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Short and Easy Computer Proofs of the RogersRamanujan Identities and of Identities of Similar Type
, 1994
"... New short and easy computer proofs of finite versions of the RogersRamanujan identities and of similar type are given. These include a very short proof of the first RogersRamanujan identity that was missed by computers, and a new proof of the wellknown quintuple product identity by creative teles ..."
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Cited by 24 (4 self)
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New short and easy computer proofs of finite versions of the RogersRamanujan identities and of similar type are given. These include a very short proof of the first RogersRamanujan identity that was missed by computers, and a new proof of the wellknown quintuple product identity by creative telescoping. AMS Subject Classification. 05A19; secondary 11B65, 05A17 1 Introduction The celebrated RogersRamanujan identities stated as seriesproduct identities are 1 + 1 X k=1 q k 2 +ak (1 \Gamma q)(1 \Gamma q 2 ) \Delta \Delta \Delta (1 \Gamma q k ) = 1 Y j=0 1 (1 \Gamma q 5j+a+1 )(1 \Gamma q 5j \Gammaa+4 ) (1) where a = 0 or a = 1, see e.g. Andrews [6] which also contains a brief historical account. It is wellknown that number theoretic identities like these, or of similar type, can be deduced as limiting cases of qhypergeometric finitesum identities. Due to recent algorithmic breakthroughs, see for instance Zeilberger [24], or, Wilf and Zeilberger [23], proving th...
The journey of the four colour theorem through time
 The NZ Math. Magazine
"... This is a historical survey of the Four Colour Theorem and a discussion of the philosophical implications of its proof. The problem, first stated as far back as 1850s, still causes controversy today. Its computeraided proof has forced mathematicians to question the notions of proofs and mathematical ..."
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Cited by 8 (0 self)
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This is a historical survey of the Four Colour Theorem and a discussion of the philosophical implications of its proof. The problem, first stated as far back as 1850s, still causes controversy today. Its computeraided proof has forced mathematicians to question the notions of proofs and mathematical truth.
A pretty binomial identity
 Elem. Math
, 2012
"... Abstract. An identity involving binomial coefficients that appeared in the evaluation of a definite integral is established by a variety of methods. k=0 1. ..."
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Abstract. An identity involving binomial coefficients that appeared in the evaluation of a definite integral is established by a variety of methods. k=0 1.
What’s experimental about experimental mathematics? ∗
, 2008
"... From a philosophical viewpoint, mathematics has often and traditionally been distinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments — one of the corner stones of most modern natural science — have had no role to play in mathematics. However, dur ..."
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From a philosophical viewpoint, mathematics has often and traditionally been distinguished from the natural sciences by its formal nature and emphasis on deductive reasoning. Experiments — one of the corner stones of most modern natural science — have had no role to play in mathematics. However, during the last three decades, high speed computers and sophisticated software packages such as Maple and Mathematica have entered into the domain of pure mathematics, bringing with them a new experimental flavor. They have opened up a new approach in which computerbased tools are used to experiment with the mathematical objects in a dialogue with more traditional methods of formal rigorous proof. At present, a subdiscipline of experimental mathematics is forming with its own research problems, methodology, conferences, and journals. In this paper, I first outline the role of the computer in the mathematical experiment and briefly describe the impact of high speed computing on mathematical research within the emerging subdiscipline of experimental mathematics. I then consider in more detail the epistemological claims put forward within experimental mathematics and comment on some of the discussions that experimental mathematics has provoked within the mathematical community in recent years. In the second part of the paper, I suggest the notion of exploratory experimentation as a possible framework for understanding experimental mathematics. This is illustrated by discussing the socalled PSLQ algorithm.
The Use of Experimental Mathematics in the Classroom
"... The use of computers is gaining importance in education today. Experimental Mathematics is particularly suitable for teaching (and learning) mathematics in a computer supported learning environment. In this manuscript, we show how Experimental Mathematics works in the classroom. We demonstrate that ..."
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The use of computers is gaining importance in education today. Experimental Mathematics is particularly suitable for teaching (and learning) mathematics in a computer supported learning environment. In this manuscript, we show how Experimental Mathematics works in the classroom. We demonstrate that computers can be used in each phase of the whole learning process (formulating definitions, problems and proofs, detecting finite patterns, conjecturing, falsifying, and applying math knowledge). 1.