By Konrad Jacobs
Based on a well-received direction designed for philosophy scholars, this e-book is a casual creation to mathematical considering. The paintings could be worthwhile not just for philosophers taken with mathematical questions but in addition for critical beginner mathematicians with an curiosity within the "frontiers" in addition to the rules of arithmetic. In what should be termed a sampler of the self-discipline, Konrad Jacobs discusses an strangely wide selection of themes, together with such goods of latest curiosity as knot thought, optimization idea, and dynamical platforms. utilizing Euclidean geometry and algebra to introduce the mathematical mode of notion, the writer then turns to contemporary advancements. within the method he deals what he calls a "Smithsonian of mathematical showpieces": the 5 Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot desk, the airplane embellishes, Alexander's Horned Sphere, and Antoine's Necklace. The remedies of geometry and algebra are by way of a bankruptcy on induction and one on optimization, video game conception, and mathematical economics. The bankruptcy on topology features a dialogue of topological areas and non-stop mappings, curves and knots, Euler's polyhedral formulation for surfaces, and the basic crew. The final bankruptcy offers with dynamics and comprises fabric at the online game of lifestyles, circle rotation, Smale's "horseshoe," and balance and instability, between different topics.