Syllabus & Assignments: INFS 501  Fall 2010
Revised 8/30/2010 for the new Edition 4 of the textbook.
See courses.gmu.edu after each class for an updated Syllabus & Assignments.
Instructor: William D. Ellis Email: wellis1@gmu.edu
Office Hours: By appt. (usually Wed. 56 pm) Room 5323, Engineering Building
Teaching Asst: Sheng Li Email: sli8@gmu.edu
Office Hours: By appointment
Web Site: http://courses.gmu.edu . Your ID = 1^{st} part of your GMU emailaddress, before the @; Password = your email password.
Schedule: 14 Classes all on Wednesdays, 7:20  10:00 pm in Innovation 208
9/1/2010 – 12/8/2010, except 11/24/2010
Final Exam on Wednesday 12/15/2010, 7:30  10:15 pm.
Prerequisite: “Completion of 6 hours of undergraduate mathematics.” As a practical matter, you need a working knowledge of algebra, including the laws of exponents. Several free tutorials may be found on the Internet. The textbook’s Appendix pages A1A3 (or 821823) are helpful, too.
Topics: We will follow the topics textbook in the following order: Ch. 5, 4, 6, 7, 8, 10, 2, and 9. Note there is a glossary of symbols inside the front and back covers. We will focus more on problem solving and less on semantics.
Textbook: Discrete Mathematics with Applications, 4^{th} ed. (8/4/2010) By Susanna S. Epp, ISBN10: 0495391328; ISBN13: 9780495391326.
A copy of the 4^{th} edition is on order at the GMU library
A copy of the prior edition is now on 2hour reserve at the Johnson Center Library. Give the call number QA39.3 E65 2004. The prior edition is reserved under the librarian’s name: Theresa Calcagno.
Calculator: You will need a calculator capable of raising numbers to powers. No cellphone calculators or calculatorsharing during exams.
Exams: We will have: (i) 2 Quizzes, (ii) 2 Hour Exams, and (iii) a comprehensive Final Exam (Wednesday December 15, 2010). Quizzes will be “closed book,” Exams will be “open book & notes.” Exams and Quizzes will be given only time. During exams and quizzes, students should use available space & not sit close together.
Grades: 1 Final Exam: 45% of final grade.
2 Hour Exams: 40% of the final grade (20% each)
Homework and Quizzes together: remaining 15% of final grade.
Help: Questions? Send me an email! If you email anything more than simple text, please send a pdf.
Homework: Homework assignments will always be on the Syllabus. The Syllabus will be updated each week after class. See courses.gmu.edu. Homework will never be accepted late. Of the 13 Homework assignments, only the 12 with the highest percentage scores will be counted toward your grade.
Honor Code: Honor Code violations will be reported to the Honor Committee.
Tentative Schedule: Exam and Quiz Dates Are Subject to Change
Class 
Date 
Event 
Details 
(1) 
Sep 1, 2010 
1st Class 

(2) 
Sep 8, 2010 


(3) 
Sep 15, 2010 
Quiz 1 
On everything covered to date 
(4) 
Sep 22, 2010 


(5) 
Sep 29, 2010 


(6) 
Oct 6, 2010 


(7) 
Oct 13, 2010 
EXAM I 
On everything covered to date 
(8) 
Oct 20, 2010 


(9) 
Oct 27, 2010 


(10) 
Nov 3, 2010 


(11) 
Nov 10, 2010 
Quiz 2 
On everything covered since Exam I 
(12) 
Nov 17, 2010 



Nov 24, 2010 
No Class 
Thanksgiving Recess 
(13) 
Dec 1, 2010 


(14) 
Dec 8, 2010 
EXAM II & Review 
On everything we covered in class that was not on Exam I 

Dec 15, 2010 7:30–10:15 pm 
FINAL EXAM 
Will be on everything covered during the entire semester. Problems will be like in the quizzes & hour exams (including samples), and homework. 
Homework assignments are updated within 24 hours after each class
Row 
Sec 
Problems are from the textbook or written out here 
Due 
(1) 
5.1 
2, 7, 13, 16, 32, 61, 72, 76. (For #72 & 76, besides the examples on page 239, page 569 might help.) 

(2) 
5.2 
22, 26, 28. Use Examples 5.2.23. 

(3) 
5.2 
7, 11, 12. Use mathematical induction. 

