21-127 Concepts of Mathematics 21-127 Concepts of Mathematics, Lecture 2

Time and place: 3:30PM-4:20PM, DH 2315

Text: "Classical algebra" by Gilbert and Vanstone.

Instructor: Prof. Rami Grossberg

Office: WEH 7204

Phone: x8482 (268-8482 from external lines), messages at 268 2545

email: Rami@cmu.edu

URL: www.math.cmu.edu/~rami

Office Hours: 11:00-12:15PM MWF or make an appointment.

THE FINAL: I have turned in to the HUB the course grades on 12/20/00, 6:50PM. According to university regulations I am not permitted to return the final examination. In case you are interested to see it please come to my office hours during the first week of the spring semester. My office hours for the spring will be posted.

Section D

Section E

Section G Section F

Evaluation: There will be two one hour tests (in class), homework assignments, and a three hour final. The final will cover all the course material. These will be weighted as follows:

The letter grade will be computed as follows: 85-100 A, 70-84 B, 60-69 C, 50-59 D and 49 or below R.

Test Dates: The first midterm will be held on October 11 (Wedensday) instead of a regular lecture. The second midterm will held on November 29 (Wedensday) instead of a regular lecture. Both midterms will be held instead of a regular lecture. Please notice that the final will be scheduled by the HUB and the fall semester will end later than usual. The last day of classes is Dec 12, and the last possible time for a final is the evening of December 21. Please make your travel plans accordingly! No consideration will be given to students who make travel plans that conflict with exams. You may reschedule an exam in case of documented illness, family emergency or University sponsored trips.

The standards of academic honesty as stated in the Student Handbook will be enforced.

Assignments: Will be from the textbook, a list will be handed out at the lectures (and posted on the web). The homework is due at the start of recitation on Tuesday. Late homework will not be accepted. The homework is graded by your TA and graders and will be returned to you by your TA at the recitation in the following week. It is strongly recommended to do all assignments, and in case of difficulties you should consult your TA. If your TA can not help you please don't hesitate and contact me.

Goals: The main purpose of this course is to teach you to be able to understand, and to write mathematical proofs. Proofs, and not prescriptions, are the central part of mathematics, and give it the rigor and absoluteness that is not present in any of the other sciences. The language of mathematical proofs is formal logic, so the course will include a short study of formal logic. But it must be emphasized that this is the language of proofs only, and that in order to do proofs there must be some content. We will emphasize proof by induction, and use several induction techniques to derive some fundametal properties of numbers.

In the early twentieth century, an attempt was made to put mathematics on a completely rigorous footing, based on well accepted and fundamental axioms (this program was advocated by David Hilbert). A large part of modern mathematical practice stems from this program. The basic theory on which most parts of abstract mathematics rest is the theory of sets. We will discuss some of this theory, including the very important notion, discovered (or created) by Cantor, of how to compare the relative sizes of infinite sets. As a postscript, it should be added that Hilbert's ideals, in their fullest form, were shown by Godel to be unrealizable. However, this in no way diminishes the importance of the axiomatic method in modern mathematics.

Material to be covered: I plan to cover most of the non-trivial material of the first five chapters of the book, with a special emphasis on chapters 3, and 5 that are the more interesting (and the hardest) chapters in the book. If time permits we will cover little from Chapter 8.

Important: Due to several reasons at certain parts of the course (especially in the begining) the lecture will not follow the order of presentation of the material in the text book. You should attend all lectures and take carefull notes. In case you will miss a lecture you should try to get a copy of the notes from one of your classmates. While attending the lectures is not a formal requirement, based on my exprience if you will not attend all the lectures and attempt to do all the homework almost certainly you will fail the course. While I plan to post some information about the course on the web (including HW assignments), the web or email are not substitutes for attending lectures and recitations.

Rami's home page.
Last modified: December 20th, 2000