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We're Swarming Again! Swarming, Collectivity, And Trope: The Case Of Extinction Rebellion, Tyler J. Behymer Aug 2024

We're Swarming Again! Swarming, Collectivity, And Trope: The Case Of Extinction Rebellion, Tyler J. Behymer

Department of Communication Studies: Dissertations, Theses, and Student Research

This thesis explores the rhetoric of the eco-movement Extinction Rebellion, focusing on the use of swarming and nature tropes to mobilize collective action and revivify contemporary notions of collectivity. Drawing on rhetoric of social movement scholarship, cultural studies, and psychoanalysis, this essay theorizes swarming as a tropological economy that expands the conditions of propriety in the context of collectivity. Through an analysis of Extinction Rebellion’s discourse, this study demonstrates how the naturalization of swarming tropes works in various ways to rewild conventional political discourse, galvanize disruptive collective assembly, and challenge green neoliberalism.

Advisor: Casey Ryan Kelly


Bayesian Approaches In Multi-State Markov Models And High Dimensional Time-To-Event Data., Yuchen Han Aug 2024

Bayesian Approaches In Multi-State Markov Models And High Dimensional Time-To-Event Data., Yuchen Han

Electronic Theses and Dissertations

This dissertation consists of two projects. The first one involves nonparametric methods on Continuous Time Markov Chains (CTMCs). The second one is centered around Bayesian shrinkage models for detecting prognostic and predictive biomarkers in high-dimensional clinical data. Both these projects build on methods from across the frequentist and Bayesian paradigm to offer novel solutions. In the first project, we aim to model the nonlinear effects of continuous variables within multistate framework in a non-parametrically by appealing to the rich mathematical framework of Reproducing Kernel Hilbert Spaces (RKHS). Then we adapted the classical Representer Theorem to penalized (squared norm) log-likelihood which …


Leveraging International Large-Scale Assessments: Insights From An Item-Writing Professional Development Program For High School Mathematics Teachers, Mark Lester B. Garcia, Catherine P. Vistro-Yu Aug 2024

Leveraging International Large-Scale Assessments: Insights From An Item-Writing Professional Development Program For High School Mathematics Teachers, Mark Lester B. Garcia, Catherine P. Vistro-Yu

Mathematics Faculty Publications

The Philippine Department of Education, despite seeing minimal improvements in the country’s score and rankings in the recent cycles of international large-scale assessments (ILSAs) such as TIMSS and PISA, maintained that it shall continue to participate in ILSAs to monitor the progress of educational effectiveness and benchmark with other countries by observing and adopting commendable practices. While legislators and other stakeholders push for increased financial resources in the education sector as part of the country’s preparations for upcoming ILSAs, one crucial aspect that is largely overlooked is teacher training. This paper presents a viable yet contentious way of upskilling teachers …


Nonfactoid Question Answering As Query-Focused Summarization With Graph-Enhanced Multihop Inference, Yang Deng, Wenxuan Zhang, Weiwen Xu, Ying Shen, Wai Lam Aug 2024

Nonfactoid Question Answering As Query-Focused Summarization With Graph-Enhanced Multihop Inference, Yang Deng, Wenxuan Zhang, Weiwen Xu, Ying Shen, Wai Lam

Research Collection School Of Computing and Information Systems

Nonfactoid question answering (QA) is one of the most extensive yet challenging applications and research areas in natural language processing (NLP). Existing methods fall short of handling the long-distance and complex semantic relations between the question and the document sentences. In this work, we propose a novel query-focused summarization method, namely a graph-enhanced multihop query-focused summarizer (GMQS), to tackle the nonfactoid QA problem. Specifically, we leverage graph-enhanced reasoning techniques to elaborate the multihop inference process in nonfactoid QA. Three types of graphs with different semantic relations, namely semantic relevance, topical coherence, and coreference linking, are constructed for explicitly capturing the …


Style: Improving Domain Transferability Of Asking Clarification Questions In Large Language Model Powered Conversational Agents, Yue Chen, Chen Huang, Yang Deng, Wenqiang Lei, Dingnan Jin, Jia Liu, Tat-Seng Chua Aug 2024

Style: Improving Domain Transferability Of Asking Clarification Questions In Large Language Model Powered Conversational Agents, Yue Chen, Chen Huang, Yang Deng, Wenqiang Lei, Dingnan Jin, Jia Liu, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

