Fundamentals of Discrete Math for Computer Science: A Problem-Solving Primer

Springer Science & Business Media
2
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An understanding of discrete mathematics is essential for students of computer science wishing to improve their programming competence.

Fundamentals of Discrete Math for Computer Science provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions.

Topics and features: highly accessible and easy to read, introducing concepts in discrete mathematics without requiring a university-level background in mathematics; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner, often including a walk-through demonstrating how the algorithm performs the desired task as expected; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question.

This easy-to-understand and fun-to-read textbook is ideal for an introductory discrete mathematics course for computer science students at the beginning of their studies. The book assumes no prior mathematical knowledge, and discusses concepts in programming as needed, allowing it to be used in a mathematics course taken concurrently with a student’s first programming course.

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About the author

Dr. Tom Jenkyns is an Associate Professor in the Department of Mathematics and the Department of Computer Science at Brock University, Canada.

Dr. Ben Stephenson is an Instructor in the Department of Computer Science at the University of Calgary, Canada.

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Reviews

4.0
2 total
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Additional Information

Publisher
Springer Science & Business Media
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Published on
Oct 16, 2012
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Pages
416
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ISBN
9781447140696
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Language
English
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Genres
Computers / Data Processing
Computers / Information Technology
Computers / Programming / Algorithms
Mathematics / Discrete Mathematics
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Content Protection
This content is DRM protected.
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Reading information

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Ben Stephenson
While other textbooks devote their pages to explaining introductory programming concepts, The Python Workbook focuses exclusively on exercises, following the philosophy that computer programming is a skill best learned through experience and practice.

Designed to support and encourage hands-on learning about programming, this student-friendly work contains 174 exercises, spanning a variety of academic disciplines and everyday situations. Solutions to selected exercises are also provided, supported by brief annotations that explain the technique used to solve the problem, or highlight specific points of Python syntax. No background knowledge is required to solve the exercises, beyond the material covered in a typical introductory Python programming course.

Features: uses an accessible writing style and easy-to-follow structure; includes a mixture of classic exercises from the fields of computer science and mathematics, along with exercises that connect to other academic disciplines; presents the solutions to approximately half of the exercises; provides annotations alongside the solutions, which explain the approach taken to solve the problem and relevant aspects of Python syntax; offers a variety of exercises of different lengths and difficulties; contains exercises that help the development of programming skills using if statements, loops, basic functions, lists, dictionaries, files, and recursive functions.

Undergraduate students undergoing their first programming course and wishing to enhance their programming abilities will find the exercises and solutions provided in this book to be ideal for their needs.

Gordon J. Pace
Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science.

The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs.

The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.
David Makinson
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduate students need to enter the world of computer and information sciences. 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. In ten chapters on these topics, the book guides the student through essential concepts and techniques.

The extensively revised second edition provides further clarification of matters that typically give rise to difficulty in the classroom and restructures the chapters on logic to emphasize the role of consequence relations and higher-level rules, as well as including more exercises and solutions.

Topics and features: teaches finite mathematics as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear away confusions; provides numerous exercises, with selected solutions, to test and deepen the reader’s understanding.

This clearly-written text/reference is a must-read for first-year undergraduate students of computing. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.

Ben Stephenson
While other textbooks devote their pages to explaining introductory programming concepts, The Python Workbook focuses exclusively on exercises, following the philosophy that computer programming is a skill best learned through experience and practice.

Designed to support and encourage hands-on learning about programming, this student-friendly work contains 174 exercises, spanning a variety of academic disciplines and everyday situations. Solutions to selected exercises are also provided, supported by brief annotations that explain the technique used to solve the problem, or highlight specific points of Python syntax. No background knowledge is required to solve the exercises, beyond the material covered in a typical introductory Python programming course.

Features: uses an accessible writing style and easy-to-follow structure; includes a mixture of classic exercises from the fields of computer science and mathematics, along with exercises that connect to other academic disciplines; presents the solutions to approximately half of the exercises; provides annotations alongside the solutions, which explain the approach taken to solve the problem and relevant aspects of Python syntax; offers a variety of exercises of different lengths and difficulties; contains exercises that help the development of programming skills using if statements, loops, basic functions, lists, dictionaries, files, and recursive functions.

Undergraduate students undergoing their first programming course and wishing to enhance their programming abilities will find the exercises and solutions provided in this book to be ideal for their needs.

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