微积分手机版作者J.Keisler教授是伟大的数学思想家、教育家与贡献者

     大家知道，上世纪50-60年代，、是美国塔尔斯基学派创立数理逻辑模型轮的黄金时期。在1967年，塔尔斯基的博士生J.Keisler首先提出了数学理论按照其复杂性分层的概念，后来被称为“Keisler ‘s Order”。

五十年之后，在2017年12月，基于Keisler“数学理论复杂性”分层观念（或理论），两位数学家合作证明了集合论奠基人康托尔提出的关于连续统假设（CH）不成立，为此，两人荣获集合论顶级豪斯多夫大奖。

实际上，Keisler教授从1969年开始投身于鲁宾逊非标准分析实现“教材化”的伟大事业。前后经历了50年之久，Keisler教授精心撰写了“Elementary Calculus”（无穷小方法）微积分教材。现在，把这本具有先进数学思想的微积分教课书（称为“微积分手机版”）推向全国高校就是我们的事业。

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袁萌  陈启清  8月20日

附：Mathematicians Mure Infinities and Find They’re Equal

infinity

Mathematicians Mure Infinities and Find They’re Equal

By  Kevin Hartnett September 12, 2017

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the most famous and intractable problems in mathematics: whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers.

The problem first identified over a century ago. At the time, mathematicians knew that “the real numbers are bigger than the natural numbers, but not how much bigger. Is it the next biggest size, or is there a size in between?” said Maryanthe Malliaris of the University of Chicago, co-author of the new work along with Saharon Shelah of the Hebrew University of Jerusalem and Rutgers University.（由于文件太长，以下省略）