HMC Math 55: Discrete Mathematics (Spring, 1999)
Typo Tracking for Mathematics: A Discrete Introduction

What this page is for

Mathematics: A Discrete Introduction by Edward R. Scheinerman is a discrete mathematics text in preperation. This semester, we're taking a preliminary copy of it for a test drive. This page contains a list of all errors found by Harvey Mudd discrete students in the Nov. 9, 1998 version of the text.
For Math 55 Students: If you find an error in our spring version of the text, e-mail it to me at, and tell me where and what the error is. If it's not already on the list below, I'll add it, along with your name (so you know I gave you credit for it), and the date it was submitted. Each error submitted is good for an extra credit homework point, up to a total of 10 (so if you submit 10 errors, you'll get half an assignment's worth of extra credit)... and some more credit after that, perhaps with diminishing returns. In addition, Ed (the author) is going to thank everyone who sends him an error in the final version of the book, so you'll get to see your name in print! (if that's any kind of motivation for you) So if you want your name in the book to be different from what I have below, you have to let me know. Whether or not you're planning on sending me typos, you may want to check this page periodically so you can make corrections to your own text. And if you are sending me a typo, make sure it's not on this list first. Note that while errors were found by persons indicated, they were reworded by me, and any comments added to them or errors in the notes are probably mine.
-Professor Greg

05/10/99: pg79, #4... The problem claims that the "big U" notation is developed in Section 8. But since "union" isn't even defined until Section 10, this seems unlikely. "Big U" notation seems to be first introduced on pg58 in Section 10. -Shane Markstrum
05/08/99: pg313, line #7... "We show that if G is connected does not contain an odd cycle" should read "is connected and does not contain an odd cycle". -Jason Yelinek
05/08/99: pg311, 6th line from bottom... "Let v be a leaf of T and let T'=T-v. Since T is a tree with n vertices" should read "Since T' is a tree with n vertices". -Jason Yelinek
05/08/99: pg230, Def 31.10... A comma should follow "that is" in parts (1) and (2) (such commas appear correctly in (3) and (4) ). -Jason Yelinek
05/08/99: pg78-79, proof box... "Hence there is an element x \in [a] n [b], that is an element x with..." should have a comma after "that is". -Jason Yelinek
05/03/99: pg333-347, heading... The heading at the top of these pages reads "A Lots of Hints; Some Answers". While the "A" is actually the appendix "number", it looks funny at first glance. May want to add a little space in there, or something. -Masashi Ito
05/03/99: pg316, 1st line of Section 44... "We are especially interested in graph that can be drawn" should be "graphs that can be drawn". -Jocelyn Chew
05/03/99: pg312, 12th line from bottom... "There is not way this graph can be 2-colored" should read "no way". -Eric Huang, Jocelyn Chew & Symon Harada
04/30/99: pg296, Def 41.1... It is grammatically incorrect to say, "...but no other vertices are repeated." Since there is none, it cannot be plural. I'm sure of this. It must be, "...but no other vertex is repeated." (I'm not at all sure... I haven't a clue... just passing it along... -GL) -Richard Trinh
04/30/99: pg280, middle of page... The neighborhood of vertex 3 should be N(3)={1,2,4}, not N(3)={1,2,3}. -Greg Mulert
04/29/99: pg354, index... In the index entry for "truth, vacuos" (bottom of first column), "vacuous" is mispelled. -Sandra Cheng
04/29/99: pg346, #43.4... "and the corresponding fiver vertices" should be "five vertices". -Sandra Cheng
04/29/99: pg346, #42.2... "Does K_n have an Euler tour?" should be "Eulerian tour". -Jocelyn Chew & Richard Trinh
04/29/99: pg308, #1... "cannot have an Euler trail" should be "Eulerian trail". -Jocelyn Chew
04/28/99: pg289, 8th line from bottom... "On the other hand, suppose d(v)<2" should be "d(v)<3" (the other case mentioned above). -Kyle Lampe
04/21/99: pg283, #5... "You may, of course, take advantage of the fact that a pipe can 'wrap' from the left side of the screen across to the exact same point on the right." This has the potenial to be confusing, since it does not restate the fact that a line can wrap top-to-bottom (which, if not allowed, changes the answer). Instead, perhaps something like, "You may, of course, still 'wrap' from left to right and from top to bottom." -Brad Forrest
04/21/99: pg280, Def. 38.4... "The degree of v is denote d_G(v)" should read "is denoted". BTW, it may not come up in the text, but you may want to mention that this definition is inaccurate for multigraphs (specifically, loops). It suggests that a loop only contributes 1 to degree. -GL) -Dale Lovell
04/21/99: pg277, 7 lines from bottom... While nothing is technically wrong here, we have three consecutive sentences starting with "It", which sounds awkward. Perhaps instead...
