Learn how to use discrete mathematics to become a better programmer. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in. If youre having a hard time with concrete mathematics, some of the suggestions in the first link in the parent post might be helpful. The subject matter is primarily an expansion of the mathematical preliminaries section in knuths classic art of. Pdf concrete mathematics a foundation for computer. Is there any prerequisite necessary to read concrete. Concrete mathematics is a different kind of book altogether and doesnt really belong in the discussion. Discrete math deals with values that come in indivisible units. Think of digital watches versus analog watches ones where the. Were not bold enough to try distinuous mathematics. I recommend the book concrete mathematics by ronald graham, donald knuth, and oren patashnik. More concretely, the authors explain, it is the controlled manipulation of. This book focuses on practical skills rather than theory.
In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Youll take probability theory even further within concrete mathematics and use practice problems to hone your skills. Whats the difference between concrete and discrete. The distinction between discrete and calc is arbitrary to begin with, or at least does not appear in applications, hence the concrete math. Pdf concrete mathematics download full pdf book download. Adu was a oneyear, intensive postbaccalaureate program in computer science based on the undergraduate course of study at the massachusetts institute of technology mit. What books do you recommend before concrete mathematics. This book is written as a companion to concrete mathematics graham, knuth, and patashnik 1. I read mathematics for computer science mcs and found it excellent. Calculus is frequently used in the explanations and exercises. An invitation to discrete mathematics by jiri matousek and jaroslav nesetril is quite nice.
We usually draw our distinctions between discrete and continuous, or between abstract and concrete. Number theory, which concerns itself with such problems involving natural numbers as divisibility and remainders, is discrete math. It should therefore relate to solving practical problems with the appropriate tools instead of seizing a problem as a way to construct an abstract structure and dig into its properties with full generalizati. However, it seems you are looking for a book to cram for a test in discrete math. Also, i totally second concrete mathematics that book rocks. More concretely, the authors explain, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. It contains many examples, tricks of trade, and problems with solutions. The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. Because this book is written in an executable notation, any expression can be entered directly on a computer for experimentation. We discuss the idea of concrete mathematics inspired by hilberts idea of finitistic mathematics as the part of mathematics not engaged into actual infinity. The role of discrete mathematics in applications in computer science. In contrast, continuous mathematics deals with objects that vary continuously, e.
Why is discrete mathematics required for data structures. Recurrences and generating functions in algorithms. Data can be descriptive like high or fast or numerical numbers. The book is based on a course begun in 1970 by knuth at stanford university. Why does undergraduate discrete math require calculus. I sampled discrete mathematics and its applications rosencurrently recommended in miris research guideas well as concrete mathematics and discrete mathematics with applications epp, which appear to be mcss competition. It is an indispensable text and reference not only for computer scientists the authors themselves rely heavily on it. Concrete mathematics wikimili, the best wikipedia reader. Based on these partial readings, i found mcs to be the best overall text. You can also take classes on programming methods, propositional logic, and theory of computation. The role of formal definitions, formal and informal mathematical proofs, and underlying algorithmic thinking, and be able to apply them in problem solving. Concrete and abstract representations using mathematical. Then i abruptly end the conversion by saying, wait whats discrete again and he says look it up.
Discrete mathematics for computer science some notes jean gallier abstract. Discrete mathematics is math that makes use of discrete structures. Learn discrete mathematics with online courses edx. 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. Therefore the subject needs a distinctive name, and \ concrete mathematics has proved to be as suitable as any other. Discrete mathematics for computer science some notes. The intriguing title concrete math is explained as being in contrast to abstract math, and a little less plausibly as a portmanteau of continuous and discrete math. Often undergraduate discrete math classes in the us have a calculus prerequisite. Rosen discrete math, cormen algorithms will find this book both. Whats the difference between concrete and discrete mathematics. The analysis of algorithms requires the ability to count the number of operations in. A foundation for computer science, 2nd edition by ronald l. It advertises itself as introductory, and can certainly be used as an introduction, but it has a great load of interesting problems and is a lot of fun to read. Concrete mathematics is the second most accessible book by knuth as one of the coauthors.
The majority of the instructors were professors from mit and the program was tuition free. Discrete mathematics deals with objects that come in discrete bundles, e. Concrete mathematics a blend of continuous and discrete mathematics. According to the preface, the topics in concrete mathematics are a blend of continuous and discrete mathematics. One of the first and most important steps to implementing the cra approach in the classroom is to use appropriate concrete objects to teach particular math conceptsskills. In reality, discrete mathematics is just that, math dealing with discrete values. Donald knuth my class on concrete mathematics 7997. Or you can explore other avenues of discrete mathematics such as game theory or discrete. Personally i would suggest kenneth rosens discrete mathematics and its applications if you want an easier first discrete math book. These are notes on discrete mathematics for computer scientists. I was talking to my classmate on how mathematics everything is rational, fact and possesses concrete ideas. For this reason, discrete mathematics often come up when studying the complexity of algorithms on data structures. Emphasis will be placed on providing a context for the application of the mathematics within computer science. You have to really read the work, and really work the problems.
According to the preface, the topics in concrete mathematics are a blend of continuous and discrete. Graham, discrete mathematics with applications by su. The term concrete mathematics also denotes a complement to abstract mathematics. I sampled discrete mathematics and its applications rosencurrently recommended in miris research guideas well as concrete. Find out about the role of math in programming, and how to use discrete math. I said that the word concrete doesnt really mean the opposite of abstract, its a. Here is the description of the discrete math course from my undergrad. The original textbook for stanfords course on concrete mathematics was. Concrete mathematics a foundation for computer science graham knuth patashnik contents.