注：本文为 "数学基础学习" 相关合辑。
英文引文，机翻未校。
如有内容异常，请看原文。
The Definition of Mathematics（数学的定义）
Mathematics is one of the most important subjects. Mathematics is a subject of numbers, shapes, data, measurements and also logical activities. It has a huge scope in every field of our life, such as medicine, engineering, finance, natural science, economics, etc. We are all surrounded by a mathematical world.
数学是最重要的学科之一。数学是一门研究数、形、数据、测量以及逻辑活动的学科，在我们生活的各个领域都有广泛的应用，例如医学、工程、金融、自然科学、经济学等。我们都被一个数学世界所包围。
The concepts, theories and formulas that we learn in Maths books have huge applications in real-life. To find the solutions for various problems we need to learn the formulas and concepts. Therefore, it is important to learn this subject to understand its various applications and significance.
我们在数学书中学习的概念、理论和公式在现实生活中有着广泛的应用。要找到各种问题的解决方案，我们需要学习这些公式和概念。因此，学习这门学科对于理解其各种应用和意义至关重要。
What Is The Definition of Mathematics?（数学的定义是什么？）
Mathematics simply means to learn or to study or gain knowledge. The theories and concepts given in mathematics help us understand and solve various types of problems in academic as well as in real life situations.
数学的字面意思是学习、研究或获取知识。数学中的理论和概念帮助我们理解和解决学术以及现实生活中的各种类型的问题。
Mathematics is a subject of logic. Learning mathematics will help students to grow their problem-solving and logical reasoning skills. Solving mathematical problems is one of the best brain exercises.
数学是一门逻辑性学科。学习数学有助于学生培养解决问题和逻辑推理能力，解决数学问题是最好的脑力锻炼之一。
Basic Mathematics（基础数学）
The fundamentals of mathematics begin with arithmetic operations such as addition, subtraction, multiplication and division. These are the basics that every student learns in their elementary school. Here is a brief of these operations.
数学的基础始于算术运算，如加法、减法、乘法和除法。这些是每个学生在小学阶段都会学习的基础知识。以下是对这些运算的简要说明。
-
Addition: Sum of numbers (Eg. 1 + 2 = 3 1 + 2 = 3 1+2=3)
加法：数的和（例： 1 + 2 = 3 1 + 2 = 3 1+2=3）
-
Subtraction: Difference between two or more numbers (Eg. 5 − 4 = 1 5 - 4 = 1 5−4=1)
减法：两个或多个数之间的差（例： 5 − 4 = 1 5 - 4 = 1 5−4=1）
-
Multiplication: Product of two or more numbers (Eg. 3 × 9 = 27 3 \times 9 = 27 3×9=27)
乘法：两个或多个数的积（例： 3 × 9 = 27 3 \times 9 = 27 3×9=27）
-
Division: Dividing a number into equal parts (Eg. 10 ÷ 2 = 5 10 \div 2 = 5 10÷2=5, 10 is divided in 2 equal parts)
除法：将一个数分成相等的部分（例： 10 ÷ 2 = 5 10 \div 2 = 5 10÷2=5，即将 10 分成 2 个相等的部分）
History of Mathematics（数学史）
Mathematics is a historical subject. It has been explored by various mathematicians across the world since centuries, in different civilizations. Archimedes, from the BC century is known to be the Father of Mathematics. He introduced formulas to calculate surface area and volume of solids. Whereas, Aryabhatt, born in 476 CE, is known as the Father of Indian Mathematics.
数学是一门具有历史渊源的学科。几个世纪以来，世界各地不同文明的众多数学家都对其进行了探索。公元前的阿基米德被称为"数学之父"，他提出了计算立体表面积和体积的公式。而出生于公元 476 年的阿耶波多被称为"印度数学之父"。
In the 6th century BC, the study of mathematics began with the Pythagoreans, as a "demonstrative discipline". The word mathematics originated from the Greek word "mathema", which means "subject of instruction".
公元前 6 世纪，毕达哥拉斯学派将数学研究作为一门"论证性学科"开创。"数学"一词源于希腊语"mathema"，意为"教学科目"。
Another mathematician, named Euclid, introduced the axiom, postulates, theorems and proofs, which are also used in today's mathematics.
另一位名叫欧几里得的数学家提出了公理、公设、定理和证明方法，这些至今仍在现代数学中使用。
History of Mathematics has been an ancient study and is described by each part of the world, in a varying method. There were many mathematicians who have given different theories for many concepts, which we are applying in modern mathematics.
数学史是一门古老的研究领域，世界各个地区都以不同的方式对其进行了记载。许多数学家为众多概念提出了不同的理论，这些理论至今仍在我们的现代数学中得到应用。
Numbers, which we use for calculations, had variations in the medieval period. The Romans introduced the Roman numerals that uses English alphabets to represent a number, such as:
我们用于计算的数字在中世纪有不同的形式。罗马人发明了罗马数字，这种数字使用英文字母来表示数值，例如：
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| I | II | III | IV | V | VI | VII | VIII | IX | X |
Branches of Mathematics（数学的分支）
The main branches of mathematics are:
数学的主要分支包括：
- Number System（数系）
- Algebra（代数）
- Geometry（几何）
- Calculus（微积分）
- Topology（拓扑学）
- Trigonometry（三角学）
- Probability and Statistics（概率论与统计学）
These mathematical concepts fall under pure mathematics . These form the base of mathematics. In our academics we will come across all these theories and fundamentals to solve questions based on them.
这些数学概念属于纯数学范畴，它们构成了数学的基础。在学术学习中，我们会接触到所有这些理论和基础知识，并基于它们解决相关问题。
Applied mathematics is another form, where mathematicians, scientists or technicians use mathematical concepts to solve practical problems. It describes the professional use of mathematics.
应用数学是另一种形式，数学家、科学家或技术人员利用数学概念解决实际问题，它体现了数学的专业应用价值。
Symbols in Mathematics（数学中的符号）
Some of the basic and most important symbols, used in mathematics, are listed below in the table.
