By Ranjan Roy

The invention of limitless items by means of Wallis and limitless sequence by means of Newton marked the start of the fashionable mathematical period. It allowed Newton to unravel the matter of discovering parts lower than curves outlined through algebraic equations, an fulfillment past the scope of the sooner tools of Torricelli, Fermat, and Pascal. Newton and his contemporaries, together with Leibniz and the Bernoullis, targeting mathematical research and physics. Euler's prodigious accomplishments confirmed that sequence and items deal with difficulties in algebra, combinatorics, and quantity thought. sequence and items have persisted to be pivotal mathematical instruments within the paintings of Gauss, Abel, and Jacobi in elliptic features; in Boole's and Lagrange's endless sequence and items of operators; in paintings by way of Cayley, Sylvester, and Hilbert in invariant idea; and within the present-day conjectures of Langlands, together with that of Shimura-Taniyama, resulting in Wiles's evidence of Fermat's final theorem. during this ebook, Ranjan Roy describes many elements of the invention and use of endless sequence and items as labored out by way of their originators, together with mathematicians from Asia, Europe, and the United States. The textual content offers context and motivation for those discoveries; the unique notation and diagrams are awarded whilst functional. a number of derivations are given for lots of effects, and exact proofs are provided for vital theorems and formulation. each one bankruptcy comprises attention-grabbing routines and bibliographic notes, supplementing the result of the bankruptcy. those unique mathematical insights provide a beneficial viewpoint on sleek arithmetic. Mathematicians, arithmetic scholars, physicists, and engineers will all learn this ebook with profit and delight.