At the Edge of Infinity and Beyond
Aleph-null is the cardinality, or size, of the set of natural numbers, and is a ‘countably infinite cardinal’. Remarkably, whereas 1 + 1 = 2, 1 + aleph-null = aleph-null. The authors of this advanced maths explainer utilize plain English in an attempt to understand difficult mathematical concepts, including large numbers, higher dimensions, computation and primes, fusing historical, philosophical and anecdotal aspects of each concept with the decidedly technical. Slightly off-mint.
The Quality of Numbers One to Thirty-one
In these essays – one for each day of the month – Held demonstrates the fascinating qualities and associations, both cultural and scientific, of the first 31 integers. His ‘excursions into the realm of number’ visit such varied calling-points as the eleven-year sunspot cycle, humans’ 23 pairs of chromosomes, Snow White’s seven dwarves and Judas’ 30 pieces of silver.
The Puzzler's Dilemma
From the Lighthouse of Alexandria to Monty Hall, a Fresh Look at Classic Conundrums of Logic, Mathematics, and Life
‘A man is found hanging in a locked room with no furniture and a puddle of water under his feet. What happened?’ From ancient Greek paradoxes to the role of probability in television game shows (via the Rubik’s Cube, chess problems and crosswords) this entertaining book illustrates eleven classic types of logic puzzle, tells the stories behind their creation and shows how to go about solving them.
Number Treasury 3
Investigations, Facts and Conjectures About More than 100 Number Families
Written as a resource for both teachers and students, this enlarged third edition of Number Treasury is designed to guide readers through the steps that will help them to think critically, to provide explanations and to formulate conjectures about different families of positive integers. Its 137 exercises and 28 'investigations', at three levels of difficulty, cover such intriguing topics as magic squares, palindromic numbers and twin primes. Detailed solutions are provided at the back of the book.
A Brief Guide to the Great Equations
The Hunt for Cosmic Beauty in Numbers
From 1+1=2 and Pythagoras' theorem to the work of Einstein and Heisenberg, Crease tells the stories and personal struggles behind the creation of the most fundamental, powerful and influential equations. He also considers what each equation reveals about the cultural and historical background that produced it and the effects, often unforeseen by their originators, which these pithy distillations of knowledge have had on later generations.