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Changes seem to come to the math universe slowly. From that forgotten day in antiquity when the first math teacher gathered a group of students to teach them the fundamentals of working with numbers, there have been accepted right ways and wrong ways to figure out a problem. Every few years an innovator comes along and introduces a new technique at arriving at a mathematical answer, but it often is a long time before the method is fully accepted and trickles down to the classroom. Despite this challenge, in some ways this is exactly what the author is trying to do in this book. In an attempt to make the expansion of binomials with large indices easier for students, he quite literally turns the standard horizontal foil method on its head.
Dubbing his creation Salcido's Vertical Foil, the author demonstrates how binomial expansion with large indices can be performed in a simpler way than having to string things out horizontally or resort to the rather cumbersome Binomial Theorem when dealing with binomial expressions. Salcido does not stop here, though. He goes on to introduce a "cousin" of the binomial which he calls a nanomial. A nanomial differs from a binomial in that it includes a denominator in each of its terms when expanded. The author then details Salcido's Nanomial Theorem and Salcido's Nanomial Vertical Foil.
Although not a professional mathematician, Salcido shows courage and great diligence in his presentation of his theories. His book is filled with useful diagrams and formulas that explain step-by-step how to put his concepts into practice. The result is an intriguing and thought-provoking look at what might possibly be the future of mathematics instruction.
RECOMMENDED by the US Review