Fundamental Mathematics

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

Classroom: Section F1, 341AH MWF 2:00-2:50pm, Section G1, 241A, MWF 3:00-3:50pm

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

Office: 353 Altgeld Hall

Email: ruan@math.uiuc.edu

Web page: http://www.math.uiuc.edu/~ruan/347.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:
Part I: Jan 25. Feb 1, 8 and 15;
Part II: Feb 29, Mar 7, 14, and 28;
Part III: Apr 11, 18, 25, and May 2.
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. Practice Homework: Page 20, 1.15, 1.20, 1.41, 1.43, 1.49.
Hand-in Homework: Page 20, 1.13, 1.14, 1.32, 1.44, 1.47a, 1.50. (Due Wednesday, Jan 25)

HW #2. Practice Homework: Page 44, 2.4, 2.9, 2.23, 2.25, 2.27.
Hand-in Homework: Page 44, 2.21, 2.26, 2.38 (prove if true, or give an example if false), 2.47, 2.49, and the following problem:
``Let n be a positive integer. Show that \sqrt 2 + \sqrt n is an irrational number'' (Due Wednesday, February 1).

HW #3. Hand-in Homework: Page 71, 3.17, 3.26, 3.49b), 3.56 a) and b), 3.57. (Due Wednesday, February 8).

HW #4. Hand-in Homework: Page 95, 4.6; 4.20 a), b); 4.24; 4.25 a), c), e); 4.33 a), b); 4.34 b), d); and the following problem:
Show that N x N and N have the same cardinality. (Due Wednesday, February 15).

1st Exam on February 20, 2012

HW #5. Hand-in Homework: Book Page 268: 13.22 a), b). Handout Material Page 38: 6, 8, 10, Page 43: 2, 6, 7, 13. (Due Wednesday, 29).

HW #6. Hand-in Homework: Handout Material Page 43: 4 a) sup part, 18, Page 50: 3, 12, and the following problem:
Let S be the set of all irrational numbers in [0, 2]. Show that sup S = 2.(Due Wednesday, March 7).

HW #7. Hand-in Homework: Handout Material Page 59: 5c, 5d, 8, 10, and the following problem:
Show that the sequence (-1)^n + 1/n does not converge to 1. (Due Wednesday, March 14).

HW #8. Hand-in Homework: First use definition to show lim (n+5)/(2n-7) = 1/2.
Then do the following problems from the handout: Page 67: 7, Page 74: 1, 2 (assume 1 < x_1 < 2), Page 80: 4a, 9 (Due Wednesday, March 28)


2nd Exam: Monday, April 2, 2012.

HW#9. Hand-in Homework: Book Page 134: 6.8 a), b), 6.9 b), c), 6.17, 6.28, 6.46, 6.47 (Due Wednesday April 11, 2012).

HW#10. Hand-in Homework: Book Page 134: 6.18, 6.29, 6.37 a), and Prove that 2^{1/3} is an irrational number; Page 151: 7.5, 7.6 and 7.9 (Due Wednesday April 18, 2012).

HW #11 Hand-in Homework: Problem 1: Let a = 3, 4, 5, 7. Find the inverse of the corresponding congruence classes represented by a in Z_{13}. Problem 2: Consider the linear congruence equations 3x= 2 and 3x = 6 in Z_9. Determine whether we have any solution. If yes, find all solutions. If no, explain why. Book Page 151: 7.1, 7.32, 7.41 b) (Due Wednesday, April 25, 2012).

HW #12 Pracrice Homework (NOT hand in): Page 151: 7.34, 7.42.

Final Review and Discussion: May 8 and May 9, noon-1pm 243AH.

Final Exam:
Section F1, Wednesday May 9, 7-10pm at 341AH
Section G1, Thursday May 10, 1:30-4:30pm at 241AH.