You always want to check your signs at the and because it's so easy to get the sign wrong, and I was hoping that it was right here because I wasn't sure, but it turned out to be right.

我们完成计算时，一定要记得检查符号,因为很容易弄错符号，刚才我就不太确定,是否弄错了符号，检查发现没有问题。

麻省理工公开课 - 热力学与动力学课程节选

At the end of the class, here's what I am hoping for, at the end of the class, if you decide to take it.

在本课程结束时，我所希望的是，在本课程结束之时，如果你打算上这门课的话。

哈佛公开课 - 幸福课课程节选

I'm hoping it was going to be obvious, what's the lesson here?

我希望大家都清楚结论是什么

耶鲁公开课 - 博弈论课程节选