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第一篇：近世代數(shù)學(xué)習(xí)心得論文中文英文對(duì)照
近世代數(shù)學(xué)習(xí)心得
《抽象代數(shù)》是一門比較抽象的學(xué)科，作為初學(xué)者的我感到虛無(wú)飄渺，困難重重。我本來(lái)英語(yǔ)學(xué)的就不好，看到全英的《近世代數(shù)》我似乎傻眼了。通過(guò)兩個(gè)月的學(xué)習(xí)，發(fā)現(xiàn)它還是有規(guī)律有方法的。
針對(duì)“近世代數(shù)”課程的概念抽象、難于理解的特點(diǎn)，我認(rèn)為理解概念的一種有效方法是多舉已學(xué)過(guò)的典型例子。多看多做，舉一反三。比如群論里面有一個(gè)最基本的問(wèn)題就是n階有限群的同構(gòu)類型有多少。圍繞這個(gè)問(wèn)題可以引出很多抽象的概念，比如元素的階數(shù)，abel群，正規(guī)子群，商群，Sylow定理等，同時(shí)也會(huì)學(xué)到如何把這些理論應(yīng)用到具體的例子分析中學(xué)習(xí)“近世代數(shù)”時(shí)，就僅僅背下來(lái)一些命題、性質(zhì)和定理，并不意味著真正地理解。要想真正理解，需要清楚這些命題、性質(zhì)和定理的前提條件為什么是必要的？而達(dá)到這個(gè)目的的最有效的方法就是構(gòu)造反例。
其次是通過(guò)變換角度尋求問(wèn)題的解法，通常是將已知或未知較復(fù)雜的問(wèn)題變換為等價(jià)的較簡(jiǎn)單的問(wèn)題，或者是將新問(wèn)題變換為已經(jīng)解決的問(wèn)題，或者是將未知與已知關(guān)系較少的問(wèn)題變?yōu)橐阎c未知關(guān)系較多的問(wèn)題等等
先參考著答案做題，然后自己總結(jié)方法思路，自己就開始會(huì)做了。問(wèn)題在是否善于總結(jié)歸納。
以前學(xué)代數(shù)的時(shí)候從來(lái)沒(méi)有意識(shí)到代數(shù)是門很抽象的學(xué)科，總在練習(xí)的過(guò)程中靠點(diǎn)小聰明學(xué)過(guò)來(lái)，也由于這段路一直走得非常平坦，我從來(lái)沒(méi)停下來(lái)去想想其本身的理論體系的問(wèn)題。現(xiàn)在想想，也許這就是我一直停留在考試成績(jī)一般，卻難以有所作為的原因吧。所以有時(shí)走得太快可能未必時(shí)間好事。很可惜現(xiàn)在才了解到這一點(diǎn)，同時(shí)也還算幸運(yùn)，畢竟人還在青年，還來(lái)得及改正
Modern Algebra learning experience “Abstract Algebra” is a more abstract subjects, as a beginner , I feel vague , difficult.I had to learn English is not good to see the UK 's “Modern Algebra” I seem dumbfounded.Through two months of the study, it is found that there is a regular method.For the “ Modern Algebra ” course abstract concept , difficult to understand the characteristics , I believe that an effective way to understand the concept is to have learned to cite a typical example.See more and more , by analogy.Such as group theory which has a fundamental problem is a finite group of order n is isomorphic to type numbers.Around this problem can lead to many abstract concepts , such as the order of elements , abel group , normal subgroups , quotient groups , Sylow theorems , etc., but also learn how to put these theories to the analysis of specific examples to learn “ Modern Algebra ”, it is just back down a number of propositions , properties and theorems , does not mean that truly understand.To truly understand the need to clear these propositions , properties and theorems prerequisite Why is necessary ? To achieve this purpose the most effective way is to construct counterexample.Followed by changing the angle seek a solution, usually known or unknown to the more complex problem is converted into an equivalent simpler problem , or is transformed into a new problem has been solved , or is unknown with the known relations fewer problems become more known and unknown relationship problems, etc.Do question the answer to the first reference , and then summarize their way thinking that he began to do it.Whether good at summarizing the problem.Previously learned algebra algebra is never realized when the door is very abstract subject , always in the process of practice by learning a little smarter over, but also because this section has gone very flat , I never stopped to think about their own theoretical system problems.Now think about it , maybe this is what I have been stuck in test scores in general, but the reason it is difficult to make a difference.So sometimes a good thing going too fast may not be time.Unfortunately now I understand this, but also lucky , after all, people are still young , still have time to correct
