One of the best way to learn mathematics is by following its history and see how new ideas were formed/discovered. It makes the concepts less abstract (less seemed pulled out of thin air by ur dull prof) and A WHOLE LOT more interesting. One book that offers such a perspective is:
http://www.amazon.com/exec/obidos/tg/detail/-/0393 04002X/ref=cm_wl_vvu-pg.1-pos.1/104-4995310-126551 5?v=glance&coliid=I13AVPIN0XVDBH&me=ATVPDKIKX0DER# product-details
I don't believe that argument for a minute! Given an open-source project with sufficient complex code base, it takes some expertise within to be able to understand the code and point out problems. Sure a casual bystander may point out some trivial problems, but to contribute meaningfully, you'll be digging deep into the code and most people will not do.
There's also ton of evidence that shows that well-designed and large projects are best done with small groups of people. (See The Mythical Man-Month and troll book of Tao of Programming)
Does this mean China will start writing more software than pirating from others?;)
(It's nice to see fellow country-men taking good use of their math prowess. Since the problems in these contests are math problems in disguise, they may start dominating this area in the future, after becoming comfortable at expressing with keyboards than pens.)
Hopefully the book mentioned how the Chinese court later turned sour on foreign explorations and destroyed most of the records by Zhang He. (I venture to guess that much of the historical facts about Zhang He are not from China but inferred unfortunately from European sources.) The unwillingness to open its borders for trade of goods and knowledge has been the prevailing force behind its ultimate fall from being the most advanced civilization at the time (Ming and Tang Dynasty) to a later weakling carved up by Europeans (Opium Wars at the end of Qing Dynasty).
The world is infinitely complex in any subject. Once you've grasped the basics of subject (from studying in college), you develope a tolerance to the known material and it becomes boring with repetition. This will not change if you simply change your major out of curiousity for some other field. The key is continously challenge yourself in some field in which you have basic knowledge and discover in it the 99.99% that you don't know about. Remember, it was your facination with computer science in the beginning that got you interested. You can apply the same facination in the next level.
In general it's hard work (but extremely exciting and rewarding) to develope depth in anything where as skin-deep breadth in many subjects only speaks of one's lack of perseverance. If that's what you lack, you won't cure with it new major.
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One of the best way to learn mathematics is by following its history and see how new ideas were formed/discovered. It makes the concepts less abstract (less seemed pulled out of thin air by ur dull prof) and A WHOLE LOT more interesting. One book that offers such a perspective is: http://www.amazon.com/exec/obidos/tg/detail/-/0393 04002X/ref=cm_wl_vvu-pg.1-pos.1/104-4995310-126551 5?v=glance&coliid=I13AVPIN0XVDBH&me=ATVPDKIKX0DER# product-details
I don't believe that argument for a minute! Given an open-source project with sufficient complex code base, it takes some expertise within to be able to understand the code and point out problems. Sure a casual bystander may point out some trivial problems, but to contribute meaningfully, you'll be digging deep into the code and most people will not do.
There's also ton of evidence that shows that well-designed and large projects are best done with small groups of people. (See The Mythical Man-Month and troll book of Tao of Programming)
Does this mean China will start writing more software than pirating from others? ;)
(It's nice to see fellow country-men taking good use of their math prowess. Since the problems in these contests are math problems in disguise, they may start dominating this area in the future, after becoming comfortable at expressing with keyboards than pens.)
Hopefully the book mentioned how the Chinese court later turned sour on foreign explorations and destroyed most of the records by Zhang He.
(I venture to guess that much of the historical facts about Zhang He are not from China but inferred unfortunately from European sources.) The unwillingness to open its borders for trade of goods and knowledge has been the prevailing force behind its ultimate fall from being the most advanced civilization at the time (Ming and Tang Dynasty) to a later weakling carved up by Europeans (Opium Wars at the end of Qing Dynasty).
The world is infinitely complex in any subject. Once you've grasped the basics of subject (from studying in college), you develope a tolerance to the known material and it becomes boring with repetition. This will not change if you simply change your major out of curiousity for some other field. The key is continously challenge yourself in some field in which you have basic knowledge and discover in it the 99.99% that you don't know about. Remember, it was your facination with computer science in the beginning that got you interested. You can apply the same facination in the next level. In general it's hard work (but extremely exciting and rewarding) to develope depth in anything where as skin-deep breadth in many subjects only speaks of one's lack of perseverance. If that's what you lack, you won't cure with it new major.