Text: "The Art of Proof: Basic Training for Deeper Mathematics" by M. Beck and R. Geoghegan, 2010. The electronic version is available at http://math.sfsu.edu/beck/papers/aop.pdf

Course Content: This course will cover parts I and II of the textbook plus some additional material. This includes the following topics. Careful discussion of the real numbers, the rational numbers and the integers, including a thorough study of induction and recursion. Countable and uncountable sets. The methodology of mathematics: basic logic, the use of quantifiers, equivalence relations, sets and functions. Methods of proof in mathematics. Training in how to discover and write proofs.

Prerequisites: Math 222: Calculus II with a grade of C or better

Class web-page: http://savchuk.myweb.usf.edu/teaching/2010A_math330_number_systems/

Grading: Your grade in this course will be based on your grades from the midterm exam, the final exam, the project, as well as homework assignments and quizzes. Except in very extreme cases, there will be no make-up quizzes and no late assignments accepted. Your grade will be determined based on the following percentages. However, attendance is required, so you may be penalized for excessive absences.

Homeworks	=	40%
Quizzes	=	10%
Project Assignment	=	15%
Midterm I	=	15%
Final Exam	=	20%

I will consider the grade appeals only within 7 days after the assignment is due (or after the last revisioin of the homework was submitted).

When calculating your course grade there is one more rule: if your homework score is an F then your course grade is an F; in this case I will ignore your midterm, project, and final exam scores.

Homework: I will assign the homework regularly and you will be required to submit it. The assignments will be available at
http://savchuk.myweb.usf.edu/teaching/2010A_math330_number_systems/homeworks.html
Solving homework problems is a crucial part in learning process. No matter how hard you study you will not learn the material unless you solve the problems on your own. In this course the grade for homeworks constitutes a significant pat of your final grade. You can discuss homework problems with other students in the class, but you are required to write the solutions on your own.

Most of your written work will be proofs. Proofs are expected to be complete and correct—but not necessarily the first time! I allow a total of 4 (four) submissions of each assignment. That gives you three rewrites. I'll read down until I find a significant error. I'll underline the error (it may be something missing) and stop there. You should figure out what's wrong and fix it. If you can't figure it out and your friends can't help, please do come and ask. Come to talk with me if you get stuck. I encourage that.

I also expect the proofs to be well written. Writing matters: not only because this is a Writing course, but because correct math must be written clearly and precisely. You may loose points for your writing.

How to Prepare Homework Papers: Please follow these easy rules to help me grade your work. Thanks!

• Write each separate assignment on a separate paper. Clearly indicate the numer of assignment and the date (and your last name, of course!). If you use more than one page for an assignment, staple the pages (other methods don't work). I will no longer accept unstapled pages.
• To make corrections, write a new solution starting from either the beginning or the first place you went wrong. Hand in the complete solution. Don't give me the same solution with a few cross-outs and replacements. I can't grade it. (Thank you.)
• Clearly indicate the complete number of the problem you are solving.
• Solve the problems in the order they are listed in the assignment
• Remove all stubs from your papers, if you tore them out of a spiral binder. (They cause chaos!)
• Use complete sentences.
• In any proof: First, state what you are going to prove. Then prove it indicating the beginning and the end of the proof. Don't omit the final step.
• Revised papers: If there's plenty of space on the previous paper you may write the revision on it, but label it clearly! You may cut and paste the good parts of the previous write-up.
• Get rewrites in as soon as possible.
  There's no firm deadline but you'll have plenty of new work. Preferred but not required: the day after I return them.
• You may submit each assignment up to four times.

If you are unable to come to class and submit the homework due to illness, you may turn in your homework to me either via email or by putting the assignment under my office door. You must then come to my office hour or make an appointment to meet with me within the next seven days, to explain to me your situation. If your explanation is satisfactory, then I will grade and give you credit for the homework assignment.

Electronic devices: During classes and exams your cell phones should be turned off. Ringing phones in class are very distracting to the rest of the students in the room, not to mention the instructor. I appreciate your cooperation with this.

Quizzes: Quizzes occasionally will be given in class. There will be NO make-up quizzes if you miss class without a University Excused Absence. One quiz with the lowest grade will be dropped. Quizzes may or may not be announced. I will post the solutions to the quizzes at http://savchuk.myweb.usf.edu/teaching/2010A_math330_number_systems/quizzes.html

Getting Help: If you are having problems, please stop by my office LN 2212 during office hours or by appointment. Again, do not hesitate to ask questions - by far this is the most effective way of learning.

Academic Honesty: All students are expected to adhere to the Student Academic Honesty Code. Copying other people's work, either in or out of the classroom, is an act of scholastic dishonesty and will result in a zero on the assignment and may cause other penalties. For more information on Academic Honesty Code visit http://provost.binghamton.edu/honesty.html.

Americans With Disabilities Act: Students with disabilities can get assistance from the Office of Services for Students with Disabilities (607-777-2686).

Copyright Policy: All printed materials distributed in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use only. Multiple copies or sale of any of the materials is strictly prohibited.