Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs

You looking to find the "Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs" Good news! You can purchase Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs with secure price and compare to view update price on this product. And deals on this product is available only for limited time.

   

Product Description

The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition.

This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the �truths� of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ��beautiful� ? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction.

This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book ��s insights illuminating.

</p>

Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs Review

Charles Sanders Pierce urged mathematicians to present their results with demonstrations that showed how they actually got there, rather than the usual way, which is to tidy up a nicely polished pyramidal proof that leads enexorably, pontifically from axioms to Q.E.D., and then to throw away the scaffolding and sweep away all traces of the parallel paths, false starts, and tangents of the actual process. This suggests a difference between mathematical reasoning as practiced and mathematical reasoning as mathematicians feel it ought to be. We may also distinguish mathematical reasoning from mathematical knowledge, as for example the toolbox of rules and formulae that every high school student of algebra is asked to master.

Nickerson is a research psychologist inquiring into how reasoning is done in the diverse fields of mathematics as an outsider, as he presumes us, his readers, to be. This book is very readable, and also very thorough. One must be prepared to commit mental resources to taking in a lot, and one very much needs the readability lest the scope, variety, and depth of coverage appear to be too daunting. Nickerson's coverage is impressive, and his intent is very ambitious.

I think that mathematicians as well should benefit from reflecting on how they reason, perhaps agreeing at some times and then when they disagree it may be finding themselves on occasion brought to an unfamiliar but possibly fruitful self-reflection. Also, mathematicians naturally specialize, and a survey of the field can be like looking up from myopic concentration at a desk and gazing out the window to scan a distant and opening horizon.

I haven't yet read enough to comment on the success of Nickerson's project, but what I have read has led me to recommend it a few times, and I now recommend it to you.

Most of the consumer Reviews tell that the "Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs" are high quality item. You can read each testimony from consumers to find out cons and pros from Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs ...