近世代数学习心得
《抽象代数》是一门比较抽象的学科，作为初学者的我感到虚无飘渺，困难重重。我本来英语学的就不好，看到全英的《近世代数》我似乎傻眼了。通过两个月的学习，发现它还是有规律有方法的。
针对“近世代数”课程的概念抽象、难于理解的特点，我认为理解概念的一种有效方法是多举已学过的典型例子。多看多做，举一反三。比如群论里面有一个最基本的问题就是n阶有限群的同构类型有多少。围绕这个问题可以引出很多抽象的概念，比如元素的阶数，abel群，正规子群，商群，Sylow定理等，同时也会学到如何把这些理论应用到具体的例子分析中学习“近世代数”时，就仅仅背下来一些命题、性质和定理，并不意味着真正地理解。要想真正理解，需要清楚这些命题、性质和定理的前提条件为什么是必要的？而达到这个目的的最有效的方法就是构造反例。
其次是通过变换角度寻求问题的解法，通常是将已知或未知较复杂的问题变换为等价的较简单的问题，或者是将新问题变换为已经解决的问题，或者是将未知与已知关系较少的问题变为已知与未知关系较多的问题等等
先参考着答案做题，然后自己总结方法思路，自己就开始会做了。问题在是否善于总结归纳。
以前学代数的时候从来没有意识到代数是门很抽象的学科，总在练习的过程中靠点小聪明学过来，也由于这段路一直走得非常平坦，我从来没停下来去想想其本身的理论体系的问题。现在想想，也许这就是我一直停留在考试成绩一般，却难以有所作为的原因吧。所以有时走得太快可能未必时间好事。很可惜现在才了解到这一点，同时也还算幸运，毕竟人还在青年，还来得及改正
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 neceary ? 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 proce 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
