Articles tagged with Algebra
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Study of abstract structures, patterns, quantities, relationships, and logical reasoning through pure and applied mathematical disciplines. Encompasses algebra, calculus, geometry, topology, number theory, analysis, discrete mathematics, mathematical logic, set theory, probability, statistics, and computational mathematics. Investigates mathematical structures, theorems, proofs, algorithms, functions, equations, and the rigorous logical frameworks underlying quantitative reasoning. Provides the foundational language and tools for all scientific fields, enabling precise description of natural phenomena, modeling of complex systems, and the development of technologies across physics, engineering, computer science, economics, and all quantitative sciences.
Researcher Manuel Krannich has been awarded a five-year ERC starting grant to investigate the connections between symmetries of high-dimensional manifolds and laws of algebra. His project, 'Manifolds and Functor Calculus' (MaFC), combines manifold theory with higher-level algebra.
Chelsea Walton, a professor of mathematics at Rice University, has been recognized as an American Mathematical Society (AMS) Fellow. Her selection acknowledges her dedication to advancing mathematical research in noncommutative algebra, quantum symmetries, Hopf algebras, and representation theory.
Researchers have developed big algebras, a new mathematical tool that connects abstract algebra and geometry, enabling unprecedented insights into symmetry groups. This breakthrough has the potential to strengthen the connection between quantum physics and number theory.
Researchers have successfully solved a problem in graph theory that has attracted attention from within the field. The team's research involves packing coloring, which deals with labelling parts of a graph to comply with certain rules and avoid specific conflicts.
Researchers at Max Planck Institute for Biological Intelligence discovered how a specific type of neuron can multiply two incoming signals in fruit flies. This finding provides insight into the algebra of neurons, which underlies various brain processes such as sound localization and visual motion detection.
A curriculum with additional math instruction led to higher attendance and degree completion rates for students in a 2003 cohort. However, similar effects were not seen in a 2004 cohort, suggesting that pairing high- and low-skilled students undermines positive impacts of extra math support.
Graspable Inc. will develop its app prototype into a classroom-ready product, providing instant step-by-step feedback and creating teacher reports for formative assessment. The company aims to increase engagement and algebra performance in students, particularly those struggling with algebraic notation.
A research team developed a method for constructing an aggregated model of a power network that can efficiently analyze and control generator groups. The symmetry of the network in graph theory is the fundamental principle for realizing the synchronization of generator groups. This achievement aims to develop analysis and control metho...
A University of Missouri team is investigating the effectiveness of flipped instruction in Missouri high school algebra classrooms, with a focus on how teachers use technology to support student learning. The researchers aim to identify the most successful strategies for teaching math using this approach.
Xia emphasizes that big data is about more than just numbers and requires new mathematical methods to analyze. Researchers in mathematics, signal processing, and computer science must develop these new tools to unlock the full potential of big data.
A study published in Psychological Science reveals that an innate ratio processing ability may play a role in determining aptitude for mathematical concepts. Researchers found that students' ability to gauge nonsymbolic ratios was correlated with their competence in symbolic math, including fractions and algebraic equations.
A new study at Southern Methodist University is testing whether students can learn algebra by authoring their own stories based on their personal interests. The research aims to improve long-term understanding of algebraic ideas and make math more accessible and captivating for students.
A recent study published in Developmental Science found that preschoolers (4-6 years old) can do basic algebra naturally, leveraging their Approximate Number System. The study used magic cups filled with objects to test children's ability to solve for a hidden variable.
The study found that practicing different types of math skills can lead to expertise in those areas. This approach helps students identify their strengths and weaknesses, allowing them to focus on areas where they need improvement.
A study published in Child Development found that instructors who use hand gestures while teaching math problems outperform those without gestures. Students who learned from gesture videos performed better on tests compared to those who learned from speech-only videos, with improved retention over time.
Physicist-turned-author Simon Singh has won the Leelavati Award for his outstanding contributions to public outreach in mathematics. The award, named after a 12th-century Indian mathematician, carries a citation and cash prize of one million Indian rupees.
A North Carolina high school teacher's algebra II textbook has scored a 96 on California's state textbook standards, meeting 26 of the 27 standards tested. The book was created by Kenny Felder and is one of the first open-source texts submitted for California's K-12 initiative.
A new study finds that Black and Latino males struggle in math classes despite positive feedback, due to a tendency to ignore institutional cues. Meanwhile, female students of the same racial groups are more resilient and less affected by low grades.
Gregory Margulis has been recognized for his monumental contributions to algebra and its applications in various fields. He will share this year's Wolf Prize with Sergei Novikov at the University of Maryland.