However, if you are really unsure of your capacity to master Concrete Mathematics at this point in time, then by all means, prepare using some of the suggestions cited here. Discrete math might provide some preparation prior to reading Concrete Mathematics , but it seems to me that the relevant content from discrete mathematics is covered in the text.
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It certainly wouldn't hurt to study discrete mathematics perhaps take a look at Kenneth Rosen's Discrete Mathematics and its Applications ; it all depends on the time-frame you have available, your level of commitment, your capacity to stay focused, and the confidence you have in your abilities. For those who aren't familiar with the book Concrete Mathematics , an overview of the text can be found here. To save you some "web surfing time", I'll quote from that webpage below:.
Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study Chapter 1 Recurrent Problems 1.
Chapter 2 Sums 2. Chapter 3 Integer Functions 3. Chapter 4 Number Theory 4. Chapter 5 Binomial Coefficients 5. Chapter 6 Special Numbers 6. Chapter 7 Generating Functions 7. Chapter 8 Discrete Probability 8. Chapter 9 Asymptotics 9. My own feeling on this is that if you are an undergraduate in an engineering discipline, with the usual math sequence behind you e. You would be much better served starting with an introductory text I think Epp's Discrete Mathematics with Applications is excellent , and afterwards going to that book.
Concrete Mathematics is an amazing book, but it assumes you already know the basics that would be taught in a 1-semester course on the subject. The problems are superbly gauged, and even the answers which are provided for all the exercises often require significant thought to understand.
I am currently halfway through it and am just amazed at its density, how well written it is, and how perfectly the answers help one to solve the respective exercise without just giving the result away. But I have already been exposed to the discrete math basics and still find Concrete Mathematics is hard work. The preface may imply it can be read by a wide audience - there may be college sophomores in engineering programs who can handle this material. But they would be the rare exception. Sorry for being late to the party, but I have some recommendations that I feel are very helpful for prepping for Concrete Mathematics.
I agree with all previously posted answers and think they are pretty on key. I haven't read Concrete Mathematics yet, but I am currently taking a discrete math course at Utah State. After taking Calc.
I, and II and my current Discrete Math course I feel comfortable with all the notation I have seen so far in the book. Linear Algebra was not a pre-requisite for Discrete Math at my university, but at times I wish I had taken it. If this book is a reflection of my current class which in seems in the most part to be I would say you can most likely get by without Linear Algebra by only learning as you are going , but I am considering taking a course in it online now since I wish I better understood the concepts.
Beskrivning Art. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it!
Several new topics have been added, and the most significant ideas have been traced to their historical roots. The prerequisites for the book are fairly low; it assumes that you are somewhat familiar with discrete math, but does not require deep knowledge. In fact the subject matter is much closer to discrete math, but unlike typical discrete math texts it assumes you have already analyzed the problem and you have now some unwieldy formula or recursion that needs to be put into a more useful form.
This may sound very specialized, but in fact a large part of the work in discrete math problems is of this nature. Nearly all of the book deals strictly with discrete problems, and concentrates on manipulations to bring them into a usable form. The book includes a thorough discussion of the Gosper and the WZ Wilf—Zeilberger methods for evaluating finite sums and proving identities involving finite sums. Although designed as a textbook, the book is also a valuable reference, and is loaded with useful results, especially in the exercises all of which are solved in the back of the book.
This is my go-to book for any problem dealing with binomial coefficients, Fibonacci numbers, harmonic numbers, or evaluation of finite sums. Allen Stenger is a math hobbyist and retired software developer. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.
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