COURSE: History of Mathematics
DATE: Spring 2006
TEXT BOOK Burton, The History of Mathematics, (Any edition).
McGraw Hill 1996

OTHER MATERIALS: Lecture notes from Osler (Download from my WEB page)

COURSE PREREQUISITES: Calculus Sequence

PROFESSOR'S PHILOSOPHY:
It is my pleasure to be your professor this semester. I shall do all that I can to make this an informative and interesting mathematics course. In addition I shall try to convey some of the history of this subject as well as the intense beauty that makes mathematics the language of all sciences.

ATTENDANCE AT REGULAR CLASSES:
Students are expected to develop good working habits. You should expect to attend all classes and to be on time. Naturally there might be times when illness or serious personal concerns make attendance at class impossible, we hope these will be infrequent. For each class you miss you are expected to hand me a note explaining:

1. Your name
2. The date you were absent
3. The reason for your absence
4. How you intend to make up the class you missed.

Students who miss an excessive number of classes will be required to submit written work proving that they have mastered the necessary material or their grade will be reduced appropriately. Students who provide (1) official college absence excuse, or (2) doctor’s note ordering you to remain at home, will not have such absences count against their grade.

TEXT BOOK READINGS AND OUTLINES:
Each week students are given about 25 pages of the text book to read and outline. The outline must be turned in each week. Bescause the readings help you to understand my lectures, you should not get behind. There is a penalty for being late.

CALCULATION OF GRADES:
To pass the course, you must complete all the required outlines and have good attendance at class. While at class, your participation and attention also will be part of your grade. Completion of all outlines and good class participation alone will earn you the grade of C.

Grading in History of Mathematics

To obtain the grade of “C”
1.Attend all classes and participate
2.Read and outline all assigned pages in the text. Hand the outlines in on time.

To obtain the grade of “B” do attend the above classes and hand in the outlines plus the following:
1. Select an appropriate book on a topic related to this course. (See the list from Dr Osler.) As you read the book make an outline of the appropriate ideas. (The outline should be about 8 to10 pages hand written. This is just a suggestion. )
2. Consider 5 mathematicians from 1700 or later. (See list in the back cover of your text.) Read and make outlines of mini biographies of these mathematicians (about two papges each).

To obtain the grade of “A” do two books and ten biographic outlines as described above.
ALL OUTLINES MUST BE HAND-WRITTEN

PASS NO CREDIT OPTION:
There is no such option for this course. The only grades I assign are A, B, C, D, F.
CHEATING:
Cheating on a test or assignment seriously undermines the integrity of the academic system and will not be tolerated. If I determine that a student has cheated, I will send a letter to this effect to his advisor and all sources of financial aid. In addition I will assign the grade of F for this course.
Even though a student is not cheating, he or she is expected to refrain from actions which could be suspicious. Using common sense on your part should avoid unnecessary embarrassment.
THE DROP PROCEDURE:
The registrar will assign the grade of W for this course if you make your request known before March 6, 2006. After this date a student will receive the grade of: F if withdrawing for academic reasons; WP or WF if withdrawing for unusual nonacademic reasons outside the student's control.

At times a student simply stops attending class without ever going through the necessary procedure with the registrar. In this case the grade of F is assigned.

QUESTIONS IN AND OUT OF CLASS:
Of course, I am always happy to answer your questions. The best time to ask questions is during class. Many times students fear that their questions will seem foolish, while in fact, many other students also have the same question. I urge you to ask your questions during class. By doing so, you make it easier for me to gage how effectively I am teaching. Students who find errors in my work at the board (sometimes deliberate and sometimes accidental) receive extra credit.
If you have questions that were not answered in class, I can usually answer them quickly for you right after class. You may stop by my office for answers to any remaining questions, or for any other assistance I am able to provide for this course.

BUILDING REGULATIONS:
Please no smoking, eating or drinking in the classroom.
Please do not bring children to class.

