By Sam Parc, Dara O Briain

Chill out: not anyone knows technical arithmetic with no long education yet all of us have an intuitive seize of the guidelines at the back of the symbols. To have fun the fiftieth anniversary of the founding of the Institute of arithmetic and its purposes (IMA), this e-book is designed to show off the great thing about arithmetic - together with photographs encouraged via mathematical difficulties - including its unreasonable effectiveness and applicability, with out frying your mind.

The e-book is a suite of fifty unique essays contributed through a wide selection of authors. It comprises articles by way of the very best expositors of the topic (du Sautoy, Singh and Stewart for instance) including enjoyable biographical items and articles of relevance to our daily lives (such as Spiegelhalter on danger and Elwes on clinical imaging). the themes lined are intentionally assorted and contain ideas from basic numerology to the very leading edge of arithmetic examine. each one article is designed to be learn in a single sitting and to be available to a common viewers.

There can also be different content material. There are 50 pictorial 'visions of arithmetic' which have been provided in keeping with an open demand contributions from IMA participants, Plus readers and the global arithmetic group. you will additionally discover a sequence of "proofs" of Phythagoras's Theorem - mathematical, literary and comedy - after this, you are going to by no means think about Pythagoras an analogous approach back.

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**Additional resources for 50 Visions of Mathematics**

**Example text**

E. zeros and ones, to encode black and white pictures. In this encoding technique, which was implemented by NASA in the 1960s, the picture was divided into equally sized boxes so that each box was either fully black or white; and the encoder used the digit 1 to represent every black box and 0 for every white box, eﬀectively giving rise to an array of 1s and 0s (or, in mathematical parlance, an incidence matrix). The next step after encoding is to communicate the encoded information, which we refer to as data, to a receiver.

Upside-down pendulums. Nature, vol. 366, pp. 215–216. [3] Edward Titchmarsh (1981). Mathematics for the general reader. Dover Publications. what’s the problem with mathematics? | 5 CHAPTER 2 The mathematics of messages alan j. aw W e all write messages, be they SMSs to our loved ones, emails to friends, or even telegrams. ’ Perhaps with a little help from physics, we could surmise that messages are transmitted by waves. However, this alone does not explain how the data are transmitted with high accuracy.

This turns out, somewhat unexpectedly, to be the measure of the limit of the reliable data transmission rate across a channel. In other words, the higher the mutual information, the greater the maximum rate of reliable data transmission. Additionally, whereas beyond the calculated value of mutual information data transmission indubitably becomes unreliable, it is also true that at rates below this value arbitrarily reliable levels of communication are achievable. That is, one may choose a speciﬁc degree of error (caused by noise) allowable during data transmission, and there is always a corresponding rate below the mutual information which allows errors precisely up to that degree.