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Discrete Mathematics and Applications - Kevin Ferland

Discrete Mathematics and Applications

(Autor)

Buch | Softcover
944 Seiten
2023 | 2nd edition
CRC Press (Verlag)
978-1-032-47689-6 (ISBN)
CHF 76,75 inkl. MwSt
This book is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs, then moves on to topics in number theory, employin
Discrete Mathematics and Applications, Second Edition is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book.



Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.









Emphasizes proofs, which will appeal to a subset of this course market



Links examples to exercise sets



Offers edition that has been heavily reviewed and developed



Focuses on graph theory



Covers trees and algorithms

Kevin Ferland

I Proofs



Logic and Sets



Statement Forms and Logical Equivalences



Set Notation



Quantifiers



Set Operations and Identities



Valid Arguments



Basic Proof Writing



Direct Demonstration



General Demonstration (Part 1)



General Demonstration (Part 2)



Indirect Arguments



Splitting into Cases



Elementary Number Theory



Divisors



Well-Ordering, Division, and Codes



Euclid's Algorithm and Lemma



Rational and Irrational Numbers



Modular Arithmetic and Encryption



Indexed by Integers



Sequences, Indexing, and Recursion



Sigma Notation



Mathematical Induction, An Introduction



Induction and Summations



Strong Induction



The Binomial Theorem



Relations



General Relations



Special Relations on Sets



Basics of Functions



Special Functions



General Set Constructions



Cardinality



II Combinatorics



Basic Counting



The Multiplication Principle



Permutations and Combinations



Addition and Subtraction



Probability



Applications of Combinations



Correcting for Overcounting



More Counting



Inclusion-Exclusion



Multinomial Coecients



Generating Functions



Counting Orbits



Combinatorial Arguments



Basic Graph Theory



Motivation and Introduction



Special Graphs



Matrices



Isomorphisms



Invariants



Directed Graphs and Markov Chains



Graph Properties



Connectivity



Euler Circuits



Hamiltonian Cycles



Planar Graphs



Chromatic Number



Trees and Algorithms



Trees



Search Trees



Weighted Trees



Analysis of Algorithms (Part 1)



Analysis of Algorithms (Part 2)



A Assumed Properties of Z and R



B Pseudocode



C Answers to Selected Exercises

Erscheinungsdatum
Reihe/Serie Textbooks in Mathematics
Zusatzinfo 893 Illustrations, black and white
Verlagsort London
Sprache englisch
Maße 178 x 254 mm
Gewicht 1741 g
Themenwelt Mathematik / Informatik Informatik Betriebssysteme / Server
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 1-032-47689-3 / 1032476893
ISBN-13 978-1-032-47689-6 / 9781032476896
Zustand Neuware
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