Math 260 Section 001— Intro to Abstract Math (Proofs)

Fall Semester 2004

Course Meetings: 11-12 AM MWF in Ware 110F

Instructor: Dr. Carolyn Yackel

Office: 220 Ware Hall

Office Phone Number: 301-5982

E-mail: yackel_ca@mercer.edu

Office Hours: Mondays 1-2 PM, Wednesdays 1-2 PM, Thursdays 3-4 PM, Fridays 10-11 AM and by appointment. You do not need to make an appointment in order to come during office hours. Office hours will be cancelled on days when the university is not in session. (For example, office hours are cancelled during fall break.)

Text: How to Read and Do Proofs, by Daniel Solow

Prerequisite: MAT 192 and MAT 192L

Course Objectives: The successful student will

• Acquire a standard set of proof techniques, including direct proof, proof by contradiction, proof by contrapositive, proof by induction, and existence proofs,
• Gain facility and confidence in identifying and using the proof techniques listed above,
• Understand the role of counterexamples in proving the falsity of a statement,
• Accurately judge the veracity of a mathematical proof,
• Read and understand some basic mathematical proofs (including some in set theory, calculus, and elementary number theory),
• Verbally articulate logically coherent mathematical arguments,
• Verbally explain his or her arguments,
• Write concise, yet elucidating logical proofs aimed at an audience of his or her peers,
• Use writing to explain mathematical ideas,
• Use logic when analyzing arguments,
• Use examples to arrive at reasonable conjectures, and
• Try to prove his or her conjectures true or false.

In this class we will work to achieve the above goals by using

• Reading. You are expected to read the text and keep up with the syllabus. This book makes for easy reading, as far as math books go. Reading mathematics is a slow process—most mathematicians consider a rate of 2 to 5 pages of mathematics per hour as a quick pace.
• Homework. You may discuss homework problems together, but you must write them up by yourself. Any work you submit should be substantially your own. You should not come away from a working session with a write up of your proofs. No two people write a given proof the same way, unless they’ve copied. Contrary to popular opinion, it is easy to spot copying amongst math students in proofs courses. If you are having trouble deciding what does and does not constitute permissible collaboration, err on the side of caution. For those problems on which you collaborated, list your collaborators.
• Class time. Class time will involve a mixture of interactive lecture, thought provoking activities, discussion, and presentations by students. Sometimes the in-class work will be done in pairs or in groups of three or four. Occasionally, we may meet in a computer classroom. Come to class ready to think!
• Presentations. During class, you will be asked to be an active participant. In addition to paying attention and thinking hard, you should contribute your ideas to the class. (This is different from dominating the class time.) You will be expected to present a small proof or result at least once every two weeks. Your grade for presentations will be based on their frequency, mathematical validity and rigor, and your ability to communicate.
• Reflection. It is easy to think that if you only do your assignments, you will succeed. However, without time for reflection upon the material and an attempt to integrate new ideas into your existing knowledge base, it is unlikely that you will truly learn the material. Thinking about mathematics each day will make the material easier to learn deeply and to retain. Each time you read your book, study your notes, try some homework problems, or even just think about mathematics, you are studying for the exams.

Assessment: A measure of your progress and your course grade will be based on the following distribution.

Presentations 15%

Homework 40%

Exams 1, 2, and 3 and Final 15% each, drop the lowest one

Important Dates: Labor day/No Class Mon., Sept. 6

Exam 1—In Class Fri., Sept. 10

Exam 1—Take Home Due Mon, Sept. 13

Exam 2—In Class Fri., Oct. 8

Exam 2—Take Home Due Wed., Oct. 13

Middle of the Term Fri., Oct. 8

Fall Break/No Class Mon. & Tues., Oct. 11-12

Last day to withdraw Tues., Oct. 26

Exam 3—In Class Wed., Nov. 3

Exam 3—Take Home Due Fri., Nov. 5

Thanksgiving/No Class Wed.-Fri., Nov. 24-26

Last Day of Class Mon., Dec. 6

Final Exam Fri., Dec. 10 9-12 AM

Policies:

• The exam dates are fixed. Make-up exams will be given only in extreme cases and when written, verifiable proof is provided. Such cases include death in the immediate family or severe illness. Such cases do not include conflicting weekend travel plans, failure to prepare, other exams or assignments due the same day, or forgetting about the exam.
• Regular, punctual attendance is key to success in this course; hence, it is expected. Students are responsible for obtaining information and assignments distributed during class.
• Written assignments will be accepted until 5pm on the due date, after which they will be considered late. The official course clock is the instructor’s watch. Homework consisting of more than one page must be held together with a STAPLE. Homework problems must be submitted in order. The penalty for late homework is stiff. Homework submitted n calendar days late will receive its score multiplied by (.5)ⁿ.
• Students are responsible for all material presented in class and all material in the text.
• Announcements made in class or posted on the class web page are considered official notification.
• Students who receive a D or F on any assignment need to make an appointment to meet with me as soon as possible.

Honor Code: The Mercer University Honor Code, found in The Lair, applies to all assignments and tests given in this course.

Technological Devices: Out of courtesy for all those participating in the learning experience, all cell phones and pagers must be turned off before entering any classroom, lab, or formal academic or performance event. You may not play with your cell phone or pager during class.

Students who believe that they possess disabilities for which accommodation is required must so inform the instructor at the close of their first class meeting. They must then indicate the nature of their disability and the sort of reasonable accommodation requested. If you believe that you possess a disability for which reasonable accommodation must be made, you must consult with the instructor of this class immediately after your first class meeting. You will then identify the disability and the reasonable accommodation requested. The instructor will refer you to Student Support Services for evaluation, documentation of your disability, and a recommendation as to the accommodation, if any, to be provided.

If you do not consult with the instructor and follow up at Student Support Services, as provided above, you will thereby waive any claim to a disability and the right to any accommodation pertaining thereto.

I reserve the right to alter the syllabus or course content at any time during the semester, as needed. For example, office hours may need to be changed, or the frequency of presentations may need to be altered.