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Viewing: Blog Posts Tagged with: Mathematics, Most Recent at Top [Help]
Results 1 - 25 of 78
1. How much do you know about Hypatia? [quiz]

An astronomer, mathematician, philosopher, and active public figure, Hypatia played a leading role in Alexandrian civic affairs. Her public lectures were popular, and her technical contributions to geometry, astronomy, number theory, and philosophy made Hypatia a highly regarded teacher and scholar.

The post How much do you know about Hypatia? [quiz] appeared first on OUPblog.

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2. Can design thinking challenge the scientific method?

The scientific method has long reigned as the trusted way to test hypotheses so as to produce new knowledge. Shaped by the likes of Francis Bacon, Galileo Galilei, and Ronald A. Fisher, the idea of replicable controlled experiments with at least two treatments has dominated scientific research as a way of producing accepted truths about the world around us. However, there is growing interest in design thinking, a research method which encourages practitioners to reformulate goals, question requirements, empathize with users, consider divergent solutions.

The post Can design thinking challenge the scientific method? appeared first on OUPblog.

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3. The consistency of inconsistency claims

A theory is inconsistent if we can prove a contradiction using basic logic and the principles of that theory. Consistency is a much weaker condition that truth: if a theory T is true, then T consistent, since a true theory only allows us to prove true claims, and contradictions are not true. There are, however, infinitely many different consistent theories that we can construct.

The post The consistency of inconsistency claims appeared first on OUPblog.

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4. Can a robot be conscious?

Can a robot be conscious? I will try to discuss this without getting bogged down in the rather thorny issue of what consciousness –– really is. Instead, let me first address whether robot consciousness is an important topic to think about. At first sight, it may seem unimportant. Robots will affect us only through their outward behavior, which may be more or less along the lines of what we tend to think of as coming along with consciousness, but given this behavior, its consequences to us are not affected by whether or not it really is accompanied by consciousness.

The post Can a robot be conscious? appeared first on OUPblog.

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5. Conversations in computing: Q&A with Editor-in-Chief, Professor Steve Furber

Oxford University Press is excited to be welcoming Professor Steve Furber as the new Editor-in-Chief of The Computer Journal. In an interview between Justin Richards of BCS, The Chartered Institute of IT and Steve, we get to know more about the SpiNNaker project, ethical issues around Artificial Intelligence (AI), and the future of the IT industry.

The post Conversations in computing: Q&A with Editor-in-Chief, Professor Steve Furber appeared first on OUPblog.

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6. Does the ‘Chinese room’ argument preclude a robot uprising?

There has been much recent talk about a possible robot apocalypse. One person who is highly skeptical about this possibility is philosopher John Searle. In a 2014 essay, he argues that "the prospect of superintelligent computers rising up and killing us, all by themselves, is not a real danger".

The post Does the ‘Chinese room’ argument preclude a robot uprising? appeared first on OUPblog.

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7. What is information, and should it be free?

When we pay our bills using a plastic card, we are simply authorizing alterations to the information stored in some computers. This is one aspect of the symbiotic relationship that now exists between money and information. The modern financial world is byzantine in its complexity, and mathematics is involved in many ways, not all of them transparently clear. Fortunately there are some bright spots, such as the fact that it is now possible to measure information.

The post What is information, and should it be free? appeared first on OUPblog.

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8. Earth’s climate: a complex system with mysteries abound

We are living with a climate system undergoing significant changes. Scientists have established a critical mass of facts and have quantified them to a degree sufficient to support international action to mitigate against drastic change and adapt to committed climate shifts. The primary example being the relation between increased atmospheric carbon dioxide concentrations and the extent of warming in the future.

The post Earth’s climate: a complex system with mysteries abound appeared first on OUPblog.

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9. Mary Somerville: the new face on Royal Bank of Scotland’s ten-pound note is worthy of international recognition

From 2017, ten-pound notes issued by the Royal Bank of Scotland will feature a new face: that of the great nineteenth-century science communicator Mary Somerville. Her book on mathematical astronomy, Mechanism of the Heavens -- published in 1831, when she was fifty years old -- was used as an advanced textbook at Cambridge for a hundred years. This is a phenomenal achievement for a woman who taught herself science and mathematics.

The post Mary Somerville: the new face on Royal Bank of Scotland’s ten-pound note is worthy of international recognition appeared first on OUPblog.

