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Discrete Math Textbook Recommendations? 93

Posted by Cliff from the books-and-learning-styles dept.
JonnyRo88 asks: "I am an undergraduate CS major at the University of Central Florida. I took a Discrete Math course this past semester and had a VERY difficult time with the text book the class used: 'Discrete and Combinatorial Mathematics' by R. Grimaldi. I do not attribute my difficulties to the book itself, rather I just feel that my learning style is incompatible with the way this book is laid out. I'm sure that others have had similar experiences where they could just not -click- with a book. Like many people I know I tend to learn almost all of the class material from the book. I learn really well from books that focus heavily on examples and explanations on how those examples work. I would love to hear what Slashdot readers consider their most useful Discrete Math textbook. Most interesting are books that have very good discussions on the basic strategies of proofs. I am currently preparing to take an exam that the department requires all CS majors take before they can move to higher level classes, it will test me on my knowledge of discrete math, specifically proofs (by induction, disproof by contradiction, direct proof, recursive definitions, etc)."
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Discrete Math Textbook Recommendations? More

Discrete Math Textbook Recommendations?

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  • Good Books (Score:4, Insightful)

    by Crutcher ( 24607 ) on Monday July 14, 2003 @11:44PM (#6439814) Homepage
    the following are very good books on proof and discrete math. Some of the titles are whimsical, but they are not toy books, they are very valuable.

    "How To Prove It", "How To Solve It", "Induction and Analogy in Mathematics", and "Patterns of Plausible Inference".

    However, it seems you are looking for a book to cram for a test in discrete math. Good luck, not going to find one. More so than any of the lower mathematics, discrete is the beginnings of higher logical analyisys, and you can not really 'cram' it. You have to really read the work, and really work the problems. It has to become part of you.

    There seems to be this trend to blame difficulty in learning a subject on the books or the teachers. There are many, many things in the world that you are not smart enough to do; you need to accept this, and figure out what problems you can deal with.

    I am not batman, I am not Johan Sebastian Bach, and I am not Richard Feynman, I have accepted this; perhaps you are not capable of Discrete Mathematics. If not, you need to leave CS, and go get in MIS or something, you will be happier.

    • "How To Solve It" (Score:3, Informative)

      by Pathwalker ( 103 ) *
      I have to second the recommendation of "How to Solve It".

      The professor of my first discrete math class recommended it to me, and it was very helpful.
      • Wow! I guess that really goes to show how differently various people think. I got a copy as a gift as teen in the 70s and while it's one of those rare gifts that I completely appreciate for the utter sincerity with which it was given, I never once found any use in it (despite a lifelong informal interest in heuristics and mathematics)

        My advice? It's a short, easy read outlining approaches to problem solving that some geeks will find intuitive/obvious, so skim it in a bookstore or library. You should be abl

    • Re:Good Books (Score:1, Insightful)

      by Anonymous Coward
      i agree that discrete math is not necessarily intuitive to everyone and doing well in this subject requires lots of work, however, stating that not understanding it means you should leave CS is an incredibly arrogant statement.

      i believe that learning is different for everyone, perhaps you understand a subject a way that a professor or a certain text presents the topic. others do not, there is bound to be a text or a tutor who'd be able to break down the topic and present it in a way you would understand
      • How will you fulfill your degree requirements if you can not grasp the concepts involved in discrete math? That's like saying that an English major will do fine as long as they ignore all those pesky writing courses. There are just some areas of study where you have to "pay your dues" or get out. Into social sciences? Better get used to statistics! Design and architecture students need to learn some engineering. Music geeks need to learn music theory. While it is true that anyone CAN learn just ab
    • I am not batman, I am not Johan Sebastian Bach, and I am not Richard Feynman, I have accepted this; perhaps you are not capable of Discrete Mathematics.

      <voice="Chief Wiggum">
      Oh, sure, and that's exactly what Batman would say. To preserve his anonymity to fight crime.

      I think you tried to be a little too clever there, Mr. Caped Crusader!
      </voice>

    • Re:Good Books (Score:3, Insightful)

      by HalfFlat ( 121672 )
      From my experience tutoring early-level University maths, it really seems that the overwhelming majority of people are capable of learning and understanding this level of mathematics, and it's not at all clear that the few remaining lacked capability rather than simply lacked sufficient motivation. (This is not to brush them off - maths can be really hard!)

      Almost every time it comes up in conversation that I'm working as a mathematician, I hear phrases such as: "oh, I was never any good at maths", or "I ha
      • I high school proofs were only discussed briefly in a Geometry course. In college I didnt really use proofs much until the end of Calculus 3.

        When I hit discrete math it felt like hitting a brick wall. I felt like I understood the concept of sets and logical rules fairly well, but I was weak on the area of actually knowing how to apply these concepts to the organization of a proof.

        In too many college courses I've seen professors who are extremely intelligent, but have a hard time explaining concepts,
        • I have a B.Math and after university went to Teacher's College. One of the things I found most hard to teach was mathematics becuase it was hard to remember how I learned a technique that was now almost innate. The very reason that I found it very difficult to create lessons outlining the steps to do basic operations was becuase I often never had to do those intermediate steps explicitly.
    • I am not batman, I am not Johan Sebastian Bach, and I am not Richard Feynman, I have accepted this; perhaps you are not capable of Discrete Mathematics. If not, you need to leave CS, and go get in MIS or something, you will be happier.

      Wow, thanks for your help. I'm sure the submitter really valued this input. I simply hope that you are not now, nor will ever be, someone in a position to give real advice to people. "Having trouble with division, Johnny? Well, not all people can divide big numbers. Maybe y
    • Number one might not be your cup of tea, as it is rather easy, but it might help you to get started on the subject.

      G. Baron and P. Kirschenhofer. An introduction to maths for computer scientists, Vol 1 & 3, Springer/Vienna.

      D. E. Knuth. The Art of Computer Programming, Vol 1 - 3, Addison-Wesley

      N.L. Biggs. Discrete mathematics, Oxford University Press

      R.L. Graham, D.E. Knuth, O. Patashnik. Concrete mathematics, Addison-Wesley

      S. B. Maurer, A. Ralston. Discrete Algorithmic Mathematics, A K Peters

    • "the following are very good books on proof and discrete math. Some of the titles are whimsical, but they are not toy books, they are very valuable. "How To Prove It", "How To Solve It"...

      I too highly recommend How to Prove It. [amazon.com] I thought that it was an excellent book as I found that it helped the reader understand how to approach mathematical proofs. It covers mathematical logic and set theory in much depth at first, then goes into detail about how to apply what was discussed earlier on. I'm sure that yo

    • perhaps you are not capable of Discrete Mathematics. If not, you need to leave CS, and go get in MIS or something, you will be happier.

      There are branches of CS where higher-level maths are important, this much is certain. However there are other branches where it's not very relevant at all. I never got to take some of the higher level maths I would have liked to, but I took CS electives that didn't require them.

      You might not wind up working at Wolfram or optimizing algorithms, but maybe you'll come up

  • discrete maths (Score:3, Interesting)

    by snowdropper ( 108891 ) on Monday July 14, 2003 @11:45PM (#6439819)
    Johnsonbaugh R 2001, Discrete Mathematics, 5th Ed, Prentice Hall

    We used this at my uni course, sometimes it lacks a bit of detail, but overall its quite a good book, it especially helped me with induction proof.

    • Best Book: _Discrete_Mathematics_ by Ross & Wr (Score:4, Informative)

      by reporter ( 666905 ) on Tuesday July 15, 2003 @04:24AM (#6440732) Homepage
      Please consult "The Mathematical Association of America (MAA) [maa.org]". It is the definitive source of recommendations for good textbooks on every topic in mathematics. According to the MAA, two textbooks about discrete mathematics are most highly recommended.

      They are the following.

      1. Maurer, Stephen B. and Ralston, Anthony. Discrete Algorithmic Mathematics Reading, MA: Addison-Wesley, 1991.

      2. Ross, Kenneth A. and Wright, Charles R.B. Discrete Mathematics, Englewood Cliffs, NJ: Prentice Hall, 1985, 1988, 1999. Third Edition.

      In particular, the second textbook has plenty of examples. Answers to many of the odd-numbered problems are also included in the back of the book.

      The book by Ross and Wright is essentially the best book on discrete mathematics if you are pursuing a course of self study. The best book also costs plenty of money but is worth it. You will find it to be a useful reference long after you have graduated with your degree in computer science. Discrete mathematics is, after all, the foundation of modern computer science.

  • What the hell are you doing? Shush! It's not just a clever name, you know!

