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An Introduction to Mathematics

This book serves as a foundational resource for understanding the core areas of mathematics, including arithmetic, algebra, geometry, and calculus. It is designed to provide readers with a solid grasp of mathematical theories and their applications in various fields. more

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Alfred North Whitehead
Alfred North Whitehead

Alfred North Whitehead was a British mathematician, philosopher, born on February 15, 1861, and died on December 30, 1947. He is known for his contributions to mathematics, logic, philosophy, and the philosophy of science, particularly for his co-authorship of 'Principia Mathematica' with Bertrand Russell. more

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“Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?”

“See skulking Truth to her old cavern fled, Mountains of Casuistry heap'd o'er her head! Philosophy, that lean'd on Heav'n before, Shrinks to her second cause, and is no more. Physic of Metaphysic begs defence, And Metaphysic calls for aid on Sense! See Mystery to Mathematics fly!”

“"I think you're begging the question," said Haydock, "and I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that, you would go round the bend. Let me assure you of that!"”

“There's a tendency for adults to label the math that they can do (such as identifying patterns, choosing between competing offers in a supermarket, and challenging statistics published by the government) as "common sense" and labeling everything they can't do as "math" - so that being bad at math becomes a self-fulfilling prophecy.”

“Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.”