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Author: William E. Fenton Publisher: Springer Science & Business Media ISBN: 1461240522 Category : Mathematics Languages : en Pages : 206
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
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
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: Springer Science & Business Media ISBN: 1461235928 Category : Mathematics Languages : en Pages : 427
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: Oscar Levin Publisher: ISBN: 9781792901690 Category : Mathematics Languages : en Pages : 408
Book Description
Note: This is the 3rd edition. If you need the 2nd edition for a course you are taking, it can be found as a "other format" on amazon, or by searching its isbn: 1534970746 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. The book contains over 470 exercises, including 275 with solutions and over 100 with hints. There are also Investigate! activities throughout the text to support active, inquiry based learning. 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. This third edition brings improved exposition, a new section on trees, and a bunch of new and improved exercises. For a complete list of changes, and to view the free electronic version of the text, visit the book's website at discrete.openmathbooks.org
Author: V. K . Balakrishnan Publisher: Courier Corporation ISBN: 0486140385 Category : Mathematics Languages : en Pages : 260
Book Description
This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.
Author: Ilana Arnon Publisher: Springer Science & Business Media ISBN: 1461479665 Category : Education Languages : en Pages : 254
Book Description
In spite of the fact that APOS Theory has been used extensively in numerous scholarly publications, in the design of textbooks, and in teaching practice, there is no single references that contains all the relevant information about its components, and provides guidance about its application. The goal of this book is to present the main elements of APOS theory. It should be useful for researchers who work with, or would like to learn more about, this theoretical approach, people who are interested in the way which mathematical conceptions are constructed according to this theory, Mathematics Education researchers, graduate students in Mathematics Education, and Mathematics instructors.
Author: William E. Fenton
Author: William E. Fenton
Author: Nancy Baxter
Author: Nancy Baxter
Author: Nancy Baxter
Author: Oscar Levin
Author: Edward R. Scheinerman
Author: V. K . Balakrishnan
Author: Ilana Arnon
Author: R. Hirschfelder
Author: R. Hirschfelder