Concrete Mathematics is a highly acclaimed book written by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. It is a comprehensive and engaging guide that explores the intricate relationship between mathematics and computer science.
With its rigorous yet accessible approach, Concrete Mathematics has gained popularity among students, researchers, and professionals in the field.
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Benefits of Concrete Mathematics:
- Bridging the Gap: Concrete Mathematics fills the gap between elementary mathematics and more advanced mathematical concepts. It offers a unique perspective by combining mathematical theory with practical applications, making it an invaluable resource for those seeking a deeper understanding of mathematical reasoning.
- Problem-Solving Skills: The book focuses on the development of problem-solving skills, providing readers with numerous challenging exercises and examples. Through these exercises, readers can enhance their analytical thinking and problem-solving abilities, which are essential for success in computer science and mathematics.
- Fundamental Concepts: Concrete Mathematics delves into fundamental concepts such as recurrence relations, generating functions, and combinatorial analysis. These topics are crucial in various areas of computer science, including algorithm analysis, data structures, and cryptography. Mastering these concepts can significantly enhance one’s ability to tackle complex problems.
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Main Chapters and Subchapters:
- Recurrent Problems: a. Summation Notation and Recurrences b. Solving Recurrences c. Generating Functions
- Sums: a. Sums and Asymptotics b. Special Sums c. Manipulation of Sums
- Integer Functions: a. Integer Functions and Elementary Number Theory b. Partitions c. Generating Functions Revisited
- Number Theory: a. Integer Functions Revisited b. Integer Partitions Revisited c. Floor/Ceiling Applications
- Counting: a. Counting Subsets b. Generating Functions for Counting c. More on Counting
Product details –Concrete Mathematics
- Publisher : Addison-Wesley Professional; 2nd edition
- Language : English
- Hardcover : 672 pages
- ISBN-10 : 0201558025
- ISBN-13 : 978-0201558029
- Item Weight : 2.65 pounds
- Dimensions : 9.38 x 7.82 x 1.44 inches
Questions and Answers about Concrete Mathematics:
Q: Is Concrete Mathematics suitable for beginners?
A: While Concrete Mathematics assumes some mathematical background, it can be comprehended by motivated beginners. It serves as an excellent stepping stone for those transitioning from elementary mathematics to more advanced topics.
Q: What are the prerequisites for studying Concrete Mathematics?
A: Familiarity with calculus, elementary number theory, and basic discrete mathematics is beneficial. A solid understanding of mathematical proof techniques is also recommended.
Q: Is Concrete Mathematics only applicable to computer science?
A: Although the book emphasizes the intersection of mathematics and computer science, the concepts discussed have broader applications in various fields, including physics, engineering, and operations research.
Q: Are there solutions available for the exercises in Concrete Mathematics?
A: Yes, the book provides solutions to selected exercises, allowing readers to validate their answers and gain further insights into problem-solving techniques.
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Concrete Mathematics is a remarkable book that offers a unique approach to mathematical problem-solving. It equips readers with the necessary tools and techniques to tackle complex mathematical and computational challenges.
Whether you are a student, researcher, or professional in the field, this book will undoubtedly enhance your mathematical reasoning skills and broaden your understanding of the fundamental principles that underpin computer science and mathematics.
