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Discrete Mathematics and Functional Programming, by Thomas VanDrunen
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This book provides a distinct way to teach discrete mathematics. Since discrete mathematics is crucial for rigorous study in computer science, many texts include applications of mathematical topics to computer science or have selected topics of particular interest to computer science. This text fully integrates discrete mathematics with programming and other foundational ideas in computer science. In fact, this text serves not only the purpose of teaching discrete math. It is also an introduction to programming, although a non-traditional one. Functional programming is a paradigm in which the primary language construct is the function and function here is essentially the same as what it is in mathematics. In the functional paradigm we conceive the program as a collection of composed functions, as opposed to a sequence of instructions (in the imperative paradigm) or a set of interacting objects (in the object-oriented paradigm). Dominant computer science curricula emphasize object-oriented and imperative programming, but competence in all paradigms is important for serious programmers and functional programming in particular may be appropriate for many casual programmers, too. For our purposes, the concepts underlying functional programming are especially grounded in those of discrete mathematics. Discrete mathematics and functional programming are equal partners in this endeavor, with the programming topics giving concrete applications and illustrations of the mathematical topics, and the mathematics providing the scaolding for explaining the programming concepts. The two work together in mutual illumination.
- Sales Rank: #545449 in Books
- Published on: 2012-10-16
- Binding: Paperback
- 688 pages
About the Author
Thomas VanDrunen teaches in the Department of Mathematics and Computer Science at Wheaton College in Wheaton, Illinois.
Most helpful customer reviews
41 of 42 people found the following review helpful.
A Few Missing Details
By Let's Compare Options Preptorial
Edu designers jokingly call discrete math "all the math that's now been removed from High School math requirements." In essence, discrete math is the study of logic and proof functions, and the logic behind programming and proofs in both math and programs. Functional programming captures this well, as it IS functions. This book is designed to cover 60% discrete math and 40% functional programming in ML, and pedagogically link and unite them as happens in the real world of applications. All the other texts in the field are silos, and it is really tough to "grok" either topic without the other.
Why ML? ML ("Meta Language") is a functional language that is a foundation (lamda-like proof discipline) for proof assistants like Coq and Isabelle, and this author's "hidden agenda" is writing proofs, which he (rightfully) sees at the foundation for discrete math, and how it unifies math and programming proofs. I've used ML, and in some ways it is closer to Python than Lisp!
It doesn't have the memory sparing features of Haskell like lazy evaluation, but you can fake it with closures. You'll probably never use ML again unless you get into Coq and language or compiler development, but the material in this book is an easy jump to F# if you're going .net, or Haskell if you're going more mainstream in functional, CAS, math, etc. Coq itself is OCaml (which I personally love), and ML isn't too far from that, either. I've seen four line Haskell algorithms that can solve the hardest Sudoku puzzles in a fifth of a second, so functional is not dead by any means, even though Lisp goes back to the Fortran days.
What's odd about this text, is that it covers VERY advanced topics at an undergrad sophmore level. It's targeted to math majors who "must" have a comp sci course or comp sci's who MUST have a discrete math course. You DO learn both a very cool functional language and there are a LOT of discrete math examples, but you're learning at a really high level-- frankly more about writing your own language or compiler than writing IN a language. As an engineer and roboticist I loved the digital circuit examples, worth the price of the book for me as a self study engineer and online discrete math tutor.
Because the author's book website at Wheaton has all the contents, lots of links, many sample pages, etc. (just google or bing the title of this book, then go to the publisher site, then use the top link for the book's site at Wheaton), go there and check it all out before investing in using this for a class you teach. My one caution to the author: your website is a little timid on giving answers due to not wanting to burden teachers with a place students can cheat. Many of us are now self study types, and this book (in my opinion) is just as good for solo acts, and in fact one of the few out there with a LOT of pedagogy built in for us autodidacts. Keep posting those self study solutions, please??!!
On the other hand, if you're an autodidact, engineer, self taught programmer, etc. like me, you will LOVE this book as it stands. I'm a roboticist who engineers and writes embedded domain specific languages, and this is outstanding for brushing up on discrete math, while reviewing functional programming at the same time. The practical tips and answered exercises and website code downloads make real world use immediate.
Now for some frank and painful honest issues for students. If you go on in math or engineering or programming, you're likely going to have to get into Java, C#, Matlab, etc. more than functional. Functional purists look down on Java via Lisp or Haskell just like even deeper geniuses look down on functional via Prolog. What about the real world? The real world is that Scala is probably going to replace Java in your lifetime if you are under 50! If you are over like me, it still is the heart of Netflix, LinkedIn, and even a lot of new features on that little known "Amazon" site. Scala is a combination of functional and imperative and runs on the JVM! So, I'm fully supportive of this author that you can't go wrong with a semester of functional, and since this brushes up your discrete math to boot, it's a double win!
I teach free online discrete math tutorials, from an embedded circuit - robotics point of view, and have eagerly adoped this text exclusively, and my students LOVE it. Once you use it, you will never want to go back to either an intro functional or an intro discrete text again, because the purpose of both is to integrate with each other, and this is the ONLY text that does that, with nearly 700 pages of dynamite examples that run the first time you try them. Because of the self study twist, I'd unhesitatingly use it for online classes, at community colleges, and even for AP High School classes for your brightest pre-undergrad achievers. Heck, they ARE teaching this to juniors in High School-- in China. Highly Recommended.
Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
0 of 0 people found the following review helpful.
Five Stars
By Alejandro Vasquez
It makes sence.
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