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Logical Methods
The Art of Thinking Abstractly and Mathematically
Taschenbuch von Roger Antonsen
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
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:
[...]

Zusammenfassung

Provides a solid foundation for beginning students in mathematics or computer science

Introduces the basics of set theory, logic, mathematical proofs, combinatorics, graph theory, and much more, in a clear and understandable way

Contains many colorful figures and illustrations, as well as hundreds of exercises

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2021
Genre: Informatik, Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xiv
288 S.
10 farbige Illustr.
288 p. 10 illus. in color.
ISBN-13: 9783030637767
ISBN-10: 303063776X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Antonsen, Roger
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 240 x 168 x 17 mm
Von/Mit: Roger Antonsen
Erscheinungsdatum: 11.02.2021
Gewicht: 0,514 kg
Artikel-ID: 119079161
Über den Autor
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:
[...]

Zusammenfassung

Provides a solid foundation for beginning students in mathematics or computer science

Introduces the basics of set theory, logic, mathematical proofs, combinatorics, graph theory, and much more, in a clear and understandable way

Contains many colorful figures and illustrations, as well as hundreds of exercises

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2021
Genre: Informatik, Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xiv
288 S.
10 farbige Illustr.
288 p. 10 illus. in color.
ISBN-13: 9783030637767
ISBN-10: 303063776X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Antonsen, Roger
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 240 x 168 x 17 mm
Von/Mit: Roger Antonsen
Erscheinungsdatum: 11.02.2021
Gewicht: 0,514 kg
Artikel-ID: 119079161
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