"Your small city can only afford one garbage truck, and it is your job to set the route for it to follow. The truck needs to collect along every street in the city, and it would be wasteful were it to traverse the same street more than once."
-Jesse Abrams
04/19/99: pg276, line #2... "using a most four colors" should read "at most four colors". -Alex Teoh & Elizabeth Millan
04/18/99: pg258, Thm 34.7... "If a^n (not congruent) a mod n then a is not prime" should be "then n is not prime". Also, put parenthesis around "mod n" for consistency. -Keith Ito
04/16/99: pg278, line #3... "nothing to do with the the motivational problems" has an extra "the". -Eric Huang
04/16/99: pg193, Proof of Prop 27.3... The proof begins "We are given that c = a mod b and c ~= 0". When was "c ~= 0" given? And if I just missed it, might want to rewrite "...where 0 <= c < b" as "where 0 < c < b". -Katie Ray
04/14/99: pg351, index... There is no entry in the index for Euler's Theorem (pg 256-7). -Eric Huang
04/11/99: pg271, 5th bullet... "Alice send the number N to Bob" should read "sends the number N". -Alex Teoh
04/10/99: pg270, line #13... "Alice forms her message... and send the result to Bob" should read "and sends the result". -Jesse Abrams, Dale Lovell & Alex Teoh
04/09/99: pg295, bottom line... "Therefore, G-e has at most one component" should read "at most two components" (which is, after all, what we're trying to prove). -Matt Brubeck
04/09/99: pg276, table... "courses" and "countries" are incorrectly switched. -Matt Brubeck
04/09/99: pg275, bottom line... Don't forget to replace "YEAR" and "PERSON". -Matt Brubeck
04/09/99: pg273, #3... "and send the value 289 to Bob" should read "and sends the value". -Star Roth
04/09/99: pg246, Definition 33.5... "congruent" is misspelled "conguent". -Lara Mercurio
04/09/99: pg220, 3rd equation... "y =, andy            = q1q2...qt" is poorly formatted. -Joel Miller
04/06/99: pg245, last sentence... "...suggest that if (H,*) is subgroup of (G,*)" should read "...if (H,*) is a subgroup of (G,*)" -Nate Chessin
04/06/99: pg238, line#7... Paragraph beginning "In other word," should be "In other words". -Jesse Abrams
04/05/99: pg249, #6... "H={(1)(2)(3), (1,2)(3)}"... the comma in the cycle "(1,2)" is inconsistant with the notation used in Example 33.3 (pg245)... should be "(12)". -Jordan Parker
04/05/99: pg238, below group table... "(2) aliases elements of ..." should read "(2) aliases for elements of..." as in (1). -Nate Chessin
04/03/99: pg348, Glossary ("Lemma")... Need to close the parenthesis in this entry. (Also, obviously, the Glossary needs a lot of completing.) -Richard Trinh
04/03/99: pg343, #31.7... There are two punctuation marks at the end of this hint. -Richard Trinh
04/02/99: pg243, under Example 33.2... "There are two issue to consider" should be "issues". -Star Roth
03/31/99: pg213, #13... "The notation a^b means to multiply a by itself b times", while clear and perhaps preferable, is not exactly correct. "multiply a by itself" <=> "multiply a by itself once" <=> "a squared", and similarly "multiply a by itself b times" translates literally to "a^(b+1)". What we're really doing b times is multiplying 1 by a. (this also makes a^0=1 clearer). As I said, it's sufficiently clear as is... just technically imprecise. -Joshdan Griffin
03/30/99: pg213, #10... "However, for some values of n (e.g. n = 5) this we do have..." should have a "this", and should perhaps read "...we have that...". -Nate Chessin
03/26/99: pg230, 2nd Margin note... Don't forget to put more about Abel where is says "More about Abel here!" ;-) -Eric Huang
03/26/99: pg205, 10th line from bottom... "i.e., there exits x, y \in Z" should read "there exist". -Eric Huang