Equipping a conversational search engine with strategies regarding when to ask clarification questions is becoming increasingly important across various domains. Attributing to the context understanding capability of LLMs and their access to domain-specific sources of knowledge, LLM-based clarification strategies feature rapid transfer to various domains in a posthoc manner. However, they still struggle to deliver promising performance on unseen domains, struggling to achieve effective domain transferability. We take the first step to investigate this issue and existing methods tend to produce one-size-fits-all strategies across diverse domains, limiting their search effectiveness. In response, we introduce a novel method, called STYLE, to …


On The Multi-Turn Instruction Following For Conversational Web Agents, Yang Deng, Xuan Zhang, Wenxuan Zhang, Yifei Yuan, See-Kiong Ng, Tat-Seng Chua Aug 2024

On The Multi-Turn Instruction Following For Conversational Web Agents, Yang Deng, Xuan Zhang, Wenxuan Zhang, Yifei Yuan, See-Kiong Ng, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

Web agents powered by Large Language Models (LLMs) have demonstrated remarkable abilities in planning and executing multi-step interactions within complex web-based environments, fulfilling a wide range of web navigation tasks. Despite these advancements, the potential for LLM-powered agents to effectively engage with sequential user instructions in real-world scenarios has not been fully explored. In this work, we introduce a new task of Conversational Web Navigation, which necessitates sophisticated interactions that span multiple turns with both the users and the environment, supported by a specially developed dataset named Multi-Turn Mind2Web (MT-Mind2Web). To tackle the limited context length of LLMs and the …


Watme: Towards Lossless Watermarking Through Lexical Redundancy, Liang Chen, Yatao Bian, Yang Deng, Deng Cai, Shuaiyi Li, Peilin Zhao, Kam-Fai Wong Aug 2024

Watme: Towards Lossless Watermarking Through Lexical Redundancy, Liang Chen, Yatao Bian, Yang Deng, Deng Cai, Shuaiyi Li, Peilin Zhao, Kam-Fai Wong

Research Collection School Of Computing and Information Systems

Text watermarking has emerged as a pivotal technique for identifying machine-generated text. However, existing methods often rely on arbitrary vocabulary partitioning during decoding to embed watermarks, which compromises the availability of suitable tokens and significantly degrades the quality of responses. This study assesses the impact of watermarking on different capabilities of large language models (LLMs) from a cognitive science lens. Our finding highlights a significant disparity; knowledge recall and logical reasoning are more adversely affected than language generation. These results suggest a more profound effect of watermarking on LLMs than previously understood. To address these challenges, we introduce Watermarking with …


Reinforcement Tuning For Detecting Stances And Debunking Rumors Jointly With Large Language Models, Ruichao Yang, Wei Gao, Jing Ma, Hongzhan Ling, Bo Wang Aug 2024

Reinforcement Tuning For Detecting Stances And Debunking Rumors Jointly With Large Language Models, Ruichao Yang, Wei Gao, Jing Ma, Hongzhan Ling, Bo Wang

Research Collection School Of Computing and Information Systems

Learning multi-task models for jointly detecting stance and verifying rumors poses challenges due to the need for training data of stance at post level and rumor veracity at claim level, which are difficult to obtain. To address this issue, we leverage large language models (LLMs) as the foundation annotators for the joint stance detection (SD) and rumor verification (RV) tasks, dubbed as JSDRV. We introduce a novel reinforcement tuning framework to enhance the joint predictive capabilities of LLM-based SD and RV components. Specifically, we devise a policy for selecting LLM-annotated data at the two levels, employing a hybrid reward mechanism …


Analyzing Temporal Complex Events With Large Language Models? A Benchmark Towards Temporal, Long Context Understanding, Zhihan Zhang, Yixin Cao, Chenchen Ye, Ma. Yunshan, Lizi Liao, Tat-Seng Chua Aug 2024

Analyzing Temporal Complex Events With Large Language Models? A Benchmark Towards Temporal, Long Context Understanding, Zhihan Zhang, Yixin Cao, Chenchen Ye, Ma. Yunshan, Lizi Liao, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

