Concrete Mathematics: Mathematics is the mother of all the subjects and is the base of all the important inventions and discoveries from the stone wheel to the modern computer. Mathematics is, therefore, called the mother of all the progress and development that is taking place in the world. It provides the concrete foundation and base for the world to move on the path from unknown to known.
Computer maths is also very important field and is required to understand form understanding the main working method of the computer and its programming. Concrete maths is also used in the working of the computer and its functions. One should learn the basics of the mathematics before learning the computer programming as it is the key factor and is of great value for the computer programming.
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The book of the concrete maths gives complete introduction about the basic mathematics which helps the advanced computer programming and also the analyzing the algorithms. The main focus of the writer of the book is to give the fundamental and solid foundation about the skills in mathematics and the relevant field. These skills are strongly required for the evaluation of the horrendous sums and discovery of the subtle patterns in the data. It is the integral part of the text and references for the computer as well as the computer scientists. The people concerned with the field of the computer programming have to depend on them more than anything else.
The book is also helpful for the users of the mathematics in almost all the fields. The concrete mathematics is the mixture of the continuous and discrete mathematics. The writer of the book explains and clarifies that the computer is the controlled manipulation of the formulas of the mathematics. They programmers use and apply the number of techniques to solve the specific problems. The content and the subject matter of the book are to describe the expansion of the mathematical preliminaries section in the theory of the art of the computer programming by well known author Knuth. The author of the book has presented his book in a free style with the coverage of the individual topics.
The author of the book has added many new topics for the information of the new learners. He has also traced many new ideas and their origin for better understanding of their history and their role in the computer programming. He has chosen more than five hundred exercises which are divided into 6 categories. These exercises are also solved with logical manner for the comfort of the readers. Research problems are not given any solution as it requires understanding which can come through the uses of the personal efforts and struggle.
Major topics include:
- Sums
- Recurrences
- Integer functions
- Elementary number theory
- Binomial coefficients
- Generating functions
- Discrete probability
- Asymptotic methods
Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Hafiz Abdul Hameed
Master In Islamic Studies
(Tajweed, Waqf)
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