The Derivation of Mathematics

The Derivation of Mathematics is a logical, sequential and easy-to-learn introduction to Secondary School Mathematics for students, teachers and parents. The book begins by demonstrating that elementary Arithmetic that students learn in Primary School is a model of the Physical Counting System that children are taught in modern Preschools. This modelling process is the key to giving meaning to the mathematical symbols in Secondary School Mathematics and leads to the Holy Grail of Mathematics, which is, understanding the meaning of 'meaning' in Mathematics, as well as the meaning of 'True' and 'False'. This powerful insight is applied to the Elementary Number Systems in their natural order of complexity and allows these Number Systems to be built sequential and incrementally, chapter by chapter. First, there is a full derivation of all the key results of the Natural Number System. Second, the Natural Number System is supplemented with one elementary property in order to build the Integer Number System. Third, the Integer Number System is supplemented with another elementary property in order to build the Rational Number System. The equivalence of fractions, indices, decimals and percentages as Rational Numbers is then proved over several chapters. Fourth, and finally, the Rational Number System is supplemented with the Irrational Numbers to build the Real Number System, which is the number system used to measure most quantities in the Sciences. Throughout this development of the Number Systems of Secondary School Mathematics, there is a fundamental introduction to Algebra, Geometry and Limits which provides the key insights and development in these important areas of the Mathematics curriculum.