# !!> PDF ✯ Math in Minutes (200 Key Concepts) ⚣ Autor Paul Glendinning – Andy-palmer.co.uk I have two problems with this book 1 The author doesn t explain that the term rational comes from the word ratio, meaning that rational numbers are produced via ratios fractions Why don t they just call them fractional numbers and eliminate the confusion when he first presents the term, but several pages later, by which time the reader is already feeling confused and stupid, which should be precisely the opposite thing that happens when one reads any kind of instructional textbook, which this is supposed to be.2 Author never explains that imaginary terms and complex numbers exist to capture and convey the behavior of perpendicular orthogonal and other phase shifted functions that occur right alongside some main function of interest, which is usually oscillatory in nature For example, a swinging pendulum is actually exhibiting two properties simultaneously a position function left or right of center and a velocity function maximum leftward described as negative or positive, maximum rightward described as the opposite of however you defined maximum leftward, or zero And if you look closely at these two functions, which are trigonometric waves, you will notice that they are precisely 90 degrees out of phase, meaning that while one is at its maximum positive or negative value, the other is exactly between its maximum positive and maximum negative values, at zero.This is why the sheer obnoxiousness of imaginary and complex numbers are used and tolerated because we can present two phase differing functions at once, just by slapping the letter i in front of one of them Imaginary and complex numbers exist to capture orthogonality. Paul Glendinning Is Professor Of Applied Mathematics At The University Of Manchester He Was Founding Head Of School For Mathematics At The Combined University Of Manchester And Has Published Over Fifty Academic Articles And An Undergraduate Textbook On Chaos Theory Both Simple And Accessible, Math In Minutes Is A Visually Led Introduction To Key Mathematical Concepts Each Concept Is Described By Means Of An Easy To Understand Illustration And A Compact, Word Explanation Concepts Span All Of The Key Areas Of Mathematics, Including Fundamentals Of Mathematics, Sets And Numbers, Geometry, Equations, Limits, Functions And Calculus, Vectors And Algebra, Complex Numbers, Combinatorics, Number Theory, And Fun to read about math in very short, digest form Explanations avoid long, dull derivations. This is a great little book on various topics in mathematics It is a joy to read and to dip into from here to there so one can find interesting topics to further study in mathematics An interesting little introduction to all kinds of mathematical concepts The first half or so acted for me as a refresher course for things I d learned in grammar and high school After that, it started getting into concepts that I either never learned, or had forgotten entirely At that point, it is much too superficial to help you really understand the ideas it s of a starting point for further research, if you re that interested. I loved the book As a undergraduate majoring in physics, I didn t take every math classes offered for math majors, but this is a guideline for me to have a better concept about all math classes, so later I can decide what other classes I can take that can potentially help me in physics.