By Robert L. Baber
''The topic of this booklet is how one can formulate a mathematical version from an English description of an issue. This publication perspectives mathematical notation as a language and develops the consequences of this view for translating English textual content into mathematical expressions and mathematical types, i.e. for using arithmetic to difficulties defined in English. for you to practice arithmetic to a pragmatic challenge, one must first remodel an English assertion of the matter and the necessities for its resolution into mathematical expressions. This booklet examines this procedure intimately, provides new perception into it, and develops specific instructions for this crucial step. This publication identifies the elemental parts (values, variables, and services) of the language of arithmetic and provides the grammatical principles for combining them into expressions and different buildings. various notational types for expressions are defined and outlined. Correspondences among elements of speech and different grammatical parts in English and parts of expressions within the language of arithmetic are pointed out. those result in necessary directions for translating English into the language of arithmetic. moreover, the ebook includes many examples of translating English into arithmetic. The strategy provided during this ebook makes arithmetic obtainable to many of us who've been grew to become off from arithmetic via their early publicity to it''-- Read more...
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Additional resources for The language of mathematics : utilizing math in practice
X, 1)]. , the empty sequence  is appended to the output abbreviation formed previously). 12-1 specifies the logic for all combinations of the several different cases of h at the beginning of the name, h after the beginning of the name, more than one vowel in a sequence, more than one consonant in a sequence, an h P1: TIX/XYZ JWBS073-02 P2: ABC JWBS073-Baber June 27, 2011 10:26 Printer: Markono ENERGY IN EARTH’S REFLECTED SUNLIGHT VS. 12-1 33 State Transition Table for Forming Abbreviations Input Letter Current State a, e, i, y o, u 0 initial 1 after vowel 2 after consonant (a, 1) (–, 1) (a, 1) b, p m, n c, k, q d, t g, j f, v, w h l, r s, x, z (o, 1) (b, 2) (m, 2) (q, 2) (t, 2) (g, 2) (f, 2) (–, 0) (r, 2) (s, 2) (–, 1) (b, 2) (m, 2) (q, 2) (t, 2) (g, 2) (f, 2) (–, 1) (r, 2) (s, 2) (o, 1) (–, 2) (–, 2) (–, 2) (–, 2) (–, 2) (–, 2) (–, 2) (–, 2) (–, 2) within a vowel sequence, an h within a consonant sequence, an h between a vowel sequence and a consonant sequence, and so on.
6 COMBINING DATA FILES Jane and George, two teenage friends in secondary school, helped older people in their town to use and maintain their various computer systems. Jane and George each kept a file of data on his/her own customers. They did not compete with each other, so had no customer in common. When Jane left to attend a university, she turned over her business to George, who merged the two files and sorted the combined file, which became his new customer file. As a brief homework problem, George wrote the following mathematical expression to describe the relationship between the two original files and his new, combined file.
The reader already familiar with mathematics and its application will find some material in the book to be old and familiar, especially the contents of Chapter 3. These readers should scan those parts of the book, however, as some of the material is presented in new, different, and unconventional ways. Readers will find that the topic of the book is presented in ways quite different from traditional mathematics teaching, and some might therefore question its validity. The very point of the book is that mathematics can be viewed from different standpoints and in different ways and that some of these approaches are absent from traditional mathematics teaching and learning.