Introduction

This course will mix the study of the history of mathematical ideas, the cultural environments which gave birth to them, and some experience practicing the mathematics of these cultures.

We will begin with the arithmetic, protoalgebra and geometry of the people of the fertile crescent, the Mesopotamians , the people of the valley of the Nile River, the Egyptians , and the early civilization on the island of Crete (Scroll down to the map of Minoan Crete, and click on it), the Minoans , who were the forerunners of the Mycenaean Greeks and the classical ancient Greeks.

We will go on to study the people of the middle and lower Yellow River, the Chinese and the people of the area near the Indus River valley , the Indians. The roots of all of the above cultures seem to have begun about 4,000 years ago.

Building upon the discoveries and creations of these five ancient cultures, the inheritors of Alexander the Great's conquests ( Click on the BIG MAP for more information ) , the Hellenistic Greeks and the Islamic societies made great strides in advancing mathematics. Renaissance Italy built upon this mathematical edifice. It is amazingly lucky that, with all of the burning, looting and struggles to secure political power throughout history, some books and knowledge have survived. The cultural and religious chauvinism used by those focused on power to erase the work of genius is truly sad.

However, if we want to get to the present, we will have to make a class decision to skip over some big parts of the intervening history. This will be decided about one-half of the way through the course, when the class has had some exposure to the history of mathematical ideas, about February 25th.

Archimedes

Grades and Organizational Matters

The instructor reserves the right to change this syllabus according to the needs which may arise in this class during this semester. Students are responsible to be aware of what goes on in the classroom including the announcement of exam dates, material to be covered on exams and any adjustments to this syllabus. If you have any questions that you are not comfortable asking in class please feel free to ask me after class or come to my office hours.

If I am unavailable or you wish to speak with someone else about this course, you should contact the

Chairman of the Mathematics Department, Professor Robert McOwen. Professor McOwen's office is 505 Lake Hall, his telephone number is 617-373-5635 and his e-mail address is mcowen@neu.edu

You should do all of the homework problems that we do not complete in class, and turn them in to me on the Thursday following each week's assignment. Some class problems may also be required to be written up and turned in. I'll look them over, grade them and return them to you. For mathematics credit, you must correctly do all of the "Math Credit" problems contained in both the homework sets and in the worksheets done in class.

The average homework grade you receive will count for 30% of your final grade in this course.

Ther will be a two page (or more, if you so choose ) outline of a paper which relates the material in some part of the course to an interest that you have.

This outline will count for 10% of your grade in the course.

A ten page paper is required in order to complete this course. This paper must expand your outline into a well written exposition of the mathematics contained therein, and how it relates to your personal interest. For mathematics credit, you must include a mathematical proof or two in your paper. See me by the third full week of the course, by February 1st, to modify the requirements for this paper.

This paper will account for 30% of your final grade in this course.

We will have quizzes on Wednesdays, at the start of the class, approximately every third week. There will be a mix af essays and mathematical problems on these quizzes. I will go over the material for the Wednesday quiz in class on the preceeding Monday.

The average of these quizzes will acount for 30% of your grade in this course.

Departmental Policies

In order to turn in assignments late or to take make-up quizzes and tests, students must bring written proof of some emergency situation; notes from doctors or nurses, documents verifying court appearances, receipts from having a car towed are all examples of valid documentation. Notes from family members are not acceptable. If a situation is of a personal nature, discuss the matter with your academic advisor; an e-mail message from your advisor saying that they believe that you should be allowed to make-up work is acceptable.

It will not be tolerated. The University's cheating policy and related disciplinary actions are detailed in the Student Handbook; the Handbook also includes a description of what is considered cheating by the University. Cheating in this class includes (but is not limited to): looking at the papers of others during a quiz or test, talking to other students during a quiz/test, looking at notes during a quiz/test (unless it is specifically announced that you may), copying other students' work outside of class, and obtaining help from others on take-home tests.

Plagiarism has been a problem for some students in recent sections of this course. In case you are not aware, one can find the source of plagiarised papers pretty easily on the web. Students who plagiarize will flunk this course, at the least. The student court will deal with outrageous instances of plagiarism.

In this class, working together on homework is NOT considered cheating. Please be aware that this policy on working together outside of class varies greatly from one course to the next; the policy on what is allowed, that has been described in this paragraph, may well be considered cheating in your other classes.

The use of advanced calculators is NOT considered cheating in this course. Be aware, however, that other courses may well have a policy barring such calculators. Also, your instructor reserves the right to decide on the spot between what constitutes a "calculator" and what constitutes a full-fledged "computer".

All incidents of cheating will be reported to the Office of Judicial Affairs.

If you have any questions as to what constitutes cheating, please ask me.

It is essential that you attend class regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day.Students are responsible for finding out what material has been covered or what announcements have been made on days that they miss class.

Please note that we will treat you as an adult here. If you must miss a class, be late or leave early, it is expected, as polite behavior, that you will contact the instructor involved ahead of time and reach an agreement. This sort of behavior goes a long way when you have to miss a quiz, for instance. If you do not do this, the ball is in your court to make up work or use the missed quiz as the quiz which you drop.

Schedule of Topics and Assignments

The following table includes a calendar with homework problems to be covered.