INFS 501 Syllabus & Assignments: Spring 2012
This syllabus is updated weekly at http://mymason.gmu.edu after class.
Instructor: Prof. William D. Ellis Email: wellis1@gmu.edu
Office Hours: By appt. (usually Wed. 56 pm) Room 5323, Engineering Bldg.
Teaching Asst: Mr. Nan Li Email: nli1@gmu.edu
Office Hours: (to be updtated)
Web Site: Syllabus updates, sample problems & solutions, lecture notes etc. are posted weekly at
Schedule: 14 Classes, Wed., 7:20  10:00 pm Krug Hall 242
1/25/2012 – 5/2/2012, except no class 3/14/2012
Final Exam on Wednesday 5/9/2012, 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 (which could be numbered pages 821823) are helpful, too.
Topics: We will follow the textbook in this order: Chapters 5, 4, 6, 7, 8, 10, 2, and 3. There is a glossary of symbols inside the front and back covers. We will focus on problem solving, using fundamental definitions, theorems, and algorithms.
Textbook: Discrete Mathematics with Applications, 4^{th} ed. (8/4/2010) By Susanna S. Epp, ISBN10: 0495391328; ISBN13: 9780495391326. A copy is on 2hour reserve at the Johnson Center Library. Give the call number QA 39.3 .E65 2011. The book is reserved under the librarian’s name: Theresa Calcagno.
Calculator: You will need a calculator capable of raising numbers to powers. Really! No cellphone calculators or calculatorsharing during exams will be allowed.
Exams: We will have: (i) 2 Quizzes, (ii) 2 Hour Exams, and (iii) a comprehensive Final Exam (Wednesday May 9, 2012). Quizzes will be “closed book,” Exams will be “open book & notes.” Exams and Quizzes will be given only one time  no makeup exams. During exams and quizzes, students should use available classroom space & should avoid sitting 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 http://mymason.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. See http://cs.gmu.edu/wiki/pmwiki.php/HonorCode/HomePage
Tentative Schedule: Exam and Quiz Dates Are Subject to Change
Class 
Date 
Event 
Details 
(1) 
Jan 25, 2012 
1st Class 

(2) 
Feb 1, 2012 


(3) 
Feb 8, 2012 


(4) 
Feb 15, 2012 
Quiz 1 

(5) 
Feb 22, 2012 


(6) 
Feb 29, 2012 


(7) 
Mar 7, 2012 
EXAM I 


Mar 14, 2012 
No Class 
Spring Vacation 
(8) 
Mar 21, 2012 


(9) 
Mar 28, 2012 


(10) 
Apr 4, 2012 


(11) 
Apr 11, 2012 
Quiz 2 

(12) 
Apr 18, 2012 


(13) 
Apr 25, 2012 


(14) 
May 2, 2012 
EXAM II & Review 
Exam will be on everything covered in class that was not on Exam I. Problems will be like in the Quizzes, Hour Exams (including samples), and the homework 
(15) 
May 09, 2012 7:30  10:15 PM 
FINAL EXAM 
On everything covered during the entire semester. Problems will be like in the Quizzes, Hour Exams (including samples), and the homework 
Homework assignments are updated weekly 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. Hint: For #72 & 76, the examples on pages 239 and 569 will help. 
HW1 2/01/2012 

(2) 
5.2 
23, 27, 29. Hint: Try using Example 5.2.2 on page 251 & Example 5.2.4 on page 255. 
HW1 2/01/2012 

(3) 
5.2 
2, 7, 11, 12. Use Mathematical Induction. 


(4) 
5.6 
2, 8, 14, 33, 38a & 38b. 


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


(6) 
5.8 
12, 14 


(7) 
4.1 
3, 5, 8, 12, 27, 36, 50. [#50 requires directly applying the definitions of “even” and “odd” (on pg. 147) instead of using wellknown properties of even & odd numbers. Doing #50 shows how the wellknown properties of even & odd numbers (in Ex. 4.2.3 on page 167) themselves follow from the definitions.] 


(8) 
4.2 
2, 20, 28 


(9) 
4.3 
3, 5, 21, 41 


(10) 
4.4 
6, 17, 21, 35, 42 


(11) 
4.8 
Find GCD(98741, 247021). 


(12) 
4.8 
12; 20(b) [Don’t worry too much about syntax. Just describe the steps actually needed to produce the desired output.] 


