Reasoning and Logic ME 3 4.
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- Fundamentals of Mathematics I.
Numeration System ME 4 5. Describing Sets ME 5 6.
Back to Basics: Mastering the Fundamentals of Mathematics
Divisibility ME 11 Prime and Composite Numbers ME 12 Integers and Addition and subtraction of Integers ME 14 Multiplication and Division of Integers ME 15 Introduction to Decimals ME 19 Operations on Decimals ME 20 Nonterminating Decimals ME 21 Real Numbers ME 22 The articles are well illustrated and supplied with references to the literature, both current and 'classical.
There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system.
In a few cases, more than two authors have collaborated. And the whole book has been coordinated in repeated conferences, involving altogether about authors and coordinators. Volume I opens with a section on mathematical foundations.
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It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials, rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn's lemma.
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Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology.
Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. Search Search. Search Advanced Search close Close. Preview Preview.
Fundamentals of Mathematics - Open Textbook Library
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