  • best discrete book ive seen (Score:4, Informative)

    by Anonymous Coward on Monday July 14, 2003 @11:49PM (#6439835)
    I did a lot of math tutoring in college, and I noticed that all of the discrete books were absolutely god-awful basically just TeX documents with covers, with the exception of one: Kenneth Rosen's "Discrete Mathematics and its Applications". Best. Discrete Book. Ever.
    • I have to agree here: we used Rosen in my Discrete Math class last year. Lots of good examples, plenty of problems, and pretty easy to understand descriptions. I wholly recommend it.

    • Ok, I'll take your word for it that it _may_ be the best book out there on the subject. I used it last semester and I found it to be very little english wrapped around a solid wall of figures and notation. Not a very good introductory text for this reason.

      If it's the best, then there is room for improvement in the field. Most of what made the class doable was being able to knock skulls with other people about the subject.

      Also, if you buy this book. Make sure you buy the hardback version and not the softco
  • That book is actually much better than the purple and white book they sometimes use for 4210... I think of it as a reference, though. Perhaps you should take a look at the books the math department uses for Logic and Proof, or the one for Combinatorics and Graph Theory? An introductory text on number theory should also have good examples of proof by induction.

  • Kenneth Rosen's Discrete Mathematics (Score:4, Informative)

    by zhiwenchong ( 155773 ) on Monday July 14, 2003 @11:56PM (#6439859)
    As far as I know, this is the standard text at many colleges. Rosen's approach is mathematically rigorous yet practical at the same time.
    This was also the book from which I first discovered Fermat's Last Theorem, so it is not the typical dry textbook that we all know about.
    Walmart [walmart.com] sells it for less than Amazon [amazon.com] .

  • Rosen (Score:2)

    by pcbob ( 67069 )
    Rosen's Discrete Mathematics and its Applications is best hands down. Used it in couple of courses here at SFU (sfu.ca), i just love it.
  • Jumped in to it while taking college trig. Definately doable, but also takes you to the edge, after 10 weeks we were at the level were new research could be done.

  • Long thoughts (Score:5, Funny)

    by cei ( 107343 ) on Tuesday July 15, 2003 @12:16AM (#6439918) Homepage Journal
    Discrete mathematics. Makes me want to paraphrase Lazarus Long...

    "Math is not necessarily something to be ashamed of--but do it in private and wash your hands afterwards."

    "A mathematician who calculates in public may have other nasty habits."

    and my personal addition, a variation on Clarke's Law, "Any sufficiently advanced mathematics is indistinguishable from surrealism"
  • I've had the exact same experience with that book. It's packed full of useful information, but worded in such a way that I have a very difficult time parsing what it says. Unfortunately, it's a virtual standard at my university, and many of the comp sci courses expect you to have it. I would really love a better book myself!

    • Re:Grimaldi (Score:3, Informative)

      by polymath69 ( 94161 )
      You know, if the questioner hadn't specifically said Grimaldi was no help, it would have been my recommendation. But it could be that it was more accessible to me after having digested Godel, Escher, Bach by Hofstaeder in high school. That covers much of the same subject area in a more conversational, but yet rigorous, way. I'm only the 94,161th person to recommend GEB, but I would suggest trying some of the included exercises as you read through it; they really help build an understanding for discrete m
      • Descrete math is a weak point for me. I think I'll spend some extra scratch on GEB then =)

        I grok a lot of the basic ideas behind descrete math, however, some of the more abstract concepts are difficult for me to get.

        Thanks for your advice!
  • I see about 20 replies so far, and at least a dozen unique books. Most of the suggestions have been along the lines of "This is a good book. We used it in a course and although it was X or Y, I recommend it." Others were just name dropping of 3 or 4 books at once.

    From that, and knowing that your local bookstore isn't going to stock all of these, and knowing that 12 textbooks will cost you close to $1200, how are YOU going to decide what to buy? Are you going to go on amazon and read reviews from here?
    • No, the beauty of being in a university environment is the existence of a place called the library. You can browse and borrow books for weeks, even a whole semester. Then if you decide you want to keep a certain book, you can go to a second-hand bookstore and pick up a copy, cheap. That's what I did.

