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W. Alabama | ECE 103
26 sample documents related to ECE 103
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W. Alabama ECE 103
Question 2. 2.1: Most got this wrong. Many gave an example where the proof fails, but did not identify the flaw in the \"inductive proof\". 2.2: Most students could not finish the inductive step, some mixed up variable names \'n\' and \'k\' in the i -
W. Alabama ECE 103
Midterm statistics ECE 103 Discrete Math Spring 2008 University of Waterloo Marked out of 64. total number of students who took the exam = 135 min 3 ( 4.7%) max 58.5 (91.4%) avg 32.3 (50.5%) Number of student scoring <50% 61 <60% -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 2: due May 26, in the tutorial Question 1. Recall that log2 3 is the real number x such that 3 = 2x . Prove that log2 3 is an irrational number. -
W. Alabama ECE 103
Question 1 Part 1.1 Does not know what quantiers and logical connectives are. Quantiers (, ) are all over the place. They should be placed right before the statement which they quantify. Misuse of the logical connectives , = . (e.g. a > 0 b Z.WR -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 5: due June 23, in the tutorial Question 1. Find all x such that x2 + 2x 3 (mod 8). Question 2. Prove that for every a, m Z such that gcd(a, m) -
W. Alabama ECE 103
ID NUMBER: NAME: Solutions ECE 103 Midterm Exam. Tuesday, June 12th, 2007. Non-programmable calculators are permitted, but show your work! Problem Value Mark Awarded 1 6 2 4 3 5 4 6 5 7 6 6 7 6 TOTAL 40 1(a) Apply the Extended Euclidean Algorithm -
W. Alabama ECE 103
ECE 103 Homework #2 Solutions. Thursday, May 24th, 2007. Chapter 2: Exercises 14, 17(b), 18, Chapter 3: Exercises 2, 3, 11(b,c), 17. 2.14 Let p, a, b Z with p prime. Assume that p|(a2 b2 ). Then, since (a2 b2 ) = (a b)(a + b) and p|(a b)(a + b -
W. Alabama ECE 103
ECE 103 Homework #6 Solutions. Thursday, June 14th, 2007. Chapter 6: 27, 30, 35, Chapter 8: 3, 4(a,b), ALSO: Poker Hands: When choosing a 5-card hand from a standard deck of 52 cards, calculate the number of ways to get a hand of each of the followi -
W. Alabama ECE 103
ECE 103, Spring 2008 Kayo Yoshida Extra Problems & Solutions Covered on June 9th, 2008 Question 1. Let a and b be integers that are not both zeros. Prove that gcd(a + b, a b) gcd(a, b). Solution: Note that not both a + b and a b are zeros because -
W. Alabama ECE 103
ECE 103, Spring 2008 Kayo Yoshida Extra Problems & Solutions Covered on July 14th, 2008 Question 1. Express the following statement using quantifiers and logical connectives: Any rational number can be written in the form a , where a and b are intege -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Suggested problems, August 1, 2008 (not for submission) Note: The Chapter and problem numbers below refer to the Spring 2008 edition of the course notes. -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 7: due July 14, in the tutorial Question 1. [5 marks] Let n = 7663 = 79 97. What is the private key corresponding to the public key (e, n) = (5, -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 6: due July 7, in the tutorial Question 1. [6 marks] Find all the solutions to the following two linear congruences, if there are any. 161x 49 7 -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 1: due May 12, in the tutorial Question 1. Is the following piece of reasoning valid? Explain. If you do every problem in the text book, then you -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 3: due June 2, in the tutorial Question 1. Let a, b, c Z such that ac|bc, and c = 0. Prove that a|b. Question 2. Using the Euclid Algorithm, com -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 4: due June 9, in the tutorial Question 1. For any a, b, c Z with c 0, prove that gcd(ac, bc) = c gcd(a, b). Question 2. Find, if any, all the -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Suggested problems, June 11, 2008 (not for submission) Note: The Chapter and problem numbers below refer to the Spring 2008 edition of the course notes. 1 -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 8: due July 21, in the tutorial Question 1. [5 marks] Recall that the n-cube Hn has as vertices, all n-bit strings {0, 1}n , and as edges, all pa -
W. Alabama ECE 103
ECE 103 Discrete Math for Engineers University of Waterloo Spring 2008 Instructor: Ashwin Nayak Homework 9: due July 28, in the tutorial Question 1. [5 marks] Recall that the grid graph Gn has n2 vertices (i, j), where 1 i, j n, and edges between ( -
W. Alabama ECE 103
ECE 103 Homework #5 Solutions. Thursday, June 21st, 2007. Chapter 6: Exercises 3, 4, 5, 6, 13, 15, 18. 3. (a) Seven place license plates like AB12345: the rst two positions are letters and the ve other positions are digits. There are no other restr -
W. Alabama ECE 103
ECE 103 Homework #4 Solutions. Thursday, June 14th, 2007. Chapter 5: 1, 6. 5.1. How many multiplications and modular reductions are required to compute N M 1003 (mod 2773) where 0 N < 2773, using the square and multiply algorthm? Start by writing -
W. Alabama ECE 103
ECE 103 Homework #8 Solutions. Thursday, July 12th, 2007. Chapter Chapter Chapter Chapter Chapter 6: 10, 16, 9.1: 10, 9.3: 1, 6, 10.1: 2, 6, 10.2: 3, 5. 6.10. How many ways are there to deal hands of 7 cards to each of 5 players, from a standard d -
W. Alabama ECE 103
ECE 103 Homework #3 Solutions. Thursday, May 31st, 2007. Chapter 3: 5, 13(c,e,g,h), Chapter 4: 2, 3. 3.5. Let p be prime and let a be an integer such that GCD(a, p) = 1. Let r be the smallest positive integer such that ar 1 (mod p). Prove that r d -
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W. Alabama ECE 103
ECE 103 Homework #4 Solutions. Thursday, June 14th, 2007. Chapter 8: 11. Chapter 9.1: 1, 7, 9. 8.11. Let y0 = 2 and y1 = 3 and for all n 2 let yn = (yn1 + 2yn2 )/3. The rst few values of yn can be calculated inductively from this recurrence relati -
W. Alabama ECE 103
ID number MT Q1 Q2 HW10 HW9 HW8 HW7 HW6 HW5 HW4 HW3 HW2 HW1 40 30 25 30 25 25 25 25 20 8 15 20 10 - 20115215 20 7 6 20162569 27 17 na 0 11 9 12 8 9 3 20173888 35 29 0 7 7 13 9 20174109 37 25 18 5 7 10 11 16 20 8 8 6 20185707 2
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