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钨的难易度| Alphamanbet万博app的,数学的力量:引进钨| Alpha的笔记本电脑版

September 12, 2019 —史蒂芬·沃尔夫勒manbet万博app姆

manbet万博app沃尔弗拉姆| Alpha的笔记本电脑版

The Next Big Step for Wolfram|Alpha

Wolfram|Alpha一直是一个巨大的打击了学生。无论是在大学或中学,钨|阿尔法已经成为学生获得解答一个无处不在的方式。manbet万博app但它是一个一次性的过程:学生进入他们要问的问题(说,在数学) and Wolfram|Alpha gives them the (usually richly contextualized) answer. It’s incredibly useful—especially when coupled with itsstep-by-step solution能力。

But what if one doesn’t want just a one-shot answer? What if one wants to build up (or work through) a whole computation? Well, that’s what we created数学and its whole notebook interface to do. And对于超过30年that’s how countless inventions and discoveries have been made around the world. It’s also how generations of higher-level students被教导

But what about students who aren’t ready to use Mathematica yet? What if we could take the power of Mathematica (and what’s now themanbet万博appWolfram语言), but combine it with the ease of Wolfram|Alpha?

我们ll, that’s what we’ve done inmanbet万博app沃尔弗拉姆| Alpha的笔记本电脑版

它的built on ahuge tower of technology,but what it does is to let any student—without learning any syntax or reading any documentation—immediately build up or work through computations。Just type input the way you would in Wolfram|Alpha. But now you’re not just getting a one-shot answer. Instead, everything is in aWolfram Notebook,在那里你可以保存和使用以前的结果,并通过整体计算建立或工作:

Wolfram Notebook

The Power of Notebooks

能够使用钨|阿尔法风格的自由形式的输manbet万博app入就是打开沃尔夫勒姆| Alpha的笔记本电脑版到全方位的学生。但它使用的ñotebook environment这使得它如此独特的教育价值。因为能够通过事工作的一系列步骤,让学生真正与他们正在做的计算接触。

Try one step. See what happens. Change it if you want. Understand the output. See how it fits into the next step. And then—right there in the notebook—see how all your steps fit together to give your final results. And then save your work in the notebook, to continue—or review what you did—another time.

But notebooks aren’t just for storing computations. They can also contain text and structure. So students can use them not just to do their computations, but also to keep notes, and to explain the computations they’re doing, or the results they get:

学生笔记本

而事实上,沃尔夫勒姆笔记本manbet万博app电脑实现一种全新的学生工作:计算随笔。A computational essay has both text and computation—combined to build up a narrative to which both human and computer contribute.

创建一个计算文章的过程是学生与他们正在学习材料搞的好方法。计算散文也可以提供学生的成绩有很大的展示,以及评估学生的理解的一种手段。而且他们不只是要生产用于分配:他们是活跃可计算的文件,学生可以在未来任何时间保持和使用。

Study notebook—click to enlarge

但是,学生们不是唯一的以生产笔记本电脑。在钨|manbet万博app Alpha的笔记本版,笔记本电脑也为教师为学生提供的材料一种很好的宣传。描述一个概念在笔记本上,然后让学生做自己的计算正确的,在笔记本的探索。或使确定的转让或笔记本测试,然后让学生在工作中填写(和档次它正确的,在笔记本电脑)。

Assignment

这是很常见使用钨| Alpha的笔记本版打造的概manbet万博app念可视化。通常,学生只要求可视化本身。但是,教师也可以设置为可视化模板,让学生在自己的功能或数据填充探索自己。

可视化

manbet万博app沃尔弗拉姆| Alpha的笔记本版还支持动态的交互式可视化,例如使用Wolfram语言Manipulatefunction. And in Wolfram|Alpha Notebook Edition students (and teachers!) can build all sorts of dynamic visualizations just使用自然语言

Dynamic visualizations

但是,如果你想要一些更复杂的互动演示,这可能是很难指定?那么,钨| manbet万博appAlpha的笔记本版具有直接访问manbet万博appWolfram演示项目,其中包含超过12,000演示。您可以使用自然语言要求演示,或者你可以浏览演示项目网站,选择一个示范,它复制到你的钨| Alpha的笔记本版的笔记本电脑,然后立即使用有:manbet万博app

示威

向Wolfmanbet万博appram | Alpha的笔记本版它很容易创建引人入胜的内容。内容可以涉及纯计算或可视化。但是,使用的功能manbet万博app沃尔弗拉姆知识库—it can also involve a vast range of real-world data, whether aboutcountrieschemicalswords or artworks。And you can access it using natural language, and work with it directly in a notebook:

