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YOU are better than YOU think. Show yourself how:
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-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery Logic mastery makes the hard, easier. Logic mastery leads to better, stronger and richer comprehension. Logic mastery improves reading and writing. Logic mastery ease learning difficulties. Logic mastery gives a headstart. In sum, logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6;
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-/[]\- What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts. Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice. |
Chapter 10: SetsThe mathematics curriculum has been influenced by the set theoretic and logical, that is the thought-based, codification and framework for mathematics. This framework is indispensable or at least appears sufficient for the rigorous discourse of most present-day professional mathematicians – whether or not this perspective is in favour a hundred years hence is another question. But for novices and for computations in many disciplines, this perspective is not required. In colleges where courses for mathematics students may emphasize or be presented in the set theory framework, mathematics courses for students in other disciplines will forgo the set theoretic wrappings and emphasize computation or the mastery of algebraic and geometric concepts. Intermediate level instruction in secondary school need not be more faithful to the set perspective than most college mathematics service courses – those given to students not specializing in the discipline. Intermediate instruction should emphasize sets and the allied concepts of membership, unions, intersections, ordered pairs and complements, only where their use shortens exposition, or provides a second higher math perspective. We recall a few examples where some benefit may be present. Venn diagrams have a slight advantage in illustrating logic and linking logical terms (and, or, not) with set theoretic terms (intersection, union, complement). Venn diagrams, sets and subsets provide a framework to simplify the computation of probabilities or the counting and representation of ways in which objects can be combined or arranged. Functions can be defined by means of a computation rule (for instance a formula) or by means of a set of ordered pairs which satisfies the vertical rule property. The two ways of defining functions are equivalent or interchangeable. For a set of points in the plane, the vertical rule property, if satisfied, can be employed to define a computational rule for a function, and a computational rule for a function can be employed to define a set with the vertical line property. Acknowledging this equivalence entails a comparison of a set theoretic definition, that of a function, with a non-set theoretic perspective of mathematics. The set-theoretic perspective is but a subset of the discipline. |
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