      (In Montreal, there is a bookstore on rue Milton and rue Durocher called "The Word" that sells cheap 2nd hand texts in very good condition. I picked up my copy of Rosen and the solution manual for C$2)
      • I too have heard of that beautiful thing called a University library. Let me tell you a bit about mine:

        #1 Professors could take out books for very long (months) periods of time.

        #2 Despite the wide selection of books, MANY of the books surrounding course materials were out, requiring you to put it on hold. Now, with a 3 week withdrawal time and 12 weeks in a semester, that's 1/4 of a semester to wait.

        #3 There were a set of books you could get access to any time, but the borrowing period was 2 hours with a
      • Not just the library, but any tenured faculty member is bound to have at least half a dozen texts on every undergrad subject.

    • > knowing that 12 textbooks will cost you close to $1200, how are YOU going to decide what to buy?

      As others have suggested, try before you buy. If you live in the United States, your public library will let you borrow a book from another library by filling out an Interlibrary Loan Request form. The ILRs that I've used didn't require a fee but some might. (Still be cheaper than buying the books.) The books came in a week or two after I filed the ILR.

  • Use the old COT3100 book. (Score:3, Informative)

    by innosent ( 618233 ) <jmdority.gmail@com> on Tuesday July 15, 2003 @12:53AM (#6440078)
    As I'll be graduating from UCF this fall with a CS degree, I suppose I'm qualified to answer... On with it then... First of all, if you're really having trouble with the class, it's probably best to seek help that's actually breathing, as a book often fails to give that last bit of insight that's keeping you from understanding the methods. Second, don't worry about the foundation exam, if you know the basics, and can do common proofs from discrete, it's actually quite easy. As for the book, I took Intro to Discrete in 1999, and the book we used then was excellent, James Hein's "Discrete Structures, Logic, and Computability". If automata and languages are the ones giving you trouble after reading that book, check out the upper level (COT4210) book, Sudkamp's "Languages & Machines". The first book should give you plenty for that class, though... Oh, and one more free tip: when you take 4210, don't take Torosolu's class, try for (Drs.) Llewellyn, Dutton, Workman, or Guha (Arup)'s class. Actually, in all cases, try to get those professors...
    • Hmmm, I took Discrete Structures at UCF 88/89, and there was no text. The prof had hand-written his own book. The entire class had to go to the Kinko's down the road and purchase a copy of the "book!" Very intense, and the poor handwriting making it doubly-so. I think there was a 30% fail rate in that class.

  • I used the instructor notes... (Score:3, Informative)

    by dotgod ( 567913 ) on Tuesday July 15, 2003 @12:53AM (#6440079)
    I go to UCF and I got a B in Dr. Lang's discrete class and passed the foundation. I got through just studying Lang's and Guha's notes. I didn't even touch that terrible book. For the foundations exam, the best thing is to practice using old exams.
    • I started reading Guha's notes, and they have been quite helpful.

      Do you have a link for Lang's notes?

      P.S. At first I had a problem reading most of the notes on some of the UCF sites simply because they were all in .doc format and required the symbol font. Crossover office allowed me to run Word in linux so I could read the notes.

      -Jonathan
      • Lang's website for the course I was in is here [ucf.edu]. These notes are in PowerPoint format and require the symbol font just like Guha's did. You can just copy the Windows symbol font to Linux, and they're pretty readable, but still funny. I just used windows to read them.

  • ...I'd recomend Richard Brualdi's Introductory Combinatorics [amazon.com]

  • The Best Discrete Math Textbook EVER (Score:4, Informative)

    by fosh ( 106184 ) on Tuesday July 15, 2003 @01:08AM (#6440152) Journal
    So, at Carnegie Mellon, for undergrad Discrete math we have two main courses. The first one is sort of wimpy, but the second one is AMAZING! The professor keeps the text book online as a bunch of lectures and assignments. See http://www.discretemath.com and click calendar.

    Enjoy
    --Alex
    • This is really interesting. I love how the professor has the notes available in various formats. This differs from most places where the only option to read math notes is M$ Word, because it has a built in eq. editor.