使用自然语言

manbet万博app沃尔弗拉姆| Alpha的笔记本电脑版is a great tool for students to use on their own computers. But it’s also a great tool for lectures and class demonstrations (as well as for student presentations). Go toFile>New>主持人笔记本,and you’ll get a notebook that’s set up to create a Wolfram|Alpha Notebook Editionslide show

主持人笔记本

请点击Start Presentationand you can start presenting. But what you’ll have is not just a “PowerPoint-style” slide show. It’s a fully interactive, editable, computable slide show. TheManipulateinterfaces work. Everything is immediately editable. And you can do computations right there during the presentation, exploring different cases, pulling in different data, and so on.

幻灯片放映

从自然语言使代码

我们invented notebooks more than 30 years ago和y’ve been widely used in Mathematica ever since. But while in Mathematica (andWolfram Desktop) notebooks you (by default) specify computations in the precise syntax and semantics of themanbet万博appWolfram语言,in Wolfram|Alpha Notebook Edition notebooks you instead specify them just using free-form Wolfram|Alpha-style input.

And indeed one of the key technical achievements that’s made Wolfram|Alpha Notebook Edition possible is that we’ve now developed increasingly robust natural-language-to-code technology that’s able to go from the free-form natural language input you type to precise Wolfram Language code that can be used to build up computations:

Natural language to code

默认情况下,钨| Alpmanbet万博appha的笔记本电脑版设置向你展示它生成的Wolfram语言代码。你并不需要看看这段代码(你可以将其设置为总是被隐藏)。但-令人满意的,我作为一个语言设计者—students seem to find it very easy to read, often actually easier than math. And reading it gives them an extra opportunity to understand what’s going on—and to make sure the computation they’ve specified is actually the one they want.

And there’s a great side effect to the fact that Wolfram|Alpha Notebook Edition generates code: through routinely being exposed to code that represents natural language they’ve entered, students gradually absorb the idea of表达计算语言的东西concepts of computational thinking

如果学生想,当他们正在使用沃尔夫勒姆改变计算| Alpha的笔记本版,他们可以随时修改他们给了自由形式输入。manbet万博app但他们也可以直接编辑一个已经产生的Wolfram语言,让他们真正的计算语manbet万博app言的经验。

自由格式输入

我应该怎么做?预测界面

钨的中心目标| Alpha的笔记本电manbet万博app脑版是完全“自我服务” - 所以,学生在各级都能很好的使用没有任何外部的指令或协助。当然,自由形式的输入为实现这一目标的重要组成部分。但另一部分是钨| Alpha的笔记本电脑版manbet万博app预测界面—that suggests what to do next based on what students have done.

Enter a computation and you’ll typically see some buttons pop up under the input field:

纽扣

这些按钮会提示方向走。这里step-by-step solution产生的增强交互版本Wolfram|Alpha Pro一步一步的功能,都在笔记本右侧:

Step-by-step functionality

请点击相关计算你会看到,你可能想要做不同的计算的建议:

相关计算

It suggests plotting the integrand and the integral:

Plotting the integrand and the integral

这也表明你可能想看到一系列扩展:

Series expansion

现在注意到输出下面有关于可能的后续计算上做此输出建议了吧。点击,例如,coefficient listto find the list of coefficients:

Coefficient list

现在有新的建议。点击,例如,total找到总系数:

Find the total of the coefficients

The Math Experience

manbet万博app沃尔弗拉姆| Alpha的笔记本版已经有很多的功能,以提高“数学体验”。例如,点击在笔记本电脑的顶部按钮,你会得到一个“数学键盘”,你可以用它来直接输入数学符号:

Math keyboard

该undmanbet万博apperlies沃尔夫勒姆沃尔夫勒姆语言| Alpha的笔记本版日常要处理的是年代由世界顶级数学家所需要的数学。但是,拥有所有复杂的数学有时会导致混乱的学生。因此,在钨|manbet万博app Alpha的笔记本版有办法说“保持简单的数学”。例如,你可以将其设置为使用复数的最小化:

简化

简化

manbet万博app沃尔弗拉姆| Alpha的笔记本电脑版also by default does things like adding constants of integration to indefinite integrals:

积分常数

By the way, Wolfram|Alpha Notebook Edition by default automatically formats mathematical output in elegant“传统textbook” form。但它总是包含一点点按钮旁边的每个输出,这样你就可以与“传统的形式”进行切换,并standard Wolfram Language form