以下表格列出了数学中一些最基础、最重要的符号。
| Symbol（符号） | Name（名称） | Meaning（含义） | Application（应用示例） |
|---|---|---|---|
| ≠ | not equal sign（不等号） | inequality（不相等） | 11 ≠ 6 11 \neq 6 11=6 |
| = | equals sign（等号） | equality（相等） | 4 = 2 + 2 4 = 2 + 2 4=2+2 |
| < | strict inequality（严格不等号） | less than（小于） | 6 < 11 6 < 11 6<11 |
| > | strict inequality（严格不等号） | greater than（大于） | 9 > 8 9 > 8 9>8 |
| [ ] | brackets（方括号） | calculate expression inside first（先计算括号内的表达式） | [ 2 × 5 ] + 7 = 17 [2 \times 5] + 7 = 17 [2×5]+7=17 |
| ( ) | parentheses（圆括号） | calculate expression inside first（先计算括号内的表达式） | 3 × ( 3 + 7 ) = 30 3 \times (3 + 7) = 30 3×(3+7)=30 |
| − | minus sign（减号） | subtraction（减法） | 5 − 2 = 3 5 - 2 = 3 5−2=3 |
| + | plus sign（加号） | addition（加法） | 4 + 5 = 9 4 + 5 = 9 4+5=9 |
| × | times sign（乘号） | multiplication（乘法） | 4 × 3 = 12 4 \times 3 = 12 4×3=12 |
| * | asterisk（星号） | multiplication（乘法） | 2 ∗ 3 = 6 2 * 3 = 6 2∗3=6 |
| ÷ | division sign / obelus（除号） | division（除法） | 15 ÷ 5 = 3 15 \div 5 = 3 15÷5=3 |
These are the most common symbols used in basic mathematical calculations. To get more maths symbols click here.
这些是基础数学计算中最常用的符号。
Properties in Mathematics（数学中的性质）
In mathematics, we learn about four major properties of numbers. They are:
在数学中，我们学习数字的四个主要性质，分别是：
- Commutative Property（交换律）
- Associative property（结合律）
- Distributive Property（分配律）
- Identity Property（恒等性）
These are the four basic properties of numbers. These properties are also applicable to some other mathematical concepts such as algebra.
这是数字的四个基本性质，这些性质也适用于代数等其他一些数学概念。
Rules in Mathematics（数学中的规则）
The most common rule used in mathematics is the BODMAS rule. As per this rule, the arithmetic operations are performed based on the brackets and order of operations. By the full form of BODMAS , we can easily understand this logic.
数学中最常用的规则是 BODMAS 规则。根据该规则，算术运算需按照括号和运算顺序进行。通过 BODMAS 的完整形式，我们可以轻松理解这一逻辑。
BODMAS -- Brackets Orders Division Multiplication Addition and Subtraction
BODMAS------括号（Brackets）、阶次（Orders）、除法（Division）、乘法（Multiplication）、加法（Addition）、减法（Subtraction）
Therefore, the first priority here is given to the brackets then division>multiplication>addition>subtraction.
因此，运算优先级为：
括号优先，其次是除法> 乘法> 加法> 减法。
For example, if we have to solve [ 5 + ( 3 × 5 ) ÷ 2 ] [5+(3 \times 5)\div2] [5+(3×5)÷2], then using the BODMAS rule, first multiply 3 and 5, within the brackets.
例如，若要计算 [ 5 + ( 3 × 5 ) ÷ 2 ] [5+(3 \times 5)\div2] [5+(3×5)÷2]，根据 BODMAS 规则，首先计算括号内的 3 与 5 的乘积。
→ 5 + ( 3 × 5 ) ÷ 2 = 5 + 15 ÷ 2 \to 5+(3 \times 5)\div2 = 5 + 15\div2 →5+(3×5)÷2=5+15÷2
Now divide 15 by 2
接着计算 15 除以 2
→ 5 + 7.5 → 12.5 \to 5 + 7.5\\ \to 12.5 →5+7.5→12.5
Formulas in Mathematics（数学中的公式）
Here are some common formulas used in mathematics to solve multiple problems.
以下是数学中用于解决各类问题的一些常见公式。
- Area and Perimeter Formula（面积与周长公式）
- Coordinate Geometry Formulas（解析几何公式）
- Heron's Formula（海伦公式）
- Quadratic Formula（二次方程求根公式）
- Differentiation Formulas（微分公式）
- Distance Formula（距离公式）
- Section Formula & Conic Sections（分点公式与圆锥曲线）
- Standard Deviation Formula（标准差公式）
- Trigonometry Formulas（三角公式）
Topics in Mathematics（数学中的知识点）
Let us see some important topics for each Class (from 1 to 12) that are covered under mathematics.
以下是 1 至 12 年级数学学科涵盖的一些重要知识点。
Class 1 Mathematics（一年级数学）
- Numbers In Words（数字的英文表达）
- Addition And Subtraction Of Integers（整数的加法与减法）
- Shapes（图形）
Class 2 Mathematics（二年级数学）
- Counting Numbers（计数）
- Place Value（数位）
Class 3 Mathematics（三年级数学）
- Multiplication Tables（乘法口诀表）
- Multiplication And Division Of Integers（整数的乘法与除法）
- Comparing Fractions（分数比较）
- Introduction To Data（数据入门）
Class 4 Mathematics（四年级数学）
- Factors And Multiples（因数与倍数）
- Multiplication And Division Of Decimals（小数的乘法与除法）
- Multiplying Fractions（分数乘法）
- Introduction to Large Numbers（大数入门）
Class 5 Mathematics（五年级数学）
- Dividing Fractions（分数除法）
- Addition and Subtraction of Decimals（小数的加法与减法）
- Lines and Angles Introduction（直线与角入门）
- Area Of A Square -- Introduction To Area（正方形的面积------面积入门）
Class 6 Mathematics（六年级数学）
- Whole Numbers（整数）
- Algebra（代数）
- Integers（整数）
- Fractions（分数）
Class 7 Mathematics（七年级数学）
- Lines And Angles（直线与角）
- Triangles（三角形）
- Percentage: Means Of Comparing Quantities（百分数：比较数量的方法）
- Visualising Solid Shapes（立体图形的认识）
Class 8 Mathematics（八年级数学）
- Rational Numbers（有理数）
- Mensuration（度量衡）
- Squares and Square Roots（平方与平方根）
- Exponents And Powers（指数与幂）
Class 9 Mathematics（九年级数学）
- Number System（数系）
- Polynomials（多项式）
- Quadrilateral（四边形）
- Surface Areas and Volume（表面积与体积）
Class 10 Mathematics（十年级数学）
- Quadratics（二次函数/二次方程）
- Circles（圆）
- Arithmetic Progression（等差数列）
- Co-ordinate Geometry（解析几何）
- Constructions（尺规作图）
- Probability And Statistics（概率论与统计学）
Class 11 Mathematics（十一年级数学）
- Sets（集合）
- Relations and Functions（关系与函数）
- Trigonometric Functions（三角函数）
- Linear Inequalities（线性不等式）
- Permutation And Combination（排列与组合）
- Conic Sections（圆锥曲线）
- Limits and Derivatives（极限与导数）
Class 12 Mathematics（十二年级数学）
- Matrices（矩阵）
- Inverse Trigonometric Functions（反三角函数）
- Determinants（行列式）
- Application of Integrals（积分的应用）
- Vector algebra（向量代数）
- Linear Programming（线性规划）
- Continuity And Differentiability（连续性与可导性）
Frequently Asked Questions on Mathematics（数学常见问题）
Q1: Define Mathematics.（问 1：定义数学。）
Mathematics is a subject that deals with numbers, shapes, logic, quantity and arrangements. Mathematics teaches to solve problems based on numerical calculations and find the solutions.
