大學數學自修

其實只要你不急於求成﹐這個問題是不難回答的
你只要去買套大學數學(第二版)便成
該書共七卷。分為微積分(一),微積分(二),多元微積分及其應用,代數與幾何,流形上的微积分,隨機數學,數學實驗。
你要自修數學至微分幾何﹐可以先看微積分(一),微積分(二)﹐再看多元微積分及其應用﹐最後看代數與幾何就得啦。行有餘力的話可以看看流形上的微积分﹐是深造課程來的。
不過你一定要順序看﹐雖然微積分(一),微積分(二)基本上你全部學過﹐但看多次當溫書無妨﹐而且有少部份al無教的。
你直接看"Elementary differential Geometry"也沒甚麼意思﹐因為個background不夠﹐硬來也沒用的。

2008-12-11 23:21:41 補充：
代數與幾何最後那篇便是說微分幾何的。

2008-12-11 23:23:05 補充：
我不懷疑The Witch君說的是好書。不過還是認為循序漸進較好

Too lazy to type Chinese, Hope I can help you in this topic, as I did differential geometry as my dissertation, so I did kind of learn this topic by myself with a little help from my dissertation superviors, at that point he recommond two book for me as the main sourse to my project.

Geometry from a Differentiable Viewpoint and Elementary Differential Geometry (Springer Undergraduate Mathematics) (Springer Undergraduate Mathematics) (Paperback)

I found the "Elementary differential Geometry" is much easier to read, however, before you get into this topic, i think it will be better for you do some learning on Vector Calculus.

2008-12-09 22:48:23 補充：
I think you should try to read the "Elementary differential Geometry", then once you found something you dont understand then you can learn it from different sourse, but if you can do some Vector Calculus first, I think that do really help a lot.

2008-12-13 03:06:07 補充：
I just want to ask if myisland8132 is a differential geometror or not. Honestly, you really "DONT" need to have so much background to do centrain stuff. it is not about 急於求成!

2008-12-13 03:06:14 補充：
What I am going to say to you is, if you never did the subject and you never know what is that, then please keep your mouth shut. Pretty honest with you is even tho you read all the books you said, and honestly, that is not really that related at all.

2008-12-13 03:07:12 補充：
One more thing, when I did "Elementary differential Geometry" is in my first year, I dont even do the HKAL before I really read the book.