在做数学很常见功能,and just say “I want to plot that!” But what range should you use? In Mathematica (or the Wolfram Language), you’d have to specify it. But in Wolfram|Alpha Notebook Edition there’s always an automatic range that’s picked:

自动量程

但是,因为你可以看到Wolfram语言代码,包括的范manbet万博app围内,可以很容易地改变这种状况,并指定任何你想要的范围。

Specify range

如果你想要得到什么的交互式控制来改变范围,或改变功能的参数?在数学(或Wolfram语言),你必须写一个manbet万博appManipulate。但在钨| Almanbet万博apppha的笔记本版,你可以建立一个整体的人机交互界面只是用自然语言:

人机交互界面

And because in Wolfram|Alpha Notebook Edition theManipulate计算都是直接在本地计算机上运行,​​没有任何正在全速网络传输等一切动作慢了下来。(另外,如果你有一个很长的计算,你可以让它保持在您的计算机上运行;没有超时像钨|阿尔法在网络上)manbet万博app

Multistep Computation

One of the important features of Wolfram|Alpha Notebook Edition is that it doesn’t just do one-shot computations; it allows you to do multistep computations that in effect involve a back-and-forth conversation with the computer, in which you routinely refer to previous results:

多步计算

通常,这是不够的,只是说说最近的结果,并说这样的话“绘制它作为一个函数x”。但它也是相当普遍的要更早重提导致笔记本。要做到这一点的方法之一是说这样的话“前的最后一次结果” - 或者使用Out[ñ]labels for each result. But another thing that Wolfram|Alpha Notebook Edition allows you to do is to set values of variables, that you can then use throughout your session:

设定值

它也可以定义功能,全部采用自然语言:

定义功能

There are lots of complicated design and implementation issues that arise in dealing with multistep computations. For example, if you have a traditional result for an indefinite integral, with a constant of integration, what do you do with the constant when you want to plot the result? (Wolfram|Alpha Notebook Edition consistently handles arbitraryadditive constantsin plots by effectively setting them to zero.)

Integrate x

It can also be complicated to know what refers to what in the “conversation”. If you say “plot”, are you trying to plot your latest result, or are you asking for an interface to create a completely new plot? If you use a pronoun, as in “plot it”, then it’s potentially more obvious what you mean, and Wolfram|Alpha Notebook Edition has a better chance of being able to use its natural language understanding capabilities to figure it out.

世界向Wolfram | Almanbet万博apppha的笔记本电脑版

它已经非常满意地看到大量钨|阿尔法已经通过的学生。manbet万博app但大多数收养一直在教室外。现在,随着钨| Almanbet万博apppha的笔记本电脑版,我们已经得到了可以立即把在课堂上使用,在整个大学和预科谱的工具。我非常高兴看到它如何可以简化课程,加深了解,使新的概念被教导,并有效地提供的课程为基础的个人AI导师为每一个学生。

Starting today, Wolfram|Alpha Notebook Edition is适用于所有标准的计算机平台(在Mac,Windows和Linux)。(一个cloud version也可在网络上推出。)高校全manbet万博app沃尔弗拉姆技术系统的站点许可可以自动开始使用钨|今日阿尔法笔记本版;manbet万博app在学校与其他网站的许可证,它可以立即加入。它的available to K–12 schoolsandjunior collegesin classroom packs, or as a站点许可证。而且,当然,它也适用于个别教师学生们hobbyists和其他人。

(Oh, and if you have Mathematica or Wolfram Desktop, it’ll also be possible in future versions to create “Wolfram|Alpha mode” notebooks that effectively integrate Wolfram|Alpha Notebook Edition capabilities. And in general there’s perfect compatibility amongmanbet万博app沃尔弗拉姆| Alpha的笔记本电脑版数学Wolfram Desktopmanbet万博app沃尔弗拉姆云manbet万博app沃尔弗拉姆编程实验室,etc.—providing a seamless experience for people progressing across education and through professional careers.)

Like Wolfram|Alpha—and the Wolfram Language—Wolfram|Alpha Notebook Edition will continue to grow in capabilities far into the future. But what’s there today is already a remarkable achievement that I think will be transformative in many educational settings.

More than31 years ago we introduced Mathematica(and what’s now the Wolfram Language). A decade agowe introduced Wolfram|Alpha。现在,今天,随着钨发布| Alpha的笔记本电脑版我们给第一个味manbet万博app道的背景下教育的一种全新的计算方法:这是由自然语言驱动的完整的计算环境。它不会取代Wolfram语言,或钨| Amanbet万博applpha的,但它定义了一个新的方向,假以时日将带来计算的力量,整个庞大的新的观众。


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