数学是一门研究数、形、逻辑、数量和排列的学科，它教会我们通过数值计算解决问题并找到答案。
Q2: Why is Mathematics an important subject for students?（问 2：为什么数学对学生来说是一门重要的学科？）
Learning mathematics will help students to build their logical thinking and problem solving skills. It has huge applications in day to day life. The basic arithmetic operations such as addition, subtraction, multiplication and division are the most important part of our lives. Based on these operations, we do numerous calculations.
学习数学有助于学生培养逻辑思维和解决问题的能力，它在日常生活中有着广泛的应用。加法、减法、乘法和除法等基础算术运算，是我们生活中最重要的部分，我们基于这些运算进行无数次计算。
Q3: Who is the Father of Mathematics?（问 3：谁是数学之父？）
Archimedes, (287-212 BC) is known to be the Father of Mathematics.
阿基米德（公元前 287-212 年）被称为"数学之父"。
Q4: Which part of mathematics does Trigonometry belong to?（问 4：三角学属于数学的哪个分支？）
Geometry is one of the most important branches of mathematics that includes trigonometry, where we deal with sides and angles of a right triangle. It has huge applications in the fields of construction and architecture.
几何是数学最重要的分支之一，三角学隶属于几何，主要研究直角三角形的边和角，在建筑和工程领域有着广泛的应用。
Q5: What are the two forms of Mathematics?（问 5：数学的两种形式是什么？）
Mathematics is described in two forms:
数学分为两种形式：
Pure mathematics and Applied mathematics
纯数学和应用数学
Mathematical symbols
数学符号
Mathematical symbols are used to perform various operations. The symbols make it easier to refer Mathematical quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the relationship between two quantities. All mathematical symbols are mainly used to perform mathematical operations under various concepts.
数学符号用于执行各类运算，便于指代数学量。数学完全建立在数字与符号之上，数学符号既表示不同量，也体现两个量之间的关系，广泛用于各类概念下的数学运算。
As we know, the full name of Maths is Mathematics. It is defined as the science of calculating, measuring, quantity, shape, and structure. It is based on logical thinking, numerical calculations, and the study of shapes. Algebra, trigonometry, geometry, and number theory are examples of mathematical dimensions, and the concept of Maths is purely dependent on numbers and symbols.
数学的全称是 Mathematics，定义为研究计算、测量、数量、形状与结构的科学，建立在逻辑思维、数值计算与图形研究之上。代数、三角学、几何、数论均为数学分支，数学体系完全依赖数字与符号。
There are many symbols used in Maths that have some predefined values. To simplify the expressions, we can use those kinds of values instead of those symbols. Some of the examples are the pi symbol ( π \pi π), which holds the value 22 / 7 22/7 22/7 or 3.14 3.14 3.14. The pi symbol is a mathematical constant which is defined as the ratio of circumference of a circle to its diameter. In Mathematics, pi symbol is also referred to as Archimedes constant. Also, e-symbol in Maths which holds the value e = 2.718281828 ... e= 2.718281828\ldots e=2.718281828.... This symbol is known as e-constant or Euler's constant. The table provided below has a list of all the common symbols in Maths with meaning and examples.
数学中许多符号具有预设值，可用于简化表达式。例如圆周率符号 π \pi π，取值为 22 / 7 22/7 22/7 或 3.14 3.14 3.14，是圆周长与直径之比，也称为阿基米德常数。数学中的自然常数 e e e，取值 e = 2.718281828 ... e=2.718281828\ldots e=2.718281828...，称为欧拉常数。下文以表格形式列出常用数学符号的含义与示例。
There are so many mathematical symbols that are very important to students. To understand this in an easier way, the list of mathematical symbols are noted here with definition and examples. There are numerous signs and symbols, ranging from the simple addition concept sign to the complex integration concept sign. Here, the list of mathematical symbols is provided in a tabular form, and those notations are categorized according to the concept.
数学符号对学习至关重要，本文按概念分类，以表格形式整理符号、定义与示例，涵盖从简单加法到复杂积分等各类记号。
Basic Mathematical Symbols With Name, Meaning and Examples
基础数学符号：名称、含义与示例
The basic mathematical symbols used in Maths help us to work with mathematical concepts in a theoretical manner. In simple words, without symbols, we cannot do maths. The mathematical signs and symbols are considered as representative of the value. The basic symbols in maths are used to express mathematical thoughts. The relationship between the sign and the value refers to the fundamental need of mathematics. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with names and meanings. Also, an example is provided to understand the usage of mathematical symbols.
