College mathematics learning methods 1
Go ahead despite difficulties and learn by turns.
Learning mathematics must first be not afraid of setbacks, have the courage to face the difficulties encountered, and have the perseverance to continue learning, which is particularly important when you first enter the university to study mathematics.
When I was in middle school, maybe many students liked to learn math and got excellent grades in math, so they were in a virtuous circle at this time, and they didn't have too much frustration or care too much about the importance of facing it bravely. As soon as we enter the university, because the theoretical system is completely different, we will encounter a lot of troubles at the beginning of our study, and even have unsatisfactory results, such as failing the exam. At this time, we must stick to it, advance despite difficulties, and continue to learn from the teacher.
I just started school, but I've been dizzy. Although I can understand what the teacher said in class on the surface, I don't understand the real reason behind the knowledge, so I always feel that what I have learned is not true. As for doing the problem, it is even worse. I don't dare to read the exercises in Jimidovich at all, because there are few exercises in the book that can be done after class. This is really a far cry from the situation in high school. I was almost discouraged at that time. However, I happened to meet Professor Tang Tao from Baptist University who came to our school to give a lecture, so after the lecture, I went forward to talk about the difficult state of my mathematics study at that time and asked him how to solve this problem. Professor Tang saw that I was a freshman in the department of mathematics who had just come to school for more than a month, and immediately replied, "Dizziness is normal, and I may get better in a few months." When I first heard this sentence, I still couldn't believe it, but after all, it was said by an awesome person, so I did it first.
Later, I have been crustily skin of head to learn from the teacher. Although I still don't understand, I still feel very hard to do my homework, but I never give up. Now I really think that sentence is true. Perhaps this state is the only way to learn mathematics, so we must overcome this difficulty to learn the theoretical knowledge of college mathematics well.
Besides persistence, we should also be careful not to spend too much time on solving some problems. Because the theory of college mathematics is very rigorous, sometimes it is inevitable to use some theoretical ideas that can be learned later when explaining the preparatory knowledge in textbooks, so it is very uneconomical to stick to this problem when preparing for learning.
For example, at the beginning of Mathematical Analysis, I spent a lot of time thinking about the purpose of introducing this theorem. Because there was no foundation at that time, I couldn't figure out how to think about this problem, and even felt that this theorem had no substantive significance. It was not until later that I learned the mathematical analysis of multiple parts and the professional course "Real Variable Function" that I began to understand its real use. The reason why we want to explain here is that the real number system has a definite bound, that is, it has a continuous property. The purpose is to pave the way for the later limit and continuity, because it is meaningful to consider the corresponding change of the dependent variable only when the independent variable can change continuously, and then we can study the properties of the function. But if you don't learn it later, it's hard to figure it out when you only know the interval and don't know some other strange point sets.
Therefore, when you start to learn mathematics, you can consider taking a circuitous way of learning. Write down the problems that are difficult to understand at the moment, then continue to learn the subsequent knowledge, and then go back to review from time to time. In the review process, due to the accumulation of later knowledge, you may find out the problems left over from the past, which in turn can promote the profound understanding of later knowledge. This circuitous learning method makes it possible to review the past not only to learn new things, but also to better understand the past.
However, it doesn't mean that you don't think about anything when you first get started. On the contrary, diligent thinking is a good habit to learn math well. "Mathematics is the gymnastics of thinking". Only by persisting in thinking can we master its theoretical system and logical relationship. Therefore, when learning, we should master the scale, not only to ensure full thinking, but also not to be too stubborn.
Learning methods of college mathematics II
Understand the background and learn the theory.
An obvious difference between college mathematics and middle school mathematics is that college mathematics emphasizes the basic theoretical system of mathematics, while middle school mathematics pays attention to calculation and problem solving. The direct reaction is that the exams in the department of mathematics in universities are almost all about the proof of mathematical theorems or definitions, while there are many technical calculation or proof questions in middle schools. Therefore, in view of this feature, when studying college mathematics, we should pay attention to establishing our own mathematical theoretical knowledge framework.
To learn the theoretical system, we must first know why this theory is established and what its function is, which requires understanding the historical background knowledge of mathematics. Therefore, I would like to recommend two books on the history of mathematics to you: Ancient and Modern Mathematical Thoughts * * * Klein * * and 20th Century Mathematical Jingwei * * * Zhang Dianzhou * *. The former book deals with the development of mathematics from ancient Greece to19th century, while the latter book deals with the development of mathematical theory in the last century, so these two books basically record the development history of the whole mathematical theory.
In the second semester of freshman year, classes were suspended due to SARS, so I borrowed "20". After reading it, I feel that it has played a great role in my math study. After that, I felt very natural and easy to accept a lot of theoretical knowledge. For example, Mathematical Analysis emphasized the mastery of language from the beginning, and its appearance was caused by the "second mathematical crisis" in the history of mathematics. As we all know, Newton's calculus has made great achievements in application, but the theoretical basis of calculus at that time was quite chaotic. Newton took infinitesimal as a non-zero number as the denominator when calculating the derivative, and then left it at zero, which led to a logical error. Cauchy, a great mathematician, put forward the concepts of limit and derivative in language in order to lay a correct and solid foundation for calculus. With the help of language, we can clearly show the process of taking the limit of a function, which is also very clear and rigorous in logic. In this way, after understanding these historical background knowledge, I feel it is necessary to learn a language, and it will be much more natural to learn it. There are many interesting stories about mathematicians in the book 20th Century, one of which is the written record of the author's interview with Chen Shengshen, a mathematician master. In that article, Master Chen Shengshen talked about many methods and attitudes of learning mathematics by himself, especially the problem of mentality, which is very enlightening to our students in mathematics department. So I suggest that if you have time, you must read this math history book.
Besides understanding the background to help us learn theoretical knowledge, we should also study hard. After being exposed to these strange mathematical theories for a period of time, you may feel that you have understood them, but in fact you may not be able to really grasp them, especially the logical relationships contained in those proofs are the most prone to mistakes. Therefore, when studying, we should properly remember theoretical knowledge and sometimes theorems. Only by rote memorization can we find our own theoretical loopholes and cultivate our strict theoretical and logical abilities, which is very helpful for future study.
Learning method 3 of college mathematics
Natural humanities, all-round learning
All of the above are about learning mathematics knowledge, but to learn mathematics well, we should not only learn mathematics knowledge, but also learn more about other disciplines, and have a broad knowledge base. Professor Lin Jiaqiao, a famous applied mathematician, once said that every college student in MIT should study mathematics, science, chemistry and biology in an all-round way in the first year, which is a fine tradition that their school has always maintained.
Many problems in natural science are the creative source or application basis of mathematical theory. For example, Riemann Geometry, founded by the famous mathematician Riemann, did not exert its power at first, but it was not put into use until the great physicist Einstein put forward the theory of relativity. Therefore, knowing more about other natural science knowledge will help us better understand mathematical theory and discover its value.
The study of humanistic knowledge is also essential, and many mathematicians have profound humanistic knowledge literacy. For example, Professor Qiu Chengtong, the winner of the Fields Prize in China, is very proficient in our ancient literature. When writing, he often quotes or writes ancient poems such as Zuo Zhuan to reflect some of his research. In fact, when we study very basic mathematical theory knowledge, such as mathematical logic, we must use humanistic knowledge to understand mathematics from a philosophical point of view. After Godel, a famous mathematical logician, proved the "incompleteness theorem", another mathematician Weil said: "God exists because mathematics is undoubtedly compatible; The devil also exists because we can't prove this compatibility. " This philosophical statement reflects the importance of mathematical theorems from a philosophical point of view.
The above are some learning methods that I have summed up after studying mathematics in recent years, most of which come from my own personal lessons. Although I can't guarantee that I can learn math well by these methods, I believe that as long as I do it, it will be helpful and rewarding.
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