This thesis investigates the relationship between object-oriented programming languages and game models of computation. These are intuitively well matched: an object encapsulates some internal state and presents some behaviour to the world via its publicly visible methods, while a strategy for some game represents the possible interactions of a program with its environment. We work with a simple and well-understood game model. Rather than tailoring our model to match some existing programming language, we view the simplicity of our semantic setting as a virtue, and try to find the appropriate language corresponding to the model. We define a class-based, stateful object-oriented language, and give a heapbased operational semantics and an interpretation in our game model. At the heart of this interpretation lies a novel semantic treatment of the phenomenon of data abstraction. The model closely guides the design of our language, which enjoys an intermediate level of expressivity between that of first-order and general higher-order store. The agreement between the operational and game interpretations is verified by a soundness proof. This involves the development of specialised techniques and a detailed analysis of the relationship between the concrete and abstract views. We also show that definability and full abstraction hold at certain types of arbitrary rank, but are problematic at other types. We conclude by briefly discussing an extended language with a control operator, along with other extensions leading to a possible core for a more realistic programming language.

This thesis examines Recursive Markov Chains (RMCs), their natural extensions and connection to other models. RMCs can model in a natural way probabilistic procedural programs and other systems that involve recursion and probability. An RMC is a set of ordinary finite state Markov Chains that are allowed to call each other recursively and it describes a potentially infinite, but countable, state ordinary Markov Chain. RMCs generalize in a precise sense several well studied probabilistic models in other domains such as natural language processing (Stochastic Context-Free Grammars), population dynamics (Multi-Type Branching Processes) and in queueing theory (Quasi-Birth-Death processes (QBDs)). In addition, RMCs can be extended to a controlled version called Recursive Markov Decision Processes (RMDPs) and also a game version referred to as Recursive (Simple) Stochastic Games (RSSGs). For analyzing RMCs, RMDPs, RSSGs we devised highly optimized numerical algorithms and implemented them in a tool called PReMo (Probabilistic Recursive Models analyzer). PReMo allows computation of the termination probability and expected termination time of RMCs and QBDs, and a restricted subset of RMDPs and RSSGs. The input models are described by the user in specifically designed simple input languages. Furthermore, in order to analyze the worst and best expected running time of probabilistic recursive programs we study models of RMDPs and RSSGs with positive rewards assigned to each of their transitions and provide new complexity upper and lower bounds of their analysis. We also establish some new connections between our models and models studied in queueing theory. Specifically, we show that (discrete time) QBDs can be described as a special subclass of RMCs and Tree-like QBDs, which are a generalization of QBDs, are equivalent to RMCs in a precise sense. We also prove that for a given QBD we can compute (in the unit cost RAM model) an approximation of its termination probabilities within i bits of precision in time polynomial in the size of the QBD and linear in i. Specifically, we show that we can do this using a decomposed Newton’s method.

We analyse the validity of common optimisations on multi-threaded programs in two memory models—the DRF guarantee and the Java Memory Model. Unlike in the single-threaded world, even simple program transformations, such as common subexpression elimination, can introduce new behaviours in shared-memory multi-threading with an interleaved semantics. To validate such optimisations, most current programming languages define weaker semantics, called memory models, that aim to allow such transformations while providing reasonable guarantees. In this thesis, we consider common program transformations and analyse their safety in the two most widely used language memory models: (i) the DRF guarantee, which promises sequentially consistent behaviours for data race free programs, and (ii) the Java Memory Model, which is the semantics of multithreaded Java. The DRF guarantee is the semantics of Ada and it has been proposed as the semantics of the upcoming revision of C++. Our key results are: (i) we prove that a large class of elimination and reordering transformations satisfies the DRF guarantee; (ii) we find that the Java language is more restrictive—despite the claims in the specification, the Java Memory Model does not allow some important program transformations, such as common subexpression elimination. To establish the safety results, we develop a trace semantic framework and describe important program optimisations as relations on sets of traces. We prove that all our elimination and reordering transformations satisfy the DRF guarantee, i.e., the semantic transformations cannot introduce new behaviours for data race free programs. Moreover, we prove that all the transformations preserve data race freedom. This ensures safety of transformations composed from eliminations and reorderings. In addition to the DRF guarantee, we prove that for arbitrary programs, our transformations prevent values appearing “outof- thin-air”—if a program does not contain constant c and does not perform any operation that could create c, then no transformation of the program can output c. We give an application of the semantic framework to a concrete language and prove safety of several simple syntactic transformations. We employ similar semantic techniques to prove validity of several classes of transformations, such as the elimination of an overwritten write or reordering of independent memory accesses, in the Java Memory Model. To establish the iii negative results for the Java Memory Model, we provide counterexamples showing that several common optimisations can introduce new behaviours and thus are not safe.

