John Nardo

CORE 203 – GREAT IDEAS OF MODERN MATHEMATICS

DR. NARDO – SPRING 2004

"Mathematics is the queen of sciences."

– Karl Friedrich Gauss

"The universe stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics."

– Galileo Galilei

Course Purpose

The Oglethorpe University Bulletin states: 

The purpose of this course is to explore several major modern mathematical developments and to help students understand and appreciate the unique approach to knowledge which characterizes mathematics.  The mode of inquiry employed is reason.

The mathematics that you will create in this course will be fundamentally different than in your previous mathematics courses.  Rather than emulating techniques and problems solved by others, you will create your own mathematics.  Your mathematical explorations are the emphasis of this class and the true measure of both your success and the success of the course as a whole.

Course Information

Meeting Time:        Monday, Wednesday, & Friday 8:30 – 9:20 a.m.

Location:        Lupton Hall 203

Section:        01

Textbooks:        A Mathematics Sampler (5^th Edition) by Berlinghoff et al.

Contact Information

Office:        311 Lupton Hall

Telephone/Voice Mail Number:        (404) 364-8327

Electronic Mail:         jnardo@oglethorpe.edu

Internet Address:        http://www.oglethorpe.edu/faculty/~j_nardo

Office Hours

Monday & Friday 10:30 – 11:30 a.m.

Monday, Tuesday, & Wednesday 2:00 – 4:00 p.m.

Also By Appointment!

• During my office hours, I am available for consultation – no appointment is necessary.

• Specific appointments for times other than my office hours must be made in advance.  I will work hard to find a mutually agreeable time for us to meet; I expect you to make a good faith effort to use my regular, posted office hours, the ARC tutors, and the Residence Tutors.

• If my door is open, then I will be happy to see you:  come in!

• If my door is closed, then I expect you to see me during the next available office hour or to contact me (before class, after class, by voice-mail, or by e-mail) to arrange for an appointment.

Course Content

1. Graph Theory

2. Probability

3. Group Theory

Course Objectives

After the successful completion of this course, a student will have:

• Read, explored, and created mathematics in a self-directed fashion

• Demonstrated basic comprehension in several newly emerged fields of modern    mathematics

• Written simple but precise mathematical explanations and proofs

• Extended his/her spatial, geometric visualization skills

• Sharpened his/her problem solving skills.

Homework

Homework is given for every class meeting; check the course webpage for these assignments.  Even though this homework is not scored and will not account for a percentage of the course letter grade, I expect that you will complete all homework assigned.  Mathematics is not a spectator sport; you will not learn by simply watching me solve problems!  Keeping up with the homework assignments on a class-by-class basis will allow you to ask questions (in class or in office hours) that focus your learning, keep pace with the class, and progress successfully through the course.

Furthermore, you are expected to read the sections of the text that we cover in class!  You may do this reading either before the class day we discuss the material or after we have finished the material.  However, I consider this reading to be a part of your homework. 

Course Work

There will be frequent take-home quizzes.  These quizzes will promote deeper understanding of material covered in class; mathematical exploration, writing, and proof will figure prominently in these quizzes.  Though most quizzes consist of questions from your textbook, your solutions to these quizzes are not simply homework recopied from your notebook.  You are expected to submit thoughtful, complete solutions to the quiz problems articulated in a way that is clearly understood.  Each student is expected to grow in his/her ability to write and create mathematics as the semester progresses.  Quizzes will be open-book and open-notes.  Take-home quizzes are due at the beginning of class, sharp.  Quizzes may be turned in early; however, absolutely no late quizzes will be accepted! 

There is one class paper; it is a documented, grammatically correct short essay.  You will be graded on mathematical content as well as grammar and writing style.  You may choose from a list of topics provided by your professor, or you may create your own (with approval of the professor).  You must submit a one-paragraph topic/paper proposal on March 12; the paper itself is due on April 2.  Again, absolutely no late proposals/papers will be accepted!

There will be three in-class tests:  February 18, March 26, and April 29.  Tests will cover material from class, homework problems, take-home quizzes, and your textbook.  Missing a test is a very serious and grave matter.  I do not give make-up tests.  If a student misses a test, then he/she receives a zero for that test.  In computing your test average, I will drop your lowest test entirely.

EXCEPTION:        If a student is required to miss a test by a faculty/staff member because he/she is officially representing Oglethorpe (i.e. for a sports competition, university singers, etc.), then he/she may be eligible for a make-up test.  To be eligible for a make-up test, the following two conditions must be met:  (1) I must be notified in writing by the faculty/staff sponsor at least one week in advance of the test that the student will miss the in-class test and (2) the faculty/staff sponsor must proctor the make-up test and deliver it to me immediately upon the group’s return to campus.  If either condition is not met, then the student will receive a zero for the missed test.

The final examination will simply be the third test of the semester; it is not cumulative.  It will occur on:  Thursday, April 29, 2004, 8:00 to 11:00 a.m.  The final examination may be taken neither early nor late.  No exceptions are allowed to the University’s Final Examination Schedule, as published in the Schedule of Courses.

