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Elementary Logic By Michael de Villiers
Paperback: $11.96
Prints in 3-5 business days
The book is suitable for learners and students from Grade 9 upwards to undergraduate level, and provides firstly an elementary introduction to the fundamental concepts of an implication, equivalence,... More > quantifiers, necessary and sufficient conditions, etc. Thereafter, some basic laws of logic such as Modus Ponens, Contrapositive, Disjunctive Inference, Syllogism, etc. are discussed. Some basic methods of proof such as mathematical induction, direct proof, proof by contradiction, etc. are illustrated with examples from the high school mathematics curriculum. Throughout the book concepts and logical reasoning are discussed with reference to many everyday examples as well as examples from high school algebra, elementary number theory, geometry and trigonometry.< Less
Elementary Logic By Michael de Villiers
eBook (PDF): $0.00
The book is suitable for learners and students from Grade 9 upwards to undergraduate level, and provides firstly an elementary introduction to the fundamental concepts of an implication, equivalence,... More > quantifiers, necessary and sufficient conditions, etc. Thereafter, some basic laws of logic such as Modus Ponens, Contrapositive, Disjunctive Inference, Syllogism, etc. are discussed. Some basic methods of proof such as mathematical induction, direct proof, proof by contradiction, etc. are illustrated with examples from the high school mathematics curriculum. Throughout the book concepts and logical reasoning are discussed with reference to many everyday examples as well as examples from high school algebra, elementary number theory, geometry and trigonometry.< Less
Some Adventures in Euclidean Geometry By Michael de Villiers
eBook (ePub): $9.99
This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean... More > geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.< Less
Boolean Algebra at School, Vol 1 By Michael de Villiers
eBook (PDF): $0.00
The main focus of this book is on actively engaging students in the mathematical processes of modeling and axiomatization. The book starts off with some challenging problems involving switching... More > circuits. Students are then engaged in gradually developing a mathematical model in order to solve these problems. Suitable notation is firstly introduced for series and parallel switches, and then followed by truth tables, and the discovery of several interesting mathematical properties related to switching circuits. After development of the model and solution of the original problems, a section on systematization follows where students are led through some proof activities to identify a suitable set of axioms. The book concludes with a short historical overview of the development and application of Boolean Algebra.< Less
Some Adventures in Euclidean Geometry By Michael de Villiers
eBook (PDF): $4.00
This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean... More > geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.< Less
Boolean Algebra at School, Vol 2 By Michael de Villiers
eBook (PDF): $0.00
This volume is the Teacher's Guide to the student text, Boolean Algebra at School, Volume 1. It provides a more detailed discussion and formal exposition of Boolean Algebra as well as a few more... More > examples of Boolean Algebras. The Teacher's Guide also provides a rationale for the approach used in Volume 1, discussing why applications and modeling are important, aspects of pure mathematics like duality, the reconstructive teaching approach, and the promotion and development of creative problem solving. Lastly, the book provides two sample test papers with worked solutions, and further references to related resources on Boolean Algebra, Logic and Switching Circuits.< Less
Boolean Algebra at School, Vol 2 By Michael de Villiers
Paperback: $11.00
Prints in 3-5 business days
This volume is the Teacher's Guide to the student text, Boolean Algebra at School, Volume 1. It provides a more detailed discussion and formal exposition of Boolean Algebra as well as a few more... More > examples of Boolean Algebras. The Teacher's Guide also provides a rationale for the approach used in Volume 1, discussing why applications and modeling are important, aspects of pure mathematics like duality, the reconstructive teaching approach, and the promotion and development of creative problem solving. Lastly, the book provides two sample test papers with worked solutions, and further references to related resources on Boolean Algebra, Logic and Switching Circuits.< Less
Boolean Algebra at School, Vol 1 By Michael de Villiers
Paperback: $15.00
Prints in 3-5 business days
The main focus of this book is on actively engaging students in the mathematical processes of modeling and axiomatization. The book starts off with some challenging problems involving switching... More > circuits. Students are then engaged in gradually developing a mathematical model in order to solve these problems. Suitable notation is firstly introduced for series and parallel switches, and then followed by truth tables, and the discovery of several interesting mathematical properties related to switching circuits. After development of the model and solution of the original problems, a section on systematization follows where students are led through some proof activities to identify a suitable set of axioms. The book concludes with a short historical overview of the development and application of Boolean Algebra.< Less
Some Adventures in Euclidean Geometry By Michael de Villiers
Paperback: List Price: $19.99 $18.99 | You Save: 5%
Prints in 3-5 business days
This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean... More > geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.< Less
Making Democracy Fair: The mathematics of voting and apportionment By Michael de Villiers, Leslie Johnson Nielsen
Paperback: $15.00
Prints in 3-5 business days
How do you know if an election is fair? Or if the result truly represents the choice of the people? In Making Democracy Fair students use elementary mathematical methods to explore different kinds of... More > ballots, election decision procedures, and apportionment methods. In the first half of the book, students are introduced to a variety of alternatives to the “winner take all” strategy used in most elections. Determining which strategy is fairest is usually a very difficult question to answer, and many times the strategy chosen determines the winner. In the second part of the book, students investigate different methods of apportionment. How many representatives from each state will there be in the United States House of Representatives? How do countries using a proportional representation decide on the number of representatives from each political party to be seated in their government bodies?< Less