Tootfinder

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#MathsMonday #Math
There's been a buzz - mostly from Tech Bros - about AI getting gold medals in the International #Mathematics Olympiad, including a remark "Now this *is* impressi…

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
—Bertrand Russell

( \(2^{nd}\) announcement)
The #Springer Problem Book for the Indiana College Mathematics Competition (2001-2023) is now available in a (slightly less expensive) softcover format! This book, edited by me, J. Gash, R. Gillman, and @… , can be used by stu…

The Indiana College Mathematics Competition (2001⁠–2023)
This book gathers problems based on over twenty years of the Indiana College Mathematics Competition, a contest for teams of undergraduates.

Continuity Norm Framework for the Evolution of Nonsingular Matrices
L. Yildiz, D. Kayki, E. Gudekli
https://arxiv.org/abs/2507.20742 https://arxiv.org/pdf/…

Continuity Norm Framework for the Evolution of Nonsingular Matrices
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular classification. However, such binary classifications become inadequate in describing matrices whose elements vary continuously over time, thereby transitioning through intermediate states near singular configurations. To address this fundamental limitation, we develop a…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Sequence of Numbers of Linear Codes with Increasing Hull Dimensions
Stefka Bouyuklieva, Iliya Bouyukliev, Ferruh \"Ozbudak

A note on the Artstein-Avidan-Milman's generalized Legendre transforms
Frank Nielsen
https://arxiv.org/abs/2507.20577 https://arxiv.org/pdf/2507.20577

A note on the Artstein-Avidan-Milman's generalized Legendre transforms
Artstein-Avidan and Milman [Annals of mathematics (2009), (169):661-674] characterized invertible reverse-ordering transforms on the space of lower-semi-continuous extended real-valued convex functions as affine deformations of the ordinary Legendre transform. In this note, we prove that all those generalized Legendre transforms on functions correspond to the ordinary Legendre transform on dually corresponding affine-deformed functions. That is, generalized convex conjugates are convex conjugat…

Enhancing Differentially Private Linear Regression via Public Second-Moment
Zilong Cao (The School of Mathematics, Northwest University), Hai Zhang (The School of Mathematics, Northwest University)
https://arxiv.org/abs/2508.18037

Enhancing Differentially Private Linear Regression via Public Second-Moment
Leveraging information from public data has become increasingly crucial in enhancing the utility of differentially private (DP) methods. Traditional DP approaches often require adding noise based solely on private data, which can significantly degrade utility. In this paper, we address this limitation in the context of the ordinary least squares estimator (OLSE) of linear regression based on sufficient statistics perturbation (SSP) under the unbounded data assumption. We propose a novel method …

The Ingleton inequality holds for metacyclic groups and fails for supersoluble groups
David A. Craven
https://arxiv.org/abs/2505.22565 https://

The Ingleton inequality holds for metacyclic groups and fails for supersoluble groups
The Ingleton inequality first appeared in matroid theory, where Ingleton proved in 1971 that every rank function coming from a representable matroid on four subsets satisfies a particular inequality. Because this inequality is not implied by submodularity, Shannon-type axioms alone, it and various analogues play a central role in separately linear and non-linear phenomena in a variety of areas of mathematics. The Ingleton inequality for finite groups concerns the various intersections of four s…

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- Algebra of overpartitions
Robert Schneider
https://arxi…

#SMBC on the final victory of the #humanities over #mathematics #engineering and

The Unreasonable Effectiveness of Mathematical Experiments: What Makes Mathematics Work
Asvin G
https://arxiv.org/abs/2506.19787 https://

The Unreasonable Effectiveness of Mathematical Experiments: What Makes Mathematics Work
This essay proposes a reconceptualization of mathematics as an experimental science exploring patterns in computation and what the advent of AI-assited provers might imply in light of this reconceptualization. Beginning with Voevodsky's crisis of confidence, where a major result remained in limbo for 24 years, neither proven nor refuted, we argue that mathematics is not the discovery of eternal truths but theory-building in response to computational experiments. Just as physicists build theorie…

Properties of zero-determinant strategies in multichannel games
Masahiko Ueda
https://arxiv.org/abs/2505.21952 https://arxiv.org/pdf/…