基础数学符号支持以理论方式处理数学概念，是数值的代表，用于表达数学思想，清晰阐释概念与关系。下表列出常用基础数学符号的名称、含义与用法示例。
| Symbol 符号 | Symbol Name in Maths 数学符号名称 | Math Symbols Meaning 符号含义 | Example 示例 |
|---|---|---|---|
| ≠ \neq = | not equal sign 不等号 | inequality 不等关系 | 10 ≠ 6 10 \neq 6 10=6 |
| = = = | equal sign 等号 | equality 相等关系 | 3 = 1 + 2 3 = 1 + 2 3=1+2 |
| < < < | strict inequality 严格不等号 | less than 小于 | 7 < 10 7 < 10 7<10 |
| > > > | strict inequality 严格不等号 | greater than 大于 | 6 > 2 6 > 2 6>2 |
| ≤ \le ≤ | inequality 不等号 | less than or equal to 小于等于 | x ≤ y x \le y x≤y means y = x y=x y=x or y > x y>x y>x |
| ≥ \ge ≥ | inequality 不等号 | greater than or equal to 大于等于 | a ≥ b a \ge b a≥b means a = b a=b a=b or a > b a>b a>b |
| [ ] [\ ] [ ] | brackets 方括号 | calculate expression inside first 优先计算内部表达式 | [ 2 × 5 ] + 7 = 17 [ 2\times5] + 7 = 17 [2×5]+7=17 |
| ( ) (\ ) ( ) | parentheses 圆括号 | calculate expression inside first 优先计算内部表达式 | 3 × ( 3 + 7 ) = 30 3 \times (3 + 7) = 30 3×(3+7)=30 |
| − - − | minus sign 减号 | subtraction 减法 | 5 − 2 = 3 5 - 2 = 3 5−2=3 |
| + + + | plus sign 加号 | addition 加法 | 4 + 5 = 9 4 + 5 = 9 4+5=9 |
| ∓ \mp ∓ | minus--plus 减-加号 | both minus and plus operations 减与加运算 | 1 ∓ 4 = − 3 , 5 1 \mp 4 = -3,\ 5 1∓4=−3, 5 |
| ± \pm ± | plus--minus 加-减号 | both plus and minus operations 加与减运算 | 5 ± 3 = 8 , 2 5 \pm 3 = 8,\ 2 5±3=8, 2 |
| × \times × | times sign 乘号 | multiplication 乘法 | 4 × 3 = 12 4 \times 3 = 12 4×3=12 |
| ∗ * ∗ | asterisk 星号 | multiplication 乘法 | 2 ∗ 3 = 6 2 * 3 = 6 2∗3=6 |
| ÷ \div ÷ | division sign / obelus 除号 | division 除法 | 15 ÷ 5 = 3 15 \div 5 = 3 15÷5=3 |
| ⋅ \cdot ⋅ | multiplication dot 点乘号 | multiplication 乘法 | 2 ⋅ 3 = 6 2 \cdot 3 = 6 2⋅3=6 |
| / / / | division slash 斜除号 | division / fraction 除法 / 分数 | 8 / 2 = 4 8/2 = 4 8/2=4 |
| m o d \bmod mod | modulo 模运算 | remainder calculation 余数计算 | 7 m o d 3 = 1 7 \bmod 3 = 1 7mod3=1 |
| a b a^b ab | power 幂 | exponent 指数 | 2 4 = 16 2^4 = 16 24=16 |
| . . . | period 小数点 | decimal point, decimal separator 小数点 / 十进制分隔符 | 4.36 = 4 + 36 / 100 4.36 = 4 + 36/100 4.36=4+36/100 |
| a \sqrt{a} a | square root 平方根 | a ⋅ a = a \sqrt{a}\cdot\sqrt{a}=a a ⋅a =a | 9 = ± 3 \sqrt{9} = \pm3 9 =±3 |
| a 4 \sqrt[4]{a} 4a | fourth root 四次方根 | a 4 4 = a \sqrt[4]{a}^4=a 4a 4=a | 16 4 = ± 2 \sqrt[4]{16}= \pm 2 416 =±2 |
| a 3 \sqrt[3]{a} 3a | cube root 立方根 | a 3 3 = a \sqrt[3]{a}^3=a 3a 3=a | 343 3 = 7 \sqrt[3]{343} = 7 3343 =7 |
| % \% % | percent 百分号 | 1 % = 1 / 100 1\% = 1/100 1%=1/100 | 10 % × 30 = 3 10\% \times 30 = 3 10%×30=3 |
| a n \sqrt[n]{a} na | n-th root (radical) n 次方根 | a n n = a \sqrt[n]{a}^n=a na n=a | n = 3 , 8 3 = 2 n=3,\ \sqrt[3]{8} = 2 n=3, 38 =2 |
| ppm \text{ppm} ppm | per-million 百万分率 | 1 ppm = 1 / 10 6 1\ \text{ppm} = 1/10^6 1 ppm=1/106 | 10 ppm × 30 = 0.0003 10\ \text{ppm} \times 30 = 0.0003 10 ppm×30=0.0003 |
| KaTeX parse error: Undefined control sequence: \permil at position 1: \̲p̲e̲r̲m̲i̲l̲ | per-mille 千分号 | KaTeX parse error: Undefined control sequence: \permil at position 2: 1\̲p̲e̲r̲m̲i̲l̲ ̲= 1/1000 = 0.1\... | KaTeX parse error: Undefined control sequence: \permil at position 3: 10\̲p̲e̲r̲m̲i̲l̲ ̲\times 30 = 0.3 |
| ppt \text{ppt} ppt | per-trillion 万亿分率 | 1 ppt = 10 − 12 1\ \text{ppt} = 10^{-12} 1 ppt=10−12 | 10 ppt × 30 = 3 × 10 − 10 10\ \text{ppt} \times 30 = 3\times10^{-10} 10 ppt×30=3×10−10 |
| ppb \text{ppb} ppb | per-billion 十亿分率 | 1 ppb = 1 / 10 9 1\ \text{ppb} = 1/10^9 1 ppb=1/109 | 10 ppb × 30 = 3 × 10 − 7 10\ \text{ppb} \times 30 = 3\times10^{-7} 10 ppb×30=3×10−7 |
Maths Logic symbols With Meaning
数学逻辑符号及含义
| Symbol 符号 | Symbol Name in Maths 数学符号名称 | Math Symbols Meaning 符号含义 | Example 示例 |
|---|---|---|---|
| ∧ \land ∧ | caret / circumflex 与号 | and 逻辑与 | x ∧ y x \land y x∧y |
| ⋅ \cdot ⋅ | and 与 | and 逻辑与 | x ⋅ y x \cdot y x⋅y |
| + + + | plus 加号 | or 逻辑或 | x + y x + y x+y |
| & \& & | ampersand 与符号 | and 逻辑与 | x & y x \& y x&y |
| ∣ \vert ∣ | vertical line 竖线 | or 逻辑或 | x ∣ y x \vert y x∣y |
| ∨ \lor ∨ | reversed caret 或号 | or 逻辑或 | x ∨ y x \lor y x∨y |
| x ˉ \bar{x} xˉ | bar 上划线 | not -- negation 非 / 否定 | x ˉ \bar{x} xˉ |
| x ′ x' x′ | single-quote 单引号 | not -- negation 非 / 否定 | x ′ x' x′ |
| ! ! ! | Exclamation mark 感叹号 | not -- negation 非 / 否定 | ! x !x !x |
