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Categories: Science fiction Fantasy Mystery Romance Business Classic Sports Young adult Humor Memoirs See all categories... |
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Categories: Science fiction Fantasy Mystery Romance Business Classic Sports Young adult Humor Memoirs See all categories... |
I was introduced to mathematics and deduction through other treatments. But this book would have led me straight to the stuff that captivates me the most today.Would be a great book to hand to any motivated reader interested in actually understanding the fabric of the mathematical method. Proof-writing skills and such is likely to follow from dedicated study of this book.Variables and quantifiers play an essential role in reasoning about mathematics. This is tied in with proving mathematical statements with respect to properties held by an 'infinite' number of 'objects'.Equality/identity has a very specific 'meaning' in mathematics.Mathematical implications - "if...then..." statements - do not have the same 'meaning' as the ordinary language use of the terms. This causes a lot of confusion to students new to doing proof-based mathematics. The early sections of this book contains many helpful comments on mathematical implication.Modern, pure mathematics is inaccessible to one uneducated in the rudiments of modern set/class theory.Relations play a fundamental role in pure mathematics.There are wonderful explanations in this book of all the topics mentioned above, and more.Pure mathematics could be claimed to be the only deductive 'science' there is. A pure mathematician does not do experiments the same way a physicist or chemist would. We have a specific way to 'prove' things, claim something 'true', and claim which statements follow from which.Alfred Tarski revolutionised a field called mathematical logic back in the early twentieth century. This book is a window into that world. It will teach you the basics of doing mathematics, in the mathematician's sense.