Properties of zero-determinant strategies in multichannel games
Controlling payoffs in repeated games is one of the important topics in control theory of multi-agent systems. Recently proposed zero-determinant strategies enable players to unilaterally enforce linear relations between payoffs. Furthermore, based on the mathematics of zero-determinant strategies, regional payoff control, in which payoffs are enforced into some feasible regions, has been discovered in social dilemma situations. More recently, theory of payoff control was extended to multichann…

Can Structured Templates Facilitate LLMs in Tackling Harder Tasks? : An Exploration of Scaling Laws by Difficulty
Zhichao Yang, Zhaoxin Fan, Gen Li, Yuanze Hu, Xinyu Wang, Ye Qiu, Xin Wang, Yifan Sun, Wenjun Wu
https://arxiv.org/abs/2508.19069

Can Structured Templates Facilitate LLMs in Tackling Harder Tasks? : An Exploration of Scaling Laws by Difficulty
Structured, procedural reasoning is essential for Large Language Models (LLMs), especially in mathematics. While post-training methods have improved LLM performance, they still fall short in capturing deep procedural logic on complex tasks. To tackle the issue, in this paper, we first investigate this limitation and uncover a novel finding: a Scaling Law by Difficulty, which reveals that model performance follows a U-shaped curve with respect to training data complexity -- excessive low-difficu…

Banach modules, almost mathematics and condensed mathematics
Dimitri Dine
https://arxiv.org/abs/2508.11268 https://arxiv.org/pdf/2508.11268

Banach modules, almost mathematics and condensed mathematics
We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring $A$, with submetric (norm-decreasing) $A$-module homomorphisms for morphisms. If $A$ is a Banach ring with a norm-multiplicative topologically nilpotent unit $\varpi$ contained in the closed unit ball $A_{\leq1}$ such that $\varpi$ admits a compatible system of $p$-power roots $\varpi^{1/p^{n}}$ with \begin{equation*}\lVert\varpi^{1/p^{n}}\rVert=\lVe…

Visualization enhances Problem Solving in Multi-Qubit Systems: An Eye-Tracking Study
Jonas Bley, Eva Rexigel, Alda Arias, Lars Krupp, Nikolas Longen, Paul Lukowicz, Stefan K\"uchemann, Jochen Kuhn, Maximilian Kiefer-Emmanouilidis, Artur Widera
https://arxiv.org/abs/2505.21508

Visualization enhances Problem Solving in Multi-Qubit Systems: An Eye-Tracking Study
Quantum Information Science (QIS) is a vast, diverse, and abstract field. In consequence, learners face many challenges. Science, Technology, Engineering, and Mathematics (STEM) education research has found that visualizations are valuable to aid learners in complex matters. The conditions under which visualizations pose benefits are largely unexplored in QIS education. In this eye-tracking study, we examine the conditions under which the visualization of multi-qubit systems in addition to the …

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- A Tale of Santa Claus, Hypergraphs and Matroids
Sami Davies, Thomas Rothvoss, Yihao Zhang

Introduction to the Cohomology of the Flag Variety
Sara C. Billey, Yibo Gao, Brendan Pawlowski
https://arxiv.org/abs/2506.21064 https://

Introduction to the Cohomology of the Flag Variety
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumerative results for intersecting varieties defined by rank conditions on vector spaces. Today by way of many contributions in algebraic topology, geometry, and combinatorics, we consider this solved. Yet, deep questions remain about the subtleties of actually carrying out the process. In this chapter, we hope to summari…

In mathematics, we have a useful phrase I wish were more in general parlance: “necessary but not sufficient.”
This is not sufficient, but it is necessary. Call those Senators. They aren’t •completely• useless. https://mastodon.social/@indivisibleteam/114729468063702602

What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems
Weiqi Chu, Matthew Dobson
https://arxiv.org/abs/2508.18519 https://arxiv…

What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. Scientists also study what happens when we shrink the ball down to the size of an electron to a w…

On preservation of relative resolutions for poset representations
Toshitaka Aoki, Shunsuke Tada
https://arxiv.org/abs/2506.21227 https://

On preservation of relative resolutions for poset representations
The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the adjoint quadruple between the categories of persistence modules (representations) of the posets via Kan extensions. One of central subjects in multiparameter persistent homology analysis is to understand structures of persistence modules. In this paper, we mainly study a class of Galois connections whose left adjoint is…

Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology - A Review
Zhe Su, Xiang Liu, Layal Bou Hamdan, Vasileios Maroulas, Jie Wu, Gunnar Carlsson, Guo-Wei Wei
https://arxiv.org/abs/2507.19504

Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology - A Review
Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology, a technique rooted in algebraic topology. Paired with topological deep learning (TDL) or topological machine learning, persistent homology has achieved tremendous success in a wide variety of applications in science, engineering, medicine, and industry. Howev…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- An analogue of Reed's conjecture for digraphs
Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta

Iterated jump noncomputability and compactness
Gavin Dooley
https://arxiv.org/abs/2506.20620 https://arxiv.org/pdf/2506.20620

Iterated jump noncomputability and compactness
We use reverse mathematics to analyze "iterated jump" versions of the following four principles: the atomic model theorem with subenumerable types (AST), the diagonally noncomputable principle (DNR), weak weak Kőnig's lemma (WWKL), and weak Kőnig's lemma (WKL). The logical relationships between these principles are summarized in Figure 1 and include, among other things, an infinite chain and an infinite antichain, the latter of which represents a strong form of non-linearity in terms of prova…

This is such a good summary of "the problem with 'data science'", as it tries to replace any domain expertise with the misguided notion that some form of statistics.
And so you end up with (maybe even well-meaning) researchers that are so far in over their head that they don't even know what they don't know.
Case in point: the authors of the preprint come from mathematics, computer science, physics, and 'future studies' (lol)…
@…

AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?
Ori Press, Brandon Amos, Haoyu Zhao, Yikai Wu, Samuel K. Ainsworth, Dominik Krupke, Patrick Kidger, Touqir Sajed, Bartolomeo Stellato, Jisun Park, Nathanael Bosch, Eli Meril, Albert Steppi, Arman Zharmagambetov, Fangzhao Zhang, David Perez-Pineiro, Alberto Mercurio, Ni Zhan, Talor Abramovich, Kilian Lieret, Hanlin Zhang, Shirley Huang, Matthias Bethge, Ofir Press

AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?
Despite progress in language model (LM) capabilities, evaluations have thus far focused on models' performance on tasks that humans have previously solved, including in programming (Jimenez et al., 2024) and mathematics (Glazer et al., 2024). We therefore propose testing models' ability to design and implement algorithms in an open-ended benchmark: We task LMs with writing code that efficiently solves computationally challenging problems in computer science, physics, and mathematics. Our AlgoTu…

The Low Mass Dwarf Host Galaxy of Non-Repeating FRB 20230708A
August R. Muller (Maria Mitchell Observatory, Max Planck Institute for Gravitational Physics), Alexa C. Gordon (Northwestern University), Stuart D. Ryder (Macquarie University), Alexandra G. Mannings (University of California Santa Cruz), J. Xavier Prochaska (University of California Santa Cruz, Kavli Institute for the Physics and Mathematics of the Universe, National Astronomical Observatory of Japan), Keith W. Bannister (C…

The Low Mass Dwarf Host Galaxy of Non-Repeating FRB 20230708A
We present Very Large Telescope/X-Shooter spectroscopy for the host galaxies of 12 fast radio bursts (FRBs) detected by the Australian SKA Pathfinder (ASKAP) observed through the ESO Large Programme "FURBY", which imposes strict selection criteria on the included FRBs and their host galaxies to produce a homogeneous and well-defined sample. We describe the data reduction and analysis of these spectra and report their redshifts, line-emission fluxes, and derived host properties. From the present…

Well-Founded Coalgebras Meet K\"onig's Lemma
Henning Urbat, Thorsten Wi{\ss}mann
https://arxiv.org/abs/2507.18539 https://arxiv.org/pdf/2507.18539…

Well-Founded Coalgebras Meet König's Lemma
König's lemma is a fundamental result about trees with countless applications in mathematics and computer science. In contrapositive form, it states that if a tree is finitely branching and well-founded (i.e. has no infinite paths), then it is finite. We present a coalgebraic version of König's lemma featuring two dimensions of generalization: from finitely branching trees to coalgebras for a finitary endofunctor H, and from the base category of sets to a locally finitely presentable category…

Mathematics of Gozinta Boxes
Dillan Agrawal, Selena Ge, Jate Greene, Tanya Khovanova, Dohun Kim, Rajarshi Mandal, Tanish Parida, Anirudh Pulugurtha, Gordon Redwine, Soham Samanta, Albert Xu
https://arxiv.org/abs/2508.18277

Mathematics of Gozinta Boxes
We study the geometric aspects of the magic trick called Gozinta Boxes. We generalize Gozinta Boxes to other dimensions, and we show that in three and higher dimensions, the maximum number of boxes is 3, and in two dimensions, the maximum is 4. We discuss other properties of Gozinta Boxes and provide a plethora of examples.

