I know the pits of mathematics learning from the mathematics “performance line struggle” back to the 138 points of high school and university-aided mathematics: learning to forget, chapters like “no connection”, collages like cylindricals, which seem to be brushing up a lot of questions, but are scattered “scatters” that are unsolved. And then i figured out the way: math is about building knowledge systems at its core, and book-to-books are the shortcuts to building systems, and there's a lot less going around。
There's a classmate who's been stuck in high school maths at 80 points, brushed it till midnight, but didn't get any better. The problem arises from the confusion of the knowledge system, the fact that the same subject is not done with the knowledge points. And then i shared her a list of my own architecture, and she followed the system for six months, and the math was stable at over 110, and the exam was 125. Mathematics, therefore, is not "brushing as much as you can" and putting together the knowledge framework and then filling in the details to make it really work。
The following five books cover the whole process from basic awareness to institutionalization, to mental upgrading to integrated application, and can be found suitable for both secondary school students and adults who want systematic mathematics. Read it, and help you to learn from fragmentation and to build a well-developed mathematical knowledge system。
I. Introduction to ice break: the beauty of mathematics -- making math interesting
Many people are afraid of mathematics because they look at the formula theorem and don't know the logic and use behind it. "the beauty of mathematics" completely breaks that perception by explaining the practical application of mathematics in life in big white, so you know, "where does math work?"。
This book has no complex reasoning. It's all real cases around it. For example, the search engine that we use every day, behind which are mathematical graphics and probabilistic models; the smart association of cell phone input methods, which is statistically dependent; and even the distribution algorithm of micro-trusted red packets, which is closely linked to probability. Through these cases, you can understand the essence of the mathematical concept, not the dead-back formula。
That's how i got rid of the fear of math in high school. It used to feel that functions and probabilities were boring, and it was only after reading that they were ubiquitous and even began to think about “mathematical problems of life”. This book is suitable for all those with a weak mathematical base and no interest in mathematics. It helps you to build a good sense of mathematics and a cognitive base and paves the way for a follow-up system。
Frameworking: a list of high school mathematics knowledge (college) - a “knowledge network” of high school mathematics
If mathematics beauty is to help you build your consciousness, then the list of maths in high school is to help you build the “bones” of mathematics in high school. This book, called the encyclopedia of secondary math, classifies all knowledge points by modules, each of which has a clear knowledge map that allows you to see the links between the points of knowledge and never again feels fragmented。
Its central highlight is “knowledge networking”. Not only are the definitions, formulas, theorems of each knowledge point described in detail, but they also indicate the logical relationship between the knowledge point, such as the "function-librity " , "creature geometry and the resolution of geometry " , "limitation of arrays and variations". For example, when you learn "number columns " , it tells you that the essence of the columns is "special functions " , which solves the number column problem in a functional sense; when you learn "conductive numbers " , it connects the points of knowledge of functions, such as single modulations, polar values, etc., before they are joined, and links you to the web。
When i was in high school, i turned the book over, and every time i finished a chapter, i combed the knowledge points against the knowledge threads, the blurry of local priorities. Gradually, a “high-school digital knowledge network” was formed in the mind, which, regardless of the problem, was able to quickly locate the corresponding knowledge points and solve the problem. This book is suitable for secondary school students, as well as for adults who want to systematically supplement mathematics in secondary schools, and is the core of the mathematical system。
Improved thinking: mathematical thinking (king guangchang) - mastering the “bottom logic”
When the knowledge framework is put in place, it will have to be used, otherwise the point of knowledge will be “dead” and the combination of the problem will have to be cut. Mathematic thinking is the book that gives you a sense of “bottom logic”, which sums up the thinking that is common in mathematics, such as classification discussions, digital integration, transformation and reintegration, modelling, etc。
The book is characterized by a “case-plus-method” approach, each of which is accompanied by specific case-specific topics, ranging from junior high school to senior high school, which is difficult to cover and easy to understand. For example, "digital combinations" will help you to visualize abstract questions through the transformation of function images into equations, geometrics and algebraics; "classification discussion" will help you to decomplicate complex issues through variable, binary functional questions with parameters; and "model thinking" will help you transform life scenes into mathematical problems through practical application。
When i was in high school, i had a headache, and i followed the book to learn how to think. For example, a function with parameters can be quickly dismantled with a "classification discussion" and a "digital integration" can simplify the operation when a geometry is deciphered. This book helps you to “assess” the knowledge system, not only to “know the point of knowledge”, but also to “utilise the point of knowledge” for people who have a certain foundation and want to improve their ability to solve problems。
Integrated consolidation: the dictionary of mathematics (shanghai words publishing) - filling system “blood”
A better framework and a better way of thinking would need to be consolidated through practice to make knowledge systems more solid. The mathematics dictionary is the best option for filling the system's “blood and flesh”, and it captures the big subjects from the basics to the press-axis, sorted by knowledge points and the type of questions, each with a detailed idea and step to solve them for you。
The bright spots of this book are “a multi-problem” and “a thought analysis”. It not only tells you “how to do this”, but it also says “why” and “there is no other way” to broaden your thinking and understanding of knowledge systems. A function combination, for example, will solve the problem from the angle of algebra operations, geometric graphics, guidance applications, etc., so that you can understand the linkages between different knowledge points, and a geometry will give you a variety of solutions, such as traditional geometry, coordinates, etc., to use knowledge flexibly。
When i was in high school, i took three-to-five exercises a day, focusing not on doing the right thing, but on understanding the thought. Through practice, i am better equipped to access knowledge points in knowledge systems, and the speed and correctness of problem resolution has increased significantly. This book is suitable for the benefit of all those who wish to improve their ability to apply mathematics, whether they are students in secondary schools to cope with examinations or adults to consolidate their knowledge。
V. Progress extension: prince department (adrian banner) — deepening system “deepness”
The princeton microration book is absolutely the preferred if you want to further study in mathematics, or if you want to get a complete picture of core knowledge points such as calculus. The book, which is referred to as the “micro-centre bible”, uses clear logic and detailed extrapolation to help you eat through the essence of the calculus instead of remaining at the application level of the formula。
The book is suitable for those who already have basic calculus knowledge and want to deepen understanding. It starts with the concept of the limit, which leads step by step to the definition and nature of the conductors, the points and the entire logical system of calculus. For example, you can explain in detail why the index is the rate of instantaneous change, what the geometry of the points is, the essence of the calculus basic theorem, and help you to break the logical faults and build a more rigorous mathematical system。
When i studied mathematics in college, it was the calculus of the book that i used to think was obscure, and then i read it, and then i read it. It not only deepens your knowledge system, it also develops critical mathematical thinking and lays the foundation for subsequent higher levels of mathematical knowledge。
The essence of mathematics learning is the process from a “scattered knowledge point” to a “systemic knowledge network”, and the selection of a pair of books is the “accelerator” of the process. These five books, from awareness-building to foundation, to system-building, thought-raising and integrated applications, have created a complete learning loop that will help you to learn away from fragmentation and truly build a well-developed mathematical knowledge system。
Mathematics isn't really scary, it's the wrong way to learn. If the system is put in place and consolidated through practice, it will be able to integrate and cope with all kinds of mathematical problems。
How's your math base? Do you want to put the math base in high school or do you want to go to higher levels? If you pick one from the list above, which one would you prefer? Welcome to the comment section to share your experience and ideas