The digital landscape is rapidly evolving with an ever-increasing volume of online news, emphasizing the need for swift and precise analysis of complex events.We refer to the complex events composed of many news articles over an extended period as Temporal Complex Event (TCE). This paper proposes a novel approach using Large Language Models (LLMs) to systematically extract and analyze the event chain within TCE, characterized by their key points and timestamps. We establish a benchmark, named TCELongBench, to evaluate the proficiency of LLMs in handling temporal dynamics and understanding extensive text. This benchmark encompasses three distinct tasks - reading comprehension, …


Staying Fresh: Unconventional Approaches Towards Advancing Energy Sustainability, Water Resources, And Community Resiliency In The Southwestern United States, Judith Hoyt Aug 2024

Staying Fresh: Unconventional Approaches Towards Advancing Energy Sustainability, Water Resources, And Community Resiliency In The Southwestern United States, Judith Hoyt

Open Access Theses & Dissertations

This dissertation addresses critical challenges in urban heat management, sustainable energy resource utilization, and water quality communication through three studies. Study 1 investigates the impact of roof color on urban heat islands in Tucson, Arizona where approximately 70% of roofs display high albedo (i.e., light) colors. Energy consumption simulations conducted indicate that converting dark- to light-colored roofs could save Tucson approximately $1,400,000 annually in energy costs, highlighting the potential of cool roofs for energy savings and improved thermal comfort. Study 2 assesses the sources of lithium in subsurface waters in West Texas and South Central New Mexico. Water chemistry data …


Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo Aug 2024

Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo

Open Access Theses & Dissertations

The outcomes of scientific models can be hard to understand given the need for context, domain knowledge, and many variables and data being used. This research aims to provide users of scientific models with understandable information that can be automatically generated. For the context of this research, understandable is defined as being correctly interpreted (i.e., with respect to the original intent of the data). Scientific information can be conveyed to users in the form of a narrative or visualizations, and these are not necessarily separate from each other, but rather complimentary. One of the objectives of this research is to …


Bridging The Gap: Ai And The Hidden Structure Of Consciousness, Emily Barnes, James Hutson Aug 2024

Bridging The Gap: Ai And The Hidden Structure Of Consciousness, Emily Barnes, James Hutson

Faculty Scholarship

The quest to develop Artificial Intelligence (AI) systems that possess human-like consciousness necessitates a deep dive into both theoretical and practical aspects underpinning this ambitious goal. This article builds on initial philosophical explorations of AI consciousness by examining the intricate and often hidden structures that may facilitate conscious experiences in AI. Drawing from concepts in cognitive science and neuroscience, the article elucidates how AI systems can be designed to replicate the structural and functional aspects of human consciousness. The discussion includes the Hierarchy of Spatial Belongings proposed by Forti (2024), frameworks like the Integrated Information Theory (IIT), and models linking …


Larp: Language Audio Relational Pre‑Training For Cold‑Start Playlist Continuation, Rebecca Salganik, Xiaohao Liu, Yunshan Ma, Jian Kang, Tat‑Seng Chua Aug 2024

Larp: Language Audio Relational Pre‑Training For Cold‑Start Playlist Continuation, Rebecca Salganik, Xiaohao Liu, Yunshan Ma, Jian Kang, Tat‑Seng Chua

Research Collection School Of Computing and Information Systems

As online music consumption increasingly shifts towards playlist-based listening, the task of playlist continuation, in which an algorithm suggests songs to extend a playlist in a personalized and musically cohesive manner, has become vital to the success of music streaming services. Currently, many existing playlist continuation approaches rely on collaborative filtering methods to perform their recommendations. However, such methods will struggle to recommend songs that lack interaction data, an issue known as the cold-start problem. Current approaches to this challenge design complex mechanisms for extracting relational signals from sparse collaborative signals and integrating them into content representations. However, these approaches …


Self-Chats From Large Language Models Make Small Emotional Support Chatbot Better, Zhonghua Zheng, Lizi Liao, Yang Deng, Libo Qin, Liqiang Nie Aug 2024

Self-Chats From Large Language Models Make Small Emotional Support Chatbot Better, Zhonghua Zheng, Lizi Liao, Yang Deng, Libo Qin, Liqiang Nie