(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) 
4.8,5.8 
Write the Fibonacci no. F_{400} in scientific notation, e.g. F_{30} ≈ 1.35*10^{6}. Using the textbook’s closedform formula on page 324 is much faster algorithm than using the definition to calculate F_{400}... Note: Our textbook defines the Fibonacci sequence starting at F_{0}=1, while in many other texts & Wikipedia it is convenient to define the Fibonacci sequence starting at F_{1}=1. 


(15) 
1.2 
#1; #4, #7 b, e, f; #9 c, d, e, f, g, h; #12 (Section 1.2 fits with Ch. 6 on Set Theory.) 


(16) 
6.1 
#7 b; #12 a, b, gj; #13; #18 


(17) 
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? 


(18) 
6.2 
9, 14, 23(c), 32. 


(19) 
6.3 
2, 4, 7, 13 
VennDiagram solutions are OK except, any VennDiagram solutions based on shading will NOT be accepted, because often shading is confusing and unconvincing. Instead of shading, number regions and calculate a VennDiagram set as a set of regions, like we do in class. 

(20) 
6.3 
Prove or disprove: (i) ∃ sets A, B & C such that (AB)C = (AC)(BC), (ii) ∀ sets A, B & C, (AB)C = (AC)(BC). 

(21) 
6.3 
20, 21 

(22) 
1.3 
15 c, d, e; 17; 20. These problems fit with Chapter 7 on Functions. 


(23) 
7.1 
2; 5; 8 c, d, e; 14; 51 d, e, f [skip logarithms] 


(24) 
7.2 
8, 13(b), 17, 18 


(25) 
7.3 
2, 4, 11, 17 


(26) 
1.3 
2, 6. These problems fit with Chapter 8 on Relations. 


(27) 
8.1 
4, 11, 20 

(28) 
8.2 
2, 10, 13, 14, 16 

(29) 
8.3 
9; 12; 15 b, c, d; 21. For #9, define “the sum of the elements” of the empty set to be 0. On #21, just say how many equivalences classes there are and describe each class. 


(30) 
8.4 
2, 4, 8, 12b, 17, 18. Hint on 12b: If we call the hundred’s digit “h,” the tens digit “t,” and the unit’s digit “u,” then the 3digit base10 number htu = h*10^2+t*10+u. Now reduce the 10's (mod 9). The same approach works no matter how many digits a positive integer has. Problems 12b & 13b (which we will discuss in class) are the basis for problem #10 on Sample Quiz #2. 


(31) 
8.4 
20, 21, 23. [The encryptiondecryption pair (mod 55) is (3,27). Note 3*27 ≡ 1(mod 40) & 40=(51)(111).] 27, 32, 38, 42 


(32) 
8.4 
Calculate 2^{373} (mod 367). (Hint: 2, 367, and 373 are all prime numbers.) 


(33) 
8.4 
37, 40. Hint: The decryption exponent is the answer from #38 because 713 = 23*31, 660=(231)(311), and x^{660} = 1 (mod 713) when gcd(x, 660)=1. 


(34) 
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. 


(35) 
10.1 
4, 19, 20, 28, 34 


(36) 
10.2 
8 b, c, d; 9; 10 


(37) 
10.4 
#4, #11 & #13. On 4, 11, & 13, explain why the given pair of graphs cannot be isomorphic. Hint on 13: Look for circuits of length 5. #15. Hint on 15: There are 11 nonisomorphic simple graphs with 4 vertices. Note: In this class we use only an intuitive definition for graphs to be “isomorphic,” because the technical definition is so impractical to use. See the last paragraph on page 678. However, we use the technical (and practical) definition for isomorphism when using the Chinese Remainder Theorem. The CRTisomorphism exposes the modulararithmetic weakness used today for attacking RSA. 


(38) 
8.4 
Under RSA: p = 13, q = 17, n = 221, & e = 37 is the encryption exponent. Find the decryption exponent d. 


(39) 
10.5 
3, 15, 16, 17, 18 


(40) 
10.6 
15, 16, 17, 18 


(41) 
2.1 
15, 33, 43 


(42) 
2.2 
2, 15, 27 


(43) 
2.3 
10, 11 


(44) 
3.1 
17, 18, 28, 32 


(45) 
3.2 
10 
