Introduction to Discrete Mathematics with ISETL PDF Download
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Author: William E. Fenton
Publisher: Springer Science & Business Media
ISBN: 1461240522
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Intended for first- or second-year undergraduates, this introduction to discrete mathematics covers the usual topics of such a course, but applies constructivist principles that promote - indeed, require - active participation by the student. Working with the programming language ISETL, whose syntax is close to that of standard mathematical language, the student constructs the concepts in her or his mind as a result of constructing them on the computer in the syntax of ISETL. This dramatically different approach allows students to attempt to discover concepts in a "Socratic" dialog with the computer. The discussion avoids the formal "definition-theorem" approach and promotes active involvement by the reader by its questioning style. An instructor using this text can expect a lively class whose students develop a deep conceptual understanding rather than simply manipulative skills. Topics covered in this book include: the propositional calculus, operations on sets, basic counting methods, predicate calculus, relations, graphs, functions, and mathematical induction.
Author: William E. Fenton
Publisher: Springer Science & Business Media
ISBN: 1461240522
Category : Mathematics
Languages : en
Pages : 206
Get Book Here
Book Description
Intended for first- or second-year undergraduates, this introduction to discrete mathematics covers the usual topics of such a course, but applies constructivist principles that promote - indeed, require - active participation by the student. Working with the programming language ISETL, whose syntax is close to that of standard mathematical language, the student constructs the concepts in her or his mind as a result of constructing them on the computer in the syntax of ISETL. This dramatically different approach allows students to attempt to discover concepts in a "Socratic" dialog with the computer. The discussion avoids the formal "definition-theorem" approach and promotes active involvement by the reader by its questioning style. An instructor using this text can expect a lively class whose students develop a deep conceptual understanding rather than simply manipulative skills. Topics covered in this book include: the propositional calculus, operations on sets, basic counting methods, predicate calculus, relations, graphs, functions, and mathematical induction.
Author: Nancy Baxter
Publisher: Springer
ISBN: 9780387968988
Category : Mathematics
Languages : en
Pages : 416
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Book Description
The title of this book, Learning Discrete Mathematics with ISETL raises two issues. We have chosen the word "Learning" rather than "Teaching" because we think that what the student does in order to learn is much more important than what the professor does in order to teach. Academia is filled with outstanding mathematics teachers: excellent expositors, good organizers, hard workers, men and women who have a deep understanding of Mathematics and its applications. Yet, when it comes to ideas in Mathe matics, our students do not seem to be learning. It may be that something more is needed and we have tried to construct a book that might provide a different kind of help to the student in acquiring some of the fundamental concepts of Mathematics. In a number of ways we have made choices that seem to us to be the best for learning, even if they don't always completely agree with standard teaching practice. A second issue concerns students' writing programs. ISETL is a pro gramming language and by the phrase "with ISETL" in the title, we mean that our intention is for students to write code, think about what they have written, predict its results, and run their programs to check their predic tions. There is a trade-off here. On the one hand, it can be argued that students' active involvement with constructing Mathematics for themselves and solving problems is essential to understanding concepts.
Author: Nancy Baxter
Publisher:
ISBN: 9781461235934
Category :
Languages : en
Pages : 440
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Book Description
Author: Oscar Levin
Publisher: Createspace Independent Publishing Platform
ISBN: 9781724572639
Category :
Languages : en
Pages : 238
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Book Description
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Author: Calvin Jongsma
Publisher: Springer Nature
ISBN: 3030253589
Category : Mathematics
Languages : en
Pages : 482
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Book Description
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades. Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include: Mathematical and structural induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.
Author: Jon Pierre Fortney
Publisher: CRC Press
ISBN: 1000296644
Category : Mathematics
Languages : en
Pages : 272
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Book Description
Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees. Features Designed to be especially useful for courses at the community-college level Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook.
Author: Nancy Baxter
Publisher: Springer Science & Business Media
ISBN: 1461235928
Category : Mathematics
Languages : en
Pages : 427
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Book Description
The title of this book, Learning Discrete Mathematics with ISETL raises two issues. We have chosen the word "Learning" rather than "Teaching" because we think that what the student does in order to learn is much more important than what the professor does in order to teach. Academia is filled with outstanding mathematics teachers: excellent expositors, good organizers, hard workers, men and women who have a deep understanding of Mathematics and its applications. Yet, when it comes to ideas in Mathe matics, our students do not seem to be learning. It may be that something more is needed and we have tried to construct a book that might provide a different kind of help to the student in acquiring some of the fundamental concepts of Mathematics. In a number of ways we have made choices that seem to us to be the best for learning, even if they don't always completely agree with standard teaching practice. A second issue concerns students' writing programs. ISETL is a pro gramming language and by the phrase "with ISETL" in the title, we mean that our intention is for students to write code, think about what they have written, predict its results, and run their programs to check their predic tions. There is a trade-off here. On the one hand, it can be argued that students' active involvement with constructing Mathematics for themselves and solving problems is essential to understanding concepts.
Author: Steven Roman
Publisher: W.B. Saunders Company
ISBN:
Category : Mathematics
Languages : en
Pages : 480
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Book Description
Author: Jean Gallier
Publisher: Springer Science & Business Media
ISBN: 1441980474
Category : Mathematics
Languages : en
Pages : 473
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Book Description
This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs.
Author: Eric Gossett
Publisher: John Wiley & Sons
ISBN: 0470457937
Category : Mathematics
Languages : en
Pages : 932
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Book Description
A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.
