Maths SC Booklet
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You and AI Conversations About AI Technologies and Their Implications for Society
You and AI Conversations about AI technologies and their implications for society SUPPORTED BY CONVERSATIONS ABOUT AI TECHNOLOGIES AND THEIR IMPLICATIONS FOR SOCIETY DeepMind1 2 CONVERSATIONS ABOUT AI TECHNOLOGIES AND THEIR IMPLICATIONS FOR SOCIETY You and AI Conversations about AI technologies and their implications for society Artificial Intelligence (AI) is the science of making computer systems smart, and an umbrella term for a range of technologies that carry out functions that typically require intelligence in humans. AI technologies already support many everyday products and services, and the power and reach of these technologies are advancing at pace. The Royal Society is working to support an environment of careful stewardship of AI technologies, so that their benefits can be brought into being safely and rapidly, and shared across society. In support of this aim, the Society’s You and AI series brought together leading AI researchers to contribute to a public conversation about advances in AI and their implications for society. CONVERSATIONS ABOUT AI TECHNOLOGIES AND THEIR IMPLICATIONS FOR SOCIETY 3 What AI can, and cannot, do The last decade has seen exciting developments in AI – and AI researchers are tackling some fundamental challenges to develop it further AI research seeks to understand what happens or inputs do not follow a standard intelligence is, and then recreate this through pattern, these systems cannot adapt their computer systems that can automatically rules or adjust their approach. perform tasks that require some level of reasoning or intelligence in humans. In the last decade, new methods that use learning algorithms have helped create In the past, AI research has concentrated computer systems that are more flexible on creating detailed rules for how to carry and adaptive, and Demis Hassabis FRS out a task and then developing computer (co-founder, DeepMind) has been at the systems that could carry out these rules; forefront of many of these developments. -
Liverpool Capstone Theatre 25 June 2015 What’S Thepoint? Summer Shows for Year 9S and 10S
Liverpool Capstone Theatre 25 June 2015 what’s thePOINT? Summer ShowS for Year 9s and 10s A fantastic outing, all our students enjoyed it Maths Teacher, South Liverpool mathsinspiration.com what’s Matt Parker is known as the ‘stand-up mathematician’ and is the only person thePOINT? to hold the prestigious title of London SUMMER SHOWS FOR YEAR 9s AND 10s Mathematical Society Popular Lecturer while simultaneously having a sold-out comedy show at the Edinburgh Festival Fringe. A regular on Liverpool Capstone Theatre Numberphile, Matt is always keen to mix his two passions of Thurs 25 June 2015, mathematics and stand-up as well as presenting TV and 10.30am–12.30pm & 1.30pm–3:30pm radio shows. Rob Eastaway is an author whose Tickets: £7.50 (inc VAT). For each 10 student ticket books on everyday maths include the purchases we include a free Teacher ticket. bestselling Why Do Buses Come In Threes? and The Hidden Maths of Sport. Inspire your Year 9s and 10s – even the ones who He appears regularly on BBC Radio 4 and don’t love maths – with a lecture show featuring 5 Live to talk about the maths of everyday life and has given some of the country’s most entertaining maths maths talks around the world to audiences of all ages. speakers. Hannah Fry is a mathematician at Do your students wonder what’s the point of University College London (or ‘Mathmo at algebra? Who on earth needs Pythagoras? UCL’ for short) as well as being an author and science presenter. You can find her And who cares about exponentials? on YouTube, TV and radio sharing her In this highly engaging and interactive show Matt Parker, love of applied mathematics and exploring the patterns it Rob Eastaway and Hannah Fry (plus special guest) explain reveals in our human behaviour. -
