Logical Methods

The Art of Thinking Abstractly and Mathematically

Roger Antonsen

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English

Springer Nature Switzerland AG
11 February 2021

Mathematical foundations; Mathematical logic; Discrete mathematics; Maths for computer scientists

Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science,

its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more.

In the book you will, among other things, find answers to:

What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something?

How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower?

Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.

By: Roger Antonsen
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2021
Dimensions: Height: 240mm, Width: 168mm,
Weight: 518g
ISBN: 9783030637767
ISBN 10: 303063776X
Pages: 288
Publication Date: 11 February 2021
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Active

Preface.- 0 The Art of Thinking Abstractly and Mathematically.- 1 Basic Set Theory.- 2 Propositional Logic.- 3 Semantics from Propositional Logic.- 4 Concepts in Propositional Logic.- 5 Proofs, Conjectures, and Counterexamples.- 6 Relations.- 7 Functions.- 8 A Little More Set Theory.- 9 Closures and Inductively Defined Sets.- 10 Recursively Defined Functions.- 11 Mathematical Induction.- 12 Structural Induction.- 13 First-Order Languages.- 14 Representation of Quantified Statements.- 15 Interpretation in Models.- 16 Reasoning About Models.- 17 Abstraction with Equivalences and Partitions.- 18 Combinatorics.- 19 A Little More Combinatorics.- 20 A Bit of Abstract Algebra.- 21 Graph Theory.- 22 Walks in Graphs.- 23 Formal Languages and Grammars.- 24 Natural Deduction.- The Road Ahead.- Index. Symbols.

Roger Antonsen is Associate Professor in the Department of Informatics at the University of Oslo, where he has taught Logical Methods to thousands of students since 2010. He is a logician, mathematician, computer scientist, author, public speaker, science communicator, and artist. His interests range from proof theory, cellular automata, algorithms, and complexity to science communication, outreach, digital art, and visualizations.To see Roger in action as a science communicator, watch his TED Talk: ted.com/speakers/roger_antonsen

Reviews for Logical Methods: The Art of Thinking Abstractly and Mathematically

From personal teaching experience, knowledge of these mathematical areas is necessary for disparate fields of CS and informatics. These foundations are needed for many fields, from database theory to various domains of information systems applications. The book's presentation of topics and incentives for problem-solving, along with its exercises, is very useful for university-level instructors and students. The compact chapters contain clear explanations, diagrams, and brief descriptions of interesting facts. (Balint Molnar, Computing Reviews, July 27, 2021)