Elements of Mathematics takes readers on a desirable journey that starts in straightforward mathematics—but, as John Stillwell exhibits, this topic isn't really as simple or straight forward as one may imagine. now not all subject matters which are a part of ultra-modern user-friendly arithmetic have been consistently regarded as such, and nice mathematical advances and discoveries needed to happen to ensure that sure matters to turn into "elementary." Stillwell examines common arithmetic from a particular twenty-first-century standpoint and describes not just the sweetness and scope of the self-discipline, but in addition its limits.

From Gaussian integers to propositional common sense, Stillwell delves into mathematics, computation, algebra, geometry, calculus, combinatorics, likelihood, and good judgment. He discusses how every one quarter ties into extra complex issues to construct arithmetic as a complete. via a wealthy choice of uncomplicated ideas, vibrant examples, and fascinating difficulties, Stillwell demonstrates that effortless arithmetic turns into complicated with the intervention of infinity. Infinity has been saw all through mathematical historical past, however the contemporary improvement of "reverse arithmetic" confirms that infinity is key for proving recognized theorems, and is helping to figure out the character, contours, and borders of ordinary mathematics.

Elements of Mathematics offers readers, from highschool scholars to expert mathematicians, the highlights of straightforward arithmetic and glimpses of the elements of math past its boundaries.