The Binomial Theorem - A Selection of Classic Mathematical Articles Containing Examples and Exercises in Algebra (Mathematics Series)

Few results in algebra earn their keep like the binomial theorem. This gathering of classic mathematical writing sets the expansion out plainly, with worked examples and exercises at every stage.

Part of a series reissuing mathematical writing from the early 1900s and before, The Binomial Theorem brings together the lessons and articles that generations of students learnt from. The material moves from raising a two-term expression to a positive whole power, through the coefficients set out in Pascal's triangle and their link with permutations and combinations, to the general statement that holds for negative and fractional indices. Proofs are given in full, and each section closes with problems to work through.

These pages were written when an answer had to be reached with pencil and paper, so the reasoning behind every step is explained rather than reduced to a rule to be memorised. That makes them useful to anyone returning to the subject as an adult, to students who want a second explanation alongside a modern textbook, and to readers curious about how mathematics was once taught.

This edition features:

• Classic articles on the binomial theorem drawn from mathematical writing of the early 1900s and before
• Full proofs for a positive whole power and for the general case of negative and fractional indices
• An accessible route into permutations, combinations, and the coefficients of Pascal's triangle
• Exercises at the close of each section, so the reasoning can be tested rather than taken on trust
• Each article reprinted with a note of the work it was taken from, so it can be traced to its author