**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.

-Professor Greg

### This page contains errors found in January and February

More recent finds

**02/27/99: pg331, #6(g)**... "If A is an antichain and C is a chain in a poset. Then A n C must be empty." should be one sentence. *-Brad Forrest*

**02/27/99: pg329, Example 45.7**... "Problem: Why do we need speparate symbols for < and (not>=)." should end in a "?". *-Brad Forrest*

**02/27/99: pg308, 5th line from bottom**... "Of course, we could every vertex its own color" should read "could *give* every vertex". *-Brad Forrest*

**02/27/99: pg283, #4**... "Device such a computer screen" should read "*Devise*...". *-Brad Forrest*

**02/27/99: pg259, Recap**... Should "Euler's theorem" be capitalized? *-Brad Forrest* *(BTW, "Fermat's little theorem" is not fully capitolized in the index. -GL)*

**02/27/99: pg236, #16**... Should "reverse Polish notation" be capitalized? *-Brad Forrest*

**02/27/99: pg216, after Thm 29.5**... Shouldn't "Chinese remainder theorem" be capitalized? (It is a proper noun.) *-Brad Forrest* *(BTW, the CRT is not listed in the index. -GL)*

**02/27/99: pg167, after Example 23.9**... "To see that this is correct. Let Pi = ..." should be one sentence. *-Brad Forrest*

**02/27/99: pg154, above Thm 21.3**... "every sequence of ten distinct integer must contain..." should read "ten distinct *integers* must contain". *-Brad Forrest*

**02/27/99: pg154, middle of page**... "Similarly, a subsequence whose element are ..." should read "whose *elements* are..." *-Brad Forrest*

**02/27/99: random gripe**... *It is really annoying how a good many of the homework problems instruct us to "please" do something. As if we really have a choice. Please remove the "please"s. -Juser* *(Personally, I don't see anything wrong with being polite when giving someone a direct order, but I found the request amusing ;-) -GL)*

**02/27/99: pg321, 4th line from bottom**... "Not only is K 3,3 nonplanar, so is any subdivision graph we can form from K 3,3." This could sound better... maybe add a "but" or a semicolon or something. *-Juser*

**02/27/99: pg321, middle of page**... "Clearly if a graph is planar, so are any of its subdivisions, and conversely." There's *got* to be a better way of phrasing this. *-Juser*

**02/27/99: pg319, first 4 sentences**... *Notice that three of the first four sentences begin with the words "Notice that". My english teachers wouldn't let me get away with this. -Juser*

**02/27/99: pg315, 2nd & 3rd sentences**... "We know that once we color a vertex, say, black. All its neighbors must
be white." These should be one sentence. *-Juser*

**02/27/99: pg113, #1**... Should "All together" be "Altogether"? *-Juser*

**02/27/99: pg38, #9; pg86, #4; pg98, #20; pg179, #3; pg180, #6**... All these questions should end in a "?". *-Juser*

**02/25/99: pg134, below (22)**... "The verification of Equation (22) is a simple, if mildly painful, algebra exercise we leave to you" might read better as "...exercise *that* we leave to you". *-Jason Yelinek*

**02/24/99: pg104, 2nd line above lower chart**... In "The answers to these four couting problems", "counting" is misspelled. *-Jocelyn Chew*

**02/24/99: pg114, #4(b)**... This might be clarified as "The second should be a combinatorial proof using inclusion-exclusion". *-Richard Trinh*

**02/23/99: pg100, Example 15.3**... "Let n be a positive integer" should read "Let *k* be a positive integer". *-Keith Ito*

**02/23/99: pg113, 3rd formula**... After the second "=", the denominator of the formula for "n choose k" has a misplaced parenthesis... "k!(n-k!)" should be "k!(n-k)!". *-Doug Honma*

**02/23/99: pg149, 10th line from bottom**... "How many function f:A->B are one-to-one?" should read "How many *functions*". *-Jesse S. Abrams*

**02/23/99: pgs147, 178, 220, margin notes**... More margin notes mutilated by the type-setting guillotine. *-Colin Little & Mike Schubmehl*

**02/23/99: pg111, margin note**... "What is the probability that no one gets their own hat back?" should read "no one gets *his or her* hat back." *( ??? Again, something beyond the scope of my gramatical awareness. -GL)* *-Mike Schubmehl*

**02/23/99: pg106, 9th line from bottom**... "but this overcounts, so have to subtract" should read "so *we* have to subtract". *-Alex Teoh*