Eigenvalue spectrum support of paired random matrices with pseudo-inverse
Uri Cohen
https://arxiv.org/abs/2506.21244 https://arxiv.or…

Eigenvalue spectrum support of paired random matrices with pseudo-inverse
The Moore-Penrose pseudo-inverse $X^\dagger$, defined for rectangular matrices, naturally emerges in many areas of mathematics and science. For a pair of rectangular matrices $X, Y$ where the corresponding entries are jointly Gaussian and i.i.d., we analyse the support of the eigenvalue spectrum of $XY^\dagger$.

Crosslisted article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Tight Quantum-Security Bounds and Parameter Optimization for SPHINCS and NTRU
Ruopengyu Xu, Chenglian Liu

This is comparable to the rise of totalitarian regimes in the 1920s and 1930s,
when Mussolini said even a teacher of mathematics must be a fascist.
Now all who do not take positions on American politics, policies and history that comply with the administration’s views
are in danger of being denied funding, subjected to lawsuits, and derided by the White House in ways that can inspire violent private attacks.
All this has precedents, but not in America’s peacetime hist…

Lt. Gen. William J. Hartman, acting N.S.A. director, asked Tulsi Gabbard for evidence to back her claim that chief scientist Vinh Nguyen committed crimes sufficient to justify revoking his clearance and received no answer.
https://www.nytimes.com/2025/08/20/us/poli

N.S.A.’s Acting Director Tried to Save Top Scientist From Purge
Vinh Nguyen, an expert in artificial intelligence and advanced mathematics, was among the current and former officials whose security clearances were revoked by the president.

Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling
Oscar Barrera, Aur\'elien Dersy, Rabia Husain, Matthew D. Schwartz, Xiaoyuan Zhang
https://arxiv.org/abs/2507.17815

Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling
In mathematics or theoretical physics one is often interested in obtaining an exact analytic description of some data which can be produced, in principle, to arbitrary accuracy. For example, one might like to know the exact analytical form of a definite integral. Such problems are not well-suited to numerical symbolic regression, since typical numerical methods lead only to approximations. However, if one has some sense of the function space in which the analytic result should lie, it is possib…

Sources: NSA Director William Hartman unsuccessfully tried to protect Vinh Nguyen, an expert in AI and cryptology, from being fired on President Trump's orders (Julian E. Barnes/New York Times)
https://w…

N.S.A.’s Acting Director Tried to Save Top Scientist From Purge
Vinh Nguyen, an expert in artificial intelligence and advanced mathematics, was among the current and former officials whose security clearances were revoked by the president.

The physics and mathematics of living and dying matter
Tanniemola B. Liverpool, Kristian K. M\"uller-Nedebock, Xichen Chao, Chang Yuan
https://arxiv.org/abs/2507.14294

The physics and mathematics of living and dying matter
We introduce and study a class of active matter models in which we keep track of fuel (stored energy) consumption. They are by construction, thermodynamically consistent. Using these models it is possible for us to observe and follow how active behaviour develops and also how it dissipates as the energy runs out. It is also straightforward to define, calculate and keep track of macroscopic thermodynamic quantities.

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
Shun Ding, Yang Wan, Luofei Wang, Siqi Xiao
https://arxiv.org/abs/2508.11635

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological space. Now all sets open and sequentially closed. Then, we form an unextendible algorithmic function transforming positive integers to 0 and 1, looking at the preimages of these values as our sequentially closed sets. Then we show that if the Tietze theorem concl…

A Classification Program for Nonlocality Paradoxes of Three Qubits
Nadish de Silva (Department of Mathematics, Simon Fraser University), Santanil Jana (Department of Mathematics, Simon Fraser University), Ming Yin (Department of Mathematics, Simon Fraser University)
https://arxiv.org/abs/2508.14673…

A Classification Program for Nonlocality Paradoxes of Three Qubits
Nonlocality is a quintessential signature of nonclassical behaviour and a resource for quantum advantages in communication and computation. The paradoxical correlations witnessed by strong nonlocality undergird the standard probabilistic form of nonlocality and provide optimal advantages in numerous informational tasks. Three-qubit systems are the simplest ones that admit strong nonlocality. Abramsky et al. (TQC, 2017) established the existence of an infinite family of three-qubit paradoxes, …