Students are expected to participate in class.  This includes responding to questions raised by the instructor, contributing to class discussions, and making presentations of solutions to homework problems.   

Grading Policy

Course averages will be calculated using these percentages:

Letter grades will be assigned according to the Oglethorpe University scale:

Attendance

I feel strongly that regular attendance and participation is vital for your learning and your success in this course!  Collegiate mathematics proceeds at a pace that makes regular class attendance a necessity.  The Oglethorpe University Bulletin admonishes:  "Regular attendance at class sessions, laboratories, examinations, and official University convocations is an obligation which all students are expected to fulfill."

Attendance will be taken within the first five minutes of every class meeting.  Any student arriving after attendance has been taken will be counted absent for that class meeting.  It is expected that when you come to class that you remain in class.  If a student leaves class early, he/she will be counted absent for that class meeting.  

EXCEPTION:        Absences resulting from officially representing Oglethorpe, i.e. for a sports team, concert, etc., will not be counted in a student’s tally of absences and will not affect a student’s grade.  A letter from the faculty/staff sponsor is required as documentation!  Absence for an official religious holiday (as determined by Oglethorpe University) will not count in a student’s tally of absences and will not affect a student’s grade.

A student’s attendance earns the 5% Attendance Grade according to the table below.  Upon a student’s SEVENTH absence, he/she will earn the grade "FA" (Failure by Absences) which has the same effect as an "F" in the GPA.

Disabilities/Learning Disabilities

Oglethorpe University is committed to equal access to its programs, services, and activities for people with disabilities. If you need physical accommodations in this class, please consult with Human Resources in Lupton Hall.  Office hours may be arranged at an alternate campus location, i.e. classroom, library, etc., for a student unable to access the third floor of Lupton Hall. 

If you need academic accommodations in this class, please consult the Learning Disabilities Resource Center in the Library. This program is responsible for acting as liaison with the faculty and was created to ensure that all students may participate fully in the Oglethorpe experience.

Honor Code

The Oglethorpe University Bulletin states:

Persons who come to Oglethorpe University for work and study join a community that is committed to high standards of academic honesty.  The Honor Code contains the responsibilities we accept by becoming members of the community. 

The students and faculty of Oglethorpe University expect each other to be truthful in the academic endeavor they share.  Faculty assume students complete work honestly and act toward them in ways consistent with that assumption.

Oglethorpe University welcomes all admitted students who accept our principles of honest behavior.  We believe that this Code will enrich our years at the University and allow us to begin practicing the honorable, self-governed lives expected of society’s leaders.

Students pledge that they have completed assignments honestly by attaching the following statement to each test, paper, overnight work, in-class essay, or other work designated by professors:  “I pledge that I have neither given nor received any unauthorized aid on this assignment.”

All work submitted by the student for a grade must represent the individual effort of the student.  The following will be considered violations of the Honor Code in this course and will be turned over to the Honor Council for investigation:

1. Giving or receiving class notes/materials

2. Discussing the specific content of examinations/quizzes

3. Giving or receiving copies of examinations/quizzes or their solutions

4. Using books or any type of notes during examinations

5. Giving aid to or receiving aid from other students during examinations/quizzes/papers.

Incompletes

The following is University policy:

The grade of  "I" has the same effect as an "F" on the GPA.  If a student is unable to complete the work for a course on time for reasons of health, family tragedy, or other circumstances the instructor deems appropriate, the grade of "I" may be assigned.  If the student completes the work within thirty days of the last day of exams (of the semester in question), the instructor will evaluate the work and turn in a revised grade.  Any "I" not changed by the professor within forty-five days of the last day of exams will automatically be changed to a grade of  "F."

• Halmos, Problems for Mathematicians, Young and Old, MAA, Washington, D.C., 1991

• National Science Foundation, Women, Minorities, and Persons with Disabilities in Science and Engineering, NSF, 1997

• National Science Foundation, Women and Science Celebrating Achievements, Charting Challenges, NSF, 1997

• Trentacosta & Kenney, Multicultural and Gender Equity in the Mathematics Classroom:  The Gift of Diversity, NCTM, 1997

• Parker, She Does Math!, The Mathematical Association of America, 1995

After the drop/add period ends on January 21, a student may withdraw from this class before its completion and will earn either a W or a WF according to the guidelines below. 

If all paperwork is processed by the Registrar’s Office by March 26, then a student will automatically earn a W. 

Between March 27 and April 9, the professor must assign either a W or a WF.  In this class, if a student is passing the course and has missed less than seven class meetings, he/she will earn a W.  In this class, if a student is not passing the course or has missed seven or more classes, he/she will earn a WF. 

Between April 10 and the end of the semester, a student will automatically earn a WF.

American Mathematical Society

Mathematics Archives

Mathematical Association of America

Mathematics Forum

Multicultural Pavilion

Women in Mathematics

Course Schedule*

*This schedule may be altered during the semester by the professor!