Web Site: Syllabus updates, sample problems & solutions, lecture notes etc. are posted weekly at

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 A1-A3 (which could be numbered pages 821-823) 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, ISBN-10: 0495391328; ISBN-13: 978-0495391326. A copy is on 2-hour 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 cell-phone calculators or calculator-sharing 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.

Help: Questions? Send me an e-mail! If you e-mail 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.

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

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.		HW-1 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.		HW-1 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 well-known properties of even & odd numbers. Doing #50 shows how the well-known 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: 247,710² - 38,573² = 61,360,244,100 - 1,487,876,329 = 59,872,367,771 = 260,867*229,513. Now factor 260,867 in a non-trivial way.
(14)	4.8,5.8	Write the Fibonacci no. F₄₀₀ in scientific notation, e.g. F₃₀ ≈ 1.35*10⁶. Using the textbook’s closed-form formula on page 324 is much faster algorithm than using the definition to calculate F₄₀₀... Note: Our textbook defines the Fibonacci sequence starting at F₀=1, while in many other texts & Wikipedia it is convenient to define the Fibonacci sequence starting at F₁=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, g-j; #13; #18
(17)	6.1	Of a population of students taking 1-3 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	Venn-Diagram solutions are OK except, any Venn-Diagram solutions based on shading will NOT be accepted, because often shading is confusing and unconvincing. Instead of shading, number regions and calculate a Venn-Diagram set as a set of regions, like we do in class.
(20)	6.3	Prove or disprove: (i) ∃ sets A, B & C such that (A-B)-C = (A-C)-(B-C), (ii) ∀ sets A, B & C, (A-B)-C = (A-C)-(B-C).
(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 3-digit base-10 number htu = h10^2+t10+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 encryption-decryption pair (mod 55) is (3,27). Note 3*27 ≡ 1(mod 40) & 40=(5-1)(11-1).] 27, 32, 38, 42
(32)	8.4	Calculate 2³⁷³ (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=(23-1)(31-1), and x⁶⁶⁰ = 1 (mod 713) when gcd(x, 660)=1.
(34)	8.4	Solve for x: x² = 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 non-isomorphic 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 CRT-isomorphism exposes the modular-arithmetic 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