Focusing on theory more than computations, this text covers sequences, definitions, and methods of induction; combinations; and limits, with introductory problems, definition-related problems, and problems related to computation limits. 1969 edition.
Focusing on theory more than computations, this text covers sequences, definitions, and methods of induction; combinations; and limits, with introduct...
-All through both volumes Functions & Graphs and The Methods of Coordinates], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated by n ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also...
-All through both volumes Functions & Graphs and The Methods of Coordinates], one finds a careful description of the step-by-step thinking process...
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the...
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathem...
This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space. Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of "road signs" in the margins, alerting students to passages requiring...
This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space...
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even...
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of ...
Even the simplest mathematical abstraction of the phenomena of reality- the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the...
Even the simplest mathematical abstraction of the phenomena of reality- the real line-can be regarded from different points of view by different mathe...
