Fundamental Mathematics

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Instructor: Prof. Zhong-Jin Ruan (ruan@math.uiuc.edu)

Classroom: 241 Altgeld Hall; MWF 3:00-3:50pm

Office Hour: MW 1-1:50pm, or by appointment.

Office: 353 Altgeld Hall

Web page: http://www.math.uiuc.edu/~ruan/347G1.html

Textbook: Mathematical Thinking: Problem-Solving and Proofs byD'Angelo and West. 2nd edition.

Homework: A homework assignment will be due in class on the following days:
Jan 27, Feb 3, 10 and 17 (Wednesdays)
Mar 3, 10, 17, 31, April 7 (Wednesdays)
April 19, 26 and May 3 (Mondays)
No late homework will be accepted for any reason. If you have a reasonable excuse for missing an
assignment, I will score it by the average of the other assignments.

Grading policy:There will be total of 500 points computed as follows.

Homework	10 x 10 pts	100 pts
Exams	2 x 100 pts	200 pts
Final Exam		200 pts
Total		500 pts

Your final grade will be based on the total scores.

HOMEWORK ASSIGNMENTS
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HW #1. 1.13, 1.14, 1.32, 1.44a, 1.47a, 1.49a, 1.49c. (Due Wednesday, Jan 27)
HW#2. 2.22, 2.23, 2.26, 2.35, 2.47, 2.49, and the following problem:
*Use contradiction method to show that sqrt 2 + sqrt 6 < sqrt 15. (Due Wednesday, February 3)
HW#3. 2.38a, 3.14a, 3.17, 3.28, 3.49b, 3.49d, 3.55, 3.57. (Due Wednesday, February 10)
HW#4. 4.20, 4.24, 4.31, 4.33a, 4.33b, 4.36, 4.47. (Due Wednesday, February 17)

1st Exam: Friday February 19, 3-3:50pm in classroom.

HW#5 Book: 13.22a, b. Handout material: Page 38, #4, #6, #10, Page 43, #4a (show sup(aS) = a sup(S) ), #13, #18
(Due Wednesday, March 3).

HW#6 Handout material: Page 43, #7, Page 51, #12, 13a, and the following problem:
Let S={r: rational such that 0 < r < sqrt2 }. Show that sup(S) = sqrt 2. (Due Wednesday, March 10).

HW#7 Book: 13.25; Handout material: P59, #5c, #10, P67, #7, and the following problem:
Use definition to show that x_n = (-1)^n + 1/n does not converge to 1. (Due Wednesday, March 17).

HW#8 Handout material: P74, #1, #2 (let 1 < x_1 < 2), P80, #9, P86, #2b, #3b. (Due Wednesday, March 31).

Practice Homework (not hand in) Handout Page P95, #3a, #8, #9, and the following problem:
Show that if the infinite series a_1+...+ a_n + ... converges, then we must have lim a_n = 0.

2nd Exam: Wednesday, April 7, 2010, 3-3:50pm in classroom.

HW#9 Book: #5.4, #5.7, #5.8, 5.18, #5.36,#5.39, and the following problems:
(1) Suppose that we have a stack of 10 books and want to arrange them in all possible ways on a bookself.
a) How many different ways to arrange these books if all books are different ?
b) How many different ways to arrange these books if 4 of them are the same and the others are all different ?
(2) How many different strings can be made by recordering the letters of the word ``excellent'' ?
(Due Wednesday, April 21).

HW#10 Book: #6.8a, #6.8b, #6.9a, #6.9b, #6.18, #6.28, #6.46, #6.47 (Due Wednesday, April 28).

HW#11 Book: #7.5, #7.6, #7.9, #7.32, #7.41, and the following problem:
Given a non-zero element a in Z_{13}, find an element x in Z_{13} such that a x = 1 in Z_{13}. Here we let a = 3, 5, 8, and 10. (Due Wednesday, May 5).


Final Review : Monday, May 10, noon - 1pm at 241AH.


Final Exam: May 11, 7-10pm at 241 AH