Maths Bridging Work Part 2

Total Page:16

File Type:pdf, Size:1020Kb

Maths Bridging Work Part 2 Maths The Mathematics department would like you to complete the booklet found at the end of this document This is your bridging task. Further Maths students will not have an additional bridging task. Super-curricular reading (information collated by Unifrog) Interesting articles Maths How mathematicians are storytellers and numbers are the characters https://www.theguardian.com/books/2015/jan/23/mathematicians- Some specialist areas storytellers-numbers-characters-marcus-du-sautoy Statistics Marcus du Sautoy, United Kingdom, 2015 Statistics is the branch of maths involved in collecting and analysing data. Statistics is one of the fastest growing fields in maths, as technology allows mathematicians to gather 'big data' in How statistics lost their power – and why we should fear what comes enormous quantities. next https://www.theguardian.com/politics/2017/jan/19/crisis-of- statistics-big-data-democracy Game theory William Davies, United Kingdom, 2017 Game theory is the branch of mathematics concerned with the analysing strategies in competitive situations, particularly where the Podcasts outcome of a choice depends critically on the actions of other A Brief History of Mathematics participants. Game theory has significant implications in contexts of https://www.bbc.co.uk/programmes/b00srz5b/episodes/download war, business, and biology. s Marcus du Sautoy, United Kingdom This is a BBC podcast in which Marcus du Sautoy discusses data, Hot topics statistics with mathematicians, showing how history can be mapped Twin primes mathematically. A twin prime is a prime number that is either 2 less or 2 more than another prime number - for example, either member of the twin The Secrets of Mathematics https://podcasts.ox.ac.uk/series/secrets- prime pair (59,61). However, it is unknown if there are infinitely many mathematics twin primes or if there is a largest pair. Oxford Mathematicians, United Kingdom The nature of infinity A series of talks and lectures from Oxford mathematicians exploring Recently mathematicians have been interested in infinity - how big is all aspects of Maths and its ever-growing range of applications from infinity? Is infinity real? Can some infinities be greater than others? medicine to economics and beyond. These are important questions when applied to the study of our universe - if the universe is truly infinite then it follows that if Relevant films youwere to travel outwards from Earth you would eventually find an exactThe Story of 1 Nick Murphy, United Kingdom, 2005 duplicate of our planet! The Story of 1 is a BBC documentary about the history of numbers, Cross curricular ideas and in particular, the number 1. Terry Jones goes right back to when Mathematical Physics the very concept of counting came about, and the immeasurable Physical mathematicians develop mathematical methods in order to impact this has had for the human race. solve problems in physics. A very simple example of this would be the The Story of Maths calculation of a car's speed using the mathematical model: speed=distance/time. Marcus du Sautoy, United Kingdom, 2008 This is a four-part documentary series in which Marcus du Sautoy Cryptography tracks historical developments in maths and their significance in Cryptography is the practice of writing and solving codes. Today today's world. cryptography is heavily based on mathematical theory and computer Some other good stuff science practice; cryptographers create algorithms to convert data so Women in Maths podcast https://soundcloud.com/damien-adams- that it's unreadable to a computer. Cryptography is used increasingly to protect digital information, including computer passwords, online 662584563 banking, and military communications. This podcast is an effort to promote visibility of women in mathematics. Each episode focuses on a different female Some influential academics mathematician and her contribution to the study of Alan Turing USA, 1912-1954 maths. Alan Turing is most famous for his work on codebreaking during the Second World War. He played a pivotal role in cracking intercepted Mathologer Youtube channel coded messages that enabled the Allies to defeat the Nazis in many https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg crucial engagements. His Turing Machine is considered to have Mathologer' is a youtube channel which produces 15-20 minute provided the model for a general purpose computer. explanations of mathematical ideas - everything from solving a 4D rubik's cube to the maths of card counting. Ada Lovelace United Kingdom,1815-1852 Ada Lovelace was a mathematician and writer, known for her work on Charles Babbage's proposed mechanical general-purpose computer. She was the first to recognise that the machine had applications beyond pure calculation and published the first algorithm intended to be carried out by such a machine. As a result, she is often regarded as the first computer programmer. Bridging the gap to Sixth Form studies Maths Please follow this link to complete structured exercises to help the transition to A level study https://amsp.org.uk/resource/gcse-alevel-transition-resources Work through as many activities as you can before September.