| ¬ \neg ¬ | not 非号 | not -- negation 非 / 否定 | ¬ x \neg x ¬x |
| ∼ \sim ∼ | tilde 波浪号 | negation 否定 | ∼ x \sim x ∼x |
| ⊕ \oplus ⊕ | circled plus / oplus 异或号 | exclusive or -- xor 异或 | x ⊕ y x \oplus y x⊕y |
| ⇔ \Leftrightarrow ⇔ | equivalent 等价号 | if and only if (iff) 当且仅当 | p ⇔ q p \Leftrightarrow q p⇔q |
| ⇒ \Rightarrow ⇒ | implies 蕴含号 | Implication 蕴含 | p ⇒ q p \Rightarrow q p⇒q |
| ∈ \in ∈ | Belong to/is an element of 属于 | Set membership 集合属于 | 2 ∈ { 1 , 2 , 3 } 2 \in \{1,2,3\} 2∈{1,2,3} |
| ∉ \notin ∈/ | Not element of 不属于 | Negation of set membership 集合不属于 | 0 ∉ { 1 , 2 , 3 } 0 \notin \{1,2,3\} 0∈/{1,2,3} |
| ∀ \forall ∀ | for all 全称量词 | Universal Quantifier 全称量词 | ∀ n ∈ N , 2 n \forall n\in\mathbb{N},\ 2n ∀n∈N, 2n is even |
| ↔ \leftrightarrow ↔ | equivalent 等价号 | if and only if (iff) 当且仅当 | p ↔ q p \leftrightarrow q p↔q |
| ∄ \nexists ∄ | there does not exist 不存在 | Negation of existential quantifier 存在量词否定 | ∄ n ∈ N , b = n a \nexists n\in\mathbb{N},\ b=na ∄n∈N, b=na |
| ∃ \exists ∃ | there exists 存在 | Existential quantifier 存在量词 | ∃ n ∈ N , b = n a \exists n\in\mathbb{N},\ b=na ∃n∈N, b=na |
| ∵ \because ∵ | because / since 因为 | Because shorthand 因为简写 | a = b , b = c ⇒ a = c ( ∵ a = b ) a=b,\ b=c\Rightarrow a=c\ (\because a=b) a=b, b=c⇒a=c (∵a=b) |
| ∴ \therefore ∴ | therefore 所以 | Therefore shorthand 所以简写 | x + 6 = 10 ∴ x = 4 x + 6 = 10\ \therefore x = 4 x+6=10 ∴x=4 |
Calculus and Analysis Symbol Names in Maths
微积分与分析数学符号
In calculus, we have come across different math symbols. All mathematical symbols with names and meanings are provided here. Go through the all mathematical symbols used in calculus.
微积分中使用多种专用符号，下表列出微积分与分析中常用符号、名称与含义。
| Symbol 符号 | Symbol Name in Maths 数学符号名称 | Math Symbols Meaning 符号含义 | Example 示例 |
|---|---|---|---|
| ε \varepsilon ε | epsilon 艾普西龙 | small number near zero 近零小量 | ε → 0 \varepsilon \to 0 ε→0 |
| lim x → a \lim\limits_{x\to a} x→alim | limit 极限 | limit value of a function 函数极限 | lim x → a ( 3 x + 1 ) = 3 a + 1 \lim\limits_{x\to a}(3x+1)= 3a + 1 x→alim(3x+1)=3a+1 |
| y ′ y' y′ | derivative 一阶导数 | Lagrange's derivative notation 拉格朗日记号 | ( 5 x 3 ) ′ = 15 x 2 (5x^3)' = 15x^2 (5x3)′=15x2 |
| e e e | Euler's number 欧拉数 | e = 2.718281828 ... e = 2.718281828\ldots e=2.718281828... | e = lim x → ∞ ( 1 + 1 / x ) x e = \lim\limits_{x\to\infty}(1+1/x)^x e=x→∞lim(1+1/x)x |
| y ( n ) y^{(n)} y(n) | nth derivative n 阶导数 | nth order derivative n 阶导数 | D n ( 3 x n ) = 3 n ! D^n(3x^n)=3n! Dn(3xn)=3n! |
| y ′ ′ y'' y′′ | second derivative 二阶导数 | second order derivative 二阶导数 | ( 4 x 3 ) ′ ′ = 24 x (4x^3)'' = 24x (4x3)′′=24x |
| d y d x \frac{dy}{dx} dxdy | derivative 导数 | Leibniz's derivative notation 莱布尼茨记号 | --- |
| D 2 x D^2x D2x | second derivative 二阶导数 | second order derivative 二阶导数 | D 2 y + 2 D y + 1 = 0 D^2y + 2Dy + 1 = 0 D2y+2Dy+1=0 |
| D x Dx Dx | derivative 导数 | Euler's derivative notation 欧拉记号 | D y − 1 = 0 Dy - 1 = 0 Dy−1=0 |
| ∫ \int ∫ | integral 积分 | antiderivative / integration 不定积分 / 积分 | ∫ x n d x = x n + 1 n + 1 + C \int x^n dx = \frac{x^{n+1}}{n+1} + C ∫xndx=n+1xn+1+C |
| ∂ \partial ∂ | partial derivative 偏导数 | derivative w.r.t. one variable 单变量偏导 | ∂ ( x 2 + y 2 ) ∂ x = 2 x \frac{\partial(x^2+y^2)}{\partial x} = 2x ∂x∂(x2+y2)=2x |
| ∭ \iiint ∭ | triple integral 三重积分 | integration over 3 variables 三元函数积分 | --- |
| ∬ \iint ∬ | double integral 二重积分 | integration over 2 variables 二元函数积分 | ∬ ( x 3 + y 3 ) d x d y \iint(x^3+y^3)dx dy ∬(x3+y3)dxdy |
| ∯ \oiint ∬ | closed surface integral 闭曲面积分 | surface integral over closed surface 闭曲面积分 | --- |
| ∮ \oint ∮ | closed line integral 闭曲线积分 | line integral over closed curve 闭曲线积分 | ∮ C 2 / z d z \oint_C 2/z dz ∮C2/zdz |
| [ a , b ] [a,b] [a,b] | closed interval 闭区间 | [ a , b ] = { x ∣ a ≤ x ≤ b } [a,b] = \{x \mid a \le x \le b\} [a,b]={x∣a≤x≤b} | sin x ∈ [ − 1 , 1 ] \sin x \in [-1, 1] sinx∈[−1,1] |
| ∰ \oiiint ∭ | closed volume integral 闭体积分 | volume integral over closed domain 闭域体积分 | --- |
| ( a , b ) (a,b) (a,b) | open interval 开区间 | ( a , b ) = { x ∣ a < x < b } (a,b) = \{x \mid a < x < b\} (a,b)={x∣a<x<b} | f f f continuous on ( 0 , 1 ) (0, 1) (0,1) |
| z ∗ z^* z∗ | complex conjugate 共轭复数 | z = a + b i ⇒ z ∗ = a − b i z = a+bi \Rightarrow z^*=a-bi z=a+bi⇒z∗=a−bi | z = 3 + 2 i , z ∗ = 3 − 2 i z = 3 + 2i,\ z^* = 3 - 2i z=3+2i, z∗=3−2i |
