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1.
通过研究二次型的性质,利用正(负)定矩阵判断多元函数的极值、证明不等式,由矩阵的特征值求多元函数的最值,再借助非退化线性替换进行多项式因式分解和判断二次曲线的形状,展现线性代数中的二次型知识在初等数学及微积分中的应用。  相似文献   

2.
基于回归分析的粮食产量影响因素分析   总被引：4，自引：0，他引：4  
主要采用回归分析的方法对1990—2005年影响我国粮食产量变化的主要因素进行分析,建立了以粮食产量为应变量,粮食作物播种面积、有效灌溉面积、农业机械总动力、化肥施用量和成灾面积五种可量化的影响因素为自变量的多元线性回归模型,利用模型对各个因素进行了比较分析.同时,对模型进行检验,在此基础上提出了一些关于稳定发展粮食生产的可供参考的意见.  相似文献   

3.
Abstract

Rouché’s Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The winding number provides a geometric interpretation relating to the conclusion of Rouché’s Theorem, but most undergraduate texts give no geometric insights that lead to an understanding of why Rouché’s Theorem holds. In addition, most texts do not inform students that a stronger version of the theorem exists. In this paper we present a simplified proof of the stronger version, which is a suitable topic for students to pursue as a short project, and provide a geometric argument for the weaker version. Finally, as a project for advanced students, we unpack a standard application of this theorem as used in control systems: the Nyquist stability criterion.  相似文献   

4.
A number of regression studies have attempted to predict success in an MBA program. The current study extends the work of previous investigations by proposing a model that incorporates a number of terms which represent interaction of undergraduate grade point average with undergraduate institution and undergraduate major. The resulting model has a significantly largerR 2 value then previously reported studies. The largeR 2 value is attributed to a more complete model and a careful scrutinizing of the data employed in model construction.  相似文献   

5.
Padmanabhan Seshaiyer 《PRIMUS》2017,27(4-5):476-493
Abstract

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived from calculus, but can be suitably modified to solve more complex problems; and finally provide pointers on how to train students through the UR process that can help to impact student’s future academic and non-academic careers.  相似文献   

6.
悬链线是微积分、微分方程、微分几何、变分计算及数值分析中的一个重要课题.本文通过一些诸如方轮自行车、旋转的最小面积等有趣的例子,计算悬链线和相应半圆下面的面积,证明悬链线到处都有,但并不是无处不在.  相似文献   

7.
In order to self-regulate, students need to honestly reflect on their learning and to take appropriate corrective action. A simple procedure to cultivate student skills in self-regulated learning, known as the Task Evaluation and Reflection Instrument for Student Self-Assessment (TERISSA) is discussed in this paper. TERISSA guides students through two evaluations of the complexity of a task: the first is undertaken just before solving the task and the second straight after completing the task. This study involved 63 undergraduate students and observed a statistically significant difference (p = 0.007) in performance between the students who did (6.1/10) and did not (4.1/10) use TERISSA during tutorials leading up to an assessment task.  相似文献   

8.
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9.
1. Introduction In 1696, the French mathematician L. Hospital published a thesis titled Infinitesimal Analysis which dealt with differential and integral calculus created by Newton and Leibniz. The thesis attracted much worldwide attention on its appearance, especially Hospital抯 creation so called 揹ifferential solution method for unitary indeterminate form?is till popular. The author acquired in early 1936 that 22xyzxy=+ is the indeterminate form when P(x,y) O (0,0), and that dtandyykxxa…  相似文献   

10.
Valid, accessible, reusable methods for instructional video game design and embedded assessment can provide actionable information enhancing individual and collective achievement. Cyberlearning through game‐based, metaphor‐enhanced learning objects (CyGaMEs) design and embedded assessment quantify player behavior to study knowledge discovery and application. CyGaMEs is grounded by analogical reasoning theory, cognitive task analysis and knowledge representation. A construct representation argument for validity using evidence‐centered design warrants CyGaMEs, its web‐based learning environment, Selene: A Lunar Construction GaME, its embedded assessment, and a learning dynamics approach to student, measurement and statistical models. Two studies (US volunteers, Study 1: n = 267, mean (M)age = 15; Study 2: n = 90, Mage = 12) cross‐validate learning dynamics (learner progress, rate of progress and changes in that rate) for Selene's multidimensional goals while players learn and apply standard‐based science about fundamental geology and space science concepts. Gameplay data analyzed using regression, calculus and hierarchical linear modeling exhibit overall relatively high standardized rates of progress toward each goal statistically higher than zero. For example, adjusting for nesting within individual players, average rate of progress toward the goal of accreting lunar mass is a z‐score of 1.4 (99% confidence interval = 1.40lower, 1.48upper) or 1.4 standard deviations above zero.  相似文献   

11.
生师比是衡量研究生教育质量常用的表征指标。以世界高水平大学研究生生师比2：1～4：1为参照,纵向维度,运用趋势外推法预测生师比发展情况;横向维度,运用多个变量的曲线模型估计研究生教育生师比与本专科院校招生数和教师数的相关关系,并在此基础上提出结合教育政策推动,提高研究生教育质量的思路。  相似文献   

