INFS 501 Syllabus & Assignments: Spring 2014
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.
Web Site: Syllabus updates, sample problems & solutions, lecture notes etc. are posted weekly at http://mymason.gmu.edu.
Schedule: 14 Classes, Wednesdays, 7:20  10:00 pm Innovation Hall 134
• Each Wednesday 1/22/20144/30/2014, except no class 3/12/2014 • The Final Exam is Wednesday 5/7/2014, 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. Also see textbook’s Appendix pages A1A3.
Topics: We will follow the textbook in this order: Chapters 5, 4, 2, 3, 6, 7, 8, 10, and 9. We will focus on problem solving, using fundamental definitions, theorems, and algorithms.
Calculator: You will need a calculator that can display 10 digits and raise numbers to powers. Using a computer or cellphone calculator, or sharing a calculator are not permitted during an exam or quiz.
Textbook: Discrete Mathematics with Applications, 4^{th} ed. (8/4/2010) By Susanna S. Epp, ISBN10: 0495391328; ISBN13: 9780495391326. A copy will be on 2hour reserve at the Johnson Center Library under Theresa Calcagno, QA 39.3 .E65 2011. A computer cannot be used to access any electronic text during an openbook exam.
Exams: We will have: (i) 2 Quizzes, (ii) 2 Hour Exams, and (iii) a comprehensive Final Exam (Wednesday May 7, 2014). Quizzes will be “closed book,” Exams will be “open book & notes.” Exams and Quizzes will be given only one time  no makeup exams. I often give partial credit when grading. However, no partial credit will be given for a purported proof to a false statement. During exams and quizzes, students should use all 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! Use the ^ symbol for exponents, * for multiplication. You may also email a pdf or scanned image.
Homework: Homework assignments will be on the weekly Syllabus updates. See http://mymason.gmu.edu. (Your username & password match your Mason NetID & Mason email password.) The Syllabus will be updated each week after each class, the first update being on 1/23/2019. 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. Submit homework on paper, or scan & email if you cannot attend class.
Honor Code: Honor Code violations are reported to the Honor Committee. See http://cs.gmu.edu/wiki/pmwiki.php/HonorCode/CSHonorCodePolicies Special for INFS501: No Honor Code violation if you collaborate on H/W or submit solutions from class discussion.
Semester Schedule
Exam and Quiz Dates Are Subject to Change
Class 
Date 
Event 
Details 
(1) 
Jan 22, 2014 
1st Class 

(2) 
Jan 29, 2014 


(3) 
Feb 5, 2014 


(4) 
Feb 12, 2014 
Quiz 1 
Problems will be like in the Sample Quiz & in the homework. 
(5) 
Feb 19, 2014 


(6) 
Feb 26, 2014 


(7) 
Mar 5, 2014 


 
Mar 12, 2014 
no class 
 Spring Break  
(8) 
Mar 19, 2014 
• Exam 1 • Lecture 
Problems will be like in the Sample Quiz, Sample Exam, and in the homework. 
(9) 
Mar 26, 2014 


(10) 
Apr 2, 2014 


(11) 
Apr 9, 2014 
Quiz 2 
Problems will be like in the Sample Quiz & in the homework. 
(12) 
Apr 16, 2014 


(13) 
Apr 23, 2014 


(14) 
Apr 30, 2014 
• Exam 2 • Lecture 
Problems will be like in the Sample Quiz, Sample Exam, and in the homework. 

May 7, 2014 7:30  10:15 PM 
FINAL EXAM 
The Final Exam will be on everything that we covered during the entire semester. Problems will be like in the Sample Quizzes & Sample Exams, in the prior Quizzes & prior Exams themselves, and in the homework. 
Assignments are updated weekly within approximately 24 hours after each class.
Row 
§ 
Problems are from the textbook or written out below. 
Due 
(1) 
5.1 
2, 7, 13, 16, 32, 61. 
HW1 1/29/2014 
(2) 
5.2 
23, 27, 29. Hint: Try using Example 5.2.2 on page 251 & Example 5.2.4 on page 255. 
HW1 1/29/2014 
(3) 
5.6 
2, 8, 14, 33, 38a & 38b. 

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

(5) 
5.8 
12, 14 

(6) 
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. The point of #50 is to see how the wellknown properties of even & odd numbers (to be summarized in §4.2 on page 167) are themselves based on the definitions of “even” and “odd.”] 

