combinatorics

简明释义

英[ˌkɒmbɪnəˈtɒrɪks]美[ˌkɑːmbənəˈtɔːrɪks]

n. [数]组合学；组合数学（等于 combinatorial analysis, combinatorial mathematics）

英英释义

单词用法

同义词

反义词

例句

1.To study combinatorial properties of discrete sequences by means of zeros of generating functions is an important topic in combinatorics.

通过发生函数的零点来研究离散序列的组合性质是组合学中的一个重要课题。

2.Hence it contains some new and important topics of combinatorics and graph theory.

因此选择的内容主要是当前组合数学与图论中研究的十分重要课题。

3.The pigeonhole principle is a important principle in combinatorics.

鸽巢原理是组合学中一个非常重要的原理。

4.And now we have a combinatorics result that I think probably you're all familiar with from one context or another.

现在我们有组合的结果,并且我认为你们或许都,对前后内容比较熟悉。

5.Combinatorics, Complexity, and Chance: a Tribute to Dominic Welsh.

组合数学，复杂性和偶然性：献给多米尼克·威尔士。

6.If you don't know what combinatorics is, not even the first clue, then you're not very likely to be able to recognize problems for which the solution is found in combinatorics, are you?

如果你不知道组合逻辑是什么，甚至连听都没听说过，那么你是不可能意识到在组合逻辑中可以找到的答案解决的是什么问题，难道不是么?。

7.In computer science, understanding combinatorics 组合数学 is essential for algorithm design.

在计算机科学中，理解组合数学 组合数学 对于算法设计至关重要。

8.The study of combinatorics 组合数学 helps in solving problems related to counting and arrangements.

研究组合数学 组合数学 有助于解决与计数和排列相关的问题。

9.Many games involve principles of combinatorics 组合数学, such as calculating the number of possible moves.

许多游戏涉及组合数学 组合数学 的原理，例如计算可能的移动数量。

10.In probability theory, combinatorics 组合数学 is used to determine the likelihood of different outcomes.

在概率论中，组合数学 组合数学 用于确定不同结果的可能性。

11.The field of combinatorics 组合数学 includes topics like permutations and combinations.

组合数学 组合数学 领域包括排列和组合等主题。

作文

Combinatorics is a fascinating area of mathematics that deals with counting, arrangement, and combination of objects. It plays a crucial role in various fields, including computer science, statistics, and optimization. The fundamental principles of combinatorics (组合数学) can be applied to solve complex problems, making it an essential tool for researchers and professionals alike. In this essay, I will explore the significance of combinatorics (组合数学), its applications, and why it is a vital subject to study. To begin with, combinatorics (组合数学) provides methods for counting and arranging objects in specific ways. For instance, consider the problem of determining how many different ways we can arrange a set of books on a shelf. Using the principles of combinatorics (组合数学), we can calculate the total arrangements by considering factors such as the number of books and any restrictions that may apply. This ability to quantify arrangements is not only useful in theoretical mathematics but also has practical applications in everyday life, such as organizing events or managing resources. Moreover, combinatorics (组合数学) is foundational in the field of computer science, particularly in algorithm design and analysis. Many algorithms rely on combinatorial principles to optimize processes, such as sorting data or searching through large datasets. For example, understanding the combinatorial aspects of graph theory can lead to more efficient algorithms for network routing and connectivity. As technology continues to advance, the demand for professionals skilled in combinatorics (组合数学) is likely to increase, highlighting the importance of this subject in modern education. In addition to its applications in computer science, combinatorics (组合数学) is instrumental in statistical analysis. Researchers often use combinatorial methods to determine probabilities and make predictions based on data. For example, when conducting surveys or experiments, understanding the combinations of possible outcomes can help statisticians draw meaningful conclusions. This aspect of combinatorics (组合数学) is particularly relevant in fields such as economics, psychology, and biology, where data interpretation is crucial for decision-making and policy formulation. Furthermore, the study of combinatorics (组合数学) fosters critical thinking and problem-solving skills. Engaging with combinatorial problems encourages individuals to think creatively and approach challenges from different angles. This type of analytical thinking is beneficial not only in mathematics but also in various other disciplines, including engineering, finance, and social sciences. By cultivating these skills through the study of combinatorics (组合数学), students can enhance their overall academic performance and prepare for future careers. In conclusion, combinatorics (组合数学) is a vital branch of mathematics with far-reaching implications across numerous fields. Its applications in counting, arrangement, and probability make it an indispensable tool for researchers and professionals. As we continue to navigate an increasingly complex world, the principles of combinatorics (组合数学) will remain essential for solving problems and making informed decisions. Therefore, it is crucial for students to engage with this subject, as it equips them with valuable skills and knowledge that will benefit them in their academic and professional pursuits.

组合数学是一个迷人的数学领域，涉及对象的计数、排列和组合。它在计算机科学、统计学和优化等多个领域中发挥着至关重要的作用。组合数学（combinatorics）的基本原理可以应用于解决复杂问题，使其成为研究人员和专业人士的重要工具。在这篇文章中，我将探讨组合数学（combinatorics）的重要性、应用以及为什么学习这一主题至关重要。 首先，组合数学（combinatorics）提供了以特定方式计数和排列对象的方法。例如，考虑确定我们可以将一组书籍在书架上排列多少种不同方式的问题。利用组合数学（combinatorics）的原理，我们可以通过考虑书籍的数量和可能适用的任何限制来计算总排列数。这种量化排列的能力不仅在理论数学中有用，而且在日常生活中的实际应用，如组织活动或管理资源，也非常重要。 此外，组合数学（combinatorics）在计算机科学领域中是基础，特别是在算法设计和分析方面。许多算法依赖于组合原理来优化过程，例如对数据进行排序或在大型数据集中搜索。例如，理解图论的组合方面可以导致更高效的网络路由和连通性算法。随着技术的不断进步，掌握组合数学（combinatorics）的人才需求可能会增加，这突显了这一学科在现代教育中的重要性。 除了在计算机科学中的应用外，组合数学（combinatorics）在统计分析中也起着重要作用。研究人员经常使用组合方法来确定概率并根据数据进行预测。例如，在进行调查或实验时，理解可能结果的组合可以帮助统计学家得出有意义的结论。组合数学（combinatorics）的这一方面在经济学、心理学和生物学等领域尤其相关，因为数据解释对于决策和政策制定至关重要。 此外，学习组合数学（combinatorics）培养了批判性思维和解决问题的能力。处理组合问题鼓励个人创造性地思考并从不同角度接近挑战。这种分析性思维不仅在数学中有益，而且在工程、金融和社会科学等多个其他学科中也同样重要。通过学习组合数学（combinatorics）培养这些技能，学生可以提高整体学业表现，并为未来的职业生涯做好准备。 总之，组合数学（combinatorics）是一个重要的数学分支，具有广泛的影响力，涉及多个领域。它在计数、排列和概率方面的应用使其成为研究人员和专业人士不可或缺的工具。随着我们继续应对日益复杂的世界，组合数学（combinatorics）原理将继续在解决问题和做出明智决策中发挥重要作用。因此，学生参与这一学科至关重要，因为它为他们提供了宝贵的技能和知识，这些技能和知识将在他们的学术和职业追求中受益。