12.
There is consensus in the statistical literature that severe departures from its assumptions invalidate the use of regression modeling for purposes of inference. The assumptions of regression modeling are usually evaluated subjectively through visual, graphic displays in a residual analysis but such an approach, taken alone, may be insufficient for assessing the appropriateness of the fitted model. Here, an easy‐to‐use test of the assumption of equal variance (i.e., homoscedasticity) as well as model specification is provided. Given the importance of the equal‐variance assumption (i.e., if uncorrected, severe violations preclude the use of statistical inference and moderate violations result in a loss of statistical power) and given the fact that, if uncorrected, a misspecified or underspecified model could invalidate an entire study, the test developed by Halbert White in 1980 is recommended for supplementing a graphic residual analysis when teaching regression modeling to business students at both the undergraduate and graduate levels. Using this confirmatory approach to supplement a traditional residual analysis has value because students often find that graphic displays are too subjective for determining what constitutes severe from moderate departures from the equal variance assumption or for assessing patterns in plots that might indicate model misspecification or underspecification.  相似文献   

13.
Following a series of reviews every 5 years since 1998, this fourth study presents the research trends in science education based on 1,088 research articles published in Science Education, Journal of Research in Science Teaching, and International Journal of Science Education from 2013 to 2017. The top three research topics, that is, the context of students’ learning, science teaching, and students’ conceptual learning were still emphasized by researchers in the period of 2013–2017. It is also evident that researchers have undoubtedly changed their preferences of research topics in the three journals within the 2 decades. For example, the topic concerning conceptual understanding, alternative conceptions, and conceptual change (Learning-Conceptions) was in continuous decline from 2003 to 2017, although it ranked as the top topic in the 1998–2002 period. The research topic of Teaching continuously ranked second in the 2008–2012 as well as in the 2013–2017 periods. Yet, the declining trend of Goals, Policy, and Curriculum reported in the last review was not observed in the latest period. The analysis of the top 10 most-cited papers unveiled that the issues such as inequality in science education, STEM education, and undergraduate research experiences were gradually highlighted.  相似文献   

14.
Abstract

This article presents research on persistence among at-risk students using network analysis following multiple linear regression (MLR). Data on a population of enrolled undergraduate students at an urban-serving university over several years (P?=?35,239) is tested using multiple linear regression. Variables interacting at different dimensions of the model are analyzed using IBM SPSS Neural Networks (2017) and Cytoscape (2018) to show network linkages. While variables may not be significant in MLR models where anomalies are ruled out, network analysis takes these anomalies into account and reveals complex layers of interactions between and among variables. Findings show that loans of any kind contribute to attrition while financial aid of any kind contributes to persistence and offsets attrition from loans.  相似文献   

15.
This paper documents the ongoing development of a framework for reflection for undergraduate learners new to the reflective process. Motivated by the gap between students’ abilities and experience of reflection and the expectations of them at undergraduate level, the author experimented with a variety of approaches over a number of years. After much trial and error, a three-step pyramid method loosely based on Mezirow's three stages of the reflective process has been meeting with some success and is presented here. Findings indicate that recognizing the limitations in novice practitioners ability to reflect effectively, and providing them with a practical framework of initial support can empower them and result in greater expression and confidence in their reflective journal writing.  相似文献   

16.

This article proposes a unit on program verification that could be included in are intermediate‐level undergraduate course. A linked cursor implementation within an array for the binary search tree abstract data type (ADT) is used ASA case study. The proofs of correctness for the ADT operations are given in a careful, but informal style consistent with the level of formality common in discrete mathematics and calculus courses.  相似文献   

17.
Rounding is a necessary step in many mathematical processes. We are taught early in our education about significant figures and how to properly round a number. So when we are given a data set and asked to find a regression line, we are inclined to offer the line with rounded coefficients to reflect our model. However, the effects are not as insignificant as they might seem at first. In this paper, we investigate some consequences of rounding the coefficients in a least squares linear regression with respect to the calculated value of R2, and consider ways to minimize the amount of error that can arise.  相似文献   

18.
This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61 students in six small sections of a bridge course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion ofproof framework to indicate that part of a theorem's image which corresponds to the top-level logical structure of a proof. For simplified informal calculus statements, just 8.5% of unpacking attempts were successful; for actual statements from calculus texts, this dropped to 5%. We infer that these students would be unable to reliably relate informally stated theorems with the top-level logical structure of their proofs and hence could not be expected to construct proofs or validate them, i.e., determine their correctness.  相似文献   

19.
Providing effective motivational support is a critical determinant of a successful online distance learning experience for students in higher education. In this study, we examined how students’ academic level and use of 8 motivational regulation strategies influence 3 types of student engagement: behavioral engagement, emotional engagement, and cognitive engagement. A total of 95 undergraduate and graduate students enrolled in online courses in 4-year universities in the United States participated in this study. A series of hierarchical regression analyses of undergraduate and graduate online students (N = 95) showed that behavioral engagement, emotional engagement, and cognitive engagement are predicted by different motivational regulation strategies after controlling for the academic level. Additionally, students’ academic level was found to be a predictor of cognitive engagement but not a predictor of behavioral engagement or emotional engagement. The results suggest that online course instructors, tutors, and designers should provide students with differentiated motivational scaffolding based on their motivational profile in order to promote different aspects of learning engagement.  相似文献   

20.
This study employed multiple linear regression and decision tree analysis to examine the correlates of overall satisfaction with undergraduate education for white, Asian American, Latino and African American seniors enrolled at 17 doctoral/research universities. Satisfaction with the overall quality of instruction and social involvement were the strongest predictors of overall satisfaction for all seniors. The predictive importance of other measures of the academic experience, social integration and performance varied both within and across race groups. Findings argue for adopting a variety of institutional strategies to address the needs of different segments of the undergraduate population.  相似文献   

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