# More From Michael de Villiers

Making Democracy Fair: The mathematics of voting and apportionment
eBook (PDF): \$3.99
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? Is this a political or a mathematical decision? Or is it both?< Less
Elementary Logic
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
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
Making Democracy Fair: The mathematics of voting and apportionment
Paperback: \$15.00
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

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