Newborn babies seem to have a rudimentary sense of numbers, preferring smaller numbers on the left and larger ones on the right. The finding suggests that this left-to-right mental number line might be innate for humans. "Anything you want to remember that has a sense of order – be it days of the week or musical tones – you tend to map that to a spatial continuum," says Koleen McCrink at Barnard College, New York. The same is true for numbers. In Western cultures, people tend to think of numbers increasing in value along a mental number line from left to right, while people who speak Arabic and Hebrew picture numbers running in the opposite direction.
The level in this article is for college students familiar with calculus, This material will be also of interest to college professors looking for new material to teach, or for original exam questions, as well as for business data scientists with some spare time, interested in refreshing their math skills. The problems cover real analysis, mathematical algorithms and numerical precision, correct visualizations, as well as geometry. The third problem is the most interesting one in my opinion, and could become a subject of active mathematical research with one new great, unsolved conjecture being proposed, of a probabilistic nature. The last problem has many applications in engineering science. Note the alternance of the signs.
Although anyone who has completed a basic course in Maths knows what a function is, it is a good idea to review this basic concept and associated terminology, just in case you need a refresher. A function is relationship that defines how one quantity depends on another. A function takes an input from a set and maps it an output from another set. The input set is known as the domain and the output set is known as the codomain or target set of the function. There are many ways to denote functions in machine learning literature, or in Mathematics.
Square Cash has just released the latest update to their iOS app now with further support and integration with iOS 10. The update today includes the ability for users to quickly send and request money from one another using either iMessage or Siri. The update today takes advantage of the new iOS 10 features including the ability to send money through the Square Cash app using iMessage. Users can optionally chose to "gift wrap" the money so that when it's sent it appears as a surprise to the recipient. Users can also request Siri to send or receive payments thanks to the new Siri SDK.
In recent years, significant progress in the area of search, constraint satisfaction, and automated reasoning has been driven in part by the study of challenge problems from combinatorics and finite algebra. This work has led to the discovery of interesting discrete structures with intricate mathematical properties. While some of those results have resolved open questions and conjectures, a shortcoming is that they generally do not provide further mathematical insights, from which one could derive more general observations. We propose an approach that integrates specialized combinatorial search, using so-called streamlining, with a human computation component. We use this approach to discover efficient constructive procedures for generating certain classes of combinatorial objects of any size. More specifically, using our framework, we discovered two complementary efficient constructions for generating so-called Spatially Balanced Latin squares (SBLS) of any order N, such that 2N+1 is prime. Previously constructions for SBLSs were not known. Our approach also enabled us to derive a new lower bound for so-called weak Schur numbers, improving on a series of earlier results for Schur numbers.