Unlocking the potential of every student

THIS IS NOT A MATH, PHYSICS OR ENGINEERING TEXTBOOK. Instead, it is a different approach to learning STEM, designed for those who might otherwise shy away from it. The problems are presented first, before the explanation, with enough hints so that solving them requires the same skill as basic puzzle solving. Anyone who has ever solved a game puzzle can try and solve at least some of the problems. This has the effect of increasing confidence. Even though a deep understanding of the math is not achieved, the objection that "math is not my thing" is overcome by the fact that the student is already doing the math! 

With every problem (or puzzle) completed, confidence increases. After attempting a problem, the "answer" section then has an explanation of how to go about solving the problem. The student who studies the book in order will first not understand why an action was taken. It may seem arbitrary. But in the course of working through the “Guide to Answers”, the student will unravel the process of getting to the solution. Approaching quantitative fields and the math needed to do them in this way opens up math, engineering and other quantitative fields to those students who might otherwise have no inclination or interest to do so. It is intended to be used as a new, more inclusive path to these subjects. 

The book is organized into four parts: In the Math section is all the math needed to solve the application problems. Each chapter in this section is a different math category, covering the range from algebra all the way to differential equations. The next section provides lots of useful information and useful tips for problem solving. In the following section, an application is provided for each chapter which uses the math learned in that chapter. Again, strong hints ensure that the student is never stranded for what to do next. 

The final section of the book has engineering problems that are designed to show the student what real engineering problems might look like. Some use the math taught in Part I, while others are just giving the student a chance to discover interest. After going through the entire book, the student will have been exposed to three concepts: 1) The math of that chapter; 2) A specific application in the field of the problem; and 3) An introduction to a real-world problem. In the process of going through the problems - guided to the answers like in the Applications section – the student is also shown how to go about solving real engineering and physics problems, which boosts problem solving skills (and confidence!)

Each real-world problem provides a background regarding the particular topic – designed to stimulate interest and excitement. The problem is broken up into sections and has multiple hints (“What you need to know”) about solving the problem. In order to avoid some of the very common issues which cause students to get stuck on quantitative problems, the section of useful information provides guidance and pitfalls to avoid. The section warns the students about common errors such as unit errors, sign errors and the ever-present factor of two, which can lead to huge frustration and teach nothing about the field.

By the time the student gets through the application problem for a given chapter, they will have a much greater comfort with the math as well as how to go about solving a problem. This is very different from conventional approaches which lose many students early on due to lengthy explanations of concepts and details, and frustrate many students by failing to provide sufficient explanation of how to go about solving a problem. Additionally, most math textbooks present problems by using only math. But many students will turn away from that approach simply because they can’t find any part of it which has a connection to their own experiences.

The purpose of this approach is not to substitute for formal textbooks on math and engineering, but rather, to provide an introduction to engineering and other quantitative fields and hopefully spark an interest in a field that might not have otherwise been explored. Further, students who makes an effort to go through the whole book will be much better positioned to a) know if they have any interest in quantitative fields; b) feel much greater confidence if they decide to explore the path of quantitative fields, and c) already have quite a bit of understanding of what will be encountered. Finally, I feel confident that students will also improve their ability to think logically.