Many readers want me to make a list of mathematical books, and this article will recommend the excellent mathematical books in my mind.
Before recommending, first make a few tips:
The following books were selected mainly for their nature, such as the "subset of the history of the scriptures". In the vernacular, it is authentic. It's not that other books haven't been selected, but that I can think mainly of these things at the moment, and I'll continue to add them later.
The following books do not have to be purchased all at once. I also read these books little by little, and buying them at once may have psychological pressure; choose the two or three books I want to read the most, and then buy them slowly after reading them.
Some books have a slight threshold, such as requiring a large period of continuous time or requiring a basic understanding of the mathematical system. Readers who have a book that they want me to interpret or read are welcome to leave a comment.
The book list is divided into six categories, and in order to write the characteristics of each book, we will talk about the content a little. In order not to be too long, this article will first write the first three categories, and the next article will continue to write the remaining three categories.
directory
Base class
Aesthetics
General Studies
Biographical class
Subject class
Hard science
<h1 class="pgc-h-arrow-right" data-track="18" >01 base class</h1>
Recommended bibliography: Renjiao edition of "Student-based Learning Materials", Shanghai Teaching Edition of Primary School Mathematics
Suitable for: Preschool and primary and secondary school children and parents, mathematics educators
Recommended reason: The Shanghai version of mathematics textbooks is the leader in domestic mathematics textbooks, and the writing concept not only fully takes care of the learning rules of students, but also does not lose the ideological nature of mathematics. Instead of buying a variety of exercise books, parents should buy Shanghai teaching materials for their children's reference. To say more, the Shanghai version of the textbook was introduced as a textbook by the United Kingdom a few years ago.
"Student-based Learning Materials" is a trial version of the future human-taught textbook, and the concept of writing is very scientific, and it can even be said without exaggeration that it will be the benchmark for primary school mathematics textbooks in the next ten years. However, for the time being, it is only in the fourth grade, and it is said that the entire elementary school stage will be out before the end of the year.
Reading suggestion: In view of the fact that these two sets of books are textbook attributes, and each place has its own textbooks, these two sets of books can be mainly used as a reference, especially with reference to the interpretation logic of knowledge.
Purchase channel: "Student-based Learning Materials" can be purchased at the "People's Education Publishing House" on Taobao, or in the RenjiaoShuyuan next to minzu University.
<h1 class="pgc-h-arrow-right" data-track="55" >02 Aesthetics class</h1>
The reason why the aesthetic category is put so high is because it is really too important. Mathematical learning is more or less vulgarized, in fact, when you really walk in, you will find that mathematics has an aesthetic component in its essence. For mathematical people who do academics, if there is no taste, it is almost goodbye to first-class work. Children also try to establish a good "sense of numbers" at a young age.
Recommended Books: The Confession of a Mathematician, The Sigh of a Mathematician, The Lazy Collection
Suitable for: Children from the fourth grade of primary school, parents and educators
Reason for recommendation: "A Mathematician's Confession" was first translated as "Confessions of a Mathematician", which is the late work of the British mathematician Hardy. Hardy did outstanding work in mathematics, especially in the field of number theory. The story related to Hardy that the public knows is mainly that Hardy discovered the legendary Indian mathematician Ramanujin as a Bole, and interested readers can go to see the movie "The Knower".
Back to the book. Hardy begins by writing:
"A mathematician who finds himself writing something about mathematics would be sad. Because mathematicians' job is to do practical things, such as proving new theorems... instead of talking about what they or other mathematicians have done. ”
This shows Hardy's cleanliness of mathematics. In this book, Hardy uses practical examples (such as the infinity of prime numbers, the irrational proof of root number 2, etc.) to argue to the reader that mathematicians and artists are essentially the creators of patterns. True immortal mathematics, a very important criterion for judging whether it is beautiful or not.
Therefore, if you want to cultivate a good mathematical taste, the book "Confession" is an excellent choice. However, there is still a reading threshold for the book, and if the reader wants the author to read the book, he can vote at the final vote.
The threshold is not so high and it is also a good option, "A Mathematician's Sigh", which is a tribute to Hardy as soon as you hear the name. The author of the book, Paul Lockhart, graduated from Columbia University with a Ph.D. and later taught at Brown University. Suddenly, one day, he quit his college position and went to teach mathematics at a K12 consistent school in New York.
Lockhart himself said this about his choice:
“I want them to understand that there is a playground in their minds and that that is where mathematics happens.”
I want children to understand that math is all about playing freely in the playground of the mind.
In A Mathematician's Sigh, the author begins by analogy with a musician's nightmares about how terrible the current mathematical education is, as if every day you remember how each note was written but never listened to real music.
What does true mathematics look like? Mathematics should be art. As the mathematician Hardy said, mathematicians and artists are creating patterns, but mathematicians can create patterns in their minds. Then Lockhart gives an example:
How many fractions of the area of the triangle in the figure is rectangle?
