Abstract Algebra is the killer Math subject for university-bound Singaporean A-level students educated in the British GCE syllabus. Except a fews who are born with the gift, most of them get lost in the first year of university. Yet Abstract Algebra is important math “language” of science and technology : IT, Chemistry, Physics, Advanced Math… if you want to describe a complex structure (quantum physics, crystallography), algorithm (search), method (encryption), you use this precise and concise language “Abstract Algebra” (such as Group, Vector Space, …). Countries like China and USA havevmade Abstract Algebra a compulsory subject for 1st year undergrads in Science, Engineering, IT students beside Math majors …
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.”
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Mathtuition88 