MATH 347 (Spring 2006) Fundamental Mathematics MWF2 at 148 Henry Zoltan Furedi

Syllabus

Fundamental ideas used in many areas of mathematics. Topics will include: techniques of proof, mathematical induction, binomial coefficients, rational and irrational numbers, the least upper bound axiom for real numbers, and a rigorous treatment of convergence of sequences and series. This will be supplemented by the instructor from topics available in the various texts. Students will regularly write proofs emphasizing precise reasoning and clear exposition.

LECTURES, DISCUSSION: Monday, Wed. and Friday 2:00-2:50 in 148 Henry Bld.

PREREQUISITE: MATH 230

INSTRUCTOR: Prof. Zoltan Furedi, 233B Illini Hall
Telephone 333-3355.
E-mail address: z-furedi@math.uiuc.edu

OFFICE HOURS: Wednesday 10:30-11:20
I can often see you if you come by without an appointment (whether or not during office hours).

TEXT: D'Angelo and West: Mathematical Thinking, 2nd Edition, Prentice-Hall 2000.
We leave out (among others) Chapters 9, 11, 12, 16, 17, 18

HOMEWORK: Homework assigned weekly, due on WEDNESDAY at the begining of the class.
(Except HW \# 12 is due on April 24, Monday).
The lowest homework score will be dropped.

HOURLY EXAMS: Three evening exams are planned. tentetively Feb 22, March 29 and April 19 at 5-6:50 pm (all Wednesdays, locations announced later).

FINAL EXAM: The final exam will be on May 12, Friday, 1:30-4:30pm, here in our usual classroom.

NO CLASS: on Jan 30, Feb 1, Feb 3. These are cancelled for the 3 evening exams.
No classes on March 20, 22, 24 (Spring break!).
No classes on April 26, 28.

We make up these 2 classes by 11 STUDY SESSIONS:
Jan 23, Feb. 6, 13, 20, 27, March 6, 13, 27, April 17, 24, May 1. (all Mondays)
5:00-6:15 pm in 141 Altgeld.

GRADING: Homework -- 25% ; Hour Exams -- 3x15% ; Final Exam -- 30%

WEB: http://www.math.uiuc.edu/~z-furedi/math347.html




The AIM of this course is to give an introduction to basic mathematical thinking, improve the students ability to absorb, read and write proofs. This course requires to work many exercises to practice clear reasoning. It also requires independent thinking, students cannot expect all questions to be instances of procedures listed in class.

TOPICS include logical reasoning, induction, equivalence relations, counting, and limits of sequences and functions.

SYLLABUS:

Part I Elementary concepts, 13 lectures

1. Numbers, Sets, Functions 3
2. Language of Proofs 3
3. Induction 4
4. Bijection and Cardinality 3

Part II Properties of Numbers, 13

5. Combinatorial Reasoning 4
6. Divisibility 3
7. Modular Arithmetic 3
8. The Rational Numbers 3

Part III Discrete Mathematics, 2

10. Two principles of Counting 2

Part IV Continuous Mathematics, 10

13. The Real Numbers 3
14. Sequences and Series 4
15. Continuous Functions 3