Teaching Students to Communicate with the Precise Language of Mathematics: A Focus on the Concept of Function in Calculus Courses

The use of precise language is one of the defining characteristics of mathematics that is often missing in mathematics classrooms. This lack of precision results in poorly constructed concepts that limit comprehension of essential mathematical definitions and notation. One important concept that frequently lacks the precision required by mathematics is the concept of function. Functions are foundational in the study undergraduate mathematics and are essential to other areas of modern mathematics. Because of its pivotal role, the concept of function is given particular attention in the three articles that comprise this study. A unit on functions that focuses on using precise language was developed and presented to a class of 50 first-semester calculus students during the first two weeks of the semester. This unit includes a learning goal, a set of specific objectives, a collection of learning activities, and an end-of-unit assessment. The results of the implementation of this unit and the administration of the assessment indicated that when students were able to construct the concept of function themselves and formulate a formal definition, they had a deeper and more meaningful understanding of the concept. In order to demonstrate its validity, the assessment was analyzed as to its relevance, reliability, and its test items\u27 effectiveness in discriminating between different levels of achievement. The results of this analysis indicated that the assessment was relevant to both the mathematical content and learning levels indicated by the unit\u27s objectives and had a high level of reliability. Additionally, the test items contained in the assessment had a reasonable level of effectiveness in discriminating between different levels of student achievement

Trellis phase codes for power-bandwith efficient satellite communications

Support work on improved power and spectrum utilization on digital satellite channels was performed. Specific attention is given to the class of signalling schemes known as continuous phase modulation (CPM). The specific work described in this report addresses: analytical bounds on error probability for multi-h phase codes, power and bandwidth characterization of 4-ary multi-h codes, and initial results of channel simulation to assess the impact of band limiting filters and nonlinear amplifiers on CPM performance

Parents’ Ethnotheories of Maladaptive Behavior in Young Children

Parents’ culturally influenced belief systems, or ethnotheories, are critical components of children’s socialization. Beliefs about children’s desirable characteristics motivate specific parenting activities and moderate the effectiveness of childrearing practices. However, relatively little attention has been given to parents’ ethnotheories of children’s undesirable behavior. From a few studies, we know that parents have culturally specific theories about the nature and management of children’s maladaptive behavior that motivate their socialization practices. In this review, we identify gaps in the research and suggest that qualitative studies of parents’ ethnotheories about the nature and management of children’s deviant behavior have strong theoretical, empirical, and practical benefits for developmental science.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151344/1/cdep12330.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151344/2/cdep12330_am.pd

Coupled-mode theory for photonic band-gap inhibition of spatial instabilities

We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane

Mechanistic Insights into Aging, Cell-Cycle Progression, and Stress Response

The longevity of an organism depends on the health of its cells. Throughout life cells are exposed to numerous intrinsic and extrinsic stresses, such as free radicals, generated through mitochondrial electron transport, and ultraviolet irradiation. The cell has evolved numerous mechanisms to scavenge free radicals and repair damage induced by these insults. One mechanism employed by the yeast Saccharomyces cerevisiae to combat stress utilizes the Anaphase Promoting Complex (APC), an essential multi-subunit ubiquitin-protein ligase structurally and functionally conserved from yeast to humans that controls progression through mitosis and G1. We have observed that yeast cells expressing compromised APC subunits are sensitive to multiple stresses and have shorter replicative and chronological lifespans. In a pathway that runs parallel to that regulated by the APC, members of the Forkhead box (Fox) transcription factor family also regulate stress responses. The yeast Fox orthologs Fkh1 and Fkh2 appear to drive the transcription of stress response factors and slow early G1 progression, while the APC seems to regulate chromatin structure, chromosome segregation, and resetting of the transcriptome in early G1. In contrast, under non-stress conditions, the Fkhs play a complex role in cell-cycle progression, partially through activation of the APC. Direct and indirect interactions between the APC and the yeast Fkhs appear to be pivotal for lifespan determination. Here we explore the potential for these interactions to be evolutionarily conserved as a mechanism to balance cell-cycle regulation with stress responses

Flint for safer smart contracts

The Ethereum blockchain platform supports the execution of decentralised applications or smart contracts. These typically hold and transfer digital currency to other parties on the platform; however, they have been subject to numerous attacks due to the unintentional introduction of bugs. Over a billion dollars worth of currency has been stolen since its release in July 2015. As smart contracts cannot be updated after deployment, it is imperative that the programming language supports the development of robust contracts. We propose Flint, a new statically-typed programming language specifically designed for writing robust smart contracts. Flint's features enforce the writing of safe and predictable code. To encourage good practices, we introduce protection blocks. Protection blocks restrict who can run code and when (using typestate) it can be executed. To prevent vulnerabilities relating to the unintentional loss of currency, Flint Asset traits provide safe atomic operations, ensuring the state of contracts is always consistent. Writes to state are restricted, simplifying reasoning about smart contracts

Why We Read Wikipedia

Wikipedia is one of the most popular sites on the Web, with millions of users relying on it to satisfy a broad range of information needs every day. Although it is crucial to understand what exactly these needs are in order to be able to meet them, little is currently known about why users visit Wikipedia. The goal of this paper is to fill this gap by combining a survey of Wikipedia readers with a log-based analysis of user activity. Based on an initial series of user surveys, we build a taxonomy of Wikipedia use cases along several dimensions, capturing users' motivations to visit Wikipedia, the depth of knowledge they are seeking, and their knowledge of the topic of interest prior to visiting Wikipedia. Then, we quantify the prevalence of these use cases via a large-scale user survey conducted on live Wikipedia with almost 30,000 responses. Our analyses highlight the variety of factors driving users to Wikipedia, such as current events, media coverage of a topic, personal curiosity, work or school assignments, or boredom. Finally, we match survey responses to the respondents' digital traces in Wikipedia's server logs, enabling the discovery of behavioral patterns associated with specific use cases. For instance, we observe long and fast-paced page sequences across topics for users who are bored or exploring randomly, whereas those using Wikipedia for work or school spend more time on individual articles focused on topics such as science. Our findings advance our understanding of reader motivations and behavior on Wikipedia and can have implications for developers aiming to improve Wikipedia's user experience, editors striving to cater to their readers' needs, third-party services (such as search engines) providing access to Wikipedia content, and researchers aiming to build tools such as recommendation engines.Comment: Published in WWW'17; v2 fixes caption of Table