Zhou Yu, an algorithm engineer of a leading Internet company and a Ph.D. in computer science. He has been working in the fields of artificial intelligence such as machine learning, deep learning, and reinforcement learning for many years. He is good at discovering unique beauty in the combination and application of mathematics with practical work and life. The series of articles he wrote have been circulated by readers, and he was awarded the title of "the most high-quality" mathematics class.
Look at math again
Mathematics is a general method for human beings to strictly describe and deduce the abstract structure and mode of things, and it can be applied to any problem in the real world. From the description here, we can read the following information:
Things have their own structure and pattern, which is a law. Humans describe the laws of things, which requires mathematics. Human beings deduce the laws of things, which requires mathematics. Any problem in the real world requires mathematics.
Mathematics has infinite power. It helps game development engineers model the physical world, quantitative financial analysts make money, and audio processing engineers make music. In the field of data science and machine learning, mathematical knowledge is indispensable.
In the relevant majors of the university courses, there are nearly ten courses directly related to mathematics, such as advanced mathematics, line algebra, probability theory, statistics, complex variables, stochastic processes, ordinary differential equations, etc. Even when we are graduate students, we study machine learning and AI courses, and we will find that its essence is also related to optimization or convex optimization.
After getting in touch with the society, we will also surprisingly find that many industry laws are also habitually summarized with mathematical formulas . For example, a company is as good as strategy times execution.
why learn math
In fact, we encourage all staff to learn mathematics. In other words, at least a certain mathematical foundation and mathematical thinking are required. Such a knowledge reserve may greatly improve the efficiency of your work and life. Such practical problems abound in life. Turing has published many mathematics-related books, all of which prove the power of mathematics.
Let's look at a case. Damei ordered a 12-inch pizza. After placing the order, the waiter told Damei that she could not make such a large pizza temporarily due to the shortage. The waiter suggested to replace it with two 8-inch pizzas, so the price is the same.
May I ask whether the replacement of Damei is a disadvantage?
The mathematical calculation here involves a unit of measurement that is not commonly used by us, that is, how much is "inch". Some students may say, first, I don’t know the concept of “inch”, second, I don’t know whether the 8 inches mentioned here is a diameter or a radius, and third, I don’t have a calculator at hand, so I can’t judge which pizza is more affordable .
In order to know the result more accurately, we can calculate it from a mathematical point of view.
We know from Baidu Encyclopedia that the inches mentioned by pizza generally refer to the diameter in inches. Among them, 1 inch = 2.54 centimeters, π = 3.14.
According to the circle area formula, two 8-inch pizzas have an area of
Ï€
Similarly, a 12-inch pizza has an area of
Pi
Therefore, after calculation, it will be found that after replacing it with two 8-inch pizzas, Dameili actually lost money, and the loss was quite a lot.
The calculation here really depends on a calculator, and it may be difficult for us ordinary people to calculate such an accurate number as 648 or 729. But if it is just to compare the size, we can use the inequality principle of the linear relationship to get the result quickly.
The so-called inequality principle of linear relationship is actually the following formula: a, b, and n are all positive numbers, assuming a > b, then a n > b n. Back to the question here, we can write the following relationship.
We assume that 1 inch is m centimeters, pi is π, and the inch of pizza is represented by h. Then the radius of the pizza is r = h * m / 2. Then the formula for the area of pizza is
pp
Therefore, the problem is transformed into judging the magnitude relationship between π and π.
There is an item "π" on both sides, according to the inequality principle of linear relationship, the size relationship has nothing to do with it. Then the problem is transformed into the judgment of the magnitude relationship of and. At this point we can easily find that , and is 144. The latter is larger, so it's more cost-effective to buy a 12-inch pizza.
Using the above mathematical knowledge, we can make an accurate judgment without knowing the concept of "inch", whether the inch here is a diameter or a radius, and without the help of a calculator.
Take my actual work as an example. As a programmer, I often deal with codes. Do I also need to learn mathematics? To answer this question, you may first need to understand what a programmer does. A program, or code, is a language that computers only understand. A program is written to solve a simple or complex problem.
Therefore, the story chain of programmers writing code comes from a real problem. First of all, it is necessary to analyze this real problem and design an algorithm to solve it efficiently. Secondly, translate this algorithm into a language that the computer can understand to form a code. Eventually, the computer runs this code to solve this real-world problem. The analysis of problems, design of algorithms, and efficient solutions here are all inseparable from mathematics. Code and mathematics are good partners who know each other and are based on common rational thinking.
Similarly, the work of each of us comes from a certain problem in real life, and it is inseparable from the application of mathematical thinking.
how to learn math well
Students from all walks of life should have basic knowledge and skill reserves for mathematics, but this does not mean that we have to delve into various complex mathematical theories like mathematicians. Mathematics is a basic subject, and many other basic subjects and applied subjects are based on mathematics. For most people, math is more of a tool.
For ordinary people, we need to use mathematics as a tool, combined with our own professional knowledge, to scientifically, rigorously and efficiently deal with various practical problems we encounter, and constantly improve mathematical thinking in the process of practice.
However, looking back at the student days, most of the students did not seem to have a smooth journey in mathematics learning in the past. Does this mean that after we get to work, we still have to relearn so many esoteric mathematical theories as before? In fact, mathematics is a basic subject. In order to lay a good foundation in the school days, it is necessary to "drill down" to the mathematical core of theoretical knowledge.
This course is more application-oriented . After we have properly interpreted the classic mathematical theories, we will use them more "upward"; that is, to solve practical problems with mathematical tools.
The whole course revolves around mathematical theory and application and is divided into the following four modules.
Module 1 : Describes the mathematical foundations such as number system, logic, induction, and nesting that need to be mastered in this course, to help you better understand the connection between programs and mathematics. First review the basics of mathematics, and explain common problems in program development from a mathematical perspective.
Module 2 : After having a mathematical foundation, we need to use the mathematical foundation to explain foreign objects, and try to use mathematical models to understand the real world .
Module 3 : With a strong understanding of the world, we can establish mathematical models based on the information of external objects, and use the optimization methods in mathematics to decide the best actions, which is to use mathematics to decide actions .
Module 4 : Use several examples to practice how to use mathematics to solve practical problems, and help you better master mathematical thinking from practice. For example, how to manage personal connections and how to analyze store data.
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The core of the whole course is to provide Internet programmers with a mathematical perspective to solve practical business problems, with the goal of applying mathematics to solve practical problems, so that you can understand programs from a mathematical perspective, master the basic routines of mathematical applications, and have the ability to use mathematics Ability to solve general problems.
Principle + practical problems, landing application
Avoiding the textbook content of pure mathematical principles, the course strengthens the application of mathematics from the perspective of solving practical problems . After completing the course, you can use what you have learned and use it after you have learned it.
Step-by-step learning route
The content of the course is arranged around the main line of " getting started, understanding the world, and making decisions and actions ", so that it is clearer which link each knowledge point can be used for. After learning, you can have a better understanding of the application level of the mathematical theory described.
Real cases, master the routine
This course covers a large number of practical cases. On the one hand, it can make theoretical mathematical knowledge more explicit, and on the other hand, it can highlight the methods and routines of using mathematics to solve problems.
If you are a practitioner in the Internet industry, or someone who wants to improve the underlying capabilities in the AI era , then this course must not be missed. Programmers with 0-3 years of experience can use this to improve their mathematical thinking and consolidate their code foundation. Experienced programmers or enthusiasts interested in mathematics can also review what they have learned through this course, and use mathematical tools to better understand the world and solve real problems.
The course is new, the new period is 99 yuan, and the group price is 69 yuan.
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