Your search
Results 185 resources
-
The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”
-
We introduce a novel application of feature ranking methods to the fault localization problem. We envision the problem of localizing causes of failures as instances of ranking program's elements where elements are conceptualized as features. In this paper, we define features as program's statements. However, in its fine-grained definition, the idea of program's features can refer to any traits of programs. This paper proposes feature ranking-based algorithms. The algorithms analyze execution traces of both passing and failing test cases, and extract the bug signatures from the failing test cases. The proposed procedure extracts possible combinations of program's elements when executed together from bug signatures. The feature ranking-based algorithms then order statements according to the suspiciousness of the combinations. When viewed as sequences, the combination of program's elements produced and traced in bug signatures can be utilized to reason about the common longest subsequence. The common longest subsequence of bug signatures represents the common statements executed by all failing test cases and thus provides a means for identifying statements that contain possible faults. Our evaluation indicates that the proposed feature-based fault localization outperforms existing fault localization ranking schemes. © 2017 World Scientific Publishing Company.
-
Vulnerabilities need to be detected and removed from software. Although previous studies demonstrated the usefulness of employing prediction techniques in deciding about vulnerabilities of software components, the improvement of effectiveness of these prediction techniques is still a grand challenging research question. This paper employed a technique based on a deep neural network with rectifier linear units trained with stochastic gradient descent method and batch normalization, for predicting vulnerable software components. The features are defined as continuous sequences of tokens in source code files. Besides, a statistical feature selection algorithm is then employed to reduce the feature and search space. We evaluated the proposed technique based on some Java Android applications, and the results demonstrated that the proposed technique could predict vulnerable classes, i.e., software components, with high precision, accuracy and recall.
-
In this article, we derive the joint Laplace transform of the sequential probability ratio test (SPRT) and the resulting stopped random walk process for the negative exponential model. The Laplace transform is derived by solving a related difference equation. This technique is novel because it only takes advantage of the Markov structure and does not rely on the typical martingale methods used for deriving the Laplace transform of other SPRTs. The joint Laplace transform provides the joint distribution of the SPRT and the associated stopped process, which is a new result. Even the marginal distributions were hitherto unknown. © 2017 Taylor & Francis.
Explore
Department
- Mathematics
- Academic Affairs (1)
- Computer Science (1)
- Economics (1)
- Health and Human Services (College of) (1)
- Health and Movement Sciences (1)
- Information and Library Science (4)
- Nursing (1)
- Physics (1)
- Psychology (1)
Resource type
- Book (32)
- Book Section (8)
- Conference Paper (21)
- Journal Article (116)
- Report (8)
Publication year
- Between 1900 and 1999 (40)
-
Between 2000 and 2026
(145)
- Between 2000 and 2009 (25)
- Between 2010 and 2019 (77)
- Between 2020 and 2026 (43)
Resource language
- English (151)