June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings for MATHEMATICS 2014 and Events Following a Very Generous Tions Open in Late 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 437 June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings FOR MATHEMATICS 2014 and Events Following a very generous tions open in late 2014. The prize Monday 16 June donation made by Professor may be awarded to either a single Midlands Regional Meeting, Loughborough Geoffrey Shephard, the London winner or jointly to collaborators. page 11 Mathematical Society will, in 2015, The mathematical contribution Friday 4 July introduce a new prize. The prize, to which an award will be made Graduate Student to be known as the Shephard must be published, though there Meeting, Prize will be awarded bienni- is no requirement that the pub- London ally. The award will be made to lication be in an LMS-published page 8 a mathematician (or mathemati- journal. Friday 4 July cians) based in the UK in recog- Professor Shephard himself is 1 Society Meeting nition of a specific contribution Professor of Mathematics at the Hardy Lecture to mathematics with a strong University of East Anglia whose London intuitive component which can be main fields of interest are in page 9 explained to those with little or convex geometry and tessella- Wednesday 9 July no knowledge of university math- tions. Professor Shephard is one LMS Popular Lectures ematics, though the work itself of the longest-standing members London may involve more advanced ideas. of the LMS, having given more page 17 The Society now actively en- than sixty years of membership. Tuesday 19 August courages members to consider The Society wishes to place on LMS Meeting and Reception nominees who could be put record its thanks for his support ICM 2014, Seoul forward for the award of a in the establishment of the new page 11 Shephard Prize when nomina- prize. -
2011 Mathematics Newsletter
AUTUMN 2011 NEWSLETTER OF THE DEPARTMENT OF MATHEMATICS AT THE UNIVERSITY OF WASHINGTON Mathematics NEWS 1 DEPARTMENT OF MATHEMATICS NEWS MESSAGE FROM THE CHAIR It has been another exciting year The positive developments reported in this newsletter stand for our department. The work of in contrast to a backdrop of (global) financial and politi- the faculty has been recognized cal uncertainty. In the fourth year of the financial crisis, in a number of ways, includ- the end is not yet in sight. Repeated cuts in state support, ing the AMS Bôcher Prize and coupled with tuition increases, spell a fundamental shift the SIAM Kleinman Prize pre- in the funding of state universities. At the same time, the sented to Gunther Uhlmann, need to re-tool to pursue new career paths in a changing and the NSF CAREER award to economy, the return of soldiers from overseas deployments, Max Lieblich. As you will see on and the coming of age of the baby-boom echo generation page 15, the numbers of majors bring increasing numbers of students to our campus and to in the Mathematics program and the joint ACMS (Applied our department. and Computational Mathematical Sciences) program have Until the situation settles, new resources are generally made continued to rise, as have the numbers of degrees awarded. available to us in the form of temporary allocations instead In addition, these programs attract outstanding students of tenure-track faculty positions, which would require long- who continue to make us proud. For example, Math majors term financial commitments. This policy is understandable. -
JPBM Communications Award Is Given to He Takes a Particular Interest in Problems That Lie Ian Stewart of the University of Warwick
comm-jpbm.qxp 3/5/99 3:49 PM Page 568 JPBM Awards Presented in San Antonio The Joint Policy Board for Mathematics (JPBM) The sheer volume of this work is staggering, but Communications Award was established in 1988 the quality is spectacular as well. With clarity and to reward and encourage journalists and other humor, Ian Stewart explains everything from num- communicators who, on a sustained basis, bring ber theory to fractals, from Euclidean geometry to accurate mathematical information to nonmathe- fluid dynamics, from game theory to foundations. matical audiences. Any person is eligible as long He conveys both the beauty and the utility of math- as that person’s work communicates primarily ematics in a way seldom achieved by a single au- with nonmathematical audiences. The lifetime thor, and he does so with charm and eloquence. award recognizes a significant contribution or ac- cumulated contributions to public understanding Biographical Sketch of mathematics. Ian Stewart was born in 1945, did his undergrad- At the Joint Mathematics Meetings in San An- uate degree at Cambridge, and his Ph.D. at Warwick. tonio in January 1999, the 1999 JPBM Communi- He is now a professor at Warwick University and cations Award was presented to IAN STEWART. Below director of the Mathematics Awareness Centre at is the award citation, a biographical sketch, and Warwick. He has held visiting positions in Ger- Stewart’s response upon receiving the award. This many, New Zealand, Connecticut, and Texas. He has is followed by information about a JPBM Special published over 120 papers. His present field is Communications Award presented to JOHN LYNCH the effects of symmetry on nonlinear dynamics, and SIMON SINGH. -
Keep on Learning in Maths!