Senior Thesis at CMC is often described institutionally as the capstone of one’s undergraduate education. As such, I wanted my own to accurately capture and reflect how I’ve grown as a student and mathematician these past four years. What follows is my attempt to distill lessons I learned in mathematics outside the curriculum, written for incoming undergraduates and anyone with just a little bit of mathematical curiosity. In it, I attempt to dispel some common preconceptions about mathematics, namely that it’s uninteresting, formulaic, acultural, or completely objective, in favor of a dynamic historical and cultural perspective, with particular attention paid to the early twentieth century search to secure the foundations of mathematics and a detailed look at contemporary Hungarian mathematics. After doing so, I conclude that the scope of mathematics is not what one might expect but that it’s still absolutely worth doing and appreciating.

This project explains one person developing an instrument that was stripped from a young age, yet voyaged a pathway of determination to become a teacher of many things. Only nine years ago I went through something no female should ever endure in a lifetime, in a time of darkness, trying to find something to live for something was presented to me out of love, knowing it would be a challenge to achieve, there was a sense of understanding and hope of clarity. This opportunity to create and deliver an understanding for students, staff, faculty, and community members of all ages, a supportive reaction and a positive interpretation, that this can really work out in various favors throughout life. Even if there is much doubt. A chance to develop a sense of effective thinking patterns and be able to examine life as a whole, to pursue those underdeveloped questions about an academic's career to only conclude for one's self.

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The purpose of this study was to determine some of the bases of character education in United States public schools from 1607 to 1983. Research was conducted concerning persons, organizations, and movements to determine bases for character education. Teaching materials representing a variety of philosophies were also studied. The various bases of character education were grouped under four categories--religious, societal, specific traits, and individually determined. The history of each area was traced in a separate chapter. An attempt was made to include educators and materials representing various philosophies. The summary included some of the trends related to each base, major proponents, and materials. It was concluded that society-based character education has been the most prominent, even among educators who claim to have other bases for their character education. Bible-based character education has also been prevalent, but less so in recent years. Independent thinking as a base for character education has increased in popularity in recent years but is often, in reality, based on society. The trait approach is an approach used mainly in relation to other bases. It was also determined that character education in the United States has changed from mainly a biblical emphasis to more diversified bases. As society has become more pluralistic, a greater diversity of bases has become more acceptable. In addition, few educators adhere strictly to a single base. Most seem to combine bases in varying degrees to arrive at some sort of personalized base for their own philosophy of moral education. Some recommendations for further research and study were given.

Book Summary: Secondary schools are continually faced with the task of preparing students for a world that is more connected, advanced, and globalized than ever before. In order to adequately prepare students for their future, educators must provide them with strong reading and writing skills, as well as the ability to understand scientific concepts. The Handbook of Research on Science Literacy Integration in Classroom Environments is a pivotal reference source that provides vital research on the importance of cross-curriculum/discipline connections in improving student understanding and education. While highlighting topics such as curriculum integration, online learning, and instructional coaching, this publication explores practices in teaching students how to analyze and interpret data, as well as reading, writing, and speaking. This book is ideally designed for teachers, graduate-level students, academicians, instructional designers, administrators, and education researchers seeking current research on science literacy adoption in contemporary classrooms.

In a large, urban district in western Tennessee, African American students perform considerably lower in math, science, and reading than other districts. Several teachers in western Tennessee are using single-gender instruction as a practice, but little is known about its effectiveness in addressing the needs of African American students. Currently, there is a gap in scholarly and practical understanding of the effects of single-gender classrooms on the academic success of African American students in western Tennessee. This exploratory qualitative case study examined the experiences shared by teachers who use single-gender learning to educate African American students in secondary schools in western Tennessee. The social cognitive theory and brain-based learning were used as frameworks in examining the perceived effectiveness of single-gender classrooms, and the guiding research questions were designed to focus on teachers' experiences with single-gender classroom instruction for African American students. Ten teachers using single-gender classrooms to educate African American high school students in the subjects of English, math, or science were interviewed. Data were analyzed using the matrix approach, which led to the identification of 3 themes: learning styles, classroom management, and instructional strategies used in single-gender classrooms. These themes were identified as factors indicating benefits and pedagogical practices participants perceived as effective when used to educate African American students in single-gender classrooms. Insight from this study will enhance educators' ability to reach a population of underserved students, thus affecting social change by reducing racial education disparities among African American students.