在分析数学中一致收敛的重要性及几乎处处收敛不一定能够一致收敛。
To make sure under what circumstances everywhere converge can be converted into uniform convergence, a typical counter-case has to be analysed.
第四部分：从数学学习心理角度，分析数学启发式教学应遵循的原则。
Part IV: It analyses the principles the heuristic math teaching is supposed to stick to from the psychological aspect of learning math.
文中在分析数学的几个重要不等式的证明之中引进了概率方法，取得较好的效果。
Better results are got during the course of the proofs of several inequalities in analysis mathematics by using probabilistic method.
在分析数学中有些不等式的证明往往比较复杂，而且具体的直观含义也比较抽象。
In analysis mathematics, some identifications of inequalities are often more complicated, and concrete ocular meaning is more abstract.
鸽子洞原理是分析数学组合的有力工具。但是其概念简单，可以通过以下具体的问题加以阐述。
The pigeonhole principle is a powerful tool used in combinatorial math. But the idea is simple and can be explained by the following peculiar problem.
分析数学，统计，人口学，财务或经济学数据，推测和评估金融决策和计划的长期风险。
Analyses mathematical, statistical, demographic, financial or economic data to predict and assess the long-term risk involved in financial decisions and planning.
通过学习的一般心理过程，分析数学学习的感知和理解，从而对数学的教学得到一些启示。
This paper analyzed the perception and understanding for mathematical study by the psychological procedures of study, and acquired some inspirations for the mathematical study.
通过分析数学对话教学过程，探讨了对话教学的认知与情感互动、知识与能力并重等原则。
Analysis of teaching mathematics through the dialogue process, a dialogue on teaching cognitive and emotional interaction, knowledge and ability to both principles.
精算师佛祖而分析数学、统计、人口学、财务或经济学数据，推测和评估金融决策和计划的长期风险。
Analyses mathematical, statistical, demographic, financial or economic data to predict and assess the long-term risk involved in financial decisions and planning.
通过分析数学问题，构建与问题相关的系统，在系统内应用辨证的观点分析常量与变量，使孤立的变量相互联系。
Through analyzing mathematic problems, constructing a system related to the problem to study constants and variables is helpful to connect individual variables with each other.
博弈论创造了数学模型来分析像这样的不同情况以预测结果。
Game theory creates mathematical models that analyze different conditions like this to predict outcomes.
它使用定量数据和数学模型作为分析工具，研究这些物体在过去、现在和未来的数量。
It studies these populations, in the past, present and future, using quantitative data and mathematical models as tools of analysis.
它使用定量数据和数学模型作为分析工具，研究这些人口在过去、现在和未来的情况。
It studies these populations in the past, present and future using quantitative data and mathematical models as tools of analysis.
我把我成功的大部分原因归结于学习数学的收获，尤其是分析复杂原则的那些定理。
I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
本书详细介绍了数学的思维方式，包括持续的、按部就班的分析、实验和真知灼见。
This book presents the details that illustrate the mathematical style of thinking, which involves sustained, step-by-step analysis, experiments, and insights.
即将发表在杂志上的一篇荟萃分析可以作为发现男女数学能力没有显著差异的证据之一。
A meta-analysis to be published in the journal can be added to the pile of evidence that finds no significant gender difference in mathematical ability.
我在我的著作和一篇很长的同行评议论文中，分析了他们关于听力、视力、语言、数学、压力反应和“学习风格”的性别差异的观点。
I analyzed their various claims about sex differences in hearing, vision, language, math, stress responses, and "learning styles" in my book and a long peer-reviewed paper.
数学分析的结果表明，如果婚姻双方在情感上是相似的，则他们有一个‘最优努力策略’，其结果是幸福、长久的婚姻关系。
The results of the mathematical analysis showed when both members of union are similar emotionally they have an "optimal effort policy," which results in a happy, long-lasting relationship.
我甚至认为，数学分析不是研究经济理论的诸多方法之一种，它是唯一的方法。
I came to the position that mathematical analysis is not one of many ways of doing economic theory: it is the only way.
根据社交网络和数学网络分析方法的提示，城市形态研究组项目计算城市空间布局如何影响人们在其中生活的方式。
Taking a cue from social networks and mathematical network analysis methods, the City Form Research Group's program calculates how a cities' spatial layout affects the way people will live in it.
他利用晚上和周末的时间在华尔街的公司里上班，学习有关交易的知识，并发现他在数学和风险分析方面有异常的天赋。
He spent his evenings and weekends working at Wall Street companies, learning about trading, and found he was exceptionally talented in math and risk analysis.
和通常算法分析一样，最麻烦的部分是数学细节。
As is often true in algorithm analysis, the devil is in the mathematical details.
数学是程序员和分析人员的流行主题，从而导致了大量不同的工具可供选择。
Math is a popular topic with programmer and analyst types, leading to a huge diversity of tools to choose from.
与“自动数学家”及其后继者不同的是，他们的程序事先只加载了一组简单的基础数学功能和要求其分析的数据。
Unlike the Automated Mathematician and its heirs, their program is primed only with a set of simple, basic mathematical functions and the data it's asked to analyze.
尽管这看起来与计算机系统的数学分析没有太大关系，但是对于思考这些问题来说，这是非常有用的一种方法，而且也是到目前为止最好的一种方法。
While this may seem tangential to a mathematical analysis of computer systems, it is a useful way to think about them and is done haphazardly today at best.
追踪公司的员工多为精通定量分析的数学专家。
Tracking companies are often staffed by math gurus with expertise in quantitative analysis.
数量分析师在此类修补上的局限已不是数学问题而是计算机的速度、能力与成本。
The limit to the quants’ tinkering has been not mathematics but the speed, power and cost of computers.
经济学理论即数学分析。
经济学理论即数学分析。
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