Recommended publications
  • Egyptian Mathematics
    Egyptian Mathematics Dr. Carmen Bruni David R. Cheriton School of Computer Science University of Waterloo November 1st, 2017 Three Part Series • Egyptian Mathematics • Diophantus and Alexandria • Tartaglia, Cardano and the Renaissance Age Egypt and Babylon Egypt circa 1500 BCE • Egyptian civilization established on the shores of the Nile about 5000 years ago • The yearly flood of the Nile brings sediments and nutriments that enriched the surrounding soils in the valley • The Nile becomes a method of transportation for both material and people and with the flood allowing for crops to grow, Egypt becomes a self-sufficient country (unlike other civilizations) Papyrus • Egyptians were the first known source of papyrus, a writing surface made from the pith (tissue in the stems) of a papyrus plant. • A lot of what we know from Egyptian mathematics originates from papyri. • We will be discussing content from two main papyri: the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus. Rhind Papyrus Written by the scribe Ahmes (also known as Ahmose or A'hmos`e). (Source: Wikimedia Commons) Moscow Papyrus (Source: Wikimedia Commons) Mathematics Arising Out of Necessity For Egyptians, mathematics was used as a tool to solve many of the problems they encountered. • Areas • Taxes • Calendars • Food • Volumes Areas Common units of measurement: • Cubit: length from the tip of the middle finger to the bottom of the elbow. Approximately 52cm. • Khet: 100 cubits • Setat/Arura/Aroura: A square khet. (About 2.7 square km or 2=3 of an acre). • Digit, palm, hand, fist: Other smaller units of measurement. This allowed them to give parcels of land to people and to keep track of these lands for taxes.
    [Show full text]
  • An Amazing Race
    THE MATHEMATICAL THE COMMON ASSOCIATION OF VICTORIA DENOMINATOR 2/15 AN AMAZING RACE Students are totally absorbed in Lumen Christi’s mathematics challenge: The Amazing Race. INSIDE As children darted from stage to stage eagerly chatting about strategies, encouraging and praising each other’s mathematical eforts it was clear that this of all school days was one that Pattern and would be remembered. A day from which we could establish interest and engagement, a day structure from which we could raise both the profile of mathematics in our school community and in the 7 minds of the students that we teach. What had started as an ambition to host a competition Problem solving challenges had quickly permeated through the school and taken on a life of its own. Indeed, from little high ability students ideas big things grow or in this case from MAV Games Days whole school engagement grows. 8 Games: In early September 2014, our school, Lumen Christi Catholic Primary School, was fortunate just trivial pursuits? enough to host a Year 6 MAV Games Day. The day was a great success and really helped 11 students apply their knowledge of mathematics in a supportive team environment, where the Mathematica and the focus was less about getting the ‘right’ answer but more about enjoying everything that maths 14Australian Curriculum has to ofer. Continued on page 4 FROM THE PRESIDENT Associate Professor Marj Horne - Faculty of Education, Australian Catholic University THE COMMON SOAK UP MATHS DURING THE REVISED VCE MATHEMATICS DENOMINATOR SUMMER STUDY IMPLEMENTATION The MAV’s magazine SUPPORT WORKSHOPS published for its members.
