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A brief history of mathematical thought
Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, \"no mathematical knowledge required.\" Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. -- Provided by publisher.
Book
Matrices, Moments and Quadrature with Applications
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part.
Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization.
This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
eBook
Math rock
\"This first ever look at the global phenomenon known as math rock includes interviews with musicians, producers, and critics and contains a thorough breakdown of what makes up the enigmatic, complex, and largely instrumental musical genre that has been fascinating listeners for decades\"-- Provided by publisher.
BOOK
The semiclassical zeta function for geodesic flows on negatively curved manifolds
We consider the semi-classical (or Gutzwiller–Voros) zeta functions for
C
∞
contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small
τ
>
0
, its zeros are contained in the union of the
τ
-neighborhood of the imaginary axis,
|
R
(
s
)
|
<
τ
, and the half-plane
R
(
s
)
<
-
χ
0
+
τ
, up to finitely many exceptions, where
χ
0
>
0
is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.
Journal Article
Math curse
When the teacher tells her class that they can think of almost everything as a math problem, one student acquires a math anxiety which becomes a real curse.
Book
The Math Anxiety-Performance Link
Demand for science, technology, engineering, and mathematics (STEM) professionals is on the rise worldwide. To effectively meet this demand, many governments and private organizations have revamped STEM education and promoted training to enhance math and science skills among students and workers. Education and training programs typically focus on increasing individuals’ math and science knowledge. However, data from laboratory studies and large-scale international assessments suggest that fear or apprehension about math, math anxiety, should also be considered when trying to increase math achievement and, in turn, STEM career success. This article reviews findings that shed light on antecedents of math anxiety, the bidirectional math anxiety-performance relation, underlying mechanisms, and promising routes to mitigating the negative relation between math anxiety and math performance.
Journal Article
Inside Mathforum.org : analysis of an Internet-based education community
The internet has dramatically transformed social space and time for many people in many different contexts. This dramatic warping of the social fabric has happened slowly over time as digital technologies have evolved and internet speeds have increased. While we are all aware of these changes, the impact is often little understood. There are few monographs about social groups made possible by the internet, and even fewer about educational communities made possible through digital technologies. 'Inside Mathforum.org' details the ways that digital media are used to enhance the practices that teachers and students of mathematics engage in. The book also shows how different kinds of mathematical conversations and interactions become possible through the digital media. Unlike many other educational uses of digital media, the Math Forum's community has provided online resources and sustained support for teachers and students, and it leads the way in showing the power of digital media for education.
Book
Tackling Anxiety in Primary
This book provides teacher educators with an understanding of the issues around mathematics anxiety and a framework of teaching strategies to support undergraduates, trainee teachers and established professionals in primary settings in developing confidence in learning and teaching mathematics.
The existence of mathematics anxiety in adults is both prevalent and well documented, and there is a real concern that adults who are anxious or lacking in confidence in their own mathematical ability may affect the quality of teaching and learning for those in their care. Research has identified that there are lower levels of mathematical confidence in adults working with children in primary rather than secondary schools, and that where adults are anxious this can be passed on to the pupils with whom they work. This book addresses issues related to the effect that mathematics anxiety has on those teaching and working with primary aged children and supports teacher educators to develop confidence in both trainee teachers and established professionals.
eBook
Is Math Anxiety Always Bad for Math Learning? The Role of Math Motivation
The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion. In the current studies, we aimed to address the lack of attention given to the possibility of such complex interplay between emotion and cognition in the math-learning literature by exploring the relations among math anxiety, math motivation, and math cognition. In two samples—young adolescent twins and adult college students—results showed inverted-U relations between math anxiety and math performance in participants with high intrinsic math motivation and modest negative associations between math anxiety and math performance in participants with low intrinsic math motivation. However, this pattern was not observed in tasks assessing participants' nonsymbolic and symbolic number-estimation ability. These findings may help advance the understanding of mathematics-learning processes and provide important insights for treatment programs that target improving mathematics-learning experiences and mathematical skills.
Journal Article