Academic Articles & Research Papers

Mathematics and Indispensability

Mathematics plays an indispensable role in the explanations that modern science provides of empirical phenomena. From this unexceptionable observation, a controversial philosophical conclusion is sometimes drawn. The claim is advanced that ...

Mathematics and Reality

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for e...

The Language of Mathematics

A History of Mathematics: An Introduction

Part I. Ancient Mathematics 1. Egypt and Mesopotamia 1.1 Egypt 1.2 Mesopotamia 2. The Beginnings of Mathematics in Greece 2.1 The Earliest Greek Mathematics 2.2 The Time of Plato 2.3 Aristotle 3. Euclid 3.1 Introduction to the Elements 3.2 ...

Mathematics, Statistics, and Teaching

How does statistical thinking differ from mathematical thinking? What is the role of mathematics in statistics? If you purge statistics of its mathematical content, what intellectual substance remains?In what follows, we offer some answers ...

The indispensability of mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to our best scientific t...

Methods of Mathematical Physics

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors...

Mathematics anxiety and mathematics achievement

With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics

Ideas like "understanding," "authenticity," and "community" are central in current debates about curriculum, instruction, and assessment. Many believe that teaching and learning would be improved if classrooms were organized to engage stude...

Mathematical Models in Biology

Life scientists are not always fully aware of the powerful role that mathematical models have in both answering biological research questions and in making predictions. Scientists have a clear view of the problem; they know the questions; t...

Mathematical Ideas in Biology

This is a lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathema...

On practical ℎ-observer design for nonlinear non-autonomous dynamical systems with disturbances

In this paper, a particular form of practical ℎ-observers for piecewise continuous Lipschitz, one-sided piecewise continuous Lipschitz systems and quasi-one-sided piecewise continuous Lipschitz systems is extended to nonlinear non-autonomou...

A local meshless method for the one-dimensional Fisher’s equation

This study presents a novel local meshless approach for solving one-dimensional Fisher’s equation, combining a local scheme, Gaussian radial basis functions (G-RBF), and a collocation technique. The method leverages the Gaussian basis’s non...

A Novel MRAC Scheme for Output Tracking

This paper puts forward a novel output feedback model reference adaptive control (MRAC) scheme for solving an adaptive output tracking problem. The proposed control scheme only needs a scalar function to be updated online, which decreases t...

Self-Organized Criticality of Rainfall in Central China

Rainfall is a complexity dynamics process. In this paper, our objective is to find the evidence of self-organized criticality (SOC) for rain datasets in China by employing the theory and method of SOC. For this reason, we analyzed the long-...

Retracted: A Novel Multicriteria Decision-Making Approach for Einstein Weighted Average Operator under Pythagorean Fuzzy Hypersoft Environment

Advancing Children's Mathematical Thinking in Everyday Mathematics Classrooms

Judith L. Fraivillig, Lauren A. Murphy, Karen C. Fuson, Advancing Children's Mathematical Thinking in Everyday Mathematics Classrooms, Journal for Research in Mathematics Education, Vol. 30, No. 2 (Mar., 1999), pp. 148-170...

Mathematics-for-Teaching: an Ongoing Investigation of the Mathematics that Teachers (Need to) Know

The Heart of Mathematics

(1980). The Heart of Mathematics. The American Mathematical Monthly: Vol. 87, No. 7, pp. 519-524....

Mathematics as a science of patterns

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has ...