| i i i | imaginary unit 虚数单位 | i = − 1 i = \sqrt{-1} i=−1 | z = 3 + 2 i z = 3 + 2i z=3+2i |
| ∇ \nabla ∇ | nabla / del 纳布拉算子 | gradient / divergence operator 梯度 / 散度算子 | ∇ f ( x , y , z ) \nabla f(x,y,z) ∇f(x,y,z) |
| ⋅ ⃗ \vec{\cdot} ⋅ | vector 向量 | magnitude + direction 大小 + 方向 | --- |
| x ∗ y x * y x∗y | convolution 卷积 | function convolution 函数卷积 | y ( t ) = x ( t ) ∗ h ( t ) y(t) = x(t) * h(t) y(t)=x(t)∗h(t) |
| ∞ \infty ∞ | infinity 无穷大 | infinite quantity 无穷大量 | x ∈ ( 0 , ∞ ) x \in (0, \infty) x∈(0,∞) |
| δ \delta δ | delta function δ 函数 | Dirac delta function 狄拉克 δ 函数 | --- |
Combinatorics Symbols Used in Maths
组合数学符号
The different Combinatorics symbols used in maths concern the study of the combination of finite discrete structures. Some of the most important combinatorics symbols used in maths are as follows:
组合数学研究有限离散结构的组合方式，常用符号如下：
| Symbol 符号 | Symbol Name 符号名称 | Meaning or Definition 含义与定义 | Example 示例 |
|---|---|---|---|
| P ( n , k ) P(n,k) P(n,k) | Permutation 排列 | permutation 排列 | --- |
| n ! n! n! | Factorial 阶乘 | n ! = 1 × 2 × ⋯ × n n! = 1\times2\times\cdots\times n n!=1×2×⋯×n | 5 ! = 120 5! = 120 5!=120 |
| ( n k ) \binom{n}{k} (kn) | Combination 组合 | combination 组合 | --- |
Greek Alphabet Letters Used in Maths
数学中使用的希腊字母
Mathematicians frequently use Greek alphabets in their work to represent the variables, constants, functions and so on. Some of the commonly used Greek symbols name in Maths are listed below:
数学中常用希腊字母表示变量、常数、函数等，常用希腊字母如下：
| Greek Symbol 希腊符号 | Greek Letter Name 希腊字母名称 | English Equivalent 英文对应 | Pronunciation 读音 |
|---|---|---|---|
| A \Alpha A | Alpha 阿尔法 | A | al-fa |
| B \Beta B | Beta 贝塔 | B | be-ta |
| Γ \Gamma Γ | Gamma 伽马 | G | ga-ma |
| Δ \Delta Δ | Delta 德尔塔 | D | del-ta |
| E \Epsilon E | Epsilon 艾普西龙 | E | ep-si-lon |
| Z \Zeta Z | Zeta 泽塔 | Z | ze-ta |
| H \Eta H | Eta 伊塔 | H | eh-ta |
| Θ \Theta Θ | Theta 西塔 | Th | te-ta |
| I \Iota I | Iota 约塔 | I | io-ta |
| K \Kappa K | Kappa 卡帕 | K | ka-pa |
| Λ \Lambda Λ | Lambda 拉姆达 | L | lam-da |
| M \Mu M | Mu 缪 | M | m-yoo |
| N \Nu N | Nu 纽 | N | noo |
| Ξ \Xi Ξ | Xi 克西 | X | x-ee |
| O \Omicron O | Omicron 奥密克戎 | O | o-mee-c-ron |
| Π \Pi Π | Pi 派 | P | pa-yee |
| P \Rho P | Rho 柔 | R | row |
| Σ \Sigma Σ | Sigma 西格玛 | S | sig-ma |
| T \Tau T | Tau 陶 | T | ta-oo |
| Υ \Upsilon Υ | Upsilon<br | 宇普西龙 | U |
| Φ \Phi Φ | Phi 斐 | Ph | f-ee |
| X \Chi X | Chi<br | 希 | Ch |
| Ψ \Psi Ψ | Psi<br | 普西 | Ps |
| Ω \Omega Ω | Omega<br | 欧米伽 | O |
Common Numeral Symbols Used in Maths
常用数字符号
The roman numerals are used in many applications and can be seen in our real-life activities. The common Roman numeral symbols used in Maths are as follows.
罗马数字广泛应用于多种场景，数学中常用罗马数字与其他记数系统对照如下：
| Name 名称 | European 欧洲数字 | Roman 罗马数字 | Arabic 阿拉伯数字 | Hebrew 希伯来数字 |
|---|---|---|---|---|
| zero 零 | 0 | n/a | ٠ | n/a |
| one 一 | 1 | I | ١ | א |
| two 二 | 2 | II | ٢ | ב |
| three 三 | 3 | III | ٣ | ג |
| four 四 | 4 | IV | ٤ | ד |
| five 五 | 5 | V | ٥ | ה |
| six 六 | 6 | VI | ٦ | ו |
| seven 七 | 7 | VII | ٧ | ז |
| eight 八 | 8 | VIII | ٨ | ח |
| nine 九 | 9 | IX | ٩ | ט |
| ten 十 | 10 | X | ١٠ | י |
| eleven 十一 | 11 | XI | ١١ | יא |
| twelve 十二 | 12 | XII | ١٢ | יב |
| thirteen 十三 | 13 | XIII | ١٣ | יג |
| fourteen 十四 | 14 | XIV | ١٤ | יד |
| fifteen 十五 | 15 | XV | ١٥ | טו |
| sixteen 十六 | 16 | XVI | ١٦ | טז |
| seventeen 十七 | 17 | XVII | ١٧ | יז |
| eighteen 十八 | 18 | XVIII | ١٨ | יח |
| nineteen 十九 | 19 | XIX | ١٩ | יט |
| twenty 二十 | 20 | XX | ٢٠ | כ |
| thirty 三十 | 30 | XXX | ٣٠ | ל |
| forty 四十 | 40 | XL | ٤٠ | מ |
| fifty 五十 | 50 | L | ٥٠ | נ |
| sixty 六十 | 60 | LX | ٦٠ | ס |
| seventy 七十 | 70 | LXX | ٧٠ | ע |
| eighty 八十 | 80 | LXXX | ٨٠ | פ |
| ninety 九十 | 90 | XC | ٩٠ | צ |
| one hundred 一百 | 100 | C | ١٠٠ | ק |
These are some of the most important and commonly used symbols in mathematics. It is important to get completely acquainted with all the maths symbols to be able to solve maths problems efficiently. It should be noted that without knowing maths symbols, it is extremely difficult to grasp certain concepts on a universal scale. Some of the key importance of maths symbols are summarized below.
