What’s in this website ?
Welcome ! I’m Jonathan Chen and this is a subdomain website of my blog.
As an undergraduate student majored in math, I have read plenty of books. During these years, I have developed my own way to read math books —- by skiming through the chaper to draw a “big picture” in my mind and picking out the definitions and theorems without knowing the proof of them, then I would head for the exercises of the chapter. In this way, I could know “Why the definition of a specific concept is the way it is and what the theorm is for.” After finishing the exercises, I would head back to figure out the proof. Usually, this step is simple as long as I have already worked out the exercise.
Reading math books in this way, however, has an obvious drawback, inefficient, actually. One must be patient enough, because, you might be stunned in some problem for weeks even months. But I think it is worth doing so. For most of math problems outsdide the textbook, they might be unspecific, even the statement of the problem is not clear enough. What a real mathematics do is probably the same way as I read these math books.
Workig on problems is a crutial part of learning mathematics
no one would regard the exercises of each chapter as a sidekick of the book. So, I launched this website to post my original solution to each (mainly) exercise of the books I read. But I can’t present all of then, since the typing them all on line a tiresome job. Only the tricky and confusing one would be presented.
The Reason for doing so can be summarized as follow:
- First, it serves as a reminder. Because I would certainly forget the definition, the lemma, the theorem. Consequencetly, I will need to pick out my notes to “refresh my memory”, and this website is a good resource for that purpose, since these are written in my own though.
- Second, It’s hard to gurantee that evey solution every detail is correct, so I post them on the internet and let the people all around the world to judge them, modify them. I would be glad and appreciated, if you could point out the erros in my solutions or provide a much more elegent solution. Actually, I take this as a way to make new friends and exchange ideas.
Oh, yes! One more thing, here is the book list:
- Â Topology – by James Munkres. [Reviews]