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Reviews
1. Concrete Mathematics: A Foundation for Computer Science (2nd Edition)
Description
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. 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! - but for serious users of mathematics in virtually every discipline.
Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study.
Major topics include:
- Sums
- Recurrences
- Integer functions
- Elementary number theory
- Binomial coefficients
- Generating functions
- Discrete probability
- Asymptotic methods
This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. 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.
2. Concrete Mathematics: A Foundation for Computer Science
Description
Will be shipped from US. Used books may not include companion materials, may have some shelf wear, may contain highlighting/notes, may not include CDs or access codes. 100% money back guarantee.3. Sets, Logic and Maths for Computing (Undergraduate Topics in Computer Science)
Description
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof.4. Introductory Discrete Mathematics (Dover Books on Computer Science)
Description
Chapters 03 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material.
Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization the minimal spanning tree problem and the shortest distance problem are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix.
5. Concrete Mathematics: A Foundation for Computer Science by Ronald L. Graham (1988-09-01)
6. Foundation Mathematics for Computer Science: A Visual Approach
Description
John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approachwill greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications.Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts.
Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the authors literary style refreshingly lucid and engaging, and prepare you for more advanced texts.
7. Mathematics for Computer Science
Description
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
8. Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More!
Feature
No Starch PressDescription
Doing Math with Python shows you how to use Python to delve into high schoollevel math topics like statistics, geometry, probability, and calculus. Youll start with simple projects, like a factoring program and a quadratic-equation solver, and then create more complex projects once youve gotten the hang of things.Along the way, youll discover new ways to explore math and gain valuable programming skills that youll use throughout your study of math and computer science. Learn how to:
Describe your data with statistics, and visualize it with line graphs, bar charts, and scatter plots
Explore set theory and probability with programs for coin flips, dicing, and other games of chance
Solve algebra problems using Pythons symbolic math functions
Draw geometric shapes and explore fractals like the Barnsley fern, the Sierpinski triangle, and the Mandelbrot set
Write programs to find derivatives and integrate functions
Creative coding challenges and applied examples help you see how you can put your new math and coding skills into practice. Youll write an inequality solver, plot gravitys effect on how far a bullet will travel, shuffle a deck of cards, estimate the area of a circle by throwing 100,000 "darts" at a board, explore the relationship between the Fibonacci sequence and the golden ratio, and more.
Whether youre interested in math but have yet to dip into programming or youre a teacher looking to bring programming into the classroom, youll find that Python makes programming easy and practical. Let Python handle the grunt work while you focus on the math.
Uses Python 3
9. From Mathematics to Generic Programming
Description
In this substantive yet accessible book, pioneering software designer Alexander Stepanov and his colleague Daniel Rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based, helping you write code that is both simpler and more powerful.
If youre a reasonably proficient programmer who can think logically, you have all the background youll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem.
As you read this book, youll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. Youll also gain deep insight into the value of mathematics to programminginsight that will prove invaluable no matter what programming languages and paradigms you use.
You will learn about
- How to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiency
- Ancient paradoxes, beautiful theorems, and the productive tension between continuous and discrete
- A simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on it
- Powerful mathematical approaches to abstraction
- How abstract algebra provides the idea at the heart of generic programming
- Axioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structures
- Surprising subtleties of simple programming tasks and what you can learn from them
- How practical implementations can exploit theoretical knowledge
10. Companion to Concrete Mathematics (Dover Books on Mathematics)
Description
Since it addresses topics of varying complexityfrom number-multiplication games and other recreational mathematics to the zeros of the Riemann zeta function and the presumed transcendence of Euler's constantthis volume can be used by readers of every background. Beginners will find it a source of useful techniques and subjects not usually taught in standard courses. They'll also discover connections between seemingly unrelated aspects of mathematics. Experienced mathematicians can rely upon the book as a source of problems and information on branches beyond their specialties. Other professionalstheoretical physicists and chemists, engineers, numerical analysts, and computer scientistswill also consider it a valuable reference.