Titlebook: Easy as π?; An Introduction to H O. A. Ivanov Book 1999 Springer Science+Business Media New York 1999 Combinatorics.Higher Mathematics.Matr

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,Enumeration and Pölya’s Theorem,We begin with three problems.

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Induction,The phrases “the method of mathematical induction,” “the principle of mathematical induction,” and “an inductive argument” are sometimes used synonymously. One of the goals of the present section is to highlight their intrinsic differences of meaning.

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Combinatorics,Combinatorics is the art of counting sets of configurations of things of one sort or another (or sometimes, in more complicated contexts, is concerned rather with the problem of the existence of certain configurations, or with finding the optimal one, in some sense, among all possible ones of a certain type).

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Geometric Transformations,We begin with the following four problems.

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Inequalities,The theme of this chapter is vast, and the author has here intentionally limited himself (and the reader) to the classical inequalities [12].

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Sets, Equations, and Polynomials,Problem 1. Sketch the plane sets defined by (i.e., the graphs of) each of the following equations and inequalities: .. = 1; .. + .. = 2. − 1; .. + .. = 2.; .+1 = .+.; ..+.. = 2.; ...+.. = 2.; |.−.| = 1;..+.−2.. = 0; ..≡ |.|; max{|.|, |.|} ≡ 1; |. + .| + |. − .| ≡ 2.

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The Quaternions,s an archetype of a general (and important) kind of algebraic structure, namely that of an “algebra,” and so serves as a “jumping-off point” for studying such objects. Lastly, we have as a consequence of one of the main theorems of this chapter that the chain of number-fields ℚcℝ⊂ℂ extends no further.

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Book 1999 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 h

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