so that you may leave with minimum disturbance to the class.

No IPods, or similar devices, will be in evidence during class time.

On exam days be sure to stop at the restroom on your way to class.  Sharpen all pencils before you get to class.  Remove Bluetooth ear pieces.  The only things visible should be your exam and pen or pencil.
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All Faculty are requested to add the following statement to our syllabi

Definition and assignment of credit hours

Federal regulations and a new WSU policy now require all faculty and course instructors to communicate to students in their course syllabi how a credit hour is defined.

According to the U.S. Department of Education a "credit hour" is a measure of graduate or undergraduate academic work represented in intended learning outcomes and verified by evidence of student achievement that reasonably approximates not less than one hour of classroom or direct faculty instruction and a minimum of two hours of out-of-class student work for each week of instructional time for approximately 15 weeks for one semester, or an equivalent amount of work over a different amount of time.

As an example, for a three-credit hour course, this translates to 135 hours of student work.
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Please be aware of the Statement  of Academic Honesty

A standard of honesty, fairly applied to all students, is essential to a learning  environment. Students abridging a standard of honesty must accept the consequences; penalties are assessed by the appropriate classroom instructors or other designated people. Serious cases may result in discipline at the college or University level and may result in suspension or dismissal. Dismissal from a college for academic dishonesty constitutes dismissal from the University.                        
                                         (WSU Student Code of Conduct)
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All work assigned to you for grading will be given a point value. Your grade will be determined by the percentage of the possible points you received. 50% midterm exams and quizzes, 40% homework and 10% Final exam.

The following scale gives an idea of the worst grade you would receive.

				100 - 94      A
				 93 - 90      A-
				 89 - 86      B+
				 85 - 82      B
				 82 - 80      B-
				 79 - 74      C+
				 73 - 68      C
				 67 - 65      C-
				 64 - 60      D+
				 59 - 55      D
				 54 - 50      D-
				 49 ->        F

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