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Excerpt from Myers Arithmetic, Vol. 1: Book I The ideas of number and of the numerical material. Processes must be derived from the concrete. Form and number are the two main develop ments of quantity. The process of numbering in its varied aspects is very closely paralleled in the physical world by the process of measuring in its varied applications. This does not imply that numbering and measuring are one and the same process, or set of processes. What it does imply is that numbering is the mental side of the same problem of adjustment of activity that has its physical expression in measurement. It means that measurement is the most direct and certain route to correct notions of number, for one who has not yet acquired them. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from Myers Arithmetic: Elementary He is next led to apply his facts to other concrete problems, such as: If John has one marble and Henry has three, how many have both? Which are not constructive, but which oblige him to use his judgment. Finally the number combinations thus learned and applied are fixed by a series of drills. An essential feature Of these drill tables is that they make the subject less formidable to the child. For example, the tables on page 43 show that if the child adds three, say, to a series Of numbers ending in six, all the sums will end in nine. As soon as the child masters the develop ment of a number, he is taught to associate it with certain facts Of his daily life; as, for example, in connection with the number eight, is given the table Of dry measure, and with the number twelve, the foot, the months, and the mysteries of the clock face. In this way the child is sure to be interested, and his powers both of memory and of judgment are developed. Throughout the book much use is made Of graphic illustrations and concrete problems, such as drawing to scale. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Excerpt from Myers Arithmetic: Elementary Many and substantial gains have been made in the last decade in both theory and practice in elementary education, and arithmetic has gained largely from this general advance. We have learned much of late as to practical ways of securing in the teaching of the elements of mathematical science the larger and the more significant educational aims - strengthening the judgment and the will, the power to think and to do. The writer of an arithmetic who cuts himself off from these advances and satisfies himself with mere "figuring," or the mere meeting of an existing "consensus," cheapens his effort by denying the higher purposes of education and renounces his opportunity to help even the makers of programs by pointing the direction whence improvement must come. Without neglecting either of these two important requirements, the authors of this book have striven to make the arithmetic work more thoughtful, and even the drill purposeful and educative. There is no school subject in which foreshortened views and distorted perspective work more harm than in elementary mathematics. Children as well as adults, learn new ideas by meeting them first in simple forms, intermingled with familiar ideas and fairly well-understood uses of the new ideas. After a little, the new idea makes itself felt as something new. This is the time to differentiate it for formal study, to learn what it really is. This is the stage for the study of process and for drill enough to fix it and to make its use easy and facile. The learner then desires to experience the added power the mastery of the process has given him, and this calls for the application stage. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Excerpt from Myers Arithmetic: For Grammar Schools This book continues the work of the Myers Elementary Arithmetic and covers comprehensively the work of the last four years of the elementary school. It is a topical treatment of the subject and is thus in itself a complete arithmetic. The educational reason for arithmetic as a school subject is that it is a type of the organization of experience that the world deems useful in daily life. The experiences which arithmetic should organize are sensations of measuring and numbering. In order that this measuring and numbering experience may be organized into the most efficient practical knowledge, the work must be done in harmony with the minds way of construing these sensations into relationships. Nothing is more fundamentally important than that the pupil actually have the experiences that are to be organized. The ready-made experiences of others cannot be substituted for those of the learner himself. Furthermore, the pupil should organize as well as experience these sensations. The requirement that the sensations to be organized shall be the pupils own can be met only by the plentiful use of concrete material. The objects, pictures, real problems, and other concrete materials must be not merely talked about by the teacher, the pupil passively listening and looking on. The pupil must handle the objects, draw the sketches, examine them and even make verbal problems. He must be allowed to make discoveries for himself. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.