Sets, Logic and Maths for Computing

This easy-to-understand textbook introduces the mathematical language and problem-solving tools essential to anyone wishing to enter the world of computer and information sciences. Specifically designed for the student who is intimidated by mathematics, the book offers a concise treatment in an engaging style.

The thoroughly revised third edition features a new chapter on relevance-sensitivity in logical reasoning and many additional explanations on points that students find puzzling, including the rationale for various shorthand ways of speaking and 'abuses of language' that are convenient but can give rise to misunderstandings. Solutions are now also provided for all exercises.

Topics and features:

• Presents an intuitive approach, emphasizing how finite mathematics supplies a valuable language for thinking about computation
• Discusses sets and the mathematical objects built with them, such as relations and functions, as well as recursion and induction
• Introduces core topics of mathematics, including combinatorics and finite probability, along with the structures known as trees
• Examines propositional and quantificational logic, how to build complex proofs from simple ones, and how to ensure relevance in logic
• Addresses questions that students find puzzling but may have difficulty articulating, through entertaining conversations between Alice and the Mad Hatter

• Provides an extensive set of solved exercises throughout the text

  This clearly-written textbook offers invaluable guidance to students beginning an undergraduate degree in computer science. The coverage is also suitable for courses on formal methods offered to those studying mathematics, philosophy, linguistics, economics, and political science. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.

Dr. David Makinson has taught courses related to the material of this book at the American University of Beirut, King's College London and, in recent years, the London School of Economics, UK.

Autorentext

Dr. David Makinson has taught courses related to the material of this book at the American University of Beirut, King's College London and, in recent years, the London School of Economics, UK.

Zusammenfassung
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.

Inhalt

Part I: Sets

Collecting Things Together: Sets

Comparing Things: Relations

Associating One Item with Another: Functions

Recycling Outputs as Inputs: Induction and Recursion

Part II: Math

Counting Things: Combinatorics

Weighing the Odds: Probability

Squirrel Math: Trees

Part III: Logic

Yea and Nay: Propositional Logic

Something about Everything: Quantificational Logic

Just Supposing: Proof and Consequence

Sticking to the Point: Relevance in Logic