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10. Diamonds are forever, and so are mathematical truths?

Try googling 'mathematical gem'. I just got 465,000 results. Quite a lot. Indeed, the metaphor of mathematical ideas as precious little gems is an old one, and it is well known to anyone with a zest for mathematics. A diamond is a little, fully transparent structure all of whose parts can be observed with awe from any angle.

The post Diamonds are forever, and so are mathematical truths? appeared first on OUPblog.

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11. The real charm of imaginary numbers

Few elementary mathematical ideas arouse the kind of curiosity and astonishment among the uninitiated as does the idea of the “imaginary numbers”, an idea embodied in the somewhat mysterious number i. This symbol is used to denote the idea of , namely, a number that when multiplied by itself yields -1. How come?

The post The real charm of imaginary numbers appeared first on OUPblog.

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12. World Statistics Day: a reading list

On 20 October 2015, the global mathematical community is celebrating World Statistics Day. In honour of this, we present here a reading list of OUP books and journal articles that have helped to advance the understanding of these mathematical concepts.

The post World Statistics Day: a reading list appeared first on OUPblog.

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13. Better medical research for longer, healthier lives

When I started my career as a medical statistician in September 1972, medical research was very different from now. In that month, the Lancet and the British Medical Journal published 61 research reports which used individual participant data, excluding case reports and animal studies. The median sample size was 36 people. In July 2010, I had another look.

The post Better medical research for longer, healthier lives appeared first on OUPblog.

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14. From number theory to e-commerce

The American Mathematical Society held on October 1903 its regular meeting in New York City. The program announced a talk by Frank Nelson Cole (1861-1921), with the unpretending title of 'On the factorization of large numbers'. In due course, Cole approached the board and started to multiply the number 2 by itself, step after step and without saying a word, sixty seven times.

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15. Why know any algebra?

A recent meme circulating on the internet mocked a US government programme (ObamaCare) saying that its introduction cost $360 million when there were only 317 million people in the entire country. It then posed the rhetorical question: "Why not just give everyone a million dollars instead?"

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16. Can one hear the corners of a drum?

Why is the head of a drum usually shaped like a circle? How would it sound if it were shaped like a square instead? Or a triangle? If you closed your eyes and listened, could you tell the difference? The mathematics used to prove that “one can hear the corners of a drum” are founded on […]

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17. Very Short Resolutions: filling the gaps in our knowledge in 2016

Why make New Year's Resolutions you don't want to keep? This year the Very Short Introductions team have decided to fill the gaps in their knowledge by picking a VSI to read in 2016. Which VSIs will you be reading in 2016? Let us know in the comment section below or via the Very Short Introductions Facebook page.

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18. How do people read mathematics?

At first glance this might seem like a non-question. How do people read anything? All suitably educated people read at least somewhat fluently in their first language – why would reading mathematics be different? Indeed, why would mathematics involve reading at all? For many people, mathematics is something you do, not something you read.

But it turns out that there are interesting questions here. There are, for instance, thousands of mathematics textbooks–many students own one and use it regularly. They might not use it in the way intended by the author: research indicates that some students–perhaps most–typically use their textbooks only as a source of problems, and essentially ignore the expository sections. That is a shame for textbook authors, whose months spent crafting those sections do not influence learning in the ways they intend. It is also a shame for students, especially for those who go on to more advanced, demanding study of upper-level university mathematics. In proof-based courses it is difficult to avoid learning by reading. Even successful students are unlikely to understand everything in lectures – the material is too challenging and the pace is too fast – and reading to learn is expected.

Because students are not typically experienced or trained in mathematical reading, this returns us to the opening questions. Does this lack of training matter? Undergraduate students can read, so can they not simply apply this skill to mathematical material? But it turns out that this is not as simple as it sounds, because mathematical reading is not like ordinary reading. Mathematicians have long known this (“you should read with a pencil in hand”), but the skills needed have recently been empirically documented in research studies conducted in the Mathematics Education Centre at Loughborough University. Matthew Inglis and I began with an expert/novice study contrasting the reading behaviours of professional mathematicians with those of undergraduate students. By using eye-movement analyses we found that, when reading purported mathematical proofs, undergraduates’ attention is drawn to the mathematical symbols. To the uninitiated that might sound fine, but it is not consistent with expert behaviour: the professional mathematicians attended proportionately more to the words, reflecting their knowledge that these capture much of the logical reasoning in any written mathematical argument.