      I will definatly check this out. Thanks
      • This is really interesting. I love how the professor has the notes available in various formats. This differs from most places where the only option to read math notes is M$ Word, because it has a built in eq. editor.
        "most places"? MS Word? I thought that about any serious piece of math is written in (La)TeX nowadays.
  • I used "Mathematics: A Discrete Introduction" by Edward R. Scheinerman

    The book was pretty good at explaining stuff, usually. He often left smiley faces and sometimes wrote things like "I'll leave this easy proof to you" or "you have to prove this for yourself in the homework." Also, the answers in the back are "hints" and usually don't help much. An example might be "Remember problem 16.7" or "Its not 20." Overall, now that I'm used to it - the book is ok - not sure if I would recommended it, but its g
  • I had some difficulty clicking with Grimaldi himself at Rose-Hulman. Like most professors, he's odd. In this case, he's got this nasally but raspy monotone voice. Walks with his hands out to his sides, as if he had a stick shoved up his butt. A very anal retentive personality. Expected you to learn things the way he taught them. I don't recall him answering questions all that well. I did OK in his classes. They weren't terribly exciting. I think I got Bs, because I had missed a few classes, and he subtracte

  • Another endorsement for Rosen, and some advice... (Score:4, Insightful)

    by Farley Mullet ( 604326 ) on Tuesday July 15, 2003 @03:28AM (#6440595)

    First, my background. I did an undergraduate degree in math and philosophy, and I'm doing graduate work in Mathematics right now, and I've t/a'ed a few introductory math courses. It was suggested to me by a prof. that before I graduate I should take a basic course in discrete math, and so in my final year of my undergrad, I took the introductory course in discrete math. We used Rosen's book, which I borrowed from a friend [slashdot.org], and, as I recall, it was a clearly written book with good examples and almost all of the formulas and information where you think it should be. Plus, it's reassuringly huge.

    And now for the unsolicited advice. . .

    You absolutely can't learn math from a book; math is a learn-by-doing subject. Books and teachers can help by suggesting techniques, or walking you through things, but you get to know how to do things by doing them again and again and again. It's a bit like sports in this respect: you can watch all the basketball you want on T.V., read all the books you want, and go to as many "shot doctors" as you like, but the only way you're going to make your shot better is by putting the hours in shooting again and again. So it is with math: books and examples and teaching can make it easier for you to practice and revise, but actually working problems out, and proving things for yourself are the only ways that you'll get better.

    So how do you put this into practice?

    Well, I have two concrete suggestions: first, if it's at all possible (and in my experience, it usually is) get ahold of all the past exams you can, and start working on the problems on the tests. The first few tests you do, have your notes, and whatever books you find useful with you, so you can look at how your prof., or Rosen, or Grimaldi, or whoever does similar problems or proofs, and so you can check facts and formulas that you use. Make sure that you save a few old tests to do without aides once you're confident and comfortable. My other big piece of advice is to work in a group when you do homework or problem sets or studying. The more backgrounds and perspectives and ways of understanding that you have to bring to bear on a problem, the better off you are, and with any luck you'll learn something from the folks you're working with. Plus, it's good practice having to explain and defend your proofs and solutions to classmates, and it's worthwhile to see how other people do the same.

    This is what I've learned from taking, tutoring, T/A'ing and marking math courses for the half decade, I hope you find it helpful.

    • You most certianly can learn math from a book. Just because you have to do some work doesn't mean the problems in the book an insufficient. A lot of instructors spend their entire lectures just doing examples from the book, and almost all of them assign the from the book (and only from the book). Often taking the test problems from the assigned homework, or only slightly modifying homework problems.

      While having an instructor, and being among peers learning the same stuff, and being able to ask questions
  • Tucker, Applied Combinatorics. It has the richest problem set of any book i owned as an undergrad. I've had grad level texts use problems from the book. I'm not just saying this because i have a copy of it for sale :-)

  • Another suggestion (Score:3, Informative)

    by Pseudonym ( 62607 ) on Tuesday July 15, 2003 @03:55AM (#6440659)

    Knuth, Graham and Patashnik, Concrete Mathematics.

    Mind you, with Don Knuth and Ron Graham's names in the author list is going to be good. :-)

    • What do you have against Oren Patashnik?

      • I don't know who he is (apart from "a lecturer at Stanford"; thanks to Google I am now a little more enlightened).

        Everyone who can call themselves a programmer has read at least one Knuth book, though, so simply saying "it's a Knuth book" speaks volumes. Admittedly less so for Ron Graham.

    • This is a bit heavy for someone 'wanting to learn some discrete math'.

      The book isn't about graphs or proof or number theory. The book is about recurances, and methods of solving them. This brings in such subjects as discrete calculus, and floor and ceiling functions, but its NOT really a discrete math book.

