Mathematical Explorations
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- Publisher:
- Cambridge University Press
- Publication date:
- January 2017
- October 2016
- ISBN:
- 9781316662595
- 9781316610565
- Dimensions:
- Weight & Pages:
- Dimensions:
- (216 x 138 mm)
- Weight & Pages:
- 0.17kg, 126 Pages
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Book description
Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.
Reviews
'The broad array of mathematics that is covered in this text might provide a thought-provoking summary of topics and give students an opportunity to expand their horizons.'
Mark Hunacek Source: MAA Reviews
Contents
Contents
References
[1] , Squares on a square pinboard, triangles on a triangular pinboard, and hexagons on a hexagonal pin board, Math. Gazette LV, No. 394 (1971), 373–379.
[2] , Pell's Equation, Springer, 2003.
[3] , Sums of squares of digits, Math. Gazette
82 (1998), 379–388.
[4] , Shanks, Ferguson and p, Math. Gazette LV, No. 392 (1971), 243–248.
[5] , The Higher Arithmetic, Sixth Edition, Cambridge University Press, 1992.
[6] , Sur un problème de géométrie diophantienne linéare II, J. Reine Angew. Math.
227 (1967), 25–49.
[7] , Fibonacci and Catalan Numbers, John Wiley & Sons, 2012.
[8] and , An Introduction to the Theory of Numbers, Fifth Edition, Oxford University Press, 1979.
[9] , Euclid's algorithm and the money changing problem, Math. Gazette
92 (2008), 259–261.
[10] , Diophantine Equations, Academic Press, 1969.
[11] , The dissection of a circle by chords, Math. Gazette
56 (1972), 113–115 and 235–236.
[12] , On the volume of lattice polyhedra, Proc. London Math. Soc.
7, No. 3 (1957), 378–395.
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