Another difference appeared in patterns of behaviour, which can best be seen by watching the behaviour of one mathematician when reading a purported proof to decide upon its validity (see below). Ordinary reading, as you might expect, is fairly linear. But mathematical reading is not. When studying the purported proof, the mathematician makes a great many back-and-forth eye movements, and this is characteristic of professional reading: the mathematicians in our study did this significantly more than the undergraduate students, particularly when justifications for deductions were left implicit.

This work is captured in detail in our article Expert and Novice Approaches to Reading Mathematical Proofs. Since completing it, Matthew and I have worked with PhD and project students Mark Hodds, Somali Roy and Tom Kilbey to further investigate undergraduate mathematical reading. We have discovered that research-based Self-Explanation Training can render students’ reading more like that of mathematicians and can consequently improve their proof comprehension (see our paper Self-Explanation Training Improves Proof Comprehension); that multimedia resources designed to support effective reading can help too much, leading to poorer retention of the resulting knowledge; and that there is minimal link between reading time and consequent learning. Readers interested in this work might like to begin by reading our AMS Notices article, which summarises much of this work.

In the meantime, my own teaching has changed – I am now much more aware of the need to help students learn to read mathematics and to provide them with time to practice. And this research has influenced my own writing for students: there is no option to skip the expository text, because expository text is all there is. But this text is as much about the thinking as it is about the mathematics. It is necessary for mathematics textbooks to contain accessible text, explicit guidance on engaging with abstract mathematical information, and encouragement to recognise that mathematical reading is challenging but eminently possible for those who are willing to learn.

Feature Image: Open book by Image Catalog. CC0 1.0 via Flickr.

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19. Is an engineering mind-set linked to violent terrorism?

In a British Council report Martin Rose argues that the way STEM subjects are taught reinforces the development of a mind-set receptive to violent extremism. Well taught social sciences, on the other hand, are a potentially powerful intellectual defence against it. Whilst his primary focus was MENA (Middle East and North Africa) he draws implications for education in the West.

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20. Addressing anxiety in the teaching room: techniques to enhance mathematics and statistics education

In June 2015, I co-chaired the organising committee of the first international mathematics education conference of the Institute of Mathematics and its Applications (IMA) titled ‘Barriers and Enablers to Learning Maths’ with the University of Glasgow, who also hosted it. The two and a half day conference explored approaches to teaching and learning mathematics and was structured around ten parallel sessions that delegates could choose from, including ‘Addressing mathematics & statistics anxiety’ and ‘Enhancing engagement with mathematics & statistics.’

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21. Let us not run blindfolded into the minefield of future technologies

There is a widely held conception that progress in science and technology is our salvation, and the more of it, the better. This is the default assumption not only among the general public, but also in the research community including university administration and research funding agencies, all the way up to government ministries. I believe the assumption to be wrong, and very dangerous.

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22. The Fragility of Grand Discoveries

When I was in graduate school at Berkeley I was offered a prestigious fellowship to study for a year in Germany, but I decided it would be a disruption, so I wrote a short note declining the offer. As, letter in hand, I stepped to the mailbox, I bumped into a woman from the scholarship [...]

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23. The role of logic in philosophy: A Q&A with Elijah Millgram

Elijah Millgram, author of The Great Endarkenment, Svantje Guinebert, of the University of Bremen, to answer his questions and discuss the role of logic in philosophy. On other occasions, you’ve said that logic, at least the logic that most philosophers are taught, is stale science, and that it’s getting in the way of philosophers learning about newer developments. But surely logic is important for philosophers. Would you like to speak to the role of logic in philosophy?

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24. Will we ever need maths after school?

What is the purpose of mathematics? Or, as many a pupil would ask the teacher on a daily basis: “When are we going to need this?” There is a considerably ruder version of a question posed by Billy Connolly on the internet, but let’s not go there.

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25. Yes, maths can be for the amateur too

A friend of mine picked an argument with me the other day about how people go on about the beauty of mathematics, but this is not only not obvious to non-mathematicians, it cannot be accessed by those outside the field. Unlike, for example, the modern art, which is also not always obvious, mathematical beauty is elusive to all but the mathematicians. Or so he said.

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