[2025-05-29 Thu (UTC), no new articles found for math.GM General Mathematics]
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🇺🇦 #NowPlaying on KEXP's #StreetSounds
Mos Def:
🎵 Mathematics
#MosDef
https://samadee.bandcamp.com/album/mos-def-mathematics-samadee-remix
https://open.spotify.com/track/3gRlmtdCyNoKiyozn2pqc9

Automatic Large Language Models Creation of Interactive Learning Lessons
Jionghao Lin, Jiarui Rao, Yiyang Zhao, Yuting Wang, Ashish Gurung, Amanda Barany, Jaclyn Ocumpaugh, Ryan S. Baker, Kenneth R. Koedinger
https://arxiv.org/abs/2506.17356

Automatic Large Language Models Creation of Interactive Learning Lessons
We explore the automatic generation of interactive, scenario-based lessons designed to train novice human tutors who teach middle school mathematics online. Employing prompt engineering through a Retrieval-Augmented Generation approach with GPT-4o, we developed a system capable of creating structured tutor training lessons. Our study generated lessons in English for three key topics: Encouraging Students' Independence, Encouraging Help-Seeking Behavior, and Turning on Cameras, using a task deco…

Pictorial and Documentary Guide for Research, Teaching, and Education through Astronomy, Physics, and Mathematics Pursued under the Umbrella of the United Nations (1974-2024)
Hans J. Haubold, Arak M. Mathai
https://arxiv.org/abs/2507.17283

Pictorial and Documentary Guide for Research, Teaching, and Education through Astronomy, Physics, and Mathematics Pursued under the Umbrella of the United Nations (1974-2024)
This paper was prepared for Open-Access-only publication as a guide reporting on Education (all aspects of space science and technology), Teaching (remote sensing and GIS, satellite meteorology and global climate, satellite communication, space and atmospheric sciences, global navigation satellite systems), and Research (solar neutrino problem, formation of structure in the Universe) in astronomy (solar physics, cosmology), physics (nuclear physics, neutrino physics), and mathematics (fractiona…

Properties and Expressivity of Linear Geometric Centralities
Paolo Boldi, Flavio Furia, Chiara Prezioso
https://arxiv.org/abs/2506.19670 https://

Properties and Expressivity of Linear Geometric Centralities
Centrality indices are used to rank the nodes of a graph by importance: this is a common need in many concrete situations (social networks, citation networks, web graphs, for instance) and it was discussed many times in sociology, psychology, mathematics and computer science, giving rise to a whole zoo of definitions of centrality. Although they differ widely in nature, many centrality measures are based on shortest-path distances: such centralities are often referred to as geometric. Geometric…

Generalized Multiple Operator Integrals for Operators with Finite Dimensions
Shih-Yu Chang
https://arxiv.org/abs/2506.19971 https://a…

Generalized Multiple Operator Integrals for Operators with Finite Dimensions
Multiple Operator Integrals (MOIs) have played a foundational role in operator theory and functional calculus, particularly for analyzing Hermitian matrices via spectral decomposition. Conventional MOIs rely on the assumption of self-adjointness, making them analytically tractable for computing Frechet derivatives, establishing trace formulas, and deriving commutator estimates. However, many problems in mathematics, science, and engineering involve matrices that are fundamentally non-Hermitian,…

Oh! #Tumblr is on a purge again, likely all these new age restrictions or such, because I've been warned against mentions of mathematics, showing chrome toggle switches being fondled on vintage computers or perhaps early 60s academic fashion, I don't know, I've requested clarification.