Reading Assignments:

Number Sections

1 1.1 to 2.6 (skim read quickly)
2 3.1 to 3.3
3 3.4 to 3.5
4 4.1 to 4.3
5 4.4 to 4.5
6 4.6 to 5.4
7 6.1 to 6.2
8 7.1 to 7.4
9 8.1
10 8.2
11 8.3
12 8.4
13 9.1
14 10.2

Notes: You will be expected to outline the historical material in each of the above portions of the text. Outlines should be from two to six hand written pages. You are to stress historical topics,. Mathematical topics can be ignored on the outline. You must hand in a new outline each week. Since these reading correspond with my lectures, you must not fall behind. There is a penalty for being late. Please write both your name and the number of the outline at the top of the first page, and staple the pages. Thank you.
ALL OUTLINES MUST BE HAND-WRITTEN.

STUDY GROUPS

Studies of successful college students show that the best students often work in groups. For this reason I am asking that you form a study group of about two to four students from your fellow classmates. I will first ask each of you to introduce yourself to the class to let us know your interests as well as the times you could meet with a study group. Later you can form your group based on common interests and availability. I will ask you to hand in on paper a list of those in your group and a group “leader” before you leave today. If you wish to change study groups later, this is always easily done.

Here are just a few of the reasons the study group will be of value to you:

1. You can phone study group members to get information about classes you might miss. (You are responsible for all assignments, even if you miss a class.)

2. You can go over hard homework problems together.

3. You can review for tests.

4. By talking over the mathematics you will bet experience in the difficult art of verbally communicating technical information. This is not easy and there is rarely time to develop this skill in the classroom. You will find that it is often not easy to formulate mathematical ideas in a way that another student can understand. This is a most important and valuable addition to your education.

5. To encourage your group to meet and work together, I often give “Group Projects” in which the entire group works on one problem and hands in to me one folder for the entire group. These group projects are scored as part of your “Class Grade”.

I recommend that you also share phone numbers with your study group members.

NAME: PHONE:

_________________________________ ____________________________

_________________________________ ____________________________

_________________________________ ___________________________

________________________________ ____________________________

SOME THOUGHTS ON MATHEMATICS AND LEARNING

Why is mathematics different from all other academic subjects?

Some 2300 years ago Euclid, a Greek mathematician, wrote a 13 volume treatise on geometry called The Elements. It contained hundreds of theorems. During the past 2300 years, not one of these theorems has been proven wrong. No other subject is like this. Once a mathematical fact has been demonstrated, its truth is evident to all who make the effort to understand it. It remains true forever. All other ancient subjects have changed drastically since they first appeared. Only mathematics remains unchanged, and universally unchallenged.

Also, mathematics is truly universal. A number, a triangle, and a circle are perceived in the same way by a male, female, European, African, Asian, etc. There is no cultural bias in mathematics.

Who is responsible for my mathematical education?

YOU ARE!!! You are an adult attending a university. What you learn from this course depends on how seriously YOU pay attention in class and study outside of class.

How should I learn mathematics?

Begin by doing the homework your professor assigns. You must practice doing mathematics by yourself. Mathematics is not a spectator activity. It is important to attend class, pay attention and ask questions, but watching the professor solve problems is no substitute for your doing problems yourself. Hours and hours of problem solving are necessary to master complex mathematical ideas. Don’t be afraid to repeat the homework by doing it a second or third time. Try other problems from your textbook that have not been assigned. Finally look at other books available in our library and Mathematics Department Conference Room. The Internet is now a valuable source of material.

If I get an A or B in the course, have I mastered the subject?

Maybe yes, but maybe no. Some students are able to “ace the test” by cramming a few days before it, and doing little else. In this case, the student might get a high grade, but also quickly forget the material. There is no substitute for spending hours and hours wrestling with the complex ideas presented in a mathematics course. At times students with a high GPA do poorly on national exit examinations such as the Graduate Record Exam or National Teachers Exams. This often reflects their study habits. They work just hard enough to get good grades, but not hard enough to really master the ideas.

Also consider that your professor’s exams have been composed largely of very short, routine questions. There is no time on a one or two hour test to put really difficult problems. The better test of mathematical ability and mastery comes from problems requiring solution in days, weeks, months or years.

I plan to go to graduate school in mathematics or a related field, what should I do?

In addition to the required course work, you should spend considerable time in the library browsing through books and journals. Consider doing a student research project under the guidance of a faculty member. This could lead to a STEM Symposium presentation or even a possible paper for publication in a suitable journal.

Remember, there is no substitute for hard work. No one ever made a significant contribution to mathematics without spending enormous amounts of time thinking about it.