你至少需要一些微积分、线性代数、概率、统计学、数值分析、蒙特卡罗方法、偏微分方程和随机微积分。 Paul Wilmott 的Paul Wilmott 介绍量化金融是一个很好的介绍。 这将为您提供上述主题的参考，并汇集必要的想法，以对定量金融有基本的了解。
You want some calculus, linear algebra, probability, statistics, numerical analysis, Monte Carlo methods, partial differential equations, and stochastic calculus at a minimum. A good introduction is Paul Wilmott's Paul Wilmott Introduces Quantitative Finance. That will provides you references for the aforementioned subjects as well as drawing together the necessary ideas to have a basic understanding of quantitative finance.
Generally, individuals who fill positions in computational finance are known as “quants”, referring to the quantitative skills necessary to perform the job. Specifically, knowledge of the C++ programming language, as well as of the mathematical subfields of stochastic calculus, multivariate calculus, linear algebra, differential equations, probability theory and statistical inference are often entry level requisites for such a position. C++ has become the dominant language for two main reasons, the computationally intensive nature of many algorithms and the focus on libraries rather than applications.
It might be interesting to look at artificial intelligence, and therefore mathematical logic as well, like neural networks, pattern matching, knowledge databases, inference, ...
I graduated with a math major. With that background the book you linked to is an introduction and it's painless. Without that background it's still an introduction and hopefully the pain isn't agonizing. (That you've survived long enough to ask a question here about it suggests that it's not.)
I read over the first 36 pages of the PDF you linked to (i.e. through chapter 4). It's highly technical and found I the following areas of math.
First semester calculus
Second semester calculus
Linear algebra (just a little)
Probability
Mostly the calculus is used to compute probability related things so if you're seroius about diving in to this stuff then I recommend that you start with algebraic probability and then work your way through the calculus.
A book that I got a lot out of was Time Series Analysis. You do need a lot of "basic math" including every topic mentioned by other responses. The thing is that computational finance is relentlessly mathematical and the more math you know often the better off you will be.
那么我建议您阅读 Mark Joshi 的书“数学金融的概念与实践”并完成所有练习和计算机项目。 里面有很多很棒的东西。
I liked "Paul Wilmott on Quantitative Finance, 2nd. Ed". It's a three volume set, lots of good math and explanations presented in an accessible way. I put up videos of concepts from the first volume on YouTube, check them out. http://www.youtube.com/user/NathanWhitehead
Then I would recommend reading Mark Joshi's book "The Concept and Practice of Mathematical Finance" and working through all the exercises and computer projects. Lots of great stuff in there.
我真的很喜欢阅读卡内基梅隆大学计算金融专业硕士课程的教学大纲。 Steven Shreve 写了一本很好的金融随机微积分教科书。 您可以在此处查看详细的课程描述
I really like reading through the syllabus for Carnegie Mellon's Professional Master's program in Computational Finance. Steven Shreve has written a good textbook in Stochastic Calculus for Finance. You can see the course descriptions in detail here
First you should know probability (combinatorics,probability density function PDF, random variable), types of PDF and work your way into calculus - differential, integral and partial derivatives. They are rather simple conceptually. Matrix helps you solve simultaneous linear equations.
For non-linear models, in nature, most processes are non-linear, depending on your rigor, you can make things as complex as you want.
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你至少需要一些微积分、线性代数、概率、统计学、数值分析、蒙特卡罗方法、偏微分方程和随机微积分。 Paul Wilmott 的Paul Wilmott 介绍量化金融是一个很好的介绍。 这将为您提供上述主题的参考，并汇集必要的想法，以对定量金融有基本的了解。
You want some calculus, linear algebra, probability, statistics, numerical analysis, Monte Carlo methods, partial differential equations, and stochastic calculus at a minimum. A good introduction is Paul Wilmott's Paul Wilmott Introduces Quantitative Finance. That will provides you references for the aforementioned subjects as well as drawing together the necessary ideas to have a basic understanding of quantitative finance.
