YOU are better than YOU think. Show yourself how:
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No matter how patterns are met and mastered, careful and observable combination, one at a time, one after another, shows in part an operational command of an art or discipline, a reflex- thought-based. Take your pick. Online Postscripts explore methods of indirect reason.
The title is misleading. A 4th skill appears in chapter 14. Appendices include advice for students. Starts with logic chapters to introduce the use of implication rules in maths, and to develop lawyer like, precision reading and writing skills - two musts for less confusion and better performance in work and studies. This work aims make logic and algebra more accessible.
For Calculus, includes geometric & algebraic starter lessons. See chapters 2 to 6. Appendices are online in separate site area Real Analysis with some duplication in site area Calculus Introduction. Volume 3 aims to make calculus and real analysis more accessible.
Where an art or discipline is based on observable movements or patterns, inductive principles for their mastery call for larger movements or patterns to be decomposed into smaller movements or patterns which can be mastered immediately or in sequence. Occam's Razor may yet favour this approach in mathematics education if its methods are statistically effective and are clearly and well-documented in course delivery how-TOs, easily understood and followed. |
Quantitative Skills - Ideas for a New Site AreaThis site area to grow will cover or point to numerical skills and concepts appearing in all walks of life at work, at home and in-between. The aim is to include common calculations of potential interest on a daily or long-term basis. For example, one of the books I am reading or have read on learning French gives many examples of visiting a places, a store or restaurant, a train station, etc, and introducing the words needed or likely to met in such a place or situation. This site area will offer examples (vignettes) where we describe the calculation likely to occur in each place or activity. Any place, trade or activity in which elementary mathematics appears provides material for a webpage in this (future) area. These examples may be useful for instruction and self-instruction. Money Matters The site pages provide an elementary to advance view of money related calculations.
The further pages review arithmetic and try to teach some algebra and logic
Logic Lessons 2 to 5 could and should lead to precision reading and writing, two musts for studies and work!
Site Content GuideChapter 14 on the Compound Interest Formula shows there is more to mathematics than doing arithmetic. Formulas can be used directly and indirectly. This chapter shows how. In this discussion of the compound interest formula, I just want to show you how to use it and how to manipulate or change it to extract other formulas from it. Examples with and without numbers will be given. Explanations of why the compound interest works may be found elsewhere. When times permits, the explanation why will be posted here.The next group of chapters describe ideas and mathematical methods which can be used in money computations. The methods should be used carefully. Errors here could be costly. Opinion: Everyone regardless of academic or work destination, should meet and master such calculations because they might be useful in daily life.The first two chapters Geometric Sums Etc and Notation for Sums and describe the mathematical ideas and methods needed in to explain the calculations involving compound interest, loans and pensions in the chapter Personal Money Matters. Note this chapter provides only one motivation for mastering the mathematical ideas and methods employed or shown. The chapter Some Finite Mathematics shows how the principle of mathematical induction can be used to justify or confirm again the summation shortcut formulas given earlier. (Mathematicians favor math induction in place of more relaxed methods of justification.) The ideas and methods in this chapter Some Finite Mathematics are re-cycled or re-used in many further parts of mathematical thought.
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