The power and properties of numbers, from basic addition and sums of
squares to cutting-edge theory
We use addition on a daily basis-yet how many of us stop to truly
consider the enormous and remarkable ramifications of this mathematical
activity? Summing It Up uses addition as a springboard to present a
fascinating and accessible look at numbers and number theory, and how we
apply beautiful numerical properties to answer math problems.
Mathematicians Avner Ash and Robert Gross explore addition's most basic
characteristics as well as the addition of squares and other powers
before moving onward to infinite series, modular forms, and issues at
the forefront of current mathematical research.
Ash and Gross tailor their succinct and engaging investigations for math
enthusiasts of all backgrounds. Employing college algebra, the first
part of the book examines such questions as, can all positive numbers be
written as a sum of four perfect squares? The second section of the book
incorporates calculus and examines infinite series-long sums that can
only be defined by the concept of limit, as in the example of
1+1/2+1/4+. . .=? With the help of some group theory and geometry, the
third section ties together the first two parts of the book through a
discussion of modular forms-the analytic functions on the upper
half-plane of the complex numbers that have growth and transformation
properties. Ash and Gross show how modular forms are indispensable in
modern number theory, for example in the proof of Fermat's Last Theorem.
Appropriate for numbers novices as well as college math majors, Summing
It Up delves into mathematics that will enlighten anyone fascinated by
numbers.