A bibliometric study on mathematical oncology: interdisciplinarity, internationality, collaboration and trending topics
Kira Pugh, Linn\'ea Gyllingberg, Stanislav Stratiev, Sara Hamis
https://arxiv.org/abs/2506.20684

A bibliometric study on mathematical oncology: interdisciplinarity, internationality, collaboration and trending topics
Mathematical oncology is an interdisciplinary research field where mathematics meets cancer research. The field's intention to study cancer makes it dynamic, as practicing researchers are incentivised to quickly adapt to both technical and medical research advances. Determining the scope of mathematical oncology is therefore not straightforward; however, it is important for purposes related to funding allocation, education, scientific communication, and community organisation. To address this i…

"Airdrops would usually be ordered as a last resort to feed people in emergency situations where hostile armed forces or geography make road deliveries impossible. In Gaza the only obstacles to driving aid across the border are restrictions imposed by Israel, an ally of many western nations including Britain, and armed with British and US weapons"
#GazaGenocide

[2025-08-28 Thu (UTC), 1 new article found for cs.DM Discrete Mathematics]
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Mathematics education research must be useful for the classroom
Anthony A. Essien, Tanya Evans, Maitree Inprasitha, Salome Martinez Salanzar, Demetra Pitta-Pantazi
https://arxiv.org/abs/2508.14433

Mathematics education research must be useful for the classroom
The theme of the PME-48 conference, Making sure that mathematics education research reaches the classroom, highlights a key concern: not all mathematics education research informs classroom practice. This raises several fundamental questions: Which research fails to reach the classroom? Why? And should all research be expected to do so? Accordingly, it is fitting that the plenary panel engages with these important issues by debating the following motion: Mathematics education research must be u…

Friezes and continued fractions
Evgeny Smirnov
https://arxiv.org/abs/2508.17074 https://arxiv.org/pdf/2508.17074 …

Friezes and continued fractions
We explore basic properties of number friezes, due to Conway and Coxeter, and their relations to decompositions of rational numbers into continued fractions, Farey sequences, and the modular group acting on the hyperbolic plane. These are notes from a mini-course for undergraduate students given at the 19th Summer School ``Modern Mathematics'', Dubna, Russia, July 18-29, 2019.

[2025-08-28 Thu (UTC), 1 new article found for math.GM General Mathematics]
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[2025-07-28 Mon (UTC), 2 new articles found for cs.DM Discrete Mathematics]
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Controlling Casimir Effect in Networks
Tian-Ming Zhao, Rong-Xin Miao
https://arxiv.org/abs/2506.20405 https://arxiv.org/pdf/2506.2040…

Controlling Casimir Effect in Networks
Networks have played a pivotal role in physics, mathematics, and biology, propelling the recent revolution in artificial intelligence. This paper studies quantum field theories on networks and proposes a novel junction condition on the node. The junction condition is consistent with energy conservation in the sense that the total energy flow into the node is zero. As an application, we explore the Casimir effect on networks. Remarkably, the Casimir force on one edge can be changed from attracti…

This is comparable to the rise of totalitarian regimes in the 1920s and 1930s,
when Mussolini said even a teacher of mathematics must be a fascist.
Now all who do not take positions on American politics, policies and history that comply with the administration’s views
are in danger of being denied funding, subjected to lawsuits, and derided by the White House in ways that can inspire violent private attacks.
All this has precedents, but not in America’s peacetime hist…

Opinion | The Mind-Boggling Intrusiveness of Donald J. Trump
The president is driving the tentacles of the federal government deep into the nation’s economy, culture and legal system.

Closed-Form Decomposition for Simplicial Cones and PDBarv Algorithm for Lattice Point Counting
Sihao Tao, Guoce Xin, Zihao Zhang
https://arxiv.org/abs/2506.19322

Closed-Form Decomposition for Simplicial Cones and PDBarv Algorithm for Lattice Point Counting
Counting lattice points within a rational polytope is a foundational problem with applications across mathematics and computer science. A key approach is Barvinok's algorithm, which decomposes the lattice point generating function of cones to that of unimodular cones. However, standard implementations face difficulties: the original primal method struggles with points on cone boundaries, while the alternative dual method can be slow for certain cone types. This paper introduces two main contr…

[2025-07-29 Tue (UTC), 2 new articles found for cs.DM Discrete Mathematics]
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[2025-07-29 Tue (UTC), 3 new articles found for math.GM General Mathematics]
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[2025-05-29 Thu (UTC), no new articles found for cs.DM Discrete Mathematics]
#toXiv_bot_toot

[2025-07-28 Mon (UTC), no new articles found for math.GM General Mathematics]
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Exploring collaboration: The effect of gender on mathematics learning preferences
Sang Hyun Kim, Tanya Evans
https://arxiv.org/abs/2508.14426 https://arxiv…

