Top Mathematics discussions
NishMath - #university
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@phys.org
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phys.org
, www.sciencedaily.com
Researchers at the Technical University of Munich (TUM) and the University of Cologne have developed an AI-based learning system designed to provide individualized support for schoolchildren in mathematics. The system utilizes eye-tracking technology via a standard webcam to identify students’ strengths and weaknesses. By monitoring eye movements, the AI can pinpoint areas where students struggle, displaying the data on a heatmap with red indicating frequent focus and green representing areas glanced over briefly.
This AI-driven approach allows teachers to provide more targeted assistance, improving the efficiency and personalization of math education. The software classifies the eye movement patterns and selects appropriate learning videos and exercises for each pupil. Professor Maike Schindler from the University of Cologne, who has collaborated with TUM Professor Achim Lilienthal for ten years, emphasizes that this system is completely new, tracking eye movements, recognizing learning strategies via patterns, offering individual support, and creating automated support reports for teachers. Recommended read:
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Michael Weiss@Diagonal Argument
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Diagonal Argument
, nLab
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Research at the intersection of logic, descent theory, and category theory is currently underway, focusing on advanced mathematical concepts. Key areas of exploration include Galois descent in algebraic contexts, a concept with applications in algebraic geometry as detailed in texts by James Milne and lecture notes by Keith Conrad and Joshua Ruiter. Additionally, researchers are investigating equivariant bicategorical shadows and traces, aiming to generalize topological Hochschild homology.
This research extends to first-order categorical logic and quantum observables, contributing to a broader understanding of these abstract mathematical structures. A recent seminar at Vanderbilt University highlighted "Equivariant Bicategorical Shadows and Traces," where the presenter discussed a new framework of equivariant bicategorical shadows and explained why twisted THH is a g-twisted shadow, also exploring g-twisted bicategorical traces. This work builds upon the foundations laid by Ponto in defining bicategorical shadows, offering potential advancements in algebraic K-theory. Recommended read:
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Tom Bridges@blogs.surrey.ac.uk
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blogs.surrey.ac.uk
, The Quantum Insider
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Recent breakthroughs are pushing the boundaries of quantum theory and quantum randomness, paving the way for commercial applications and more reliable quantum technologies. A paper by Dorje Brody, along with collaborators Eva-Maria Graefe and Rishindra Melanathuru, has been published in Physical Review Letters, exploring decoherence resulting from phase-space measurements. Their work addresses the question of decoherence resulting from a monitoring of position and momentum, i.e., a phase-space measurement, by the environment.
Researchers have also made strides in protecting quantum information from environmental disruptions, offering hope for more stable quantum computers and networks. Scientists have demonstrated how certain quantum states can maintain their critical information even when disturbed by environmental noise. This could lead to more reliable quantum technology, enhanced medical imaging techniques, improved AI-driven diagnostics, and stronger data security. Simultaneously, a joint research team consisting of members from JPMorgan Chase, Quantinuum, multiple national labs, and UT Austin, has achieved certified quantum randomness, turning once theoretical experiments into first commercial applications for quantum computing. The team demonstrated a certified randomness protocol using Quantinuum's 56-qubit H2 trapped-ion system, showcasing a quantum computer's ability to generate entropy beyond classical reach. Furthermore, the high cost of quantum randomness is dropping due to advancements in pseudorandomness techniques, which may open new doors for quantum computing and cryptography research. Recommended read:
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Tom Bridges@blogs.surrey.ac.uk
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Math Department
Academic institutions are hosting a variety of mathematics-related events and activities. The Department of Mathematics hosted its first annual "Pi Your Professor" event on March 20, 2025, a belated celebration of Pi Day. Undergraduate students were invited to throw pies made of paper plates with Reddi Wip at participating professors, including Maddie Brandt, Spencer Dowdall, and Dan Margalit.
Math Game Monday featured "Make a Square," a strategic game designed to build 2-D visualization skills for all ages. The game involves players marking symbols on a grid, aiming to form a square with their marks. Additionally, the One World Approximate Bayesian Inference (OWABI) Seminar is scheduled for March 27th, featuring Meïli Baragatti from the Université de Montpellier discussing Approximate Bayesian Computation with Deep Learning and Conformal Prediction. Recommended read:
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Mike Watts@computational-intelligence.blogspot.com
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computational-intelligence.blo
, computational-intelligence.blo
Recent developments highlight advancements in quantum computing, artificial intelligence, and cryptography. Classiq Technologies, in collaboration with Sumitomo Corporation and Mizuho-DL Financial Technology, achieved up to 95% compression of quantum circuits for Monte Carlo simulations used in financial risk analysis. This project explored the use of Classiq’s technology to generate more efficient quantum circuits for a novel quantum Monte Carlo simulation algorithm incorporating pseudo-random numbers proposed by Mizuho-DL FT, evaluating the feasibility of implementing quantum algorithms in financial applications.
Oxford researchers demonstrated a fast, 99.8% fidelity two-qubit gate using a simplified circuit design, achieving this using a modified coaxmon circuit architecture. Also, a collaborative team from JPMorganChase, Quantinuum, Argonne National Laboratory, Oak Ridge National Laboratory, and the University of Texas at Austin demonstrated a certified randomness protocol using a 56-qubit Quantinuum System Model H2 trapped-ion quantum computer. This is a major milestone for real-world quantum applications, with the certified randomness validated using over 1.1 exaflops of classical computing power, confirming the quantum system’s ability to generate entropy beyond classical reach. The 2025 IEEE International Conference on Quantum Artificial Intelligence will be held in Naples, Italy, from November 2-5, 2025, with a paper submission deadline of May 15, 2025. Vanderbilt University will host a series of workshops devoted to Groups in Geometry, Analysis and Logic starting May 28, 2025. Recommended read:
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