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Easy As π? : An Introduction to Higher Mathematics by Oleg A. Ivanov (1998, Trade Paperback)

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Title: Easy As π?. : An Introduction To Higher Mathematics. Number of Pages: 190. Weight: 0.67 lbs. Publication Date: 1998-12-04. Publisher: Springer.

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The 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.

Product Identifiers

Publisher
Springer New York
ISBN-10
0387985212
ISBN-13
9780387985213
eBay Product ID (ePID)
866485

Product Key Features

Author
Oleg A. Ivanov
Publication Name
Easy As π? : an Introduction to Higher Mathematics
Format
Trade Paperback
Language
English
Publication Year
1998
Type
Textbook
Number of Pages
Xviii, 190 Pages

Dimensions

Item Length
9.3in
Item Height
0.2in
Item Width
6.1in
Item Weight
16 Oz

Additional Product Features

Number of Volumes
1 Vol.
Lc Classification Number
Qa297.4
Table of Content
1 Induction.- 1.1 Principle or method'.- 1.2 The set of integers.- 1.3 Peano's axioms.- 1.4 Addition, order, and multiplication.- 1.5 The method of mathematical induction.- 2 Combinatorics.- 2.1 Elementary problems.- 2.2 Combinations and recurrence relations.- 2.3 Recurrence relations and power series.- 2.4 Generating functions.- 2.5 The numbers ?e, and n-factorial.- 3 Geometric Transformations.- 3.1 Translations, rotations, and other symmetries, in the context of problem-solving.- 3.2 Problems involving composition of transformations.- 3.3 The group of Euclidean motions of the plane.- 3.4 Ornaments.- 3.5 Mosaics and discrete groups of motions.- 4 Inequalities.- 4.1 The means of a pair of numbers.- 4.2 Cauchy's inequality and the a.m.-g.m. inequality.- 4.3 Classical inequalities and geometry.- 4.4 Integral variants of the classical inequalities.- 4.5 Wirtinger's inequality and the isoperimetric problem.- 5 Sets, Equations, and Polynomials.- 5.1 Figures and their equations.- 5.2 Pythagorean triples and Fermat's last theorem.- 5.3 Numbers and polynomials.- 5.4 Symmetric polynomials.- 5.5 Discriminants and resultants.- 5.6 The method of elimination and Bézout's theorem.- 5.7 The factor theorem and finite fields.- 6 Graphs.- 6.1 Graphical reformulations.- 6.2 Graphs and parity.- 6.3 Trees.- 6.4 Euler's formula and the Euler characteristic.- 6.5 The Jordan curve theorem.- 6.6 Pairings.- 6.7 Eulerian graphs and a little more.- 7 The Pigeonhole Principle.- 7.1 Pigeonholes and pigeons.- 7.2 Poincaré's recurrence theorem.- 7.3 Liouville's theorem.- 7.4 Minkowski's lemma.- 7.5 Sums of two squares.- 7.6 Sums of four squares. Euler's identity.- 8 The Quaternions.- 8.1 The skew-field of quaternions, and Euler's identity.- 8.2 Division algebras. Frobenius's theorem.- 8.3 Matrix algebras.- 8.4 Quaternions and rotations.- 9 The Derivative.- 9.1 Geometry and mechanics.- 9.2 Functional equations.- 9.3 The motion of a point--particle.- 9.4 On the number e.- 9.5 Contracting maps.- 9.6 Linearization.- 9.7 The Morse-Sard theorem.- 9.8 The law of conservation of energy.- 9.9 Small oscillations.- 10 The Foundations of Analysis.- 10.1 The rational and real number fields.- 10.2 Nonstandard number lines.- 10.3 "Nonstandard" statements and proofs.- 10.4 The reals numbers via Dedekind cuts.- 10.5 Construction of the reals via Cauchy sequences.- 10.6 Construction of a model of a nonstandard real line.- 10.7 Norms on the rationals.- References.
Copyright Date
1999
Target Audience
Scholarly & Professional
Topic
Algebra / Linear, General, Number Theory, Combinatorics
Lccn
98-016710
Illustrated
Yes
Genre
Mathematics

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item 1 Easy as x3C0: An Introduction to Higher Mathematics - Paperback - GOOD
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item 2 Easy as ?: An Introduction to Highe..., Ivanov, Oleg A.
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Picture 1 of 1

Easy As π? : An Introduction to Higher Mathematics by Oleg A. Ivanov (1998, Trade Paperback)

About this product

Product Information

Product Identifiers

Product Key Features

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Additional Product Features

All listings for this product

item 1 Easy as x3C0: An Introduction to Higher Mathematics - Paperback - GOOD

item 2 Easy as ?: An Introduction to Highe..., Ivanov, Oleg A.

item 3 Easy As π?: An Introduction To Higher Mathematics

item 4 Easy as ?: An Introduction to Higher Mathematics by Oleg Ivanov (English) Paperb

Best Selling in Textbooks

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Self Heal by Design : The Role of Micro-organisms for Health by Barbara O'Neill (2018, Trade Paperback)

Research Design : Qualitative, Quantitative, and Mixed Methods Approaches by J. David Creswell and John W. Creswell (2022, Trade Paperback)

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Cognitive Behavior Therapy : Basics and Beyond by Judith S. Beck (2020, Hardcover)

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