I've been very interested in the book Concrete Mathematics (Graham,Knuth,Patashnik) and I've been reading it for the past few weeks.

I'm at the chapter about Sums (Chapter 2), specificaly, the lesson about Finite and Infinite Calculus. My question is if any serious calculus or advanced math background will be needed from this point on?

I'm going into 10th grade and the highest math I can take as a 10th grader is Precalculus (in my school at least), so anything I would want to do with calculus at school would have to wait until I'm in 11th grade.

I know a few topics about Calculus due to my own interest in the topic, but they've been entirely self-taught and no formal lecturing about them ( maybe this will hold me back?). I seem to understand this part of the book without too much difficulty, but should I first complete a Calculus course before moving on with the book and gather a firm background, or is it not needed?


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    $\begingroup$ If I were you I wouldn't wait. It is often helpful to read about topics you don't fully understand. And if you do get stuck on a specific point...well...that's what stackexchange is for! :) $\endgroup$
    – Bill Cook
    Jun 12, 2013 at 20:10
  • $\begingroup$ Thanks @BillCook, I'm willing to do calculus before this, I have a textbook at home, and an entire summer of free time :) On top of that, the topic itself really interests me. Thanks for your opinion! $\endgroup$
    – Alejandro
    Jun 12, 2013 at 20:11
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    $\begingroup$ Sounds like a good use of your free time. :) You might benefit from having an extra calculus text or two to look at (there's lot of free stuff online, but there's something about having a physical book to flip through). I put a few links to cheap standard calculus text at the beginning of my calc III course syllabus: mathsci2.appstate.edu/~cookwj/courses/math2130-spring2013/… You can pick up a copy of Artin, Stewart, etc. (old editions anyway) for $4. $\endgroup$
    – Bill Cook
    Jun 12, 2013 at 20:16
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    $\begingroup$ Never wait for school especially with the lousy curriculum these days. Follow what Samuel Johnson said, "A man ought to read just as inclination leads him; for what he reads as a task will do him little good." Good luck and have fun :) $\endgroup$
    – user70962
    Jun 12, 2013 at 20:20
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    $\begingroup$ Just to echo the previous comments, never wait for anyone to teach you anything. If you need to learn more about some field of mathematics in order to further your interests, do what the pros do, crack open a book and start learning! $\endgroup$
    – treble
    Jun 12, 2013 at 21:34

1 Answer 1


You do not need calculus to understand the material on finite calculus; you’ll simply miss some of the analogies until you actually learn the calculus side of them. Most of the material through Section $5.3$ is also accessible without calculus, at least in principle, though some of it is far from easy. The same applies to much of Chapter $6$. On the whole I’d say that you should give it a try if you find it interesting (as I certainly would have done, had it existed when I was that age).

  • $\begingroup$ Thanks Brian! I appreciate your advice :) Do you think that having a calculus background would help me better understand the topics from here to 5.4 though? $\endgroup$
    – Alejandro
    Jun 12, 2013 at 20:24
  • $\begingroup$ @user1274223: Very little, I think. That nebulous and elusive thing called mathematical maturity is far more important. If you’ve seen a little modular arithmetic, that would be of some help. $\endgroup$ Jun 12, 2013 at 20:29

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