The Riemann zeta function plays an important role in number theory. Its analytic properties encode subtle information about arithmetic, although proving these properties can seem difficult and unwieldy. In this tutorial, we will follow Tate's streamlined approach to proving these properties for a useful generalization of Riemann zeta functions: Hecke L-functions. Tate's approach is remarkable for its systematic application of Pontryagin duality (a generalization of Fourier analysis) to the adele ring, which smoothly unifies algebraic and analytic aspects of number theory. Not only does this result in a much more elegant proof, but it also serves as a gateway to understanding automorphic forms (a generalization of modular forms). Prerequisites include complex analysis, real analysis, and a one-year course in algebra. Familiarity with algebraic number theory is highly recommended. by Daniel Li, [email protected]
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Mathematics education is like many scientific disciplines witnessing an increase in scientific output. Examining and reviewing every paper in an area in detail are time-consuming, making comprehensive reviews a challenging task. Unsupervised machine learning algorithms like topic models have become increasingly popular in recent years. Their ability to summarize large amounts of unstructured text into coherent themes or topics allows researchers in any field to keep an overview of state of the art by creating automated literature reviews. In this article, we apply topic modeling in the context of mathematics education and showcase the use of this data science approach for creating literature reviews by training a model of all papers ( n = 336) that have been presented in Thematic Working Groups related to technology in the first eleven Congresses of the European Society for Research in Mathematics Education (CERME). We guide the reader through the stepwise process of training a model and give recommendations for best practices and decisions that are decisive for the success of such an approach to a literature review. We find that research in this period revolved around 25 distinct topics that can be grouped into four clusters: digital tools, teachers and their resources, technology experimentation, and a diverse cluster with a strong focus on student activity. Finally, a temporal analysis of these topics reveals a correlation between technology trends and research focus, allowing for reflection on future research in the field.
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The material generated and analyzed during the current study are available in the Zenodo repository (CERN’s repository service for open science) in Herfort et al. ( 2022 ).
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Herfort, J.D., Tamborg, A.L., Meier, F. et al. Twenty years of research on technology in mathematics education at CERME: a literature review based on a data science approach. Educ Stud Math 112 , 309–336 (2023). https://doi.org/10.1007/s10649-022-10202-z
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An international survey in two rounds. Around the time when Educational Studies in Mathematics (ESM) and the Journal for Research in Mathematics Education (JRME) were celebrating their 50th anniversaries, Arthur Bakker (editor of ESM) and Jinfa Cai (editor of JRME) saw a need to raise the following future-oriented question for the field of mathematics education research:
Education-Related Research Topics & Ideas. ... 2020) A study of the elementary math program utilized by a mid-Missouri school district (Barabas, 2020) Instructor formative assessment practices in virtual learning environments : a posthumanist sociomaterial perspective (Burcks, 2019) ...
Harvard Mathematics Department Tutorial Topics, Fall 2019, Spring 2020 Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
Mathematics education is like many scientific disciplines witnessing an increase in scientific output. Examining and reviewing every paper in an area in detail are time-consuming, making comprehensive reviews a challenging task. Unsupervised machine learning algorithms like topic models have become increasingly popular in recent years. Their ability to summarize large amounts of unstructured ...