3 Wide Discomforts For Abstract Math Students
1. Group : Coset, Quotient group, morphism...
2. Limit ε-δ: Cauchy
3. Bourbaki Sets: Function f: A-> B is subset of Cartesian Product AxB.
Students should learn from their historical genesis rather than the formal abstract definitions
<a href="http://http://en.wikipedia.org/wiki/Wu_Wenjun">Wu Wenjun (吳文俊) on Learning Abstract Math
"...It is more important to understand the 'Principles' 原理 behind, à la Physics (eg. Newton's 3 Laws of Motion), and not blinded by its abstract 'Axioms' 公理."
Prof I.Herstein http://en.wikipedia.org/wiki/Israel_Nathan_Herstein
“... Seeing Abstract Math for the first time, there seems to be a common feeling of being adrift, of not having something solid to hang on to.”
“Do not be discouraged. Stick with it! The best road is to look at examples. Try to understand what a given concept says, most importantly, look at particular, concrete examples of the concept.”
"Abstract Math plays a dual role: that of unifying link between disparate parts of math and that of a research subject with a highly active life of its own. It plays an ever more important role in physics, chemistry, and computer science, etc."
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