查看维基百科条目，它会告诉您：
看看人工智能，以及数学逻辑可能会很有趣，比如神经网络、模式匹配、知识数据库、推理……
Look at the wikipedia entry and it will tell you:
It might be interesting to look at artificial intelligence, and therefore mathematical logic as well, like neural networks, pattern matching, knowledge databases, inference, ...
我毕业于数学专业。 有了这个背景，您链接到的书就是一个介绍，而且很轻松。 如果没有这些背景，它仍然只是一个介绍，希望痛苦不会令人痛苦。 （你已经活了足够长的时间在这里提出一个问题，这表明事实并非如此。）
我阅读了你链接到的 PDF 的前 36 页（即通过第 4 章）。 它的技术性很强，我发现了以下数学领域。
微积分主要用于计算与概率相关的事物，因此，如果您认真研究这些内容，那么我建议您从代数概率开始，然后按自己的方式工作通过微积分。
I graduated with a math major. With that background the book you linked to is an introduction and it's painless. Without that background it's still an introduction and hopefully the pain isn't agonizing. (That you've survived long enough to ask a question here about it suggests that it's not.)
I read over the first 36 pages of the PDF you linked to (i.e. through chapter 4). It's highly technical and found I the following areas of math.
Mostly the calculus is used to compute probability related things so if you're seroius about diving in to this stuff then I recommend that you start with algebraic probability and then work your way through the calculus.
我受益匪浅的一本书是时间序列分析。 您确实需要大量“基础数学”，包括其他回复中提到的每个主题。 问题是，计算金融学本质上是数学性的，你知道的数学越多，你的生活就会越好。
A book that I got a lot out of was Time Series Analysis. You do need a lot of "basic math" including every topic mentioned by other responses. The thing is that computational finance is relentlessly mathematical and the more math you know often the better off you will be.
成为一名真正的量化分析师而不仅仅是在量化公司工作的 IT 程序员所需的技能：
The skills you will need for being a real quant not just an IT programmer working in a quant company:
我喜欢“保罗·威尔莫特论定量金融，第二版”。 这是一套三卷本，以通俗易懂的方式提供了大量优秀的数学知识和解释。 我在 YouTube 上发布了第一卷的概念视频，请观看。 http://www.youtube.com/user/NathanWhitehead
那么我建议您阅读 Mark Joshi 的书“数学金融的概念与实践”并完成所有练习和计算机项目。 里面有很多很棒的东西。
I liked "Paul Wilmott on Quantitative Finance, 2nd. Ed". It's a three volume set, lots of good math and explanations presented in an accessible way. I put up videos of concepts from the first volume on YouTube, check them out. http://www.youtube.com/user/NathanWhitehead
Then I would recommend reading Mark Joshi's book "The Concept and Practice of Mathematical Finance" and working through all the exercises and computer projects. Lots of great stuff in there.
我真的很喜欢阅读卡内基梅隆大学计算金融专业硕士课程的教学大纲。 Steven Shreve 写了一本很好的金融随机微积分教科书。 您可以在此处查看详细的课程描述
I really like reading through the syllabus for Carnegie Mellon's Professional Master's program in Computational Finance. Steven Shreve has written a good textbook in Stochastic Calculus for Finance. You can see the course descriptions in detail here
首先，您应该了解概率（组合学、概率密度函数 PDF、随机变量）、PDF 的类型，并学习微积分 - 微分、积分和偏导数。 它们在概念上相当简单。
矩阵可帮助您求解联立线性方程。
对于非线性模型，本质上，大多数过程都是非线性的，根据您的严谨程度，您可以使事情变得像您想要的那样复杂。
信心非常重要。
First you should know probability (combinatorics,probability density function PDF, random variable), types of PDF and work your way into calculus - differential, integral and partial derivatives. They are rather simple conceptually.
Matrix helps you solve simultaneous linear equations.
For non-linear models, in nature, most processes are non-linear, depending on your rigor, you can make things as complex as you want.
Confidence is very important.