接着，如果你学过本科阶段的代数课程（或者具备足够的数学成熟度，能啃得下一些代数定义），我推荐泰特（Tate）和西尔弗曼（Silverman）合著的《Rational Points on Elliptic Curves》。这本书没有特别死抠严谨性，但在椭圆曲线入门方面讲得非常好。https://link.springer.com/book/10.1007/978-3-319-18588-0
Subsequently, if you've taken an undergraduate level algebra class (or just have mathematical maturity and can work through some algebraic definitions) I suggest Tate and Silverman's Rational Points on Elliptic Curves. It's not super rigorous but it's good at introducing elliptic curves. https://link.springer.com/book/10.1007/978-3-319-18588-0
……每一步单独拿出来都不算太难，但又足够深入，能逼着我思考，从而靠自己形成一些深刻的理解。（不过这种方法也可能会翻车。西尔弗曼那本本来极好的《Rational Points on Elliptic Curves》在附录里给出了贝祖定理（Bezout's theorem）的引导式证明，但切得太碎了，反而很难让人真正理解。）
…the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own. (This approach can also fail. Silverman's otherwise excellent book Rational Points on Elliptic Curves has a guided proof of Bezout's theorem in the appendix that is just too atomized to engender much understanding.)
我1972年的硕士论文题目就是《椭圆曲线上的有理点》（Rational Points on Elliptic Curves）。在我的书架上吃灰整整50年了。一个月前，我发现 EC（椭圆曲线）居然成了现代加密技术的基础。去研究1972年以来的新进展挺有意思的。不过，就我所知，加密货币（Cryptocurrencies）……
My Masters Thesis in 1972 was “Rational Points on Elliptic Curves”. It’s been sitting on my shelf for 50 years. A month ago, I discovered that EC’s are now the basis for encryption. Been fun exploring what’s been done since 1972. However, based on what I know, Cryptocurrencies…
伊恩·斯图尔特（Ian Stewart）写的任何书都行。西尔弗曼（Silverman）的《椭圆曲线上的有理点》（Rational points on elliptic curves）
Anything written by Ian Stewart. "Rational points on elliptic curves" by Silverman
接着，如果你学过本科阶段的代数课程（或者具备足够的数学成熟度，能啃得下一些代数定义），我推荐泰特（Tate）和西尔弗曼（Silverman）合著的《Rational Points on Elliptic Curves》。这本书没有特别死抠严谨性，但在椭圆曲线入门方面讲得非常好。https://link.springer.com/book/10.1007/978-3-319-18588-0
Subsequently, if you've taken an undergraduate level algebra class (or just have mathematical maturity and can work through some algebraic definitions) I suggest Tate and Silverman's Rational Points on Elliptic Curves. It's not super rigorous but it's good at introducing elliptic curves. https://link.springer.com/book/10.1007/978-3-319-18588-0
……每一步单独拿出来都不算太难，但又足够深入，能逼着我思考，从而靠自己形成一些深刻的理解。（不过这种方法也可能会翻车。西尔弗曼那本本来极好的《Rational Points on Elliptic Curves》在附录里给出了贝祖定理（Bezout's theorem）的引导式证明，但切得太碎了，反而很难让人真正理解。）
…the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own. (This approach can also fail. Silverman's otherwise excellent book Rational Points on Elliptic Curves has a guided proof of Bezout's theorem in the appendix that is just too atomized to engender much understanding.)
我1972年的硕士论文题目就是《椭圆曲线上的有理点》（Rational Points on Elliptic Curves）。在我的书架上吃灰整整50年了。一个月前，我发现 EC（椭圆曲线）居然成了现代加密技术的基础。去研究1972年以来的新进展挺有意思的。不过，就我所知，加密货币（Cryptocurrencies）……
My Masters Thesis in 1972 was “Rational Points on Elliptic Curves”. It’s been sitting on my shelf for 50 years. A month ago, I discovered that EC’s are now the basis for encryption. Been fun exploring what’s been done since 1972. However, based on what I know, Cryptocurrencies…