iwrite math foundations of mathematics 11

#Iwrite math foundations of mathematics 11 series#

His method anticipated that of the Dedekind cut in the modern definition of real numbers by Richard Dedekind (1831–1916). The discrepancy between rationals and reals was finally resolved by Eudoxus of Cnidus (408–355 BC), a student of Plato, who reduced the comparison of two irrational ratios to comparisons of multiples of the magnitudes involved. The discovery of the irrationality of √ 2, the ratio of the diagonal of a square to its side (around 5th century BC), was a shock to them which they only reluctantly accepted.

The Pythagorean school of mathematics originally insisted that only natural and rational numbers exist. 430 BC) produced four paradoxes that seem to show the impossibility of change. While the practice of mathematics had previously developed in other civilizations, special interest in its theoretical and foundational aspects was clearly evident in the work of the Ancient Greeks.Įarly Greek philosophers disputed as to which is more basic, arithmetic or geometry. Its high level of technical sophistication inspired many philosophers to conjecture that it can serve as a model or pattern for the foundations of other sciences.įurther information: Ancient Greek mathematics

#Iwrite math foundations of mathematics 11 series#

It went through a series of crises with paradoxical results, until the discoveries stabilized during the 20th century as a large and coherent body of mathematical knowledge with several aspects or components ( set theory, model theory, proof theory, etc.), whose detailed properties and possible variants are still an active research field. The systematic search for the foundations of mathematics started at the end of the 19th century and formed a new mathematical discipline called mathematical logic, which later had strong links to theoretical computer science. Mathematics' many developments towards higher abstractions in the 19th century brought new challenges and paradoxes, urging for a deeper and more systematic examination of the nature and criteria of mathematical truth, as well as a unification of the diverse branches of mathematics into a coherent whole. Mathematics plays a special role in scientific thought, serving since ancient times as a model of truth and rigor for rational inquiry, and giving tools or even a foundation for other sciences (especially Physics). The development, emergence, and clarification of the foundations can come late in the history of a field, and might not be viewed by everyone as its most interesting part. Generally, the foundations of a field of study refers to a more-or-less systematic analysis of its most basic or fundamental concepts, its conceptual unity and its natural ordering or hierarchy of concepts, which may help to connect it with the rest of human knowledge. The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic. The search for foundations of mathematics is a central question of the philosophy of mathematics the abstract nature of mathematical objects presents special philosophical challenges. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be vague.įoundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. Investigations, Explorations, or Review which include inquiry based learning that can be teacher led, student led, or a combination of both.Ĭlass Examples which are applications of the investigations, explorations or review.Īssignments which include short response, extended response, multiple choice, and numeric response questions provided for student practice.Īnswer Key which contains the answers to the assignment questions.Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. Most lessons can be covered in one hour (plus homework time), but some may require more time to complete. The last lesson in each unit is a practice test containing 15 multiple choice questions, 5 numeric response questions, and 1 extended response question.

Each curricular unit is subdivided into individual lessons. In addition, there is some enrichment material which can be completed individually or in groups. The Foundations of Mathematics 11 BC Edition Workbook is a complete resource and a 100% fit for the new British Columbia curriculum.