Discrete Mathematics DeMYSTiFied

by Steven G. Krantz

Publisher's Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product.




MULTIPLY your chances of understanding DISCRETE MATHEMATICS If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts. Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and enlightening way. You will learn about logic, proofs, functions, matrices, sequences, series, and much more. Concise explanations, real-world examples, and worked equations make it easy to understand the material, and end-of-chapter exercises and a final exam help reinforce learning. This fast and easy guide Simple enough for a beginner, but challenging enough for an advanced student, Discrete Mathematics Demystified is your integral tool for mastering this complex subject.

Genres: Mathematics, Textbooks

364 pages, Paperback

First published January 1, 2008

Reviews

[Alberto Tebaldi · Rating 3 out of 5]

book explains well the concepts, however a minimum or algebra revision is required for the general reader

[Erickson · Rating 5 out of 5]

Quite clear in presentation, though more suitable for those who have studied the topic and need clarification.

[Muriel · Rating 1 out of 5]

I did not finish this book because some of the examples were wrong, not just a typo, the logic and the answer were wrong. It will only confuse people trying to learn.

[William Cruise · Rating 3 out of 5]

I'd give this a higher rating if not for the many examples where algebraic leaps are taken in a single bound.

[Lars Westergren · Rating 2 out of 5]

Started out good, but a bit of a disappointment. Needs more polish - by chapter 2 and onwards some exercises appear which are much more difficult than the examples in the chapter, and also uses concepts and notations that aren't explained until later in the book.

It is of course difficult to explain complex topics in a way simple enough for *everyone* to understand, but I think he could have done a lot better in some places. For instance on the chapter on "generating functions", this is part of his step by step example:

F(x)=(1/(1-x-x^2)
It is convenient to factor the denominator as follows:
F(x)=1/[(1-((-2)/(1-sqrt(5)))x:]*[1-((-2)/(1+sqrt(5)))x):]
A little more algebraic manipulation yields that
F(x)=(5+sqrt(5)/10)[1/(1+(2/(1-sqrt(5)))x):]+(5-sqrt(5)/10)[1/(1+(2/(1+sqrt(5)))x):]

Now we want to apply the formula in Eq. (6.2) from Sec. 6.4 to each of the fractions in brackets ([:]). For the first fraction, we think of -(2/(1-sqrt(5)))x as lambda. Thus the first expression in brackets equals
(sigma(j=0->infinity)(-(2/(1-sqrt(5)))x))^j
Likewise the second sum equals
(sigma(j=0->infinity)(-(2/(1+sqrt(5)))x))^j
All told, we find that
F(x)=((5+sqrt(5))/(10))(sigma(j=0->infinity)(-(2/(1-sqrt(5)))x))^j+ ((5-sqrt(5))/(10))(sigma(j=0->infinity)(-(2/(1-sqrt(5)))x))^j
Grouping terms with like powers of x, we finally conclude that
F(x)=(sigma(j=0->infinity)[((5+sqrt(5))/(10))(-(2/(1-sqrt(5))))^j+((5-sqrt(5))/(10))(-(2/(1+sqrt(5))))^j:])x^j

This example is about 4 pages long, with these step by steps where he doesn't explain how to think in order to see where to go next! A few pages later he goes "Now you try it!" It's like seeing a parashute pro do all sorts of tricks with no explanation and then get pushed out of the plane on your first lesson.

"It is conventient to write it like..." Convenient why? Not to mention he uses vastly more complex factorisations than before, with no explanation.

Not all the book is like this fortunately, and I think I learned enough from the better chapters to tackle a more complex book next time, which is why I give it two stars instead of one.