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An Introduction to Real Mathematics. A manual for mathematics teachers based on Alexey Savvateev's "100 Lessons in Mathematics" course.

Alexey Savvateev, Nikolai Kazimirov
29.99 €
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An Introduction to Real Mathematics. A manual for mathematics teachers based on Alexey Savvateev's "100 Lessons in Mathematics" course.
29.99 €
The publication is a detailed and finalized lecture notes of the video course "100 Lessons in Mathematics" by Alexey Savvateev, which was delivered at the Filippovskaya School (Moscow) in 2014-2018. The book presents the concept of number at different levels of rigor and complexity. Starting from simple geometric images describing ordinary arithmetic operations to complex algebraic concepts, the authors introduce the reader to the beginnings of number theory, group theory, linear algebra and complex ´ analysis. The book focuses on the following topics: motions and similarities of a straight line and plane, linear equations in integers, residue arithmetic, the ring of polynomials, the group of permutations, complex numbers, models of real numbers, and limit theory. The book deals with a number of well-known mathematical facts: the Main theorem of arithmetic, Schall's theorem, Fermat's theorem at n = 4, the insolubility of the problem of doubling the cube, Euler's formula, Cantor's theorem. The book pays special attention to the group-theoretic approach to the description of mathematical concepts and deals in detail with the structure of the permutation group and related problems. In addition, the completeness axiom (continuity principle) of the real numbers is studied in some detail, and the construction of the real and complex exponent is done. The book is provided with a large number of auxiliary drawings and illustrations (more than 100), as well as problems of varying complexity for independent solution (more than 800). The content covers such topics as: geometry, linear algebra, motions, group theory, complex numbers, mathematical analysis, polynomials, and the ring of Gaussian numbers.
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Author Alexey Savvateev, Nikolai Kazimirov
EDITORIAL. Dmitry Pozharsky University
ISBN 978-5-91244-307-7
BELOW solid
COUNTRIES 408
WEIGHT 0.76 kilogram
SIZE (WIDTH × HEIGHT) 171 x 242 mm
Format 70х100/16
YEAR OF PUBLICATION 2022

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