03/23/99: pg203, Margin note... "and we have mod as in operation" should (I believe) read "as an operation". -Elizabeth Millan
03/21/99: pg191, #4... The meat of this problem, "Repair these statements and prove your revised versions", should come before the statements. Many students said what was wrong with the statements, but didn't see the last (and most important) part. -Lizz Norton, grader
03/20/99: pg172, #4... "Permutation" should be pluralized. -Jesse S. Abrams
03/19/99: pg225, #9... "Prove: Let a \in Z and suppose a^2 is even. Prove that a is even." The leading "Prove:" should be excommunicated. -Rob Adams
03/19/99: pg341, #28.1(g)... The back of the book lists "4x4 mod 10" as "4". It should be "6". -Jesse S. Abrams
03/10/99: pg201, #9d... "Prove that if gcd(a,b,c) = d, then d is the smallest positive integer of the form ax+by+cz where x,y,z \in Z." The wording of this problem is misleading. First, it sounds like an if-then proof, which it's not. Second, the student is, presumeably, supposed to mimic the proof of Thm 27.6. But in this proof, "d" is the smallest element of {ax+by>0: x,y \in Z}, not the gcd. In fact, gcd is never assigned a variable in this proof. Since "gcd(a,b,c)=d" is then presumeably not used in the exercise, (while d=min{ax+by..} would be), a rewording seems in order, perhaps by simply deleting "if" and "=d, then d". -Greg Mulert & Doug Honma
03/10/99: pg201, #6... This problem refers to a non-existant "Proposition 18.6". Obviously, the correct proposition (whatever it may be) needs to be referenced instead. -GL
03/10/99: pg202, #17... At various places in the problem we see "8 ounces", "one ounce", and "1 ounce". Consistancy of words or numbers should be established. -Richard Trinh
03/09/99: pg201, #9... "We can extend the definition of the gcd of two numbers, to the gcd of 3 or more numbers." First, there shouldn't be a comma in this sentence. Second, for consistancy, "3" should be "three". -Jesse Abrams & Richard Trinh
03/09/99: pg189, Def 26.4... "By Thm 26.1 there exist a unique pair of numbers q and r". "exist" should, I believe, be "exists". While we are talking about numbers, plural, "exist" is actually referring to "a pair", which is a singular ("numbers q and r" are hinding in the prepisition). -Jason Yelinek
03/08/99: pg202, #15... "Let x be rational number" should read "be a rational number". -Brandon Duncan
03/08/99: pg188, 2nd margin note... In the set "B={2, 3, 8, 11, 14,...}", the 3 should be a 5. -Elizabeth Millan
03/08/99: pg187, line #3... Since there are 6 children, this should read "The problem is to divide 25 by 6 (not 4). The quotient is 4 (not 6) and the remainder is 1." -Jesse Abrams
03/07/99: pg202, #17(a)... "Show how to use the 13-ounce and 5-ounce measuring cups" should be "13-ounce and 8-ounce" to remain consistant with the problem statement. -Rob Adams & Gillian Allen
03/07/99: pg202, #17(a)... "but his large bowl" should read "this large bowl". -Rob Adams, Jocelyn Chew & Gillian Allen
03/07/99: pg201, #8... The question "Approximately how long..." should end in a "?". -Jocelyn Chew
03/07/99: pg188, 6th line from bottom... "Suppose, for sake of contradiction there are two different pairs..." should have a comma after "contradiction". -Steve Yan
03/05/99: pg188, middle of page... Right below "r>=0", "We still need to show is that r < b." shouldn't have the "is". -Nate Chessin
03/01/99: pg150, Thm 20.26(3)... In the formula for the number of onto functions, (b choose a) should be (b choose j). -Nate Chessin
This page was getting too long, so I move the older finds to their own page (errors reported in January and February... there are about 75).
More errors
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