CMPSCI 250: Introduction to Computation

David Mix Barrington and Hava Siegelmann

Fall, 2010

Errata in the Textbook

This is a list of errors discovered in Dave's draft textbook Discrete Mathematics: A Foundation for Computer Science, Chapters 1-5, 9, 14, and 15, as printed for CMPSCI 250 this term.

Volume I: Chapters 1-4 and Solutions

• Page 1-49, Problem 1.7.6: Replace the last sentence with "Why didn't our substitution lead to a valid tautology?"

• Page 1-50, footnote 24: "see Chapter 15"

• Page 2-45: Section 2.11 is missing! I will print up copies of it to be handed on in lecture on 23 September. Pages 2-45 and 2-46 in the printed version should be renumbered 2-50 and 2-51.

• Page 2-47: (in handout) at end of last full paragraph, "transitivity"

• Page 3-9: In the display equation, should be "17256" not "17526" with correpsonding changes in the sums.

• Page 3-11: Add period after item 4 of list.

• Page 3-33: Problem 3.6.5 (c), "Prove that any nonzero Gaussian integer..."

• Page 3-35 (not used this term), end of text: "in Chapter 15"

• Page 3-51, footnote: "a field that is the subject of Chapter 13 of this book."

• Page 3-52 (not used this term), footnote 65: "in Chapter 15"

• Page 4-8, Problem 4.1.5: "write a pseudo-Java method"

• Page 4-12, Writing Exercise prompt: "following four questions"

• Page 4-22, Problem 4.4.5: This should be rewritten to make it clearer that there is conceivably more than one Elvis. "Containing Elvis" throughout should be "containing an Elvis", and on line 2 of the proof it should say "all are Elvises".

• Page 4-35: In E4.7.2, E4.7.4, P4.7.3 (b), and P4.7.4 (a), replace "Java-syntax" by "pseudo-Java". In Problem 4.7.3, "The pseudo-Java function..."

• Page 4-37, last paragraph: "as pseudo-Java functions.."

• Page 4-49 (not used this term): line 1, "pseudo-Java methods"

• Page 4-52 (not used this term): Problems 4.10.1 and 4.10.2, "pseudo-Java code", "pseudo-Java methods"

• Page 16-7, Figure 16-2: The region for P ∩ (Q ∪ R) should be shaded.

• Page 16-22, Exercise 3.1.3: delete extra right paren

Volume II: Chapters 5, 9, 14, 15 and solutions

• Page 5-3, footnote: "In Chapter 14"

• Page 5-4, last line: "Chapter 14:"

• Page 5-5, footnote 8: "in Chapter 14"

• Page 5-6, middle of page and in footnote: "Chapter 14"

• Page 5-9, Problem 5.2.2: "if w is any string of..."

• Page 5-14, second paragraph: "a recursively defined set"

• Page 5-15, Problem 5.4.2: Replace entire problem with this -- "Prove that if S and T are any regular expressions over a one-letter alphabet, e.g., Σ = {a}, and if n is any natural, then the languages (ST)ⁿ and SⁿTⁿ are equal. (Hint: Use ordinary induction on n and the result of Exercise 5.4.5.) Give examples of two regular expressions S and T, again with Σ = {a}, such that the languages (ST)^* and S^*T^* are not equal."

• Page 5-21, next to past paragraph: "in Chapter 14"

• Page 5-22, Problem 5.5.2: "in Chapter 14"

• Page 5-23, Problem 5.5.5: "⊂" should be "⊆"

• Page 9-2, first bullet: "∀x: P(x,x)"

• Page 9-8, code: last character of the first constructor should be "}" and not "]", end of class needs another "}"

• Page 9-14: Problem 9.3.1: type of method should be "integer"

• Page 9-14, Problem 9.3.2: "of Exercise 9.3.2"

• Page 9-22, Problem 9.4.5: "the number of Rubik's Cube positions", change the sum to "1 + 18 + 18(15) + 18(15² + ... + 18(15)^k-1", "at least 16 moves"

• Page 9-32, Problem 9.6.3: "between nodes at the same level in its BFS tree"

• Page 9-38, Problem 9.8.3: third and fourth bullets, "to (i, j+1)" and "to (i, j-1)" respectively. Change the weight function so that each north-south edge has weight 1 and each east-west edge has weight 3.

• Page 9-41, Problem 9.9.1: "of Problem 9.8.3", "s = (1,1) and t = (3,3)", and "with h(i,j) as the pedestrian distance from (i,j) to (3,3), where edges may be traversed either forward or backward"

• Page 9-47, Problem 9.10.1: Near end of paragraph, "can then also move" In part (a), add "Make an overestimate, as finding the exact number of positions that could actually occur in a game would require a search of the whole game tree."

• Page 14-11, footnote 6: "in Chapter 15"

• Page 14-41, Problem 14.7.1: "such that λ ∉ L(M)"

• Page 14-49, Figure 14-37: Diagram is missing the transition (r,a,f)

Last modified 14 January 2011