**02/22/99: pg146, above "Inverse functions"**... "It is tempting for pronounce..." should read "It is tempting *to* pronounce..." *-Nate Chessin*

**02/22/99: pg145, g**... The function **g** includes "(1,4)", but in the diagram at right shows 1->3. *-Nate Chessin*

**02/21/99: pg143, Mathspeak!**... In the margin comment, "And there a notation for this." should read "And there *is* a notation for this." *-Nate Chessin*

**02/21/99: pg108, 9th line from bottom**... In the first sentence after *How to use inclusion-exclusion*, "and replaces is by" should read "and replaces *it with*". *-Roy Shea & Nate Chessin*

**02/21/99: pg107, proof chart**... In the chart, the element 6 is listed as being in A1 & A2, but appears in A1 & A3 in the diagram at right. *-Nate Chessin*

**02/21/99: pg113, formulas**... In two of the first three formulas reading "# derangements", "derrangements" is spelled with two "r"s. *-Masashi Ito*

**02/19/99: pg102, line#3**... While the use of "xor" here is correct and presumeably deliberate, it should perhaps be reconsidered. "Xor" is only defined in Problem #5.15, so unless its usage is present throughout the text (and maybe even if it is), it could be confusing to students who did not encounter this exercise. As a side note, while "exclusive or" appears in the index, "xor" does not.*-Gillian Allen, Katie Ray & Titus Winters*

**02/18/99: pg339, #19.4**... In the last equation line, "2^{k+2}-2+1" should equal "2^{k+2}-1",not "2^{k+2}+1". *-Nate Chessin*

**02/18/99: pg101, above Prop. 15.6**... In "The number to the left of ((n k)) is ((n-1 k)) and number above is ((n k-1))", the "((n-1 k))" and "((n k-1))" are reversed. *-Nate Chessin*

**02/18/99: pg88, line#11**... "the subset look like this" should read "*looks* like this". *-Nate Chessin*

**02/17/99: pg121, After 1st box**... To introduce the second box, "Next we could unravel definitions to yield." shouldn't end in a period. *-Elizabeth Millan*

**02/17/99: pg119, Margin note**... In the second paragraph of the note, "Let *x* and *y* be two integer..." should read "integer*s*". *-Elizabeth Millan*

**02/17/99: pg96, #5**... This problem should end in a question mark. *-Elizabeth Millan*

**02/17/99: pg96, above "Recap"**... "we might be tempted just to do the remaining multiplications" has misleading connotations. The "tempted" suggests the temptation of evil, and that that which is tempting us is wrong and incorrect. Since what is tempting us is, in fact, quite valid, you might replace "...tempted..." with "might want to just do" or "we can just", or something a little safer-sounding.*-Elizabeth Millan*

**02/16/99: pg120, #7**... Don't forget to put something here. *-Doug Honma*

**02/16/99: pg140, #4a**... In the second line, "a0, a1, a2, a3 ..." should have a comma after the "a3" to be consistant with the rest of the page. *-Rob Adams*

**02/14/99: pg119**... Another instance of a margin note running off the bottom of the page. *-Colin Little*

**02/10/99: Sections 12 & 13**... We speak of "an equivalence relation *on* a set" and "a partition *of* a set", but is it more proper to say "the equivalence classes *of* a set" or "the equivalence classes *on* a set"? The later seems to be the text's usage, but we thought we'd mention it anyway. *-Elizabeth Millan & GL*

**02/10/99: index**... The index entry for "combinatorial proof" mistakenly lists it as being on page 93 (they're on page 56). *-Titus Winters*

**02/10/99: pg48, line#12**... "more than one objects" should read "more than one *object*" *-Elizabeth Millan*

**02/10/99: pg39, line#5**... "let us rethink out list counting problem" should read "*our* list counting problem" *-Elizabeth Millan*

**02/10/99: pg32, Second sentence**... Consistancy... should make the "1" a "one" or the "two" a "2". *-Elizabeth Millan*

**02/10/99: pg32, First sentence**... This sentence is awkward, and might be better phrased "Notice how we organized the
lists so it is clear that we have neither repeated nor omitted a list." *-Elizabeth Millan*

**02/10/99: pg97, #9**... "Move all the negative terms over to the right-hand side to give." should either have a colon or nothing at all after "give" before the equation. *-Doug Honma*

**02/10/99: pg96, #3**... The last sentence "The race is an Olympic final event..." should end in a period. *-Doug Honma & Elizabeth Millan*

