Easy as p?: An Introduction to Higher MathematicsThe present book is rare, even unique of its kind, at least among mathematics texts published in Russian. You have before you neither a textbook nor a monograph, although these selected chapters from elementary mathematics certainly constitute a fine educational tool. It is my opinion that this is more than just another book about mathematics and the art of teaching that subject. Without considering the actual topics treated (the author himself has described these in sufficient detail in of the book as a whole, the Introduction), I shall attempt to convey a general idea and describe the impressions it makes on the reader. Almost every chapter begins by considering well-known problems of elementary mathematics. Now, every worthwhile elementary problem has hidden behind its diverting formulation what might be called "higher mathematics," or, more simply, mathematics, and it is this that the author demonstrates to the reader in this book. It is thus to be expected that every chapter should contain subject matter that is far from elementary. The end result of reading the book is that the material treated has become for the reader "three-dimensional" as it were, as in a hologram, capable of being viewed from all sides. |
Contents
IV | 1 |
V | 3 |
VI | 5 |
VII | 6 |
VIII | 8 |
IX | 13 |
X | 16 |
XI | 21 |
XXXVI | 98 |
XXXVII | 100 |
XXXVIII | 103 |
XXXIX | 105 |
XL | 107 |
XLI | 110 |
XLII | 113 |
XLIII | 115 |
XII | 23 |
XIII | 28 |
XIV | 32 |
XV | 35 |
XVI | 37 |
XVII | 39 |
XVIII | 42 |
XIX | 46 |
XX | 50 |
XXI | 54 |
XXII | 57 |
XXIII | 59 |
XXIV | 63 |
XXV | 66 |
XXVI | 70 |
XXVII | 71 |
XXVIII | 74 |
XXIX | 79 |
XXX | 82 |
XXXI | 85 |
XXXII | 88 |
XXXIII | 89 |
XXXIV | 92 |
XXXV | 94 |
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Common terms and phrases
a₁ algebra angle arbitrary Cauchy Cauchy sequences chapter circle coefficients contains contracting maps coordinates Corollary corresponding curve defined denote diagram differential equation disk distinct edges elementary problems elementary symmetric polynomials elements equation f(x equivalence classes Euclidean Euler's formula Euler's identity Exercise exists fact finite function ƒ ƒ and g geometric given graph Hence highschool identity infinite integers intersection isomorphic lattice least line segment linear map F mathematical induction matrix motion multiplication natural number nonempty nonzero norm obtain ordered field pair partition pigeonhole principle plane polygonal polygonal arc positive real number proof properties Prove quaternions rational numbers relatively prime respect result roots rotation satisfying sequence Show solving square subset Suppose symmetric polynomial symmetry group theorem trajectory translation principle tree triangle vector space verify vertex vertices whence zero