中英文翻译：数学论文题目、摘要、关键词

Question

解数学竞赛题的若干思想方法
摘要：以数学竞赛题为载体,阐述了数学思想方法的涵义：数学思想就是对数学知识的本质认识，是从某些具体的数学内容和对数学的认识过重中提炼上升的数学观点，是数学知识结构的精髓和灵魂，它起到统帅和支配数学知识的作用。它在认识活动中被反复运用，带有普遍的指导意义，是建立数学和运用数学解决问题的指导思想。数学方法是指数学在提出问题、解决问题的过程中，所采用的各种方式、手段、途径等；列举了代数代换法、增设有效条件在数学竞赛在解题中的应用；展示了数学的统一美、简单美、对称美、奇异美
关键词：数学思想；数学方法；竞赛；代换法；增设条件

Answer 1

摘要（abridgement ）：Mathematics Olympiad entitled to carriers, a mathematical way of thinking on the meaning: mathematical thinking is to understand the nature of mathematical knowledge, from some of the specific content of mathematics and mathematical understanding of the excessive rise in refining a mathematical point of view, is a mathematics knowledge Structure of the essence and soul of the commander in chief and it played the dominant role of mathematical knowledge. It was in the awareness activities in the use of repeated, with the guidance of universal significance, is the establishment of mathematics and use mathematics to solve the problem of guiding ideology. Is the index of mathematical methods in question, problem-solving process, used in various ways, means and ways; cited the algebra substitution law, created conditions for effective problem solving in mathematics competition in the application; demonstrated the mathematical The unity of the United States, the United States and simple, symmetrical the United States, the United States and singular

关键词：
Mathematical thinking 数学思想
Mathematical Methods 数学方法
Competition 竞赛
Replacement Act 代换法
Additional conditions 增设条件

Answer 2

Solves mathematics competition topic certain thinking method
Take mathematics competition topic as the carrier, elaborated mathematics thinking method implication: Mathematics thought is knew to mathematics knowledge essence that is overweight refines the rise from certain concrete mathematics content and to mathematics understanding mathematics viewpoint, is mathematics knowledge structure essence and the soul, it the command and the control mathematics knowledge function. It is utilized repeatedly in the understanding activity, has the universal guiding sense, is establishes mathematics and solves the question guiding principle using mathematics. The mathematical method refers to mathematics, in proposed that the question, solves in the question process, uses each way, method, way and so on; Has enumerated the algebra substitution law, the addition effective condition in mathematics competition in the problem solving application; Has demonstrated mathematics unification beautifully, simple beautiful, symmetrical beautiful, strange beautiful
数学思想；Mathematics thought
数学方法；Mathematical method
竞赛；Competition
代换法；Substitution method
增设条件Addition condition

Answer 3

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