(4) 
5.6 
2, 4, 8, 14, 38a & 38b. Skip set partitions 

(5) 
5.7 
1c, 2b & 2d, 4, 20, 23, 25 

(6) 
5.8 
12, 14. Write the Fibonacci no. F_{400} in scientific notation, e.g. F_{30} ≈ 1.35*10^{6}. 

(7) 
4.1 
3, 5, 12, 27, 36, 50. [#27 & #50 directly apply the definitions of “even” and “odd.” Similarly applying those definitions produces the well known properties of the integers listed in Ex. 4.2.3 on page 167.] 

(8) 
4.2 
2, 20, 22, 28 

(9) 
4.3 
3, 5, 16, 21, 23, 41 

(10) 
4.4 
6, 21, 30, 35, 42 

(11) 
4.8 
12, 20, 25. On #20(b), don’t worry too much about syntax. Mainly what you need to do is describe the steps actually needed to produce the desired output. 

(12) 
4.8 
Find GCD(98,741 ; 247,021). 

(13) 
4.8 
Observe: 247,710^{ 2}  38,573^{ 2} = 61,360,244,100  1,487,876,329 = 59,872,367,771 = 260,867*229,513. Now factor 260,867 in a nontrivial way. 

(14) 
1.2 
#1; #4, #7 b, e, f; #9 c, d, e, f, g; #12 [Section 1.2 fits with Chapter 6 on Set Theory.]. 

(15) 
6.1 
#7 b; #12 a, b, gj; #13 a, c, e, g, i; #18 

(16) 
6.1 
Of a population of students taking 13 classes each, exactly: 19 are taking English, 20 are taking Comp Sci, 17 are taking Math, 2 are taking only Math, 8 are taking only English, 5 are taking all 3 subjects, and 7 are taking only Computer Science. How many are taking exactly 2 subjects? 

(17) 
6.2 
9, 14, 23(c), 32. [Using Venn is OK on all except 14. On #32: Instead of shading, number the regions of each diagram (the same way) and represent each constructed set as a set of regions, like in class.] 

(18) 
6.3 
4, 7, 20, 21 

(19) 
1.3 
15 c, d, e. These problems fit with Chapter 7 on functions. 

(20) 
7.1 
2; 7; 8 c, d, e; 14; 51 d, e, f [skip logarithms] 

(21) 
7.2 
8, 13(a), 18, 19 

(22) 
7.3 
2, 4, 17, 18 

(23) 
1.3 
2, 6. These problems fit with Chapter 8 on relations. 

(24) 
8.1 
4, 11, 20 

(25) 
8.2 
2, 10, 13, 14, 16 

(26) 
8.3 
9 (For #9, define “the sum of the elements” of the empty set to be 0.); 12; 15 b, c, d; 21 

(27) 
8.4 
2, 4, 5, 8, 17, 18 

(28) 
8.4 
Calculate 17^{40} mod 83,523. Your answer should be between 0 and 83,522. 

(29) 
8.4 
20, 23, 27, 32, 38, 42 

(30) 
8.4 
37, 40 

(31) 
8.4 
Under RSA: p = 13, q = 17, n = 221, & e = 37 is the encryption exponent. Find the decryption exponent d. 

(32) 
8.4 
Solve for x: x^{2} = 4 (mod 675,683). Give all 4 solutions. Your answers should be between 0 & 675,682. Note: 675,683 = 821 * 823, the product of 2 prime numbers. 

(33) 
10.1 
4, 19, 20, 28, 29, 34 

(34) 
10.2 
8 b, c, d; 9 b, c; 10 

(35) 
10.4 
In each problem 4, 11 & 13, explain why the given pair of graphs cannot be isomorphic. #13 Hint: Look for circuits of length 5. 

(36) 
10.4 
17 

(37) 
8.4 
Find the integer x satisfying: 1 ≤ x ≤ 2,622,187, x = 510 (mod 661), and x = 479 (mod 3967) 

(38) 
10.4 
Draw all nonisomorphic simple graphs on 4 vertices. Hint: There are 11. 

(39) 
11.5 
3, 1521 

(40) 
11.5 
1216, 18 

(41) 
2.1 
15, 33, 43 

(42) 
2.2 
2, 15, 27 

(43) 
2.3 
10, 11 

(44) 
9.5 
6, 9, 14 