Research Collection School Of Computing and Information Systems

Large Language Models (LLMs) have shown strong generalization abilities to excel in various tasks, including emotion support conversations. However, deploying such LLMs like GPT-3 (175B parameters) is resource-intensive and challenging at scale. In this study, we utilize LLMs as “Counseling Teacher” to enhance smaller models’ emotion support response abilities, significantly reducing the necessity of scaling up model size. To this end, we first introduce an iterative expansion framework, aiming to prompt the large teacher model to curate an expansive emotion support dialogue dataset. This curated dataset, termed ExTES, encompasses a broad spectrum of scenarios and is crafted with meticulous strategies …


Planning Like Human : A Dual-Process Framework For Dialogue Planning, Tao He, Lizi Liao, Yixin Cao, Yuanxing Liu, Ming Liu, Zerui Chen, Bing Qin Aug 2024

Planning Like Human : A Dual-Process Framework For Dialogue Planning, Tao He, Lizi Liao, Yixin Cao, Yuanxing Liu, Ming Liu, Zerui Chen, Bing Qin

Research Collection School Of Computing and Information Systems

In proactive dialogue, the challenge lies not just in generating responses but in steering conversations toward predetermined goals, a task where Large Language Models (LLMs) typically struggle due to their reactive nature. Traditional approaches to enhance dialogue planning in LLMs, ranging from elaborate prompt engineering to the integration of policy networks, either face efficiency issues or deliver suboptimal performance. Inspired by the dual-process theory in psychology, which identifies two distinct modes of thinking—intuitive (fast) and analytical (slow), we propose the Dual-Process Dialogue Planning (DPDP) framework. DPDP embodies this theory through two complementary planning systems: an instinctive policy model for familiar …


Sibo : A Simple Booster For Parameter-Efficient Fine-Tuning, Zhihao Wen, Jie Zhang, Yuan Fang Aug 2024

Sibo : A Simple Booster For Parameter-Efficient Fine-Tuning, Zhihao Wen, Jie Zhang, Yuan Fang

Research Collection School Of Computing and Information Systems

Fine-tuning all parameters of large language models (LLMs) necessitates substantial computational power and extended time. Latest advancements in parameter-efficient fine-tuning (PEFT) techniques, such as Adapter tuning and LoRA, allow for adjustments to only a minor fraction of the parameters of these LLMs. Concurrently, it has been noted that the issue of over-smoothing diminishes the effectiveness of these Transformer-based LLMs, resulting in suboptimal performances in downstream tasks. In this paper, we present SIBO, which is a SImple BOoster to enhance PEFT, by injecting an initial residual. SIBO is straightforward and readily extensible to a range of state-of-the-art PEFT techniques to alleviate …


Synergizing Large Language Models And Pre-Trained Smaller Models For Conversational Intent Discovery, Jinggui Liang, Lizi Liao, Hao Fei, Jing Jiang Aug 2024

Synergizing Large Language Models And Pre-Trained Smaller Models For Conversational Intent Discovery, Jinggui Liang, Lizi Liao, Hao Fei, Jing Jiang

Research Collection School Of Computing and Information Systems

In Conversational Intent Discovery (CID), Small Language Models (SLMs) struggle with overfitting to familiar intents and fail to label newly discovered ones. This issue stems from their limited grasp of semantic nuances and their intrinsically discriminative framework. Therefore, we propose Synergizing Large Language Models (LLMs) with pre-trained SLMs for CID (SynCID). It harnesses the profound semantic comprehension of LLMs alongside the operational agility of SLMs. By utilizing LLMs to refine both utterances and existing intent labels, SynCID significantly enhances the semantic depth, subsequently realigning these enriched descriptors within the SLMs’ feature space to correct cluster distortion and promote robust learning …


A Survey On Neural Question Generation : Methods, Applications, And Prospects, Shasha Guo, Lizi Liao, Cuiping Li, Tat-Seng Chua Aug 2024

A Survey On Neural Question Generation : Methods, Applications, And Prospects, Shasha Guo, Lizi Liao, Cuiping Li, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

In this survey, we present a detailed examination of the advancements in Neural Question Generation (NQG), a field leveraging neural network techniques to generate relevant questions from diverse inputs like knowledge bases, texts, and images. The survey begins with an overview of NQG’s background, encompassing the task’s problem formulation, prevalent benchmark datasets, established evaluation metrics, and notable applications. It then methodically classifies NQG approaches into three predominant categories: structured NQG, which utilizes organized data sources, unstructured NQG, focusing on more loosely structured inputs like texts or visual content, and hybrid NQG, drawing on diverse input modalities. This classification is followed …


