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Mathematics (from Ancient Greekμάθημα; máthēma: 'knowledge, study, learning') is an area of knowledge that includes such topics as numbers (arithmetic and number theory),[1] formulas and related structures (algebra),[2] shapes and the spaces in which they are contained (geometry),[1] and quantities and their changes (calculus and analysis).[3][4][5] One whose occupation involves the pursuit or study of mathematical truths or objects is known as a mathematician.
Level 1
从"功能"角度出发可以分为如下主题:
Number theory (数论)
Geometry (几何)
Algebra (代数)
Calculus and analysis (微积分和分析)
Discrete mathematics (离散数学)
Mathematical logic and set theory (数理逻辑和集合论)
Applied mathematics (应用数学)
Statistics and other decision sciences (统计学和其他决策科学)
Structure (algebra): 结构, 对应的是代数: 个人理解代数就是用符号(变量)代替具体数字, 不再研究具体数字, 而是研究各种抽象化的结构, 比如f(x)=x+1, 我们并不关心具体x到底是几, 而是关心f这个模型的结构。这里包括了Combinatorics(组合数学), Number theory(数论), Group theory(群论), Graph theory (图论), Order theory (序理论), Algebra(代数),
意图:
Mathematics - Wikipedia
Level 1
从"功能"角度出发可以分为如下主题:
但我非常喜欢wikipedia定义的划分角度:
f(x)=x+1
, 我们并不关心具体x到底是几, 而是关心f这个模型的结构。这里包括了Combinatorics(组合数学), Number theory(数论), Group theory(群论), Graph theory (图论), Order theory (序理论), Algebra(代数),大体可以分为以下3类:
在集合论的基础上,现代数学有两大家族: 分析(Analysis)和代数(Algebra)。
事实上, 对于CS来说, 也恰恰就是线性代数和微积分这两个概念。
以吴军"数学通识50讲"模块划分为例:
1-5年级
五年级第二学期最后的总复习整理了1-5年级的内容:
小结:
6-9年级
小结:
10-12年级
小结:
大概7个方面:
下一步行动: 通过中考高考试卷反推各类占比。
高等数学
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