Instructor: William D. Ellis Email: wellis1@gmu.edu
Office Hours: By appointment (usually Wed. 56 pm) Rm. #335, Sci & Tech. II
Teaching Asst: Hanjo Jeong Email: hjeong@gmu.edu
Office Hours: By appointment
Class Web http://courses.gmu.edu . Your ID = 1^{st} part of your GMU email
Site: email address, before the @, Password = your email password.
Schedule: Classes Wednesdays 7:20  10 pm Sci & Tech. I Rm. 131
1/21/2009 – 4/29/2009, except 3/11/2009 (14 classes);
Final Exam on Wednesday 5/6/2009, 7:30  10:15 pm
Prerequisite: “Completion of 6 hours of undergraduate mathematics.”
As a practical matter, you must have a working knowledge of algebra. Several free tutorials may be found on the Internet.
Topics: Course Catalog: “Study of discrete and logical structures for information systems analysis and design including basic set theory and proof techniques, propositional and predicate logic, trees and graphs, finite state machines, formal languages and their relation to automata, computability and computational complexity, formal semanticsoperational, axiomatic and denotational approaches.” We will focus on problem solving.
Textbook: Discrete Mathematics with Applications, 3 edition (Dec. 22, 2003) By Susanna S. Epp, Publ: Brooks Cole; ISBN10: 0534359450; ISBN13: 9780534359454. We will start with mathematical induction, a method of proof with maybe the least conceptual and notational overhead. With that apology, we’ll follow the textbook in this order: Chapters 4, 3, 5, 7, 10, 11, 1, and 12. Note the glossary of symbols inside the front and back covers.
Calculator: You will need a calculator capable of raising numbers to powers. No calculator sharing or using cellphone calculators during exams.
Exams: We will have: (i) 2 Quizzes, (ii) 2 Hour Exams, and (iii) a comprehensive Final Exam on May 6, 2009. Quizzes will be “closed book,” Exams will be “open book & notes.”
Grades: 1 Final Exam: 40% of final grade.
2 Hour Exams: 20% of final grade each, 40% total.
Homework and Quizzes together: remaining 20% of final grade.
Help: Questions? Send me an email! If you email anything more than simple text, please send a .pdf.
Homework: Homework will never be accepted late. Exams and Quizzes will never be given late. Of the 13 Homework assignments, only the 12 with the highest percentage scores will be counted toward your grade. Always check courses.gmu.edu after class for an updated syllabus with the next week’s homework assignment.
Honor Code: Any Honor Code violations will be reported to the Honor Committee.
Homework Problems from Sections in our Textbook
Row 
Sec. 
Problems 
Due 
(1) 
4.1 
2, 13, 16, 21, 31, 60 
1/28/2009 
(2) 
4.2 
2, 11, 20, 22 
1/28/2009 
(3) 
3.1 
3, 5, 12, 27, 32, 46 

(4) 
3.2 
2, 15, 21, 27 

(5) 
3.3 
2, 9, 16, 18, 38 

(6) 
3.4 
17, 18, 24, 35, 50 

(7) 
3.8 
2, 12, 16, 20, 25 

(8) 
3.8 
Observe: 247,710^{ 2}  38,573^{ 2} = 61,360,244,100  1,487,876,329 = 59,872,367,771 = 260,867*229,513 Factor 260,867 in a nontrivial way. 

(9) 
5.1 
#2; #3; #7; #11 a, b, gj; #12 a, c, e, g, i; #15 

(10) 
5.1 
Of a population of students taking 13 classes each, exactly: 22 are taking English, 19 are taking Comp Sci, 21 are taking Math, 5 are taking only Comp Sci, 8 are taking only Math, 11 are taking only English, 3 are taking only Comp Sci and English. How many are taking all 3 subjects? 

(11) 
5.2 
#4; #9; #13; #21, b, c; # 30 

(12) 
5.3 
2, 4, 7, 16, 17 

(13) 
7.1 
2; 11; 14; 35 d, e, f 

(14) 
7.2 
8, 13, 18, 19 

(15) 
7.4 
2, 4, 11, 17 

(16) 
10.1 
2, 6, 18, 30 

(17) 
10.2 
2, 13, 16, 17, 19 

(18) 
10.3 
11; 12; 13 b, c, d; 19 

(19) 
10.4 
2, 4, 5, 8, 17, 18, 27, 32 

(20) 
10.4 
20, 23, 37, 38, 40 

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

(21) 
11.1 
4, 17, 18, 29, 34 

(22) 
11.2 
8, 9, 10 

(23) 
Solve for x: x^{2} = 4 (mod 4,269,389). Give all 4 solutions. Your answers should be between 0 & 4,269,388. Here, 4,269,389 = 1,033*4,133, the product of two prime numbers. (Finding multiple square roots, of 4 in this example, is the classic way to attack RSA.) 


(24) 
11.4 
4, 7, 9, 11, 13 

(25) 
11.5 
3, 1520, 4347, 49 

(26) 
1.1 
2, 17, 36, 44, 46 

(27) 
1.2 
2, 15, 27 

(28) 
1.3 
10, 11 

(29) 
1.3 
Show whether the following syllogism is valid: Some scientists are not mathematicians; all scientists are people; therefore, some people are not mathematicians. 

Tentative Schedule of Events
Class 
Date 
Event 
Details 
(1) 
Jan 21, 2009 


(2) 
Jan 28, 2009 


(3) 
Feb 04, 2009 


(4) 
Feb 11, 2009 
Quiz 1 
The Quiz date is subject to change. 
(5) 
Feb 18, 2009 


(6) 
Feb 25, 2009 


(7) 
Mar 04, 2009 
EXAM I 


Mar 11, 2009 

No Class  Spring Recess 
(8) 
Mar 18, 2009 


(9) 
Mar 25, 2009 


(10) 
Apr 01, 2009 
Quiz 2 
The Quiz date is subject to change. 
(11) 
Apr 08, 2009 


(12) 
Apr 15, 2009 


(13) 
Apr 22, 2009 


(14) 
Apr 29, 2009 
EXAM II and Review 

(15) 
May 06, 2009 
FINAL EXAM 
7:30 p.m.10:15 p.m. The Final will cover everything we study during the entire semester. Problems will be like in the quizzes & hour exams, including samples, and homework. 