Mathematics for the General Reader (Dover Books on Mathematics) by E.C. Titchmarsh (PDF)

Description

“A first-class mathematician’s lucid, unhurried account of the science of numbers from arithmetic through the calculus.” — James R. Newman, The World of Mathematics.This highly accessible introduction to mathematics is geared toward readers seeking a firm grasp of the essentials of mathematical theory and practice. The treatment also offers a concise outline of mathematical history and a clearer notion of why mathematicians do what they do.Author E. C. Titchmarsh, who served for many years as Savilian Professor of Geometry at Oxford University, begins with counting and the fundamentals of arithmetic. He guides readers through the complexities of algebra, fractions, geometry, irrational numbers, logarithms, infinite series, complex numbers, quadratic equations, trigonometry, functions, and integral and differential calculus. Titchmarsh’s graceful, fluid style helps make complicated topics easier to grasp, and his inclusion of numerous examples will prove especially helpful to readers with little or no background in mathematics.

User’s Reviews

Editorial Reviews: About the Author British mathematician Edward Charles Titchmarsh (1899–1963) was Savilian Professor of Geometry at the University of Oxford from 1932 to 1963 and the author of several books in advanced mathematics, including Introduction to the Theory of Fourier Integrals and The Theory of the Riemann Zeta-Function.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a Dover reprint of Titchmarsh’s little book “Mathematics for the General Reader”. I am not sure how a “general reader” will feel about this book, but I would recommend it to all school teachers, because the author had raised some subtle points that are often neglected in class.For example, when discussing an infinite decimal such as 0.999…, the focuses are usually placed on why THIS particular expression does represent a number and what value it is, but Titchmarsh didn’t forget to mention that EVERY infinite decimal is actually a valid representation of a real number, because it is a convergent infinite series.Another example is geometry. Many school teachers tend to pass geometrical theorems as physical realities, but Titchmarsh had made it very clear that geometry is only an idealised way to think about our world.Despite the title and thin size, this is not a “popular mathematics” book. Titchmarsh did try to explain mathematics to laymen, but the book wasn’t written in an entertaining style like those written by Martin Gardner or Ian Stewart were. It is more appropriate to view it as a distinctly introductory text to the very bare essentials of algebra, geometry and analysis. Many topics in this book are actually discussed from university-level perspectives. E.g. fractions are explained using equivalence classes and part of the discussion on irrational numbers is reminiscent of Dedekind cuts. Most proofs (e.g. that e is irrational) are rigorous. When a hand-wavy argument must be made because a rigorous proof is beyond the scope of the book, the author will explicitly say so.

⭐This was one of the two books that I read nearly eight years ago that renewed my interest in mathematics. The other book was An Introduction to Mathematics by Alfred North Whitehead. Any one interested in mathematics can with an investment of perhaps of only 10 hours or less (took me only a weekend to get through this book) can come away with a good grasp of the underlying principles of arithmetic, algebra, trigonometry and calculus that is often overlooked in dry and uninspiring textbooks that most of us encounter during our school or university years. Both these books will be part of my treasured collection of great books for years to come. Will make you fall in love with mathematics if you haven’t already. A must read!

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