How can I learn mathematical analysis well?

It is necessary to listen carefully in class and complete homework after class. In addition, you should do some corresponding extracurricular exercises to further improve your ability, the most representative exercise set is "Jimidovich Mathematical Analysis Problem Collection" (that has six fascicle recommendations), this is the original exercise problem, the questions in it are more difficult, not recommended for first-year freshmen, and now there are many solutions to this exercise set, too simple and too difficult questions are removed, recommended.

I usually have time to check more ** suitable for undergraduates, which is very helpful for learning.

The first thing to understand is to understand the concept, and then to practice a certain amount of exercises.

Typical Problems and Methods in Mathematical Analysis (Pei Liwen).

The "Mathematical Analysis Problem Solving Guide" and "Advanced Mathematics Problem Solving Guide" published by Peking University Press, as well as the "Mathematical Analysis Problem Exercise" (Zhou Minqiang), one of the exercise collections used by the School of Mathematical Sciences of Peking University, are all good, and the "Jimmy Dovich Problem Manual" is not recommended.

Some of the contents of Fishingolz's "Tutorial of Calculus" and Zorich's "Mathematical Analysis" provide a deeper understanding and improvement of mathematical analysis.

I think it is very important to learn mathematics well and exercise your logical thinking ability, and you should strengthen the training of logical thinking, so that mathematical analysis is naturally not a problem.

Exercise is the most important thing, and you should strengthen the training of logical thinking!

Mathematical analysis can be difficult in some ways compared to other mathematics courses

1.Strong abstraction. Mathematical analysis studies concepts such as functions, limits, and integrals, which are more abstract and not as intuitive as algebra and geometry, which can be more difficult to learn.

2.Strong reasoning. Mathematical analysis requires a lot of logical reasoning and deduction, which requires strong reasoning skills. Especially when it comes to proving theorems and solving problems, the importance of reasoning is even more apparent.

3.There are many theorems. Mathematical analysis involves a lot of theorems, which must be mastered and used flexibly, which also increases the difficulty of learning and memorizing.

4.Computationally complex. Compared to other mathematics, the calculations of mathematical analysis can be relatively complex, especially in terms of integration. This will also make it difficult for learners to have numeracy skills and habits.

5.Difficult to solve. Mathematical analysis exercises and test questions are difficult and require a comprehensive application of the knowledge and skills learned to perform step-by-step reasoning and calculations. This also makes it more difficult to learn and practice.

6.Logical and strong. Mathematical analysis requires rigorous logical reasoning and argumentation, and it is necessary to understand the premises, theorem content and deductive process, which requires strong logical thinking ability and also increases the difficulty.

In summary, the reason why mathematical analysis is difficult is because of its strong abstraction, strong reasoning, many theorems, complex calculations and strong logic. If you want to learn mathematical analysis well, you must have strong abstract thinking ability, logical reasoning ability and calculation ability, and at the same time, you must be proficient in theorems and formulas, and practice more in order to truly understand the mysteries. I hope these analyses are helpful to my classmates!

Mathematical analysis is a core course in advanced mathematics, which is a discipline that studies the laws of mathematical change, limits, and the foundations of calculus. Here are a few things that I think are difficult in mathematical analysis:

For example, calculus, limits, and continuity of functions, students need to master the relevant definitions and theorems first.

2.Strong logic: Mathematical analysis has a rigorous logical structure and proof methods, which requires a large number of proofs and deductions, and requires students to have profound mathematical skills and rigorous logical thinking ability. Understanding and applying proof methods takes a lot of time and effort.

3.Mathematical Logical Thinking: Mathematical analysis not only requires students to be proficient in various mathematical formulas and operation rules, but also requires students to have mathematical logical thinking, that is, to have a thorough understanding and mastery of mathematical thinking structures and reasoning methods.

This is the natural reasoning ability required by mathematical analysis, and it is not achieved overnight.

4.Understanding and application: Most of the classical theorems or results of mathematical analysis require the depth and breadth of rational understanding, as well as a higher level of application ability. Through a large number of knowledge points understanding and practice, students can truly grasp and appreciate the excitement of project export.

In short, mathematical analysis requires students to have solid mathematical professional knowledge, Hu Wang's excellent logical thinking, broad mathematical vision, in-depth understanding of mathematical analysis knowledge points, and mathematical "intuition". Only in the process of continuous practice and application can we gradually grasp and understand.

The first is the concept of "limit", that is, "you must learn it well, and you must be careful at the beginning", which means that you must strictly follow this definition, so that you can avoid the question of "why does this need to be proven, why is it so troublesome to prove".

The second: destroy one's own three views. Look at some more counter-examples:

Continuous but non-derivable, original functions exist but Riemann are non-integrable, functions that are discontinuous everywhere, functions that are continuous everywhere but not monotonic everywhere, functions that are continuous everywhere but not derivable everywhere, functions that are derivable everywhere but not monotonic everywhere. As long as you know that these deep ice-like functions exist, you will not dare to be arbitrary when you do proofs. Welcome to "Counterexamples in Real Analysis", which is really a functional psychiatric hospital.

Third: do the right amount of questions, don't brush a few meters, the efficiency is too low, you can do some condensed versions, understand first, and then calculate. Don't swap the limit and the integral at every turn, and swap the two limits without moving.

Don't dare Taylor for any function. I think Pei Liwen's "Typical Examples in Mathematical Analysis" is better, but it is a bit difficult. Beginners don't look at any rudin, it's not fun to play yourself to death.

There is a three-volume "Selected Translations of Russian Mathematics Textbooks" "A Course in Calculus" (by Fichkingolz) (said to be calculus, but the rigor is sufficient), which is written in a relatively unpretentious manner, suitable for beginners, with a lot of content, and you can omit the parts that you dare not be interested in when you read it. When I was a freshman in the physics department, I read this set, and then I went to the mathematics department and read Rudin's "Principles of Mathematical Analysis" again, and I thought it was best for Rudin to read it a second time (when I reviewed). Also, if you are interested in how to calculate integrals, you can read a book:

paul j. nahin inside interesting integrals

Fourth: The topic still has to be done, and I am afraid of the situation that I think I know when I learn mathematics, and many high school students in Zhihu claim to have learned mathematical analysis. In order to test yourself, you still have to do the exercises after class, at least 80%-90% of them are correct, do more questions on understanding and proof, and do the calculation questions in moderation.

Even if you can't do it, you have to ask people, and you can't give up quality for the sake of learning speed, and the final result is to kill yourself.

1. Pragmatic foundation.

The review process is an advanced stage of mastering knowledge, and the quality of review depends on the mastery of basic knowledge. Therefore, when learning new knowledge in ordinary times, we should "work steadily and steadily" and "step by step" according to the normal pace to lay a good foundation.

2. Self-study and induction. Peerless.

At the beginning of the review, first read and study the books according to the textbook units, review systematically, summarize and organize, and take good notes.

3. Check and fill in the gaps.

When reviewing, on the basis of your own induction, you should compare it with the teacher's comprehensive and systematic summary. Identify gaps, analyze the causes, and further strengthen the understanding of knowledge, and for problems that are not clearly understood, it is necessary to have a thorough understanding.

4. Intensive exercises.

Under the guidance of the teacher, you should choose a high-quality reference book to improve your thinking ability and problem-solving skills through problem solving, and deepen your in-depth understanding of what you have learned. Magnanimous.

5. Summarize and improve.

The purpose of the post-revision follow-up test is to check the effectiveness of the review and develop the ability to take the test, so it should be taken seriously. On the basis of the teacher's analysis of the test papers, the teacher will conduct a self-summary, mainly summarize the thinking methods and learning methods, find out the problems and deficiencies in learning, and clarify the direction of future efforts.

Preview well before class, so that when the teacher explains, he also has a bottom in his heart, and he can also keep up with the teacher's rhythm slowly.

Review the content in time after class, and don't know how to ask teachers or classmates quickly, or search for answers online.

Read more books and thoroughly understand every knowledge point in the books.

You can take a proper look at extracurricular materials, learn different methods of solving problems from books, and spread your thinking.

Then do more questions, if you do the questions, prepare a wrong question book, record the wrong questions in time, read it repeatedly, figure out why you are wrong, which knowledge point you have not mastered well, and then you can draw inferences from one another, change the value of one of the conditions, and see if you can still make it.

In the end, you must have confidence, believe in yourself, hehe.

I'm a math major.,This question depends on whether you just want to take the exam without failing the subject.,Or decide whether you want to go to graduate school in the future.,If you just don't want to fail the subject.,Then do the exercises in the first part of the book and the homework assigned by the teacher.,There is also a half-term exam to mention,That's it! If you want to go to graduate school, it's not just the things in the old model master's class, but also the library!

No matter how difficult the mathematical analysis is, there is no complex variable function, and the real variable function is difficult!

There is no square circle method that can guarantee that people can learn well, if there is a closed matter, the textbook and the teacher will copy it, how can there be such a cheap thing.

This is nothing more than talking about liquid, which is to read more books, do more questions, and do more research.