Eng Guan Tay - Böcker

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory.The book builds on the verity that graph theory even at high school level is a subject that lends itself well to the development of mathematical reasoning and proof.This is an updated edition of two books already published with World Scientific, i.e., Introduction to Graph Theory: H3 Mathematics & Introduction to Graph Theory: Solutions Manual. The new edition includes solutions and hints to selected problems. This combination allows the book to be used as a textbook for undergraduate students. Professors can select unanswered problems for tutorials while students have solutions for reference.

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory.The book builds on the verity that graph theory even at high school level is a subject that lends itself well to the development of mathematical reasoning and proof.This is an updated edition of two books already published with World Scientific, i.e., Introduction to Graph Theory: H3 Mathematics & Introduction to Graph Theory: Solutions Manual. The new edition includes solutions and hints to selected problems. This combination allows the book to be used as a textbook for undergraduate students. Professors can select unanswered problems for tutorials while students have solutions for reference.

This book provides a one-stop resource for mathematics educators, policy makers and all who are interested in learning more about the why, what and how of mathematics education in Singapore. The content is organized according to three significant and closely interrelated components: the Singapore mathematics curriculum, mathematics teacher education and professional development, and learners in Singapore mathematics classrooms. Written by leading researchers with an intimate understanding of Singapore mathematics education, this up-to-date book reports the latest trends in Singapore mathematics classrooms, including mathematical modelling and problem solving in the real-world context.

This edited volume explores key areas of interests in Singapore math and science education including issues on teacher education, pedagogy, curriculum, assessment, teaching practices, applied learning, ecology of learning, talent grooming, culture of science and math, vocational education and STEM.

This edited volume explores key areas of interests in Singapore math and science education including issues on teacher education, pedagogy, curriculum, assessment, teaching practices, applied learning, ecology of learning, talent grooming, culture of science and math, vocational education and STEM.

This book is a useful, attractive introduction to basic counting techniques for upper secondary and junior college students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills.

This book is a useful, attractive introduction to basic counting techniques for upper secondary and junior college students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills.

This book is the essential companion to the authors' earlier book Counting (World Scientific, 2002), an introduction to combinatorics for junior college students. It provides supplementary material both for the purpose of adding to the reader's knowledge about counting techniques and, in particular, for use as a textbook for junior college students and teachers in combinatorics at H3 level in the new Singapore mathematics curriculum for junior college. The emphasis in combinatorics within the syllabus is to hone basic skills and techniques in general problem solving and logical thinking. The book also gives solutions to the exercises in Counting. There is often more than one method to solve a particular problem and the authors have included alternative solutions whenever they are of interest.

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college.The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college.The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

This is a companion to the book Introduction to Graph Theory (World Scientific, 2006). The student who has worked on the problems will find the solutions presented useful as a check and also as a model for rigorous mathematical writing. For ease of reference, each chapter recaps some of the important concepts and/or formulae from the earlier book.

This book is the first of its kind, as it includes both mathematics content and pedagogy. It is a professional instructional manual on how mathematical problem solving curriculum can be implemented in the classrooms. The book develops from the theoretical work of Polya and Schoenfeld, and explicates how these can be translated to the actual implementation in schools. It represents the work of a group of researchers from the Singapore National Institute of Education, after experimenting with it in the Singapore school classrooms.This book includes a set of scheme of work, lesson plans and a choice of mathematics problems that teachers can actually use in teaching problem solving. Certain pedagogical considerations are developed and suggested in this book. In addition, the book includes an assessment framework on how mathematical problem solving can be assessed.

This book in its Second Edition is a useful, attractive introduction to basic counting techniques for upper secondary to undergraduate students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills.New chapters originally from a supplementary book have been added in this edition to substantially increase the coverage of counting techniques. The new chapters include the Principle of Inclusion and Exclusion, the Pigeonhole Principle, Recurrence Relations, the Stirling Numbers and the Catalan Numbers. A number of new problems have also been added to this edition.

This book in its Second Edition is a useful, attractive introduction to basic counting techniques for upper secondary to undergraduate students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills.New chapters originally from a supplementary book have been added in this edition to substantially increase the coverage of counting techniques. The new chapters include the Principle of Inclusion and Exclusion, the Pigeonhole Principle, Recurrence Relations, the Stirling Numbers and the Catalan Numbers. A number of new problems have also been added to this edition.

This book is the essential companion to Counting (2nd Edition) (World Scientific, 2013), an introduction to combinatorics for secondary to undergraduate students. The book gives solutions to the exercises in Counting (2nd Edition). There is often more than one method to solve a particular problem and the authors have included alternative solutions whenever they are of interest.The rigorous and clear solutions will aid the reader in further understanding the concepts and applications in Counting (2nd Edition). An introductory section on problem solving as described by George Pólya will be useful in helping the lay person understand how mathematicians think and solve problems.

The book Making Mathematics Practical (published by World Scientific in 2011) proposes a new paradigm in teaching problem solving in secondary school mathematics classrooms. It is a report of the research project “Mathematical Problem Solving for Everyone” (MProSE), which attempts to provide all the necessary resources for teachers to teach problem solving in schools. This book reports as a follow-up on the actual enactment of the proposed MProSE problem solving curriculum in five Singapore schools. The experimental schools, which span across the entire spectrum of all Singapore secondary schools, report how they tweak the MProSE proposal to fit into their school curriculum, together with issues, challenges and success stories in implementing such an innovative curriculum in Singapore schools. It is an ideal handbook for educators who believe in problem solving as the core of mathematics curriculum and who wish to implement such an approach in their schools.

This book is an expansion of our first book Introduction to Graph Theory: H3 Mathematics. While the first book was intended for capable high school students and university freshmen, this version covers substantially more ground and is intended as a reference and textbook for undergraduate studies in Graph Theory. In fact, the topics cover a few modules in the Graph Theory taught at the National University of Singapore. The reader will be challenged and inspired by the material in the book, especially the variety and quality of the problems, which are derived from the authors' years of teaching and research experience.