Exploring collaboration: The effect of gender on mathematics learning preferences
This study examines the influence of gender on students' collaborative preferences for learning mathematics (CPLM) over time in an undergraduate mathematics context. Data collected at three points during the semester were analyzed using a two-way mixed analysis of variance (ANOVA). Results showed no significant interaction between gender and time, nor a main effect of gender, indicating stable CPLM scores and comparable preferences between male and female students. These findings challenge prio…

"In the first 21 months of war, 104 flights supplied the equivalent of just four days of food for Gaza, Israeli data shows, for a cost running to tens of millions of dollars. Spent on trucks, the same budget would deliver much more food"
#GazaGenocide
#GazaStarvation …

[2025-08-29 Fri (UTC), no new articles found for math.GM General Mathematics]
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Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification
Juan E. N\'apoles Vald\'es
https://arxiv.org/abs/2508.19253 https://

Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification
In this paper, we present an overview of the development of one of the most dynamic areas of mathematics today: local differential operators of non-integer order. The underlying question is whether we are witnessing a period of consolidation and are on the way to a general formulation of this fascinating topic.

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- A Row-wise Algorithm for Graph Realization
Rolf van der Hulst, Matthias Walter

“Our analysis of the food packages supplied by the [Gaza Humanitarian Foundation] shows that their distribution plan would lead to mass starvation, even if it was able to function without the appalling levels of violence that have been reported”
#GazaGenocide
#GazaStarvation

Student explanation in middle and secondary mathematics and statistics: A scoping literature review
Huixin Gao, Tanya Evans, Anna Fergusson
https://arxiv.org/abs/2508.14417 http…

Student explanation in middle and secondary mathematics and statistics: A scoping literature review
This scoping review examines the literature on student explanation strategies in middle and secondary mathematics and statistics education from 2014 to 2024. Following the PRISMA protocol, we analyzed 41 studies that met the inclusion criteria. The findings classify student explanations into two types: self-explanation (SE) and peer explanation (PE). Both approaches enhance conceptual understanding and procedural knowledge, though each offers distinct benefits and challenges. SE is particularly…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- An abstract structure determines the contextuality degree of observable-based Kochen-Specker proofs
Axel Muller, Alain Giorgetti

Crosslisted article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Generalizing Brooks' theorem via Partial Coloring is Hard Classically and Locally
Jan Bok, Avinandan Das, Anna Gujgiczer, Nikola Jedli\v{c}kov\'a

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- P-adic integrals: A solution to the p-adic Schrodinger Equation
Haonan Gu

"data compiled and published by Israel’s own government makes clear that it has been starving Gaza. Between March and June, Israel allowed just 56,000 tonnes of food to enter the territory, Cogat records show, less than a quarter of Gaza’s minimum needs for that period"
#GazaGenocide
#GazaStarvation

Examining Gender Differences in the Impact of Instructional Clarity on Year 9 Students' Mathematics Interest in New Zealand: A Multi-Group Comparison of 2019 TIMSS Data
Huayu Gao, Tanya Evans, Gavin T. L. Brown
https://arxiv.org/abs/2508.13502

Examining Gender Differences in the Impact of Instructional Clarity on Year 9 Students' Mathematics Interest in New Zealand: A Multi-Group Comparison of 2019 TIMSS Data
Grounded in Social Cognitive Career Theory (SCCT), this study explores how teacher instruction clarity impacts Year 9 students' mathematics interest through the mediating roles of confidence and value, with a focus on gender differences. Structural equation modelling applied to the 2019 New Zealand TIMSS dataset (2,594 girls and 2,651 boys) supports the SCCT framework. While confidence and value have similar mediating effects for boys, confidence plays a more pivotal role for girls. Gender diff…

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- Bent functions using Maiorana-McFarland secondary construction
Juan Carlos Ku-Cauich, Javier Arturo D\'iaz-Vargas, Sara Mandujano-Velazquez

[2025-06-27 Fri (UTC), 2 new articles found for cs.DM Discrete Mathematics]
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Collaborative Preferences for Learning Mathematics: A Scale Validation Study
Sang Hyun Kim, Tanya Evans
https://arxiv.org/abs/2508.12199 https://arxiv.org/…

Collaborative Preferences for Learning Mathematics: A Scale Validation Study
Collaboration within mathematics has been established as being effective in providing students with crucial opportunities to develop critical thinking, effective communication, and teamwork skills. By engaging in group problem-solving and shared learning experiences, students may gain deeper insights into mathematical concepts and learn to approach challenges from multiple perspectives. However, there remains a need for a reliable instrument to capture students' preferences for collaboration. T…

[2025-08-27 Wed (UTC), no new articles found for cs.DM Discrete Mathematics]
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Exploring Gender Differences in Tertiary Mathematics-Intensive Fields: A Critical Review of Social Cognitive Career Theory
Huayu Gao, Tanya Evans, Gavin Brown
https://arxiv.org/abs/2508.12180

Exploring Gender Differences in Tertiary Mathematics-Intensive Fields: A Critical Review of Social Cognitive Career Theory
Social Cognitive Career Theory (SCCT) has been extensively employed to elucidate the enduring gender differences in mathematics-intensive fields, with a particular emphasis on the complex interplay of motivational factors and extra-personal influences contributing to the underrepresentation of women. Although a plethora of empirical studies corroborate SCCT, three crucial aspects for refinement have come to the fore. First, the theory should place a more substantial emphasis on how cultural and…

[2025-06-27 Fri (UTC), no new articles found for math.GM General Mathematics]
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Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Local Search Improvements for Soft Happy Colouring
Mohammad Hadi Shekarriz, Dhananjay Thiruvady, Asef Nazari, Wilfried Imrich

[2025-08-27 Wed (UTC), 3 new articles found for math.GM General Mathematics]
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Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Structure and growth of $\mathbb{R}$-bonacci words
Sergey Dovgal, Sergey Kirgizov
h…

Crosslisted article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Toward Vu's conjecture
Peter Bradshaw, Abhishek Dhawan, Abhishek Methuku, Michael C. Wigal

Homotopy classification of closed polygonal lines: results and problems
E. Alkin, O. Nikitenko, A. Skopenkov
https://arxiv.org/abs/2508.16287 https://arxiv…

Homotopy classification of closed polygonal lines: results and problems
In this text we expose (as a sequence of problems) basic cases of some fundamental ideas and methods of mathematics. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal lines in a subset of the plane. Although these ideas and methods are parts of topology, they are used in many other areas including computer science. This text is expository and is accessible to mathematicians not specialized in …

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- A closed-form expression for $\zeta(3)$
Tobias Kyrion
https://

[2025-06-26 Thu (UTC), 1 new article found for cs.DM Discrete Mathematics]
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[2025-08-26 Tue (UTC), no new articles found for cs.DM Discrete Mathematics]
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[2025-06-26 Thu (UTC), 2 new articles found for math.GM General Mathematics]
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Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- On solving basic equations over the semiring of functional digraphs
Alberto Dennunzio, Enrico Formenti, Luciano Margara, Sara Riva

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- On the generalized coloring numbers
Sebastian Siebertz
https://

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- Efficient application of the Voigt functions in the Fourier transform
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal, Brendan M. Quine

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- A unified worst case for classical simplex and policy iteration pivot rules
Yann Disser, Nils Mosis

Crosslisted article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Exhaustive Generation of Pattern-Avoiding s-Words
Buick, Goertz, Lastmann, Pal, Qian, Tacheny, Williams, Williams, Zhai

[2025-08-26 Tue (UTC), no new articles found for math.GM General Mathematics]
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Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- Legendre duality for certain summations over the Farey pairs
Nikita Kalinin
h…

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Computation of Immediate Neighbours of Monotone Boolean Functions
Jos\'e E. R. Cury, Patr\'icia Tenera Roxo, Vasco Manquinho, Claudine Chaouiya, Pedro T. Monteiro

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- The Price of Upwardness
Angelini, Biedl, Chimani, Cornelsen, Da Lozzo, Hong, Liotta, Patrignani, Pupyrev, Rutter, Wolff

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- The Collatz Conjecture & Non-Archimedean Spectral Theory -- Part II -- $\left(p,q\right)$-Adic Fo...
Maxwell C. Siegel

[2025-07-25 Fri (UTC), 1 new article found for cs.DM Discrete Mathematics]
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[2025-06-25 Wed (UTC), 2 new articles found for cs.DM Discrete Mathematics]
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[2025-08-25 Mon (UTC), no new articles found for cs.DM Discrete Mathematics]
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Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- Unavoidable induced subgraphs in graphs with complete bipartite induced minors
Maria Chudnovsky, Meike Hatzel, Tuukka Korhonen, Nicolas Trotignon, Sebastian Wiederrecht

[2025-07-24 Thu (UTC), no new articles found for cs.DM Discrete Mathematics]
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