重新学习享受数学
我是计算机科学专业一年级的学生,高中毕业几年后返回。
当我深入研究兔子洞时,我对数学在计算机科学中的重要性有了更大的认识。
问题是我不喜欢数学,我读了一篇名为 Lockhart 的挽歌 的文章我想总结一下我在高中数学方面的经验。我想学习更多的数学来提高我的编程能力并扩大我解决问题的能力,目前我正在学习罗森的离散数学文本,但感觉很辛苦。
我小时候就喜欢数学,自然而然地喜欢解决问题和逻辑。我希望能以某种方式重新点燃我对数学的兴趣。有没有人为了数学本身而重新燃起对数学的兴趣?
你从哪里开始,做了什么类型的事情?我有兴趣听听其他人的经历,也许是鼓舞人心的书籍或优秀的教科书
I'm a first year computer science student, having returned several years after finishing high school.
As I delve deeper down the rabbit hole I am gain a greater appreciation for the importance of math in computer science.
The problem is I don't enjoy math, I read an article called Lockhart's Lament that I think sums up my experience with math in high school. I want to learn more math to improve my programming abilities and broaden my problem solving abilities and at the moment I am working through Rosen's discrete math text but it feels like a grind.
I used to enjoy math as a kid, and I naturally enjoy problem solving and logic. I am hoping to somehow rekindle my interest in math. Has anyone managed to rekindle their interest in math for its own sake?
Where did you start, what type of things did you do? I'd be interested to hear other peoples experiences, maybe inspiring books or good text books
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当你学习数学时,你用数学解决的问题必须对你来说很重要,那么数学就会值得。仅仅读一本让你感到无聊的书而不同时解决你喜欢的问题可能不会有很好的效果。
如果您遇到需要数学的编程,请找到对您来说重要的编程变体,并解决它,同时学习所需的数学。
The problem your solving with the math as you learn it must to be important to you, then the math will be worth it. Just reading a book that bores you without working on a problem you enjoy simultaneously probably won't work very well.
If you have been running into programming that requires math, find some variant of that programming that is important to you, and solve it, learning the math required as you go.
我非常喜欢解决项目欧拉问题。它们本质上是数学的,可能会激发您的兴趣。
I enjoy solving project euler problems a lot. They are mathematical in nature and may sparkle your interest.
数学成为苦差事(从教师的角度来看)的问题在于符号。大多数人阅读问题或概念描述时都不会遇到任何问题。当引入符号来以数学方式描述问题时,人们往往会感到惊慌。
您的问题表明您对离散数学特别感兴趣。在我介绍过的许多离散数学中,解决一个有趣的谜题是很有帮助的,这个谜题是专门设计用于关注手头问题的逻辑和独立元素的。
不过,尝试拼图只是其中的一部分,因为你可以在任何书店买到拼图。但是,如果您无法以数学方式描述问题,那么除了您头脑中的算法之外,您还没有真正学到任何东西,而您可能无法以编程方式描述这些算法。解决密码是一种简单的字典攻击,大多数人都可以通过自己的语言经验来管理。尝试编写一个算法来逻辑地完成这件事完全是另一回事。
当您发现您喜欢解决(或尝试解决)的难题时,请使用教科书尝试通过适当的符号来描述所涉及的逻辑问题。一个很好的例子就是许多骑士、无赖和普通人 互联网上的谜题。获取常规逻辑问题,并尝试通过符号写出每个线索/推论的逻辑描述。
当您使用 Big O/Big Theta 表示法时……祝您好运。除了对这些概念的基本理解之外,我仍然在努力解决这个问题。
The problem with math becoming a grind (from an instructor's perspective) is the notation. Most people read problems or descriptions of concepts and have no trouble. The moment a notation is introduced to describe a problem mathematically, people tend to freak out.
Your question indicates you are specifically interested in discrete mathematics specifically. In a lot of discrete mathematics that I've covered, it is helpful to have a fun puzzle to solve that is specifically designed to focus on the logical and separate elements of a problem at hand.
Attempting puzzles is only one part of it though, because you can get puzzles at any bookstore. If you can't describe the problem mathematically, though, you haven't really learned anything beyond the algorithm in your mind which you may or may not be able to describe programmatically. Solving a cryptogram is a simple dictionary attack that most people can manage through their own experience with language. Trying to program an algorithm to do it logically is another story altogether.
As you find the puzzles you enjoy solving (or attempting to solve), use your textbook(s) to attempt to describe the logical problems involved through appropriate notation. A good example of this would be the many Knights, Knaves, and Normals puzzles on the internet. Get regular logic problems and attempt to write the logical descriptions of each clue/deduction through the notation.
When you get to Big O/Big Theta notation... good luck. I still struggle with this beyond basic understanding of the concepts.
我也不喜欢数学,获得工程学位也不是那么简单……我在高中和大学勉强取得了不错的成绩!当我毕业并开始在一家 IT 公司工作时,我开始对财务和会计产生兴趣。数字上的薄弱使得这变得更加困难。因此,我在网上搜索并发现了这个 YouTube 频道:可汗学院。这家伙太棒了!他发布了我们在高中学到的几乎所有内容的视频教程,包括代数、概率和算术等等。他的教程很容易理解,并且是与学习曲线上与您处于相同位置的其他人互动的好方法。
更好的是,比尔·盖茨和他的儿子们也遵循这些教程。在这里阅读更多相关信息:http://money.cnn.com /2010/08/23/technology/sal_khan_academy.fortune/
I never enjoyed math either and getting a degree in Engineering was not as simple...I barely managed to get decent grades in high school and college! As I graduated and started working at an IT company, I started gaining interest in finance and accounting. Being weak with numbers made this even more difficult. So, I searched online and came across this YouTube Channel: The Khan Academy. This guy is amazing! He has posted video tutorials on pretty much everything that we learnt in high school, including algebra, probability and arithmetic and much more. His tutorials are easy to understand and a great way to engage with other people who are on the same position as you on the learning curve.
Even better, Bill Gates and his sons follow the tutorials too. Read more about it here: http://money.cnn.com/2010/08/23/technology/sal_khan_academy.fortune/