(7) 
4.2 
2, 7, 20, 28 

(8) 
4.3 
3, 5, 21, 41 

(9) 
4.4 
6, 21, 25, 35, 42, 44 

(10) 
4.8 
Find GCD(98741, 247021). 

(11) 
4.8 
12, 16; 20(b) [Don’t worry too much about syntax. Just describe the steps actually needed to produce the desired output.] 

(12) 
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. 

(13) 
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 a faster algorithm than using the definition to calculate F_{400}... Note: Be careful if you try using formulas on the Internet. Epp defines the Fibonacci sequence starting at F_{0}=1 while some others start the sequence at F_{1}=1. 

(14) 
2.1 
12, 15, 33, 43 

(15) 
2.2 
2, 4, 8, 15, 27 

(16) 
2.3 
10, 11 

(17) 
3.1 
Suppose we are given an integer x. Now call the statement s = “(x^{2}x) is exactly divisible by 3.” Complete one of the following answers (a), (b), or (c): (a) Prove s is true; (b) Prove s is not true; (c) Explain why (a) and (b) are impossible. 

(18) 
3.1 
12, 17, 18, 28, 32 

(19) 
3.2 
10, 17, 25b, 25c, 38 

(20) 
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.) 

(21) 
6.1 
#7 b; #12 a, b, g, j; #18 

(22) 
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? 

(23) 
6.2 
10, 14, 32 

(24) 
6.3 
2, 4, 7, 13 Using the isanelementof method is always good for verifying a “forallsets” identity. It is also OK instead if we verify (or find a counterexample) by calculating with numbered VennDiagram regions. However, any VennDiagram solution based on shading will NOT be accepted  shading alone is usually confusing & unconvincing. 

(25) 
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). 

(26) 
6.3 
20, 21 

(27) 
1.3 
15 c, d, e; 20. These problems fit with Chapter 7 on Functions. 

(28) 
7.1 
2; 5; 14; 51 d, e, f 

(29) 
7.2 
8, 13(b), 17, 18 

(30) 
7.3 
2, 4, 11, 17 

(31) 
8.1 
3(c),(d). Use the definition of a relation on page 14. 

(32) 
8.3 
10; 15 b, c, d 

(33) 
8.4 
2, 4, 8, 17, 18 

(34) 
8.4 
Calculate 2^{373} (mod 367). [Hint: If it matters, 2, 367, and 373 are all prime numbers.] 

(35) 
8.4 
12b, 13b [Hint: 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.] These problems are like #3 on Sample Quiz #2. 

(36) 
8.4 
Solve for x: 1014*x ≡ 7 (mod 4,157), 0 ≤ x ≤ 4,156. 

(37) 
8.4 
20, 21, 23, 27. [The encryptiondecryption pair (mod 55) is (3,27). The pair works because 3*27 ≡ 1 (mod 40) where 40=(51)(111).] 37, 38, 40 [The decryption exponent is from #38 because 713 = 23*31, 660=(231)(311), and x^{660} = 1 (mod 713) when gcd(x, 660)=1.] 

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

(39) 
8.4 
Solve for x: x^{2} ≡ 4 (mod 675,683). Give all 4 solutions. All 4 answers should be between 0 & 675,682. Use 675,683 = 821 * 823, the product of 2 prime numbers. The general technique is at Square roots (mod pq) two examples.pdf, on BlackBoard. 

(40) 
10.1 
4, 19, 20, 28, 34 

(41) 
10.2 
8 b, c, d; 9; 10 

(42) 
10.5 
3, 15, 16, 17, 18, 19 

(43) 
10.6 
15, 16, 17, 18 

(44) 
10.4 
#4, #11 & #13, #15. On #13: Only explain why the given pair of graphs cannot be isomorphic. Hint: Look at the length of circuits. On #15, Hint: There are 11 nonisomorphic simple graphs with 4 vertices. Note: We are using only an intuitive definition for graphs to be “isomorphic,” because using an exact definition is impractical. See the last paragraph on page 678. However, we will see the technical definition of isomorphism is practical for producing “weird square roots” like in line (39) above, the standard approach for attacking RSA. 

(45) 
9.1 
7, 10, 12(b)(ii)(iii), 14(b)(c) 

(46) 
9.2 
10, 12(b), 16(b)(d), 33, 40 