熟练掌握数学符号是高效解题的基础，数学符号具有通用性，是理解通用数学概念的必要工具，其重要意义归纳如下。
Importance of Mathematical Symbols
数学符号的重要性
-
Helps in denoting quantities
用于表示数量
-
Establishes relationships between quantities
建立量之间的关系
-
Helps to identify the type of operation
标识运算类型
-
Makes reference easier
便于指代与引用
-
Maths symbols are universal and break the language barrier
数学符号具有通用性，消除语言障碍
Frequently Asked Questions on Math Symbols
数学符号常见问题
Q1: What is the pi symbol in Maths?
数学中的圆周率符号是什么？
The pi symbol is a mathematical constant, which is approximately equal to 3.14 3.14 3.14. The symbol of pi is π \pi π and it is a Greek alphabet. Pi is an irrational number which is defined as the ratio of circle circumference to its diameter.
圆周率符号 π \pi π 是希腊字母，为数学常数，近似值 3.14 3.14 3.14，是圆周长与直径之比，属于无理数。
Q2: What is e symbol in mathematics?
数学中的 e e e 符号是什么？
The " e e e" symbol in maths represents Euler's number which is approximately equal to 2.71828 ... 2.71828\ldots 2.71828... It is considered as one of the most important numbers in mathematics. It is an irrational number and it cannot be represented as a simple fraction.
数学符号 e e e 表示欧拉数，近似值 2.71828 ... 2.71828\ldots 2.71828...，是数学中重要常数，为无理数，不能表示为简单分数。
Q3: Write down the symbols for basic arithmetic operations.
写出基础算术运算符号。
The symbols for basic arithmetic operations are addition ( + + +), subtraction ( − - −), Multiplication ( × \times ×), Division ( ÷ \div ÷).
基础算术运算符号为：加法 + + +，减法 − - −，乘法 × \times ×，除法 ÷ \div ÷。
Q4: Why do we use mathematical symbols?
为什么使用数学符号？
Mathematics is a universal language and the basics of maths are the same everywhere in the universe. Mathematical symbols play a major role in this. The definition and the value of the symbols are constant. For example, the Roman letter X represents the value 10 10 10 everywhere around us.
数学是通用语言，数学符号定义与数值具有统一性，例如罗马数字 X X X 在全球均表示 10 10 10。
Q5: Mention the logic symbols in maths.
列举数学中的逻辑符号。
The logic symbols in maths are:
AND ( ∧ \land ∧), OR ( ∨ \lor ∨), NOT ( ¬ \neg ¬), Implies ( ⇒ \Rightarrow ⇒), Equivalent ( ⇔ \Leftrightarrow ⇔), For all ( ∀ \forall ∀), There exists ( ∃ \exists ∃).
数学逻辑符号包括：与 ∧ \land ∧、或 ∨ \lor ∨、非 ¬ \neg ¬、蕴含 ⇒ \Rightarrow ⇒、等价 ⇔ \Leftrightarrow ⇔、全称量词 ∀ \forall ∀、存在量词 ∃ \exists ∃。
HOW TO STUDY MATH
如何学习数学
Before I get into the tips for how to study math let me first say that everyone studies differently and there is no one right way to study for a math class. There are a lot of tips in this document and there is a pretty good chance that you will not agree with all of them or find that you can't do all of them due to time constraints. There is nothing wrong with that. We all study differently and all that anyone can ask of us is that we do the best that we can. It is my intent with these tips to help you do the best that you can given the time that you've got to work with.
在给出数学学习的具体建议之前，我需要首先说明，每个人的学习方式各不相同，数学课程并不存在唯一正确的学习方法 。本文包含大量学习建议，你很可能不会认同全部内容，或因时间限制无法全部执行。这并无不妥。我们的学习方式本就存在差异，每个人只需尽力而为即可。本文的目的，是在你可支配的时间内，帮助你尽可能取得更好的学习效果。
Now, I figure that there are two groups of people here reading this document, those that are happy with their grade, but are interested in what I've got to say and those that are not happy with their grade and want some ideas on how to improve. Here are a couple of quick comments for each of these groups.
我认为阅读本文的读者可分为两类：一类对现有成绩满意，但希望了解相关内容；另一类对成绩不满意，希望找到提升方法。下面针对这两类读者分别给出简要说明。
If you have a study routine that you are happy with and you are getting the grade you want from your math class you may find this an interesting read. There is, of course, no reason to change your study habits if you've been successful with them in the past. However, you might benefit from a comparison of your study habits to the tips presented here.
如果你拥有满意的学习习惯，且能在数学课程中取得理想成绩，本文可作为参考阅读。如果以往的学习方式已经带来良好效果，自然无需改变。不过，将自身学习习惯与本文建议进行对比，或许会带来收获。
If you are not happy with your grade in your math class and you are looking for ways to improve your grade there are a couple of general comments that I need to get out of the way before proceeding with the tips. Most people who are doing poorly in a math class fall into three main categories.
如果你对数学课程成绩不满意，希望寻找提升途径，在给出具体建议前，我需要先说明几点概况。数学课程成绩不理想的人群，大多可分为三类。
The first category consists of the largest group of students and these are students that just do not have good study habits and/or don't really understand how to study for a math class. Students in this category should find these tips helpful and while you may not be able to follow all of them hopefully you will be able to follow enough of them to improve your study skills.
第一类 人数最多，这类学生缺乏良好的学习习惯 ，或不理解数学课程的学习方式。这类学生可从本文建议中获得帮助，即便无法遵循全部内容，也可通过执行其中多条建议提升学习能力。
The next category is the people who spend hours each day studying and still don't do well. Most of the people in this category suffer from inefficient study habits and hopefully this set of notes will help you to study more efficiently and not waste time.
第二类 学生每天投入大量时间学习，却仍无法取得理想成绩。这类学生大多存在学习效率偏低的问题，希望本文内容能帮助你提升学习效率，减少时间浪费。
The final category is those people who simply aren't spending enough time studying. Students are in this category for a variety of reasons. Some students have job and/or family commitments that prevent them from spending the time needed to be successful in a math class. To be honest there isn't a whole lot that I can do for you if that is your case other than hopefully you will become a more efficient in your studies after you are through reading this. The vast majority of the students in this category unfortunately, don't realize that they are in this category. Many don't realize how much time you need to spend on studying in order to be successful in a math class. Hopefully reading this document will help you to realize that you do need to study more. Many simply aren't willing to make the time to study as there are other things in their lives that are more important to them. While that is a decision that you will have to make, realize that eventually you will have to take the time if you want to pass your math course.
第三类 学生未投入足够的学习时间 。学生处于这类情况的原因多种多样。部分学生因工作或家庭事务，无法保证数学学习所需的时间。坦白说，对于这类情况，我能提供的帮助有限，只希望你读完本文后能提升学习效率。遗憾的是，这类学生中的大多数并未意识到自己的问题 。很多人不了解，学好数学课程需要投入的时间量级。希望本文能帮助你认识到增加学习时间的必要性。还有许多人不愿为学习分配时间，因为生活中存在对其更重要的事务。这是你需要自行做出的选择，但也要明白，若想通过数学课程，最终仍需投入相应时间。
Now, with all of that out of the way let's get into the tips. I've tried to break down the hints and advice here into specific areas such as general study tips, doing homework, studying for exams, etc. However, there are three broad, general areas that all of these tips will fall into.
完成以上说明后，我们进入具体建议部分。我将相关提示与建议分为通用学习、作业完成、考试复习等具体板块。而所有建议，均可归入三个宏观方向。
Math is Not a Spectator Sport
数学不是观赏性运动
You cannot learn mathematics by just going to class and watching the instructor lecture and work problems. In order to learn mathematics you must be actively involved in the learning process. You've got to attend class and pay attention while in class. You've got to take a good set of notes. You've got to work homework problems, even if the instructor doesn't assign any. You've got to study on a regular schedule, not just the night before exams. In other words you need to be involved in the learning process.
仅通过听课、观察教师讲解与解题，无法掌握数学知识 。学习数学，需要主动参与 整个学习过程。你需要按时上课并保持专注 ，需要整理完整的笔记 ，需要完成习题练习 ，即便教师未布置作业也应自主练习。你需要制定规律的学习计划，而非仅在考试前一晚突击。换言之，你需要深度参与学习过程。
The reality is that most people really need to work to pass a math class, and in general they need to work harder at math classes than they do with their other classes. If all that you're willing to do is spend a couple of hours studying before each exam then you will find that passing most math classes will be very difficult.
事实是，大多数人需要付出切实努力 才能通过数学课程，且通常需要比其他课程投入更多精力。如果你只愿意在每次考试前学习几小时，会发现多数数学课程都难以通过。
If you aren't willing to be actively involved in the process of learning mathematics, both inside and outside of the class room, then you will have trouble passing any math class.
若不愿在课上与课后主动参与数学学习过程，通过任意数学课程都会存在困难。
Work to Understand the Principles
重在理解原理
You can pass a history class by simply memorizing a set of dates, names and events. You will find, however, that in order to pass a math class you will need to do more than just memorize a set of formulas. While there is certainly a fair amount of memorization of formulas in a math class you need to do more. You need to understand how to USE the formulas and that is often far different from just memorizing them.
历史课程可通过记忆日期、人物与事件通过考试，而数学课程则不能仅依靠公式记忆 。数学课程中确实需要记忆大量公式，但你需要完成更多内容。你需要理解公式的使用方法，这与单纯记忆公式存在明显区别。
Some formulas have restrictions on them that you need to know in order to correctly use them. For instance, in order to use the quadratic formula you must have the quadratic in standard form first. You need to remember this or you will often get the wrong answer!
部分公式存在使用限制 ，了解这些限制才能正确应用公式。例如，使用一元二次方程求根公式时，必须先将方程化为标准形式。牢记这一前提，否则容易得出错误结果。
Other formulas are very general and require you to identify the parts in the problem that correspond to parts in the formula. If you don't understand how the formula works and the principle behind it, it can often be very difficult to use the formula. For example, in a calculus course it's not terribly difficult to memorize the formula for integration by parts for integrals. However, if you don't understand how to actually use the formula and identify the appropriate parts of the integral you will find the memorized formula worthless.
另一些公式具有通用性，需要你在题目中找到与公式各部分对应的内容 。若不理解公式的运行方式与背后原理 ，往往难以正确使用公式。例如，微积分课程中，分部积分公式的记忆难度不高。但如果不理解实际使用方法，无法正确识别积分中的对应部分，记住的公式便失去价值。
Mathematics is Cumulative
数学是累积的学问
You've always got to remember that mathematics courses are cumulative. Almost everything you do in a math class will depend on subjects that you've previously learned. This goes beyond just knowing the previous sections in your current class to needing to remember material from previous classes.
你需要始终牢记，数学课程具有知识累积性 。数学课程中的几乎所有内容，都建立在已学知识的基础之上 。这不仅包括当前课程已学章节，还包括先修课程的知识内容。
You will find a college algebra class to be very difficult without the knowledge that you learned in your high school algebra class. You can't do a calculus class without first taking (and understanding) an Algebra and a Trigonometry class.
没有高中代数知识储备，大学代数课程会变得十分困难。未学习并掌握代数与三角学课程，便无法学习微积分课程。
So, with these three main ideas in mind let's proceed with some more specific tips to studying for a math class. Note as well that several of the tips show up in multiple sections since they are either super important tips or simply can fall under several general topics.
牢记这三个基本思路 后，我们继续学习数学课程的更具体建议。需要注意的是，部分建议会在多个板块中出现，这类建议要么具有重要意义，要么可同时归属于多个主题。
via：
- maths/what-is-mathematics
https://byjus.com/maths/what-is-mathematics/ - maths/math-symbols
https://byjus.com/maths/math-symbols/ - How To Study Math
https://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx