What books should be used for college freshmen to get started with advanced mathematics

Answer: If a freshman college student learns advanced mathematics in the first semester, the school will distribute textbooks, is there anything better than textbooks?

The teaching materials have been inspected by the National Education Bureau, and are absolutely authoritative and formal. Those extracurricular tutoring books, no matter how good they are, the core of their ideas also come from textbooks. Therefore, you must first master all the knowledge in the textbook, and in order to make perfect, you must not fail to understand it, but you must read it intensively and understand it thoroughly.

In this way, when you do the more difficult topics in the extracurricular books in the future, you don't have to think so hard about why this is the case, how many people ask why this is the case? Actually, there is no reason, it is all fashionable formulas and theorems.

It is necessary to listen carefully to the class, there are always some people who like to study on their own, and feel that the teacher's lecture is useless, and it is in vain to listen to it. That's a big mistake, the teacher is a teacher after all, he is professional in this area, even if what he says is simple, listening, will not be in vain, because the process of listening is a process of communication, pay attention to the details of the teacher's lecture process, maybe you are distracted, a very important sentence will be ignored by you. That's a wealth you've lost, and it may be just a little bit of something you've lost, and you may have to spend a hundred times more time thinking about it in the future, and the gains outweigh the losses.

Generally two books,Further MathematicsIt is divided into two volumes, and it is completed in the first year of the freshman year.

Universities (universities, colleges) are the implementation of higher education.

of a kind of school, including a comprehensive university.

It is a unique organization that is a higher education institution that inherits, researches, integrates and innovates advanced scholarship that is interrelated with the economic and political institutions of society.

Charter

The constitution of the university is the "sail of the constitution" within the university, which is dismantled by the authority of the university in accordance with the charter established by the university and the national or local education laws and regulations in order to ensure the independent status of the university.

A governing program that is formulated in accordance with certain procedures concerning the nature of the organization and basic rights of the university and has certain legal effect.

In addition to independent textbooks, most schools use the Tongji version of high mathematics.

Books of different grades are the same, but some of the content of the lower grades is not learned. Mathematics A (11 credits) is required to be learned in all of them, and Mathematics B (8 credits) is not required to be re-integral. Since you're going to count A, just learn it all.

Advanced math skills: The content of college mathematics is different from the mathematics we have learned before. In the past, in mathematics, we all knew what it was and knew why, and the derivation process, meaning, etc. of each knowledge were relatively obvious, and we were relatively understandable.

But higher mathematics.

Many of the definition languages, derivation processes, etc., are very rigorous mathematical languages, and 99% of students will be confused when they look at these related proof processes.

The above content refers to the encyclopedia - Advanced Mathematics.

1.Be understood! Be understood! Be understood!

This is the most important word, so say it three times.

To change from a high school student to a college student, you must first change your thinking.

For those of us who are non-gifted players in mathematics.

Abstract thinking may not be as big as we can't.

But often we have a natural advantage when it comes to figurative thinking.

When introducing a new concept, make sure that its image comes to mind.

and understand the meaning it represents on a perceptual level.

Example-limit", don't be intimidated by the abstract formulas in the book, think of a function in your head, such as the -1 power of e.

You'll find it as if it's never going to reach 0

But it's getting closer and closer.

So when x tends to infinity, its limit is 0

2. Derive the commonly used formulas yourself.

This process may not be useful for the exam in the short term.

But stick to it, and the results are immediate.

Benefits of doing so:

Exercise your logical thinking.

A deeper understanding of the formula with forks.

As the saying goes, if the brain doesn't turn, it will rust.

The process of deriving the formula is precisely what makes one's head spin.

Ask a few more whys, and slowly accumulate a little touch.

Of course, formulas like Fourier series are very difficult to derive.

You don't have to push it yourself, but you must read the derivation process in the book!

3. Quickly brush up on after-class questions.

In order to save time, it is not recommended that everyone brush them one by one.

Instead, first look at the classic example questions with points and faces, and then brush a few similar ideas, and then think of ways to think of the questions after class in your mind, and cross out those who can come up with ideas, and read them carefully if you can't think of them.

It's not hard to finish a book in three days!

4. Pay attention to review classes and learn to guess questions.

Cramming before the exam and engaging in some strategies is also a good choice to help you improve your scores!

I myself am very confident in guessing the questions, although I can't completely guess the questions.

But the test sites and inspection methods involved can be.

Guess nine is not far from ten.

This requires you to work the teacher's revision class.

You can record and listen to the key points and question types clearly.

If you don't focus on the key questions, you can directly memorize the second-level conclusions.

In the key part, I will read all the classic example questions, and then look at two or three difficult problems.

If you have short-answer questions, be sure to pay attention to the concepts and principles!

<> the seventh edition of Advanced Mathematics compiled by Tongji University, it is a very representative book of advanced mathematics.

In the first National Textbook Construction Award, the seventh edition of Advanced Mathematics (Volume I and Volume II) compiled by Tongji University won the "National Excellent Textbook Special Award". From the first edition to the seventh edition, the Department of Mathematics of Tongji University has collectively compiled the textbook and has achieved the ultimate goal.

Now many colleges and universities also use this version of the textbook, including my own school, and my feeling after learning is that the content of the textbook is very rigorous, committed to telling every knowledge point well, the classic example questions are worth repeatedly, and many of the after-class questions are excerpted from the postgraduate examination questions over the years. In short, it's a non-renting book.

However, learning high mathematics well is not just a good textbook, but also needs to constantly think about jujube concealment and practice.

Books required for self-study of advanced mathematics: advanced mathematics textbooks, advanced mathematics study problem workbooks.

2. After being familiar with the relevant concepts and basic knowledge, you can further increase your understanding of textbook knowledge and increase your ability to apply relevant knowledge through additional exercises in the corresponding advanced mathematics study book.

3. Be good at using the resources around you. For example, on the Internet, if you encounter knowledge that you don't understand, you need to search for relevant knowledge on the Internet to solve relevant problems. At the same time, you can also learn and consolidate the knowledge you have learned through online classes.

Here are some recommendations for advanced math books:

1.Thomas Calculus, by Finney, Vail, and Giordanno, is an intuitive and easy-to-read book that emphasizes modeling applications and skills training, while at the same time surging mathematical integrity, making it suitable for engineering use.

The above are some recommendations for advanced mathematics books, readers can choose the books that suit them according to their needs and interests.

A Course in Calculus, Introduction to Advanced Mathematics, On Calculus, etc.

Calculus Tutorial is a January 2006 issue of Higher Education Press.

Published book by (Russia) Fichkingoltz.

Calculus Course 8th Edition) is one of the series of selected translations of Russian mathematics textbooks, which is included in the series of textbooks to Moscow State University.

This book is an excellent work on mathematics and education, as well as textbooks from other well-known Russian universities. In the more than 50 years since the first edition was published, "A Course in Calculus 8th Edition" has been reprinted several times.

It is still considered a comprehensive university in Russia.

and technical and pedagogical colleges selected for mathematical analysis.

One of the basic textbooks of the course. It has been translated into many languages and is popular all over the world. It can be used as a teaching reference book for mathematical analysis and advanced mathematics courses in various colleges and universities at all levels, and is an excellent desk book for mathematical analysis teachers.

Bibliography. 1.Rational number fields.

2.Import of irrational numbers and order of real number fields.

3.Arithmetic operations on real numbers.

4.Other properties and applications of real numbers.

Universities that think they are good at have their own textbooks. However, it is generally recognized that the better is the "Advanced Mathematics" edited by Tongji University and published by the Higher Education Press, which is divided into two volumes, and has now published its sixth edition. The sixth edition of the comparative version emphasizes more on the understanding and mastery of basic concepts, and the requirements for calculation skills are relatively lower.

This is mainly due to the advancement of computing technology, and the requirements for mathematics have also changed.

But like calculating triple integrals using spherical coordinates, Stokes' formula as an asterisk is something that takes into account the learning difficulties of students nowadays. And things like least squares are the same.

If you need advanced mathematics to take the exam, this textbook can be said to be the best.

There are higher education publications, and there are Tongji University publications.