Top Mathematics discussions
NishMath - #math
|
MAA@maa.org
//
References:
maa.org
The Mathematical Association of America (MAA) has announced the recipients of the 2025 awards for expository mathematical writing in MAA publications. The awards recognize outstanding contributions to mathematical literature. Jordan S. Ellenberg was awarded the Chauvenet Prize for his work "Geometry, Inference, Complexity, and Democracy," which appeared in the Bulletin (New Series) of the American Mathematical Society. Ellenberg's work explores the challenge of fairly dividing democratic polities into legislative districts, demonstrating the practical application of mathematics to societal issues. Ismar Volíc of Wellesley College, received the Euler Book Prize for his book "Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation," which brings complex topics, such as voting theory, apportionment, gerrymandering, and the Electoral College, to life.
Awarded individuals are reciving either the Chauvenet Prize, the Euler Book Prize, the Daniel Solow Author’s Award, the George Pólya Awards, the Paul R. Halmos–Lester R. Ford Awards, the Trevor Evans Award, or the Carl B. Allendoerfer Awards. Ellenberg's article, drawn from his 2020 Current Events Bulletin lecture, showcases how mathematical approaches can measure fairness in democratic processes. Volíc's book makes complex topics accessible to readers, highlighting the crucial role of mathematics in collective decision-making, and providing essential insights without political bias. Both works exemplify clear and engaging writing, effectively communicating intricate mathematical ideas to a wider audience. As summer approaches, Denise Gaskins is offering discounts on her math game books at the Playful Math Store. This presents an opportunity for families and educators to enhance mathematical learning through playful activities. Gaskins' "Math You Can Play" series offers math games sorted by topics traditionally taught at various age levels, with teaching tips and advice aimed at parents and teachers. Her new series, "Tabletop Math Games Collection," also covers the same mathematical topics. These books are designed for direct use by players of all ages, making them ideal for spontaneous math play. These books are available in both physical and digital formats, providing flexibility for use in math centers, homeschool co-op classes, or at home. Recommended read:
References :
@Math Blog
//
References:
medium.com
, Math Blog
Percentages are a fundamental concept in mathematics, representing a fraction with a denominator of 100. The term "percent" comes from the Latin phrase "per centum," meaning "by the hundred". A percentage is denoted by the symbol %, and is used to express a part of a whole. For example, if a student scores 65 percent on a test, it means they obtained 65 marks for every 100 marks. Understanding percentages is crucial as they frequently appear in daily life, from calculating discounts to understanding statistics.
Percentages offer a standardized way to compare different quantities or proportions. To convert a fraction to a percentage, the goal is to express the fraction with a denominator of 100. If David secures 475 marks out of 500, this can be converted to a percentage by dividing both the numerator and the denominator by 5, resulting in 95/100, or 95%. Conversely, 9% is equivalent to 9/100. Visual representations can also aid in understanding percentages, such as imagining a battery made up of 100 small cells, where each cell represents 1%. If all cells are charged then the battery is at 100%. In addition to understanding percentages, other mathematical concepts like linear regression are important in more advanced applications. Linear regression is a fundamental machine learning model used to find correlations between variables and make predictions. For instance, it can be used to predict ice cream sales based on temperature data. The model identifies a relationship between the input feature (temperature) and the target feature (ice cream sales) and uses a general line to make predictions. The equation of this line, f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept, helps in understanding how changes in the input feature affect the predicted output. Recommended read:
References :
@Math Blog
//
References:
Math Blog
, denisegaskins.com
Mathematical concepts and their applications are gaining increased attention, with recent explorations into diverse areas. A blog post discusses the fundamental differences between mathematical and statistical reasoning, using the example of predicting days with the fewest noninduced births. Researchers are also delving into methods for eliminating parameters in parametric equations. A podcast delves into the philosophy of mathematics and set theory, examining the nature of mathematics itself.
The article "Eliminating the Parameter in Parametric Equations" provides a guide for expressing relationships between variables `x` and `y` when they are defined in terms of a parameter `t`. It explains the process of removing the parameter to obtain a direct equation between `x` and `y`, showcasing examples and solutions. Furthermore, there is a discussion on Charlotte Mason's approach to mathematics using living books as a method of teaching. Python's dominance in AI and machine learning is a significant development. An article explores the factors behind this, highlighting Python's readability, extensive libraries like NumPy, Pandas, Scikit-learn, TensorFlow, and PyTorch, and the role of AI hype in its rise. The Church of Logic podcast also featured a discussion with Joel David Hamkins on the philosophy of mathematics and set theory, particularly exploring differing perspectives on the nature of mathematics. Recommended read:
References :
@www.newtonproject.sussex.ac.uk
//
Recent blog posts are delving into a variety of mathematical topics, offering insights and explorations across different areas of the field. These posts cover historical aspects of mathematics, examine specific mathematical concepts, and explore the connections between mathematics and other disciplines. This collection of diverse content aims to provide readers with a broader understanding and appreciation of mathematics.
The blog posts include diverse mathematical items. For example, one post references Gemma Frisius' "Arithmeticae Practicae Methodus Facilis" (1540) and its entry in *MAA Mathematical Treasures. Another commemorates April 13 as "On This Day in Math," highlighting mathematical facts associated with the number 103. This includes its unique properties as a prime number and its presence in Ramanujan's mathematical explorations. Furthermore, the blog explores historical events like the coining of the word "microscope" in 1620 and Lord Brouncker's published mathematical result in 1668. From statistical physics to number theory, these blogs showcase the versatility and interdisciplinary nature of mathematical thought. One blog even mentions using statistical physics concepts to analyze election results. These blog postings aim to engage readers with a range of mathematical subjects, from historical figures and publications to contemporary applications and connections. Recommended read:
References :
@primes.utm.edu
//
References:
Pat'sBlog
, mathdaypballew.blogspot.com
This week saw a flurry of mathematical activity, highlighted by the 238th Carnival of Mathematics, organized by Aperiodical. The carnival showcases a variety of submissions and mathematical art, focusing on the number 238 itself. Noteworthy facts about 238 include that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime". The carnival also encourages exploration beyond pure mathematics, with community members contributing insights linking the number to uranium isotopes, birth minutes, and even hexadecimal representations. It also shines a light on #MathArtMarch, with examples of crochet, coding, and painting from around the world.
Continuing the daily exploration of numbers, several interesting facts and events were highlighted for April 6th, 7th, 8th and 10th. The number 96, the 96th day of the year, was examined for its unique properties, such as being the smallest number expressible as the difference of two squares in four different ways. Events like Euler's first paper on partitions (April 7th, 1741) and Al-Biruni's observation of a solar eclipse in 1019 were also noted, linking mathematical concepts to historical contexts. Also, the number 97 has been noted as the 97th day of the year, where 97 is the largest prime that we can ever find that is less than the sum of square of its digits. In recreational mathematics, a "Salute" game for reinforcing multiplication and division was featured, emphasizing the inverse relationship between these operations. Additionally, the concept of "truncatable primes" was explored through a game where players create strings of prime numbers by adding digits to either end of a number. The number 91 was discussed as the 91st day of the year where 10 n + 91 and 10 n + 93 are twin primes for n = 1, 2, 3 and 4. Finally, highlighting mathematics beyond academia, James Abram Garfield, a former Congressman and mathematician, was mentioned for his original proof of the Pythagorean Theorem, illustrating the interdisciplinary nature of mathematics. Recommended read:
References :
Greg Bock@thequantuminsider.com
//
Quantum computing has taken a significant leap forward with Phasecraft's development of a novel quantum simulation method called THRIFT (Trotter Heuristic Resource Improved Formulas for Time-dynamics). This breakthrough, detailed in a recent *Nature Communications* publication, drastically improves simulation efficiency and lowers computational costs, bringing real-world quantum applications closer to reality. THRIFT optimizes quantum simulations by prioritizing interactions with different energy scales within quantum systems, streamlining their implementation into smaller, more manageable steps.
This approach allows for larger and longer simulations to be executed without the need for increased quantum circuit size, thereby reducing computational resources and costs. In benchmarking tests using the 1D transverse-field Ising model, a widely used benchmark in quantum physics, THRIFT achieved a tenfold improvement in both simulation estimates and circuit complexities, enabling simulations that are ten times larger and run ten times longer compared to traditional methods. This development holds immense promise for advancements in materials science and drug discovery. Separately, mathematicians have achieved a breakthrough in understanding and modeling melting ice and other similar phenomena through a new proof that resolves long-standing issues related to singularities. A powerful mathematical technique used to model melting ice and other phenomena had been hampered by “nightmare scenarios.” A new proof has removed that obstacle. This new proof addresses concerns about "nightmare scenarios" that previously hindered the analysis of these processes, ensuring that singularities do not impede the continued evolution of the surface being modeled. The resolution, described in Quanta Magazine, allows mathematicians to more effectively assess the surface's evolution even after a singularity appears. Finally, researchers at Cornell University have introduced a novel data representation method inspired by quantum mechanics that tackles the challenge of handling big, noisy data sets. This quantum statistical approach simplifies large data sets and filters out noise, allowing for more efficient analysis than traditional methods. By borrowing mathematical structures from quantum mechanics, this technique enables a more concise representation of complex data, potentially revolutionizing innovation in data-rich fields such as healthcare and epigenetics where traditional methods have proven insufficient. Recommended read:
References :
@medium.com
//
Mathematics is a diverse field with applications spanning multiple disciplines. Recent articles and discussions have highlighted the importance of mathematics in various areas, including Artificial Intelligence (AI), data science, and quantum physics. Linear algebra, calculus, and probability are identified as essential mathematical topics for mastering AI and machine learning, while mathematical tools are enhancing learning in these complex fields.
The exploration of mathematics extends beyond its application in technology, encompassing historical perspectives, number theory, and geometric puzzles. Pi, a fundamental mathematical constant, continues to fascinate mathematicians and enthusiasts, with its presence felt across science, engineering, art, and culture. Discussions also cover the etymology of mathematical terms like logarithms, and the use of math journals and games in education. Recommended read:
References :
Denise Gaskins@denisegaskins.com
//
Recent studies and educational resources are focusing on enhancing math education through innovative approaches. Denise Gaskins' "Let's Play Math" blog offers resources for families to learn and enjoy math together, including playful math books and internet resources suitable for various age groups. Math journaling and games have been highlighted as effective tools to engage students, promote problem-solving skills, and foster a richer mathematical mindset.
Numerous games and activities can make learning fun. For instance, "Make a Square" is a game that builds 2-D visualization skills and strategic thinking. Quick number games that can be played anywhere. The divisibility rules for numbers, particularly divisibility by 2, are being emphasized to help students easily identify even and odd numbers. A megastudy also revealed that behaviorally informed email messages improved students' math progress, demonstrating how simple interventions can positively impact learning outcomes. Recommended read:
References :
Unknown (noreply@blogger.com)@Pat'sBlog
//
References:
Pat'sBlog
Recent discussions have highlighted the diverse applications and historical roots of mathematics. A blog post explored the history of mathematical terms such as billion, trillion, and others, tracing their origins back to figures like Nicholas Chuquet, a French physician from the 15th century. The evolution of these terms and their varying definitions across different countries demonstrate the rich history and changing conventions within mathematical nomenclature. This information has recently resurfaced in a post from earlier this year.
Alongside the history of math, practical math applications are being discussed. For example, recent word problems are now available that focuses on division suitable for fourth-grade students. The step-by-step solutions for problems involving dividing quantities among groups can help students improve their comprehension of division and problem solving. Mathematics continues to be the basis for many algorithms in a variety of modern technological applications and is not widely recognized as a science. Recommended read:
References :
Michael Weiss@Diagonal Argument
//
References:
Diagonal Argument
Recent discussions in mathematical concepts and programming tools cover a range of topics, including theoretical foundations and practical applications. Peter Cameron highlighted the Compactness Theorem for first-order logic, explaining its consequences and connections to topology. Also, a beginner's guide to sets has been published to explain how they work and some applications.
Noel Welsh presented a talk at Imperial College on dualities in programming, exploring the relationships between data and codata, calls and returns, and ASTs and stack machines. The use of adjoints in boolean operations was justified, and Daniel Lemire published an overview of parallel programming using Go. These discussions bridge the gap between abstract mathematical principles and their concrete uses in software development and programming paradigms. Recommended read:
References :
@medium.com
//
References:
Pat'sBlog
, medium.com
,
March 14th marks the annual celebration of Pi Day, honoring the mathematical constant π (pi), which represents the ratio of a circle’s circumference to its diameter. Pi, an irrational number approximately equal to 3.14159, holds significance across various scientific disciplines, including geometry, physics, engineering, and even music theory. Its infinite, non-repeating decimal expansion symbolizes infinity and mystery, captivating mathematicians and enthusiasts alike.
Pi Day 2025 presents an opportunity to engage students with interactive activities like Ratio Riddles, PiCraft, and Math Progress. Ratio Riddles, a lesson from Minecraft Education, introduces concepts of ratio, proportion, fractions, and scale through engaging games. PiCraft offers a student workbook blending gaming and learning, allowing students to estimate and calculate the area of a circle within the Minecraft universe, applying mathematical concepts through coding with Microsoft MakeCode. These hands-on experiences aim to make math more meaningful and strengthen students' confidence in the subject. Recommended read:
References :
Megan Murphy@Stattr@k
//
References:
Stattr@k
The Causality in Statistics Education Award, established by Judea Pearl, is seeking nominations. This award acknowledges the growing importance of incorporating causal inference into undergraduate and lower-division graduate statistics courses. The award provides a $5,000 cash prize annually, and nominations are due by April 5th. Further details regarding selection criteria and nomination requirements can be found on the American Statistical Association's STATtr@k website.
In other news, the Carnival of Maths 237, which rounds up various mathematics blog posts, is now available online. A mathematics conference organized by DEA SCUOLA is scheduled for secondary school mathematics teachers which aims to enhance mathematics teaching through innovative strategies and the integration of AI. Musically, Day 30 of a practice series features bass drum exercises from Mark Guiliana's book, highlighting complex coordination challenges in alternating snare and bass drum strokes. Recommended read:
References :
munizao@Puzzle Zapper Blog
//
References:
mathvoices.ams.org
, John D. Cook
Math enthusiasts and educators are exploring a variety of topics on blogs and websites. Puzzlezapper features geometrical puzzles like polyiamond path puzzles, while other platforms share insights into math education and mathematical concepts. Alexandre Muñiz, on Puzzle Zapper Blog, explores variations on polyiamond tiles with marked paths, constrained to straight lines connecting the midpoints of cell edges.
Donna Fernandez, Co-Director of Alliance of Indigenous Math Circles, highlights the power of indigenous approaches to math education, using the example of the Navajo Prep Math Camp and ICME-15. John D. Cook discusses the practical consequences of tokenization, noting how subtle changes in prompts can significantly impact Large Language Models (LLMs), referencing an article about LLMs and chess, and illustrating how tokenization differences can confuse the model, affecting its ability to play effectively. Recommended read:
References :
|
Blogs
|