      Its a good book to read AFTER you get the basics of discrete though.

  • One problem that affects universities is conflict of interest. The customer, the student, has very little power. So, people who staff universities often do what they want to do, even when it is not good for the customer.

    How many programming jobs require a solid understanding of mathematics? Not many, it seems to me. Instead, programming requires a solid understanding of how to be logical in solving a problem you have never seen before.

    I seem to detect a lack of caring in the approach of the univers

    • How many programming jobs require a solid understanding of mathematics? Not many, it seems to me. Instead, programming requires a solid understanding of how to be logical in solving a problem you have never seen before.

      I appologize right now for any toes I step on:

      We'll agree to disagree on this. My (admittedly limited) experience working in industry proved to me that there is a big difference between a well trained monkey and someone I would want to hire to write code. I'll admit right up front that


      • "Mathematics is primarily concerned with asking, "I accept these axioms to be true. What must be true as a consequence?", a skill crucial in pretty much every field. I've had to deal with altogether too many people who think something is true without being able to justify their beliefs. What's worse are the sheep who blindly accept what is said on faith alone. Do you want to deal with these people as team members on a project? Do you want to deal with these people as project managers?"

        I agree, exactly.

        • [Grimaldi] seems to be someone who is not in mathematics so that he can learn to be more logical, but is in mathematics because it allows him to earn a living while having very poor social skills. Do you want him as your leader?

          What is this drivel? How can you speculate about Grimaldi's motives like this? Have you met the man?

          Having had several classes from him, I can certainly tell you that you are talking out of your ass. Please know what you're talking about *before* typing.

          • It is you who is being impolite. I was merely using the description given by an earlier poster. The overall issue stands: Don't let universities and professors intimidate you. You are the customer and deserve to be served.

    • Professor Grimaldi sounds like someone whose inner conflict is a lot more important to him than anything else. He sounds like the kind of professor who doesn't care if he is communicating.

      I have to disagree, having had personal experience with him as a teacher (two different classes). At least to me, it seemed he did care very much that the students were learning (meaning he did care if he was communicating). He was incredibly helpful and accessible if you were having problems (as I did often). I can't

  • A good "helper" book for learning maths, for those who need a hand is William Curtis' "How to Improve Your Math Grades".

    It's available as an ebook (PDF) from http://www.occampress.com/#mathgrades [occampress.com]

    From the site: "This book sets forth a new method for students to organize their notes for any math course (in fact, for any technical course)..."

  • "Combinatorics: An Introduction" by K.H.Wehrhahn

    "Concrete Mathematics" by Graham, Patashnik and Knuth

    I've personally used both, and they are both great for what they cover. The Wehrhahn book would probably suit you best, whilst the GPK book would be good as a solid reference tome.
  • I used Susan Epp's "Discrete Mathematics with Applications" two years ago for my introductory descrete math course. Its hard to find used copies of this book because most students from my university (UNB) do not sell the book after, it's really that good.

  • Some books (Score:4, Funny)

    by Bluesman ( 104513 ) on Tuesday July 15, 2003 @07:59AM (#6441283) Homepage
    My favorites are "Discrete Math for Dummies" - it's very clearly written for normal people, not those math whizzes, and it has funny cartoons related to discrete math.

    Also, "Learn Discrete Math in 24 Hours" is pretty good.
  • I remember reading a section of some math book. I was completeley confused and lost. I then looked at the exercises and realized I had already knew this stuff from some other class and finished them with no problem.

    I went back and re-read the same section and still couldn't follow the book.

    What I am saying is sometimes the author of a book sucks, sometimes the book teaches in a way you find hard to understand, and sometimes the subject takes awhile to stick.

    Either way you need to get a another book or an
  • Grimaldi is a professor at my alma mater [rose-hulman.edu]. I can understand how the book might be a bit tough to crack.

    Never really had to take his discrete math class, since I was an EE major. But if you're having problems with the book, maybe you could shoot him an email about it. Rose-Hulman professors are busy, but it's not like they have 350 students in each class.

    He may be interested in knowing what you found difficult about the book, to perhaps improve the next edition. Also he might give you a few hints on how to
  • I have a book from college called "Applications for Discrete Mathematics" (or something to that effect). I use it as a $75 doorstop. Literally.

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