**02/09/99: pg97, #12**... "the factorial formula" might be clarified to "the factorial formula for n choose k". Although the "(Theorem 14.12)" makes this somewhat clear, it helps avoid confusion with the factorial formula on page 38, and perhaps lessens the need to look back at Thm. 14.12. *-Andrew "Pimp Daddy" Yamashita*

**02/09/99: pg97, #9**... The binomial theorem is Thm 14.8, not 14.12 as stated. *-Andrew "Pimp Daddy" Yamashita*

**02/09/99: pg95, 7th line up from Thm 14.12**... "We declare two of this lists equivalent" should read "these lists" *-Jocelyn Chew*

**02/08/99: pg94, 6th line from bottom**... "This is a not bad,..." should read "This is not bad". *-Nate Chessin & Zeke Burgess*

**02/08/99: pg89, 8th line from bottom**... "We can think about selected the unfortunate..." should read "selecting the unfortunate". *-Nate Chessin*

**02/07/99: pg96, #1**... "Mixed Matched Marvin has a draw full of 30 different socks". Presumeably Marvin actually has a "drawer" full of socks (tho with Marvin, who can say for sure?) *-Colin Little*

**02/07/99: pg91, 3rd line above Example**... "would simply be the all possible *k*-element subsets" should read "be all the possible". *-Leslie Joe*

**02/07/99: pg76, 10th line from bottom**... "Next, there all the subset of size 1" is just a mess. *-Leslie Joe*

**02/07/99: pg38, #10**... "...if the cards are all of different value" should read "are all of different values"
*(Is this correct? Grammar's not my strong suit -GL)* *-Leslie Joe*

**02/03/99: pg8, 7th line from bottom**... "understands the if he" should read "understands *that* if he". *-Elizabeth Millan*

**02/03/99: pg8, 10th line from bottom**... The sentence "Only one consequence is promised" is missing a period. *-Elizabeth Millan*

**02/03/99: pg3, line#7**... "There two conditions" should read "There *are* two conditions". *-Elizabeth Millan*

**02/03/99: index**... The terms "pig", "guinea" and "guinea pig" were all blatantly omitted from the index. ;-) *-Rob Adams*

**02/03/99: pg31, middle of page**... In the paragraph starting with "Lists are all pervasive in mathematics", this should read "all-pervasive" since, of course, not every list is pervasive. *-Zach Walters*

**02/02/99: General Inconsistancy**... Definitions given "on the fly" (that don't have their own numbered **Definition** or heading) are sometimes indicated via a margin note (Ex: "Nand", page 30... making it easier to find on the page if coming from the index), and sometimes not (Ex: "adjacency matrix", page 281). If this inconsistancy is undesired, then someone needs to go thru the index and check on all these. *-Colin Little*

**02/02/99: pg316, margin**... Bad formatting... 1 1/2 figures (curves) in the margin are cut off at the bottom of the page. *-Adam Fischer*

**02/02/99: pg37, #2**... The question should end with a question mark rather than a period. *-Zeke Burgess*

**02/02/99: pg45, 4th line from bottom**... "...now reduces the problem of counting lists" should read "now reduces *to* the problem...". *-Eric Huang*

**02/02/99: pg31, middle of page**... "A natural number is, when written in standard notation, is a list of digits;" should only have one "is". *-Nate Chessin*

**01/29/99: pg35, line#6**... Should "How many lines are on this chart?" be in quotes in the book (it's not), and if not, should "How" be capitalized? *(Don't ask me, I'm just a mathematician. -GL)* *-Roy Shea*

**01/28/99: pg335, #6.2**... "6 ways" should be "36 ways" *-Masashi Ito*

**01/25/99: pg21, 7th line from bottom **... "one the one hand" should read "*on* the one hand". *-Nate Chessin*

**01/24/99: pg17, line#4**... "(x+y)=c" should be "(x+y)=2c". *-Nate Chessin*

**01/23/99: pg13, #1(d)**... The statement in this part is false. While this does not affect the problem (and is probably even deliberate), it might be less startling if a second statement were false, or a caveat was added to the problem statement. *-Katie Ray*

**01/23/99: pg7, middle of page**... "with 100 meters of the surface of the earth" should read "*within* 100 meters...". *-Nate Chessin*

**01/23/99: pg1, 6th line from bottom**... "work our way up integers" should read "work our way up to the integers". *-Nate Chessin*

**01/21/99: pg1, margin**... Bad formatting... the margin note runs off the end of the page, and is not readable. *-Jay Trautman*

**12/15/98: pg308, #2**... might want to note explicitly that we're excluding dominoes that have the same number twice (even though it's implicitly clear). *-Kim Wallmark*

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