For domestic children, the problem is too simple: half of the model, so it is one half. Let's see how Lockhart does it.
What exactly does this question mean? If I find an actual rectangular cardboard and draw a triangle, can I determine the number of fractions of the area by measuring their weight?
In the process of thinking about the above problem, we can realize that the real essence of the problem is that this is a purely imaginary rectangle and triangle, and any entity in reality is only an approximation of them. What we are really asking for is that the area of this triangle that exists only in the mind accounts for a fraction of the area of the rectangle that exists only in the mind?
At this point you will find that the rectangles and triangles have fully acquired their freedom, and that after they have been freely created by your mind, the remaining problems are not for you to control. For example, you can't force a triangle to make up two-thirds of the rectangle's area, and your logic will laugh at you until you draw this dotted line, which is also in your head:
Triangles are divided into two parts, each half of which is half, so the area of the triangle is one-half of the rectangle!
From there, Lockhart takes the reader on a truly mathematical journey of how to create freely in the mind and then think logically. You will find that mathematics is really created by yourself little by little, rather than copying the blackboard and writing it down, you will experience the joy of real thinking, rather than doing a few problems.
The last book, The Lazy Collection, by Kunihiko Kohata, a Japanese mathematician and Fields Medal winner. In this book, Kunihiko Kohira talks about both mathematics education and his own mathematical study and work experience, both mathematical learning methods and anecdotes of mathematicians, which is very easy to read.
Two examples.
In the "Mathematical Impressions" section, Kunihiko Kodaira puts it this way:
Mathematics does not rely on logic, but on the sense of numbers
What is number sense
Reading advice: The above three books are written by mathematicians (two are mathematicians), and the overall technical requirements are not high, but it also takes some time. For the modern mathematical concepts mentioned in it, you can skip it, just look at mathematical ideas, methods, etc., because our purpose is to infiltrate first, and cultivate a pure mathematical taste little by little.
Purchase channels: When JD.com can buy.
<h1 class="pgc-h-arrow-right" data-track="97" >03 General education class</h1>
Recommended books: What Is Mathematics, Mathematics and Life, X's Fantastic Journey
Suitable for readers: children from junior high school, parents and educators
Recommended reason: "What is Mathematics" is written by mathematician Courant, the content starts from natural numbers, gradually introduces the operations, properties and laws of numbers, and then goes to the rational number system, the real number system, the complex number system, and the larger picture of the number layer by layer.
Of course, we know that the expansion of the mathematics system is also exactly what mathematics will learn in elementary, middle, and high schools. Next, What Is Mathematics continues to talk about basic Euclidean geometry, affine geometry, non-Euclidean geometry, and topology, thus giving the reader a basic understanding of the general outline of geometry. The third part is functions, limits, and calculus fundamentals.
That is to say, "What Is Mathematics" includes the number system of algebra, the European and non-Euclidean geometry of geometry, and the calculus foundation of analytics, so that readers have a basic understanding of the knowledge system and development of mathematics from ancient times to modern times.
The idea of Mathematics and Life is similar, covering the development of the number system, basic Euclidean geometry, and basic calculus. It can be said that "Mathematics and Life" is the best companion for students outside the textbook, because the content of the book includes the mathematical content from elementary school to junior high school to high school.
More crucially, from the title of the book, we can see that "Mathematics and Life" emphasizes the connection between mathematics and life, or the cultural background of mathematics. This provides additional nourishment for students to learn mathematics, which stimulates interest in learning.
The Fantastic Journey of X is the author of Steven Strogatz, a professor in Cornell University's Department of Applied Mathematics, and the content of this book is actually still numbers, algebra, geometry, analysis, probability and statistics, and the frontiers of mathematics, but the style is very different from the first two.
Let's get a feel for it from the first verse.
Introduce mathematics from Sesame Street
As you can see from the content of this section, the style of the book is storytelling. Introduce mathematical concepts through a variety of interesting topics, and integrate the content into the story.
Therefore, the above three books, from an interesting point of view, the order is:
"X" > "Mathematics and Life" > "What Is Mathematics"
But in terms of the systematization of knowledge, the ordering is:
What is Mathematics > Mathematics and Life > X
Readers can choose according to their own preferences and needs.
Reading suggestion: As mentioned above, "What is Mathematics" is the most technical, if the child is still only in elementary school or junior high school, in fact, you can wait; of course, if the child's mathematical level obviously belongs to the top layer, you can consider buying it to open your eyes.
In contrast, the universality of "Mathematics and Life" is much better, one content is more compatible with the textbook, and at the same time provides a large number of mathematical cultural backgrounds, which can be used as a companion for the textbook. "X" is highly interesting and can also be read as a story + mathematical culture.
Purchase channels: When JD.com can be.