    [Show full text]
  • JPBM Communications Award
    JPBM Communications Award The 2010 Communications Award of the Joint the Riemann hypothesis, entitled The Music of the Policy Board for Mathematics (JPBM) was presented Primes, is a best seller which has been translated at the Joint Mathematics Meetings in San Francisco, into ten languages. In his 2008 book, Symmetry: California, in January 2010. A Journey into the Patterns of Nature, du Sautoy The JPBM Communications Award is presented guides the reader through groups and symmetry, annually to reward and encourage journalists from Babylonia to Moonshine theory, while at the and other communicators who, on a same time giving an engaging glimpse into math- sustained basis, bring mathematical ematicians’ minds. His four-part television series, ideas and information to nonmathe- The Story of Maths, presents a fascinating look at matical audiences. JPBM represents the the development of mathematics from the design American Mathematical Society, the of the pyramids in Egypt to Perelman’s proof of American Statistical Association, the Poincaré’s conjecture. Whether it is talking about Mathematical Association of America, Beckham’s choice of number on a sports radio pro- and the Society for Industrial and Ap- gram, explaining the work of the Abel prize winner plied Mathematics. The award carries on Norwegian television, writing a weekly math a cash prize of US$1,000. column for the London Times, hosting a television Previous recipients of the JPBM game show based on math puzzles, or delivering Communications Award are: James the Royal Institution Christmas Lectures, Marcus Gleick (1988), Hugh Whitemore (1990), du Sautoy invariably seizes opportunities to make Ivars Peterson (1991), Joel Schneider mathematics more accessible and more appealing.
    [Show full text]
  • Resource Pack for Level 3 Preparation Programmes for Entry to Numeracy Teacher Training
    SkillsSkills for for LifeLife Support Programme Support Programme Resource pack for Level 3 preparation programmes for entry to numeracy teacher training The Skills for Life Support Programme CfBT Education Trust T: 0118 902 1920 is delivered on behalf of the Learning 60 Queens Road F: 0845 838 1207 and Skills Improvement Service by Reading E: [email protected] CfBT Education Trust and partners RG1 4BS W: www.excellencegateway.org.uk/sflsp Skills for Life Support Programme Acknowledgements This pack is the result of input and work from a range of individuals including the participants at the three events run by the Skills for Life Support Programme in 2010 and the members of CfBT, LLU+ at London South Bank University, LSN, NIACE and NRDC. The authors wish to thank these individuals for their input into this resource. Skills for Life Support Programme Contents Chapter 1 Introduction and rationale 3 1.1 Introduction and rationale 4 Chapter 2 Self assessment, number and geometry 8 2.1 Level 3 Self assessment carousel activity 9 2.2 Checklist of level 3 personal skills 49 2.3 Group summary checklist 53 2.4 Number systems and place value 59 2.5 Number systems 63 2.6 Egyptian multiplication 65 2.7 The commutative, associative and distributive laws 66 2.8 Approaches for dividing fractions 70 2.9 Pythagoras’ theorem 71 2.10 Discovering ratios in right angled triangles 72 2.11 Trigonometry 76 Chapter 3 Algebra and its applications 78 3.1 Kinaesthetic equations 79 3.2 Algebra carousel activity 82 3.3 I think of a number 105 3.
    [Show full text]
  • History of Mathematics in the Higher Education Curriculum
    History of Mathematics in the Higher Education Curriculum Mathematical Sciences HE Curriculum Innovation Project Innovation Curriculum HE Sciences Mathematical Edited by Mark McCartney History of Mathematics in the Higher Education Curriculum Edited by Mark McCartney A report by the working group on History of Mathematics in the Higher Education Curriculum, May 2012. Supported by the Maths, Stats and OR Network, as part of the Mathematical Sciences Strand of the National HE STEM Programme, and the British Society for the History of Mathematics (BSHM). Working group members: Noel-Ann Bradshaw (University of Greenwich; BSHM Treasurer); Snezana Lawrence (Bath Spa University; BSHM Education Officer); Mark McCartney (University of Ulster; BSHM Publicity Officer); Tony Mann (University of Greenwich; BSHM Immediate Past President); Robin Wilson (Pembroke College, Oxford; BSHM President). History of Mathematics in the Higher Education Curriculum Contents Contents Introduction 5 Teaching the history of mathematics at the University of St Andrews 9 History in the undergraduate mathematics curriculum – a case study from Greenwich 13 Teaching History of Mathematics at King’s College London 15 History for learning Analysis 19 History of Mathematics in a College of Education Context 23 Teaching the history of mathematics at the Open University 27 Suggested Resources 31 History of Mathematics in the Higher Education Curriculum Introduction Introduction Mathematics is usually, and of course correctly, presented ‘ready-made’ to students, with techniques and applications presented systematically and in logical order. However, like any other academic subject, mathematics has a history which is rich in astonishing breakthroughs, false starts, misattributions, confusions and dead-ends. This history gives a narrative and human context which adds colour and context to the discipline.