Speaker Verification In Agent-Generated Conversations, Yizhe Yang, Palakorn Achananuparp, Heyan Huang, Jing Jiang, Ee-Peng Lim Aug 2024

Speaker Verification In Agent-Generated Conversations, Yizhe Yang, Palakorn Achananuparp, Heyan Huang, Jing Jiang, Ee-Peng Lim

Research Collection School Of Computing and Information Systems

The recent success of large language models (LLMs) has attracted widespread interest to develop role-playing conversational agents personalized to the characteristics and styles of different speakers to enhance their abilities to perform both general and special purpose dialogue tasks. However, the ability to personalize the generated utterances to speakers, whether conducted by human or LLM, has not been well studied. To bridge this gap, our study introduces a novel evaluation challenge: speaker verification in agent-generated conversations, which aimed to verify whether two sets of utterances originate from the same speaker. To this end, we assemble a large dataset collection encompassing …


An Efficient Neutrosophic Approach For Evaluating Possible Industry 5.0 Enablers In Consumer Electronics: A Case Study, Mai Mohamed, Asmaa Elsayed, Bilal Arain, Jun Ye Aug 2024

An Efficient Neutrosophic Approach For Evaluating Possible Industry 5.0 Enablers In Consumer Electronics: A Case Study, Mai Mohamed, Asmaa Elsayed, Bilal Arain, Jun Ye

Neutrosophic Systems with Applications

With the use of cutting-edge technologies like artificial intelligence (AI), robotics, and the Internet of Things (IoT), Industry 5.0 represents a breakthrough move towards a sustainable and human-centered industrial future. Industry 5.0 endeavors to transform industries such as consumer electronics by emphasizing sustainability and collaboration, in contrast to its predecessors, who only concentrated on automation and efficiency. Along with improved manufacturing efficiency and product innovation, this change in the consumer electronics sector also redefines the human-machine interaction. This paper proposes a novel hybrid integrating model that combines the Entropy Weight Method (EWM), Best-Worst Method (BWM), and an acronym in Portuguese …


Heterogeneous Graph Transformer With Poly-Tokenization, Zhiyuan Lu, Yuan Fang, Cheng Yang, Chuan Shi Aug 2024

Heterogeneous Graph Transformer With Poly-Tokenization, Zhiyuan Lu, Yuan Fang, Cheng Yang, Chuan Shi

Research Collection School Of Computing and Information Systems

Graph neural networks have shown widespread success for learning on graphs, but they still face fundamental drawbacks, such as limited expressive power, over-smoothing, and over-squashing. Meanwhile, the transformer architecture offers a potential solution to these issues. However, existing graph transformers primarily cater to homogeneous graphs and are unable to model the intricate semantics of heterogeneous graphs. Moreover, unlike small molecular graphs where the entire graph can be considered as the receptive field in graph transformers, real-world heterogeneous graphs comprise a significantly larger number of nodes and cannot be entirely treated as such. Consequently, existing graph transformers struggle to capture the …


Empathyear : An Open-Source Avatar Multimodal Empathetic Chatbot, Hao Fei, Han Zhang, Bin Wang, Lizi Liao, Qian Liu, Erik Cambria Aug 2024

Empathyear : An Open-Source Avatar Multimodal Empathetic Chatbot, Hao Fei, Han Zhang, Bin Wang, Lizi Liao, Qian Liu, Erik Cambria

Research Collection School Of Computing and Information Systems

This paper introduces EmpathyEar, a pioneering open-source, avatar-based multimodal empathetic chatbot, to fill the gap in traditional text-only empathetic response generation (ERG) systems. Leveraging the advancements of a large language model, combined with multimodal encoders and generators, EmpathyEar supports user inputs in any combination of text, sound, and vision, and produces multimodal empathetic responses, offering users, not just textual responses but also digital avatars with talking faces and synchronized speeches. A series of emotion-aware instruction-tuning is performed for comprehensive emotional understanding and generation capabilities. In this way, EmpathyEar provides users with responses that achieve a deeper emotional resonance, closely emulating …


