相关论文: Why I don't like "pure mathematics"

Many undergraduate students of engineering and the exact sciences have difficulty with their mathematics courses due to insufficient proficiency in what we in this paper have termed clear thinking. We believe that this lack of proficiency…

We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…

The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].

Many important journal functions would be lost if the mathematical community replaced all paper journals with electronic media. Electronic media are useful for some purposes, but they will not be the basis for a publishing revolution in the…

Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…

Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…

What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…

Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.

What would you do if you were asked to "add" knowledge? Would you say that "one plus one knowledge" is two "knowledges"? Less than that? More? Or something in between? Adding knowledge sounds strange, but it brings to the forefront…

Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…

Mathematics as an area of study occupies an important place in higher education. Due in part to its utility in other disciplines as well as its role in student learning, institutions of higher education (IHEs) often have large numbers of…

Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…

The words ``Programming is the second literacy'' were coined more than 40 years ago but never came to life. This paper is one in the series of papers aimed at the analysis of mathematical requirements for a merge of school mathematics with…

The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…

Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and…

We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project…

From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…

Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can…

Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…

Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…