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Our department has decided to offer a "Discrete Math" course that students would take before their "Intro to Proofs" course. The idea is that the Discrete Math course would focus on the computations and techniques that are used in discrete settings similar to how a typical Calculus I course focuses on the computations and techniques of continuous situations. The problem I'm having in preparing for this course is that every Discrete Math textbook I look at spends a lot of time on proof technique and contains many "Prove that..." exercises.

Question: Does anyone know a Discrete Math textbook that emphasizes computations and applications instead of proof? (Or at least, proof at a level analogous to Calculus I.)

Here is a basic run-down of the topics chosen by the department: Boolean logic, Basic Set Theory, Counting/Combinatorics, Modular Arithmetic, Relations, Graphs/Digraphs (Eulerian Circuits, Hamiltonian Cycles, Dijkstra’s Algorithm), Trees (Minimal Spanning Tree), Sequences (Finite Difference Methods).

Bonus Points: Such a text that allows use of an online homework system (WebAssign, MyMathLab, WeBWorK, etc.)

Edit: The course has only Calculus I as a prerequisite and it will be taken by freshman/sophomore majors in Math or Math Ed.

Update: I've found that the text "Discrete Mathematics" by Dossey, Otto, Spence and Vanden Eynden seems to strike the right balance. However the latest edition is over a decade old and, hence, the internet is rife with solution manuals and the Amazon.com reviews are poor. Does anyone know of a newer/better text similar to this one?

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    $\begingroup$ Just for some further information: who is the class aimed at? What is the expected prior knowledge? $\endgroup$ – Chris C Feb 17 '15 at 17:43
  • $\begingroup$ Good question. I added that info in an edit above. $\endgroup$ – Aeryk Feb 17 '15 at 17:52
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    $\begingroup$ An aside: Do you think your department's decision was wise? To me, proofs are easier to understand in discrete math than in, say, linear algebra. $\endgroup$ – Joseph O'Rourke Mar 23 '15 at 0:18
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While not, strictly speaking, a textbook, Phillips Exeter Academy publishes their full problem set for their non-proof based discrete mathematics course (which they offer to advanced high school students). For more on how they use the problem set in their course, see my answer to this question. Re: your "Update," these problems do have the advantage of having no available solution set.

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I may suggest Discrete Mathematics by Rosen, this book has a lot of computation problems, and the sections on proof are not really that necessary to continue with the advanced material on the book.

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I hate answering my own question, but thought I should let others who find this know what I decided on:

"Applied Discrete Structures" by Alan Doerr and Kenneth Levasseur

Reasons for picking it: Light on proofs (but they're still there), good on computation problems, free online text.

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  • $\begingroup$ Let me just say, I really like the idea of teaching Discrete Mathematics to Math Ed majors. I chose to take this while Differential Equations was the recommended course, and I'm so glad I did. I'd also say this tho: my recommendation is that students would first take College Geometry so that they have knowledge of proofs before taking the Discrete Math course you recommend, as you've admitted it has minor proof content. $\endgroup$ – Elem-Teach-w-Bach-n-Math-Ed May 11 '16 at 18:35

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