Keep on learning in Maths! Are you enjoying your maths work? Are you looking for something more? Are you in Year 11 and considering maths for A-Level? This is the place for you! We have tried to put together some ideas for you to extend your mathematical knowledge beyond what MyMaths and Kerboodle. None of this work is compulsory and we will not be assessing it, BUT if you have a go at it and want to share your work then please do! We would love to hear from you all Year 7 ● Have a go at some of the MyMaths games. They can be found on the left hand side menu under Activities. The games are split into Number, Algebra, Shape and Data so you can pick different ones to play. Challenge your friends! ● Some more challenging mathematical games can be found here: https://nrich.maths.org/9465. I particularly liked Last Biscuit ● Watch a documentary or a TED talk about applied maths- a list is attached at the bottom of this document Year 8 ● Have a go at some of the MyMaths games. They can be found on the left hand side menu under Activities. The games are split into Number, Algebra, Shape and Data so you can pick different ones to play. Challenge your friends! ● Nrich have a number of short problems here https://nrich.maths.org/11993 ● Watch a documentary or a TED talk about applied maths- a list is attached at the bottom of this document Year 9 ● Do you enjoy things like Sudoku? Then the game 2048 might be the one for you! You can download it onto your phone or go to https://2048game.com/ to play ● Some challenging maths problems and games here https://wild.maths.org/. -
![2 MB 9Th Apr 2021 BBC Ideas Full Report [Final]](https://docslib.b-cdn.net/cover/9354/2-mb-9th-apr-2021-bbc-ideas-full-report-final-689354.webp)
2 MB 9Th Apr 2021 BBC Ideas Full Report [Final]
BBC IDEAS 1 CONTENTS INTRODUCTION ............................................................................................................................................................... 3 EXECUTIVE SUMMARY .................................................................................................................................................... 5 PART ONE: MONITORING STATISTICS ...................................................................................................................... 7 1.1 The BBC and its Charter Responsibilities on ‘Impartiality’ and ‘Distinctiveness’ ................................ 7 1.2 BBC Ideas ...................................................................................................................................................... 11 1.3 News-watch ................................................................................................................................................... 13 1.4 Project Overview ......................................................................................................................................... 13 1.5 The Full Sample ............................................................................................................................................ 14 1.6 Views per Day .............................................................................................................................................. 15 1.7 Presentational style .................................................................................................................................... -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Fermat's Last Theorem
Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have an infinite number of solutions.[1] The proposition was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica; Fermat added that he had a proof that was too large to fit in the margin. However, there were first doubts about it since the publication was done by his son without his consent, after Fermat's death.[2] After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995; it was described as a "stunning advance" in the citation for Wiles's Abel Prize award in 2016.[3] It also proved much of the modularity theorem and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof was in the Guinness Book of World Records as the "most difficult mathematical problem" in part because the theorem has the largest number of unsuccessful proofs.[4] Contents The 1670 edition of Diophantus's Arithmetica includes Fermat's Overview commentary, referred to as his "Last Pythagorean origins Theorem" (Observatio Domini Petri Subsequent developments and solution de Fermat), posthumously published Equivalent statements of the theorem by his son. -
Maths Resources for Schools