Clamber: A Benchmark Of Identifying And Clarifying Ambiguous Information Needs In Large Language Models, Tong Zhang, Peixin Qin, Yang Deng, Chen Huang, Wenqiang Lei, Junhong Liu, Dingnan Jin, Hongru Liang, Tat-Seng Chua Aug 2024

Clamber: A Benchmark Of Identifying And Clarifying Ambiguous Information Needs In Large Language Models, Tong Zhang, Peixin Qin, Yang Deng, Chen Huang, Wenqiang Lei, Junhong Liu, Dingnan Jin, Hongru Liang, Tat-Seng Chua

Research Collection School Of Computing and Information Systems

Large language models (LLMs) are increasingly used to meet user information needs, but their effectiveness in dealing with user queries that contain various types of ambiguity remains unknown, ultimately risking user trust and satisfaction. To this end, we introduce CLAMBER, a benchmark for evaluating LLMs using a well-organized taxonomy. Building upon the taxonomy, we construct 12K high-quality data to assess the strengths, weaknesses, and potential risks of various off-the-shelf LLMs.Our findings indicate the limited practical utility of current LLMs in identifying and clarifying ambiguous user queries, even enhanced by chain-of-thought (CoT) and few-shot prompting. These techniques may result in overconfidence …


First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat Jul 2024

First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat

Journal of Humanistic Mathematics

From August 22nd to November 21st, the first Diffusion Course on “The structure of language as a connection between artificial intelligence, information and ethics” will take place on a Thursday of each month, in Ribeirao Preto, Brazil. You are cordially invited to sign up for in-person classes and join other researchers and students on this course.


Oh Statistics!, Heather L. Cook Jul 2024

Oh Statistics!, Heather L. Cook

Journal of Humanistic Mathematics

This poem was written about statistics and the usefulness thereof.


Geometric Shapes That Sing And Move: An Interdisciplinary Lesson With Pre-Service Teachers, Gladys Krause, Gustavo Velandia Jul 2024

Geometric Shapes That Sing And Move: An Interdisciplinary Lesson With Pre-Service Teachers, Gladys Krause, Gustavo Velandia

Journal of Humanistic Mathematics

Our work shares a practical example of an interdisciplinary lesson in which two teacher educators collaborated to integrate mathematics and music in an elementary mathematics methods course. This paper describes the process of collaboration in designing the lesson and shares original instructional resources to be used in the classroom. We also discuss what the pre-service teachers participating in the lesson shared about their learning experience, and what we, the teacher educators, learned from this experience. In presenting this work we aim to promote the opening of spaces in teacher preparation programs that allow pre-service teachers to develop their own instructional …


Intuitive Explanations In Mathematical Education, Jerzy Pogonowski Jul 2024

Intuitive Explanations In Mathematical Education, Jerzy Pogonowski

Journal of Humanistic Mathematics

I discuss the role of intuitive explanations in the learning, teaching, and popularization of mathematics. Several examples of such explanations are presented, related to linguistic explanations, perception, empirical models, and internal explanations inside mathematics itself. I emphasize the fact that intuitive explanations in a sense transgress mere mathematical arguments. I also discuss in brief the role of paradox resolution in mathematical education.


Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller Jul 2024

Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller

Journal of Humanistic Mathematics

The following investigation is a cognitive-historical analysis of the conceptual development of complex numbers. The history of this development spans nearly two millennia, from the earliest appearance of the square root of a negative quantity in the calculations of Heron of Alexandra (1st Century CE) to the full flowering of complex numbers in the first half of the 19th Century. The approach used for this analysis is Nersessian's, including her formulations of model-based reasoning and mental models. Additional aspects of the analysis feature the prominent roles played by process representations, including object-process complementarities, and by core numerical systems. Our analysis …


Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson Jul 2024

Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson

Journal of Humanistic Mathematics

A permutation π in Sn can be decomposed into its runs π = τ1τ2 . . . τk, where a run of π is a maximal contiguous subsequence whose elements are in increasing order. If the first values of each run are in increasing order, then π is said to be flattened. Motivated by the study of flattened permutations, we study the words in the Danish, German, English, Spanish, French, Italian, Dutch, and Norwegian languages. In each language considered, our work provides the following: a list of the longest flattened words, histograms for the proportion …


Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl Jul 2024

Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl

Journal of Humanistic Mathematics

According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …