Twenty-one patients with right hemisphere damage were studied (11 men, 10 women; average age = 41.33; range 19-65). Patients were divided into two groups: pre-Rolandic (six patients) and retro-Rolandic (15 patients) right hemisphere damage. A special calculation test was given. Different types of calculation errors were analyzed. Spatial alexia and agraphia for numbers, loss of calculation auto...

Humans share with other animals a system for thinking about numbers in an imprecise and intuitive way. The Approximate Number System (ANS) that underlies this thinking is present throughout the lifespan, is entirely nonverbal, and supports basic numerical computations like comparing, adding, and subtracting quantities. Humans, unlike other animals, also have a system for representing exact numb...

This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.

We give a simple constructive version of Szemerédi’s Regularity Lemma, based on the computation of singular values of matrices. Mathematical Reviews Subject Numbers: 05C85, 68R10.

the zarankiewicz number z(b; s) is the maximum size of a subgraph of kb,b which does not contain ks,s as a subgraph. the two-color bipartite ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of kb,b with two colors contains a ks,s in the rst color or a kt,t in the second color.in this work, we design and exploit a computational method for bounding and computin...

Richard Dedekind's characterization of the real numbers as the system of cuts of rational numbers is by now the standard in almost every mathematical book on analysis or number theory. In the philosophy of mathematics Dedekind is given credit for this achievement, but his more general views are discussed very rarely and only superrcially. For example, Leo Corry, who dedicates a whole chapter of...

In e'ective analysis, various classes of real numbers are discussed. For example, the classes of computable, semi-computable, weakly computable, recursively approximable real numbers, etc. All these classes correspond to some kind of (weak) computability of the real numbers. In this paper we discuss mathematical closure properties of these classes under the limit, e'ective limit and computable ...

Argumentative practice in mathematics evidently takes a number of shapes. An important part of understanding mathematical argumentation, putting aside its special subject matters (numbers, shapes, spaces, sets, functions, etc.), is that mathematical argument often tends toward formality, and it often has superlative epistemic goals: often the aim of a piece of mathematical argumentation is to p...

The inverse error function erfinv is a standard component of mathematical libraries, and particularly useful in statistical applications for converting uniform random numbers into Normal random numbers. This chapter presents a new approximation of the erfinv function which is significantly more efficient for GPU execution due to the greatly reduced warp divergence.

In spite of Calvin’s discomfiture, imaginary numbers (a subset of the set of complex numbers) exist and are invaluable in mathematics, engineering, and science. In fact, in certain fields, such as electrical engineering, aeronautical engineering and quantum mechanics, progress has been critically dependent on complex numbers and their behavior. In the context of mathematical biology, a number o...