    [Show full text]
  • Mathematics in India
    TRADITIONSKnowledg & PRACTICES OF INDIA e Textbook for Class XI Module 7 Mathematics in India CENTRAL BOARD OF SECONDARY EDUCATION Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India TRADITIONSKnowledg & PRACTICESe OF INDIA Textbook for Class XI Module 7 Mathematics in India CENTRAL BOARD OF SECONDARY EDUCATION Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India No part of this publication may be reproduced or stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical photocopying, recording or otherwise, without the prior permission of the Central Board of Secondary Education (CBSE). Preface India has a rich tradition of intellectual inquiry and a textual heritage that goes back to several hundreds of years. India was magnificently advanced in knowledge traditions and practices during the ancient and medieval times. The intellectual achievements of Indian thought are found across several fields of study in ancient Indian texts ranging from the Vedas and the Upanishads to a whole range of scriptural, philosophical, scientific, technical and artistic sources. As knowledge of India's traditions and practices has become restricted to a few erudite scholars who have worked in isolation, CBSE seeks to introduce a course in which an effort is made to make it common knowledge once again. Moreover, during its academic interactions and debates at key meetings with scholars and experts, it was decided that CBSE may introduce a course titled ‘Knowledge Traditions and Practices of India’ as a new Elective for classes XI - XII from the year 2012-13. It has been felt that there are many advantages of introducing such a course in our education system.
    [Show full text]
  • Program at a Glance
    Program at a Glance This document provides a thumbnail sketch of all scientific and social events so you can easily see which events may overlap and better plan your time. Saturday, January 3 8:00 a.m.– 12:00 p.m. AMS SHORT COURSE ON QUANTUM COMPUTATION AND QUANTUM INFORMATION (PART I) 8:00 a.m.– 12:00 p.m. MAA SHORT COURSE ON DATA MINING AND NEW TRENDS IN TEACHING STATISTICS (PART I) Sunday, January 4 8:00 a.m.– 6:30 p.m. AMS DEPARTMENT CHAIRS WORKSHOP 9:00 a.m.– 5:00 p.m. AMS SHORT COURSE ON QUANTUM COMPUTATION AND QUANTUM INFORMATION (PART II) 9:00 a.m.– 4:00 p.m. MAA SHORT COURSE ON DATA MINING AND NEW TRENDS IN TEACHING STATISTICS (PART II) 9:00 a.m.– 5:00 p.m. MAA BOARD OF GOVERNORS 1:30 p.m.– 10:00 p.m. AMS COUNCIL 3:00 p.m.– 7:00 p.m. JOINT MEETINGS REGISTRATION, Marriot Ballroom Lobby, Lobby Level, Marriott Wardman Park Hotel Monday, January 5 7:30 a.m.– 4:00 p.m. JOINT MEETINGS REGISTRATION, Marriot Ballroom Lobby, Lobby Level, Marriott Wardman Park Hotel 8:00 a.m.– 10:50 a.m. AMS-MAA-SIAM SPECIAL SESSION ON RESEARCH IN MATHEMATICS BY UNDERGRADUATES, I AMS SPECIAL SESSIONS 8:00 a.m.– 10:50 a.m. Recent Trends in Coding Theory, I 8:00 a.m.– 10:50 a.m. Representation Theory of Lie Algebras and Algebraic Groups, I 8:00 a.m.– 10:50 a.m. Nonlinear Partial Differential Equations and Applications, I 8:00 a.m.– 10:50 a.m.
    [Show full text]
  • A MATHEMATICAL COLLABORATION ACROSS the ATLANTIC Elaine W. Clark, Assistant Professor University of New Mexico-Valencia Departme
    25TH ANNIVERSARY International Conference on Technology in Collegiate Mathematics A MATHEMATICAL COLLABORATION ACROSS THE ATLANTIC Elaine W. Clark, Assistant Professor University of New Mexico-Valencia Department of