By Avner Ash, Robert Gross

ISBN-10: 0691170193

ISBN-13: 9780691170190

We use addition on an everyday basis--yet what percentage folks cease to actually examine the big and memorable ramifications of this mathematical job? *Summing It Up* makes use of addition as a springboard to provide a desirable and obtainable examine numbers and quantity idea, and the way we practice attractive numerical houses to respond to math difficulties. Mathematicians Avner Ash and Robert Gross discover addition's most elementary features in addition to the addition of squares and different powers prior to relocating onward to limitless sequence, modular types, and matters on the vanguard of present mathematical examine.

Ash and Gross tailor their succinct and fascinating investigations for math fanatics of all backgrounds. utilizing university algebra, the 1st a part of the booklet examines such questions as, can all optimistic numbers be written as a sum of 4 excellent squares? the second one component to the booklet contains calculus and examines countless series--long sums that may merely be outlined through the idea that of restrict, as within the instance of 1+1/2+1/4+. . .=? With the aid of a few team thought and geometry, the 3rd part ties jointly the 1st elements of the ebook via a dialogue of modular forms--the analytic services at the higher half-plane of the complicated numbers that experience progress and transformation homes. Ash and Gross convey how modular kinds are vital in glossy quantity conception, for instance within the facts of Fermat's final Theorem.

Appropriate for numbers newcomers in addition to collage math majors, *Summing It Up* delves into arithmetic that might enlighten someone eager about numbers.