Mathematical Foundations of Computer Science:
Mathematical Foundations of Computer Science introduces students to the discrete mathematics needed later in their Computer Science coursework with theory of computation topics interleaved throughout. Students learn about mathematical concepts just in time to apply them to theory of computation idea...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
Taylor & Francis
2024
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| Schlagworte: | |
| Zusammenfassung: | Mathematical Foundations of Computer Science introduces students to the discrete mathematics needed later in their Computer Science coursework with theory of computation topics interleaved throughout. Students learn about mathematical concepts just in time to apply them to theory of computation ideas. For instance, sets motivate the study of finite automata, direct proof is practised using closure properties, induction is used to prove the language of an automaton, and contradiction is used to apply the pumping lemma. The main content of the book starts with primitive data types such as sets and strings and ends with showing the undecidability of the halting problem. There are also appendix chapters on combinatorics, probability, elementary number theory, asymptotic notation, graphs, loop invariants, and recurrences. The content is laid out concisely with a heavy reliance on worked examples, of which there are over 250 in the book. Each chapter has exercises, totalling 550. This class-tested textbook is targeted to intermediate Computer Science majors, and it is primarily intended for a discrete math / proofs course in a Computer Science major. It is also suitable for introductory theory of computation courses.The authors hope this book breeds curiosity into the subject and is designed to satisfy this to some extent by reading this book. The book will prepare readers for deeper study of game theory applications in many fields of study |
| Beschreibung: | Preface; Chapter 1 ¦ Mathematical Data Types; 1.1 WHY YOU SHOULD CARE ; 1.2 SETS ; 1.3 SET TERMINOLOGY ; 1.4 SET-BUILDER NOTATION ; 1.5 UNION, INTERSECTION, DIFFERENCE, - COMPLEMENT ; 1.6 VENN DIAGRAMS ; 1.7 POWER SETS ; 1.8 TUPLES AND CARTESIAN PRODUCTS ; 1.9 FUNCTIONS ; 1.10 STRINGS ; - 1.11 LANGUAGES ; 1.12 CHAPTER SUMMARY AND KEY CONCEPTS ; Chapter 2 ¦ Deterministic Finite Automata ; 2.1 WHY YOU SHOULD CARE ; 2.2 A VENDING MACHINE EXAMPLE ; 2.3 FORMAL DEFINITION OF A DFA ; 2.4 MATCHING PHONE - NUMBERS ; 2.5 COMPUTATIONAL BIOLOGY ; 2.6 STOP CODONS ; 2.7 DIVVYING UP CANDY ; 2.8 DIVISIBILITY IN BINARY ; 2.9 CHAPTER SUMMARY AND KEY CONCEPTS ; Chapter 3 ¦ - Logic ; 3.1 WHY YOU SHOULD CARE ; 3.2 LOGICAL STATEMENTS ; 3.3 LOGICAL OPERATIONS ; 3.4 TRUTH TABLES ; - 3.5 CONDITIONAL STATEMENTS ; 3.6 QUANTIFIERS ; 3.7 BIG-O NOTATION ; 3.8 NEGATING LOGICAL STATEMENTS |
| Beschreibung: | 228 Seiten 421 gr |
| ISBN: | 9781032467870 |
Internformat
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| 500 | |a Preface; Chapter 1 ¦ Mathematical Data Types; 1.1 WHY YOU SHOULD CARE ; 1.2 SETS ; 1.3 SET TERMINOLOGY ; 1.4 SET-BUILDER NOTATION ; 1.5 UNION, INTERSECTION, DIFFERENCE, | ||
| 500 | |a - COMPLEMENT ; 1.6 VENN DIAGRAMS ; 1.7 POWER SETS ; 1.8 TUPLES AND CARTESIAN PRODUCTS ; 1.9 FUNCTIONS ; 1.10 STRINGS ; | ||
| 500 | |a - 1.11 LANGUAGES ; 1.12 CHAPTER SUMMARY AND KEY CONCEPTS ; Chapter 2 ¦ Deterministic Finite Automata ; 2.1 WHY YOU SHOULD CARE ; 2.2 A VENDING MACHINE EXAMPLE ; 2.3 FORMAL DEFINITION OF A DFA ; 2.4 MATCHING PHONE | ||
| 500 | |a - NUMBERS ; 2.5 COMPUTATIONAL BIOLOGY ; 2.6 STOP CODONS ; 2.7 DIVVYING UP CANDY ; 2.8 DIVISIBILITY IN BINARY ; 2.9 CHAPTER SUMMARY AND KEY CONCEPTS ; Chapter 3 ¦ | ||
| 500 | |a - Logic ; 3.1 WHY YOU SHOULD CARE ; 3.2 LOGICAL STATEMENTS ; 3.3 LOGICAL OPERATIONS ; 3.4 TRUTH TABLES ; | ||
| 500 | |a - 3.5 CONDITIONAL STATEMENTS ; 3.6 QUANTIFIERS ; 3.7 BIG-O NOTATION ; 3.8 NEGATING LOGICAL STATEMENTS | ||
