An undergraduate-diploma introduction to amount precept, with the emphasis on completely outlined proofs and examples. Exercises, together with their choices are constructed-in into the textual content material, and the first few chapters assume solely main school algebra. Elementary ideas about groups and rings are then used to evaluate groups of fashions, quadratic residues and arithmetic options with functions to enumeration and cryptography. The last word half, applicable for third-yr school college students, makes use of ideas from algebra, analysis, calculus and geometry to evaluation Dirichlet assortment and sums of squares. Notably, the ultimate chapter offers a concise account of Fermat's Remaining Theorem, from its origin inside the historic Babylonian and Greek analysis of Pythagorean triples to its present proof by Andrew Wiles.
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