[learning resources] understand and love mathematics

Catalog

1. Apply mathematical and Computational Thinking in scientific and engineering practice

2. Mathematics in artificial intelligence

3. use ADEPT Models understand complex concepts

4. Reference books

5. Limitations of data and calculations

---

picture source ：Memorization vs. Automaticity: Back to Basics or Beyond the Basics?

Understand mathematics , Don't memorize math . Learn mathematics , Not to be 985 In University , There are a group of small town problem makers who call themselves waste The author of the article , Not to show off the score , But in the future scientific and engineering practice , Using mathematics and mathematical abstract modeling thinking , Make a real contribution and influence .

About Mathematics , I have written the following articles

【 Learning resources 】 Mathematical reference materials related to machine learning _ Apple II blog -CSDN Blog

Today, I would like to summarize the mathematics learning materials I collected with you , Hope to help you understand mathematics , Love math .

1. Apply mathematical and Computational Thinking in scientific and engineering practice

In scientific and engineering practice , How to use mathematical and computational thinking ？

Mathematics is a good tool , It has the communication function as one of the scientific languages and the structural function of allowing logical deduction . Mathematics can express ideas in precise form , And be able to identify new ideas about the physical world . Computing tools enhance the power of mathematics by implementing calculations that cannot be performed by analysis . Calculation method is also an effective tool for visualizing data , They can display the results of a calculation or simulation in a way that allows exploring patterns . Although there are differences in the application of mathematical and Computational Thinking in science and Engineering , But mathematics usually combines these two fields , A mathematical form that enables engineers to apply scientific theories , And enable scientists to use powerful information technology designed by engineers . 

I want to know how to cultivate students' mathematical and Computational Thinking in science education in primary and secondary schools in the United States , Listen to the following audio .

Applied mathematics and Computational Thinking in science and engineering practice 1 The meaning of mathematics and calculation _ Interpreting the United States K-12 Science education framework _ Free online reading, listening and downloading - The Himalayan

Applied mathematics and Computational Thinking in science and engineering practice 2 Learning goals _ Interpreting the United States K-12 Science education framework _ Free online reading, listening and downloading - The Himalayan

Applied mathematics and Computational Thinking in science and engineering practice 3 Specific development process _ Interpreting the United States K-12 Science education framework _ Free online reading, listening and downloading - The Himalayan

Please visit the following link to read the report A Framework for K-12 Science Education, You can get detailed information

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas |The National Academies Press

2. Mathematics in artificial intelligence

Recommend a good article for you

Shenhuawei, Institute of computing, Chinese Academy of Sciences ： Fig. review and frontier of neural network expression ability

Mr. shenhuawei explained the graph neural network in depth GNN The mathematical essence and theoretical bottleneck of , And it raises three very good questions ：

1. Is it necessary for us to construct a graph neural network with such high expression ability ？

2. GNN Can you learn structural patterns ？

3. Can you build a more powerful GNN Well ？

The specific content , You can also refer to Mr. shenhuawei's speech video ,

Figure neural network webinar 2020 The latest theoretical progress and application exploration of graph representation learning and graph neural network

source ： Figure neural network webinar 2020 The latest theoretical progress and application exploration of graph representation learning and graph neural network

In particular , Although wechat articles come from 6 In June, the second Beijing Zhiyuan conference , And the video is 3 Activities in the month , But the content is consistent .

3. use ADEPT Models understand complex concepts

Kalid stay Best Explained A very good model is presented on the website , Help people understand complex concepts .

Analogy analogy ： This concept is like something known ？

Diagram visualization ： What does this concept look like ？

Example example ： What are the cases around you ？

Plain English Explain in vernacular ： How to explain this concept to a child ？

Technical Definition： What is the definition and description of a true profession ？

Reference link ：Learn Difficult Concepts with the ADEPT Method – BetterExplained

Kalid Why we should learn mathematics is also put forward in the following paragraphs , Because mathematics is a specific and powerful vocabulary for expressing ideas . When considering new ideas , We found ourselves still a fool , You need to learn mathematics .

Why Do We Learn Math? – BetterExplained

picture source ：Why Do We Learn Math? – BetterExplained 

Special recommendation “ Simple and easy to understand ”？ Let's explain hidden Markov models One article , The above methods are used to help readers understand hidden Markov HMM.

4. Reference books

linear algebra

Recommended reasons ：

Explain the meaning and essence of linear algebra through application cases , Look at the following interesting examples .

1. How to use matrix and equations to complete the analytic hierarchy process in Management Science , Complete information retrieval , Realize the population statistics of sea turtles , Solve problems about the network ;
2. How to use determinant to complete information coding ;
3. How to use vector space to analyze population migration ;
4. How to use linear transformation to realize computer graphics and animation ;
5. How to use orthogonality to investigate information retrieval , Complete the factor analysis and element analysis of psychology ？ How to use the least square method to calculate the orbit of asteroids ？ How to do signal processing with orthogonality ？
6. How to locate the space shuttle with eigenvalues ？ Investigate the vibration of buildings ？ Predict car rental ? Search pages and graded pages ？ How to use singular value decomposition to process digital images and analyze the elements of Psychology ？
7. How to use numerical linear algebra to calculate the weight problem in analytic hierarchy process ？

5. Limitations of data and calculations

Although mathematics has its strong points , It also has its limitations . Welcome to my audio . Data or calculations can't do anything ？

I hope you can learn and explore , Understand mathematics , Love math , And make real contributions with mathematics .