A cascade of numbers: an introduction to number theory
This fascinating book introduces classical number theory using a variety of mathematical puzzles, problems and exercises, which conciously lead the reader towards rigorous proofs without assuming a love of rigour. Based on successful courses at both Exeter and Lancaster University, and written by well known authors, this unique text has a 'hands-on' approach which will bring the subject alive for most students of number theory. The text is divided into 53 sections, arranged in three parts, each section consisting of two elements. The first is raw material, encouraging student activity that leads to pattern recognition and conjecture. The second (comments and solutions) contains the identification of formal structures and provision of proofs. The raw material of each section is presented in the first half of the book, with the comments and solutions grouped together in the latter half. Part 1 could be part of a sixth form course, while part 2 is intended for first year undergraduate study and part 3 for second year undergraduates. The result is an innovative approach to number theory which encourages a more participatory style of learning than traditional lectures and enables students of all levels to expand their understanding of the subject through a variety of interesting and enjoyable puzzles.
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The magic of nines decimal place value 3
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7p stamps ball binary notation cards catching practice coconuts columns headed congruent congruent modulo conjecture coprime cricketers decoding digit number division algorithm divisor Dominoes door number encode equation Euclidean algorithm expressed factorisation Fermat's theorem Fibonacci numbers Fibonacci sequence form 4k fractions give Hence highest common factor last digit lattice points Look mathematical induction minute hand mod 9 modulo 11 multiplication table modulo negative entries non-square modulo number less number of lattice number of negative numbers of quarter-hours numerically least residue odd number positive integers possible prime factors prime number prime pairs primitive Pythagorean triples proof QRST quadratic reciprocity rectangle recurring block recurring decimal recurring digits reflexive relation result shuffling solution of x2 square modulo square numbers squares and non-squares step lengths stick of sugar sugar cane sums of squares symmetric true unreachable values Warder Wendy Toots Tweedle whole number yes yes