Maths Resources for Schools Resources for students Key Resource stage Additional Reading ALL Internet Archive has millions of free books, movies, websites and more. KS5 Worcester College Bookshelf Project Maths “Closing the Gap: The Quest to Understand Prime Numbers - Vicky Neale” KS5 Staircase 12 KS4-5 Maths questions set by Oxford tutors. KS5 Bridging Material • Alcock, Lara How to Study for a Mathematics Degree (2012) • Allenby, Reg Numbers and Proofs (1997) • Earl, Richard Towards Higher Mathematics: A Companion (2017) • Houston, Kevin How to Think Like a Mathematician (2009) • Liebeck, Martin A Concise Introduction to Pure Mathematics (2000) Popular Mathematics • Acheson, David 1089 and All That (2002), The Calculus Story (2017) • Bellos, Alex Alex’s Adventures in Numberland (2010) • Clegg, Brian A Brief History of Infinity (2003) • Courant, Robbins and Stewart What is Mathematics? (1996) • Devlin, Keith Mathematics: The New Golden Age (1998), The Millennium Problems (2004), The Unfinished Game (2008) • Dudley, Underwood Is Mathematics Inevitable? A Miscellany (2008) • Elwes, Richard MATHS 1001 (2010), Maths in 100 Key Breakthroughs (2013) • Gardiner, Martin The Colossal Book of Mathematics (2001) • Gowers, Tim Mathematics: A Very Short Introduction (2002) • Hofstadter, Douglas Gödel, Escher, Bach: an Eternal Golden Braid (1979) • Körner, T. W. The Pleasures of Counting (1996) • Neale, Vicky Closing the Gap: the quest to understand prime numbers (2017) • Odifreddi, Piergiorgio The Mathematical Century: The 30 Greatest Problems of -
The Book Review Column1 by William Gasarch Dept of Computer Science Univ
The Book Review Column1 by William Gasarch Dept of Computer Science Univ. of MD at College Park College Park, MD, 20742 email: [email protected] Slight change in information given: in the past I have provided price and ISBN numbers of books. The notion of price is ill-defined: the website www.bestbookbuys.com gives a range of prices from place to purchase books on the web. (amazon.com is usually not the cheapest, and its usually not even close.). Providing ISBN numbers is also not needed in this electronic age where such information is available at the touch of a button. If the price is notable{ either rather high or rather low, this might be mentioned in the review. Welcome to the Book Reviews Column. We hope to bring you at least two reviews of books every month. In this column five books are reviewed. 1. The Codebreakers: The story of secret writing , by David Kahn reviewed by William Gasarch. This is a rather complete history of crypto up to World War II. The key question for us is, should someone doing research in cryptography read this book? 2. The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography , by Simon Singh. This book review originally appeared in the Notices of the American Mathematical Society, March 2000, and is reprinted here with permission. Review by Jim Reeds. This is a recent book on the history of crypto that is quite popular. But is it accurate? Read the review to find out. 3. DNA Based Computers V (Proceedings of a Dimacs Workshop) edited by Eric Winfree and David K. -
Career Pathway Tracker 35 Years of Supporting Early Career Research Fellows Contents
Career pathway tracker 35 years of supporting early career research fellows Contents President’s foreword 4 Introduction 6 Scientific achievements 8 Career achievements 14 Leadership 20 Commercialisation 24 Public engagement 28 Policy contribution 32 How have the fellowships supported our alumni? 36 Who have we supported? 40 Where are they now? 44 Research Fellowship to Fellow 48 Cover image: Graphene © Vertigo3d CAREER PATHWAY TRACKER 3 President’s foreword The Royal Society exists to encourage the development and use of Very strong themes emerge from the survey About this report science for the benefit of humanity. One of the main ways we do that about why alumni felt they benefited. The freedom they had to pursue the research they This report is based on the first is by investing in outstanding scientists, people who are pushing the wanted to do because of the independence Career Pathway Tracker of the alumni of University Research Fellowships boundaries of our understanding of ourselves and the world around the schemes afford is foremost in the minds of respondents. The stability of funding and and Dorothy Hodgkin Fellowships. This us and applying that understanding to improve lives. flexibility are also highly valued. study was commissioned by the Royal Society in 2017 and delivered by the Above Thirty-five years ago, the Royal Society The vast majority of alumni who responded The Royal Society has long believed in the Careers Research & Advisory Centre Venki Ramakrishnan, (CRAC), supported by the Institute for President of the introduced our University Research Fellowships to the survey – 95% of University Research importance of identifying and nurturing the Royal Society.