第二篇：近世代數(shù)學(xué)習(xí)心得論文中文英文對(duì)照
近世代數(shù)學(xué)習(xí)心得
《抽象代數(shù)》是一門比較抽象的學(xué)科，作為初學(xué)者的我感到虛無(wú)飄渺，困難重重。我本來(lái)英語(yǔ)學(xué)的就不好，看到全英的《近世代數(shù)》我似乎傻眼了。通過(guò)兩個(gè)月的學(xué)習(xí)，發(fā)現(xiàn)它還是有規(guī)律有方法的。
針對(duì)“近世代數(shù)”課程的概念抽象、難于理解的特點(diǎn)，我認(rèn)為理解概念的一種有效方法是多舉已學(xué)過(guò)的典型例子。多看多做，舉一反三。比如群論里面有一個(gè)最基本的問(wèn)題就是n階有限群的同構(gòu)類型有多少。圍繞這個(gè)問(wèn)題可以引出很多抽象的概念，比如元素的階數(shù)，abel群，正規(guī)子群，商群，Sylow定理等，同時(shí)也會(huì)學(xué)到如何把這些理論應(yīng)用到具體的例子分析中學(xué)習(xí)“近世代數(shù)”時(shí)，就僅僅背下來(lái)一些命題、性質(zhì)和定理，并不意味著真正地理解。要想真正理解，需要清楚這些命題、性質(zhì)和定理的前提條件為什么是必要的？而達(dá)到這個(gè)目的的最有效的方法就是構(gòu)造反例。
其次是通過(guò)變換角度尋求問(wèn)題的解法，通常是將已知或未知較復(fù)雜的問(wèn)題變換為等價(jià)的較簡(jiǎn)單的問(wèn)題，或者是將新問(wèn)題變換為已經(jīng)解決的問(wèn)題，或者是將未知與已知關(guān)系較少的問(wèn)題變?yōu)橐阎c未知關(guān)系較多的問(wèn)題等等
先參考著答案做題，然后自己總結(jié)方法思路，自己就開始會(huì)做了。問(wèn)題在是否善于總結(jié)歸納。
以前學(xué)代數(shù)的時(shí)候從來(lái)沒(méi)有意識(shí)到代數(shù)是門很抽象的學(xué)科，總在練習(xí)的過(guò)程中靠點(diǎn)小聰明學(xué)過(guò)來(lái)，也由于這段路一直走得非常平坦，我從來(lái)沒(méi)停下來(lái)去想想其本身的理論體系的問(wèn)題?，F(xiàn)在想想，也許這就是我一直停留在考試成績(jī)一般，卻難以有所作為的原因吧。所以有時(shí)走得太快可能未必時(shí)間好事。很可惜現(xiàn)在才了解到這一點(diǎn)，同時(shí)也還算幸運(yùn)，畢竟人還在青年，還來(lái)得及改正
Modern Algebra learning experience “Abstract Algebra” is a more abstract subjects, as a beginner , I feel vague , difficult.I had to learn English is not good to see the UK 's “Modern Algebra” I seem dumbfounded.Through two months of the study, it is found that there is a regular method.For the “ Modern Algebra ” course abstract concept , difficult to understand the characteristics , I believe that an effective way to understand the concept is to have learned to cite a typical example.See more and more , by analogy.Such as group theory which has a fundamental problem is a finite group of order n is isomorphic to type numbers.Around this problem can lead to many abstract concepts , such as the order of elements , abel group , normal subgroups , quotient groups , Sylow theorems , etc., but also learn how to put these theories to the analysis of specific examples to learn “ Modern Algebra ”, it is just back down a number of propositions , properties and theorems , does not mean that truly understand.To truly understand the need to clear these propositions , properties and theorems prerequisite Why is necessary ? To achieve this purpose the most effective way is to construct counterexample.Followed by changing the angle seek a solution, usually known or unknown to the more complex problem is converted into an equivalent simpler problem , or is transformed into a new problem has been solved , or is unknown with the known relations fewer problems become more known and unknown relationship problems, etc.Do question the answer to the first reference , and then summarize their way thinking that he began to do it.Whether good at summarizing the problem.Previously learned algebra algebra is never realized when the door is very abstract subject , always in the process of practice by learning a little smarter over, but also because this section has gone very flat , I never stopped to think about their own theoretical system problems.Now think about it , maybe this is what I have been stuck in test scores in general, but the reason it is difficult to make a difference.So sometimes a good thing going too fast may not be time.Unfortunately now I understand this, but also lucky , after all, people are still young , still have time to correct
