INFS 501 Syllabus & Assignments: Fall 2013
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 Art & Design 2026
Every Wednesday 8/28/201312/4/2013, except no class 11/27/2013. The Final Exam is Wednesday 12/11/2013, 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 capable of raising numbers to powers. Really! Using a computer or a cellphone calculator or sharing a calculator is 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 Dec. 11, 2013). 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 8/29/2013. 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.
Tentative Schedule: Exam and Quiz Dates Are Subject to Change
Class 
Date 
Event 
Details 
(1) 
Aug 28, 2013 
1st Class 

(2) 
Sep 4, 2013 


(3) 
Sep 11, 2013 


(4) 
Sep 18, 2013 
Quiz 1 
The questions will be like the questions in: (1) the homework, (2) the Sample Sequences & Progressions pdf on Blackboard, and (3) the sample quiz. 
(5) 
Sep 25, 2013 


(6) 
Oct 2, 2013 


(7) 
Oct 9, 2013 
• Exam 1 • Lecture 
Exam problems will be like on Sample Exam 1, Quiz 1, Sample Quiz 1, the Sample Sequences & Progressions pdf on Blackboard, and the homework. 
(8) 
Oct 16, 2013 


(9) 
Oct 23, 2013 


(10) 
Oct 30, 2013 


(11) 
Nov 6, 2013 
Quiz 2 

(12) 
Nov 13, 2013 


(13) 
Nov 20, 2013 



Nov 27, 2013 

Thanksgiving Recess 
(14) 
Dec 4, 2013 
• Exam 2 • Lecture • Review 

(15) 
Dec 11, 2013 7:30  10:15 PM 
FINAL EXAM 
On everything covered during the entire semester. Problems will be like in the Sample Quizzes, Hour Exams, Sample Quizzes & Exams, and 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 9/4/2013 

(2) 
5.2 
23, 27, 29. Hint: Try using Example 5.2.2 on page 251 & Example 5.2.4 on page 255. 
HW1 9/4/2013 

(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.] 


(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 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. 


(15) 
2.1 
12, 15, 33, 43 


(16) 
2.2 
2, 4, 8, 15, 27 


(17) 
2.3 
10, 11 


(18) 
3.1 
17, 18, 28, 32 


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


(20) 
6.2 
10, 14. 


(21) 
6.3 
2, 4, 7, 13 


(22) 
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). 


(23) 
6.3 
20, 21 
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. 

(24) 
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? 


(25) 
1.3 
15 c, d, e; 17; 20. These problems fit with Chapter 7 on Functions. 


(26) 
7.1 
2; 5; 8 c, d, e; 14; 51 d, e, f [skip logarithms] 


(27) 
7.2 
8, 13(b), 17, 18 


(28) 
7.3 
2, 4, 11, 17 


(29) 
1.3 
2, 6. These problems fit with Chapter 8 on Relations. 



8.1 
3. Use the definition of a relation on page 14. 


(30) 
8.3 
15 b, c, d; 21(2). On #21(2), just give the number of equivalences classes and describe each class. 


(31) 
8.4 
2, 4, 8, 17, 18, 27 


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


(33) 
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. 


(34) 
8.4 
Solve for x: 1014*x ≡ 7 (mod 4,157), 0 ≤ x ≤ 4,156. 


(35) 
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 the answerfrom #38 because 713 = 23*31, 660=(231)(311), and x^{660} = 1 (mod 713) when gcd(x, 660)=1.] 


(36) 
8.4 
Under RSA: p = 13, q = 17, n = 221, & e = 37 is the encryption exponent. Find the decryption exponent d. 


(37) 
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. 


(38) 
10.1 
4, 19, 20, 28, 34 


(39) 
10.2 
8 b, c, d; 9; 10 


(40) 
10.4 
On #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 (36) above, the standard approach for attacking RSA. 


(41) 
10.5 
3, 15, 16, 17, 18, 19 


(42) 
10.6 
15, 16, 17, 18 


(43) 
9.1 
7, 10, 12(b)(ii)(iii), 14(b)(c) 


(44) 
9.2 
10, 12(b), 16(b)(d), 33, 40 