| 520 | |a Mathematical Foundations of Computer Science introduces students to the discrete mathematics needed later in their Computer Science coursework with theory of computation topics interleaved throughout. Students learn about mathematical concepts just in time to apply them to theory of computation ideas. For instance, sets motivate the study of finite automata, direct proof is practised using closure properties, induction is used to prove the language of an automaton, and contradiction is used to apply the pumping lemma. The main content of the book starts with primitive data types such as sets and strings and ends with showing the undecidability of the halting problem. There are also appendix chapters on combinatorics, probability, elementary number theory, asymptotic notation, graphs, loop invariants, and recurrences. The content is laid out concisely with a heavy reliance on worked examples, of which there are over 250 in the book. Each chapter has exercises, totalling 550. This class-tested textbook is targeted to intermediate Computer Science majors, and it is primarily intended for a discrete math / proofs course in a Computer Science major. It is also suitable for introductory theory of computation courses.The authors hope this book breeds curiosity into the subject and is designed to satisfy this to some extent by reading this book. The book will prepare readers for deeper study of game theory applications in many fields of study | ||
| 650 | 4 | |a bicssc / Information technology - general issues | |
| 650 | 4 | |a bicssc / Algorithms & data structures | |
| 650 | 4 | |a bicssc / Coding theory & cryptology | |
| 650 | 4 | |a bicssc / Discrete mathematics | |
| 650 | 4 | |a bisacsh / COMPUTERS / Computer Science | |
| 650 | 4 | |a bisacsh / COMPUTERS / Languages / General | |
| 650 | 4 | |a bisacsh / COMPUTERS / Mathematical & Statistical Software | |
| 650 | 4 | |a bisacsh / MATHEMATICS / General | |
| 650 | 4 | |a bisacsh / MATHEMATICS / Applied | |
| 650 | 4 | |a bisacsh / MATHEMATICS / Discrete Mathematics | |
| 650 | 4 | |a bisacsh / MATHEMATICS / Logic | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035371622 | |
Datensatz im Suchindex
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| author | Lall, Ashwin |
| author_facet | Lall, Ashwin |
| author_role | aut |
| author_sort | Lall, Ashwin |
| author_variant | a l al |
| building | Verbundindex |
| bvnumber | BV050033738 |
| ctrlnum | (DE-599)BVBBV050033738 |
| format | Book |
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| id | DE-604.BV050033738 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-19T23:00:11Z |
| institution | BVB |
| isbn | 9781032467870 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035371622 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | 228 Seiten 421 gr |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Taylor & Francis |
| record_format | marc |
| spelling | Lall, Ashwin Verfasser aut Mathematical Foundations of Computer Science Boca Raton Taylor & Francis 2024 228 Seiten 421 gr txt rdacontent n rdamedia nc rdacarrier Preface; Chapter 1 ¦ Mathematical Data Types; 1.1 WHY YOU SHOULD CARE ; 1.2 SETS ; 1.3 SET TERMINOLOGY ; 1.4 SET-BUILDER NOTATION ; 1.5 UNION, INTERSECTION, DIFFERENCE, - COMPLEMENT ; 1.6 VENN DIAGRAMS ; 1.7 POWER SETS ; 1.8 TUPLES AND CARTESIAN PRODUCTS ; 1.9 FUNCTIONS ; 1.10 STRINGS ; - 1.11 LANGUAGES ; 1.12 CHAPTER SUMMARY AND KEY CONCEPTS ; Chapter 2 ¦ Deterministic Finite Automata ; 2.1 WHY YOU SHOULD CARE ; 2.2 A VENDING MACHINE EXAMPLE ; 2.3 FORMAL DEFINITION OF A DFA ; 2.4 MATCHING PHONE - NUMBERS ; 2.5 COMPUTATIONAL BIOLOGY ; 2.6 STOP CODONS ; 2.7 DIVVYING UP CANDY ; 2.8 DIVISIBILITY IN BINARY ; 2.9 CHAPTER SUMMARY AND KEY CONCEPTS ; Chapter 3 ¦ - Logic ; 3.1 WHY YOU SHOULD CARE ; 3.2 LOGICAL STATEMENTS ; 3.3 LOGICAL OPERATIONS ; 3.4 TRUTH TABLES ; - 3.5 CONDITIONAL STATEMENTS ; 3.6 QUANTIFIERS ; 3.7 BIG-O NOTATION ; 3.8 NEGATING LOGICAL STATEMENTS Mathematical Foundations of Computer Science introduces students to the discrete mathematics needed later in their Computer Science coursework with theory of computation topics interleaved throughout. Students learn about mathematical concepts just in time to apply them to theory of computation ideas. For instance, sets motivate the study of finite automata, direct proof is practised using closure properties, induction is used to prove the language of an automaton, and contradiction is used to apply the pumping lemma. The main content of the book starts with primitive data types such as sets and strings and ends with showing the undecidability of the halting problem. There are also appendix chapters on combinatorics, probability, elementary number theory, asymptotic notation, graphs, loop invariants, and recurrences. The content is laid out concisely with a heavy reliance on worked examples, of which there are over 250 in the book. Each chapter has exercises, totalling 550. This class-tested textbook is targeted to intermediate Computer Science majors, and it is primarily intended for a discrete math / proofs course in a Computer Science major. It is also suitable for introductory theory of computation courses.The authors hope this book breeds curiosity into the subject and is designed to satisfy this to some extent by reading this book. The book will prepare readers for deeper study of game theory applications in many fields of study bicssc / Information technology - general issues bicssc / Algorithms & data structures bicssc / Coding theory & cryptology bicssc / Discrete mathematics bisacsh / COMPUTERS / Computer Science bisacsh / COMPUTERS / Languages / General bisacsh / COMPUTERS / Mathematical & Statistical Software bisacsh / MATHEMATICS / General bisacsh / MATHEMATICS / Applied bisacsh / MATHEMATICS / Discrete Mathematics bisacsh / MATHEMATICS / Logic |
| spellingShingle | Lall, Ashwin Mathematical Foundations of Computer Science bicssc / Information technology - general issues bicssc / Algorithms & data structures bicssc / Coding theory & cryptology bicssc / Discrete mathematics bisacsh / COMPUTERS / Computer Science bisacsh / COMPUTERS / Languages / General bisacsh / COMPUTERS / Mathematical & Statistical Software bisacsh / MATHEMATICS / General bisacsh / MATHEMATICS / Applied bisacsh / MATHEMATICS / Discrete Mathematics bisacsh / MATHEMATICS / Logic |
| title | Mathematical Foundations of Computer Science |
| title_auth | Mathematical Foundations of Computer Science |
| title_exact_search | Mathematical Foundations of Computer Science |
| title_full | Mathematical Foundations of Computer Science |
| title_fullStr | Mathematical Foundations of Computer Science |
| title_full_unstemmed | Mathematical Foundations of Computer Science |
| title_short | Mathematical Foundations of Computer Science |
| title_sort | mathematical foundations of computer science |
| topic | bicssc / Information technology - general issues bicssc / Algorithms & data structures bicssc / Coding theory & cryptology bicssc / Discrete mathematics bisacsh / COMPUTERS / Computer Science bisacsh / COMPUTERS / Languages / General bisacsh / COMPUTERS / Mathematical & Statistical Software bisacsh / MATHEMATICS / General bisacsh / MATHEMATICS / Applied bisacsh / MATHEMATICS / Discrete Mathematics bisacsh / MATHEMATICS / Logic |
| topic_facet | bicssc / Information technology - general issues bicssc / Algorithms & data structures bicssc / Coding theory & cryptology bicssc / Discrete mathematics bisacsh / COMPUTERS / Computer Science bisacsh / COMPUTERS / Languages / General bisacsh / COMPUTERS / Mathematical & Statistical Software bisacsh / MATHEMATICS / General bisacsh / MATHEMATICS / Applied bisacsh / MATHEMATICS / Discrete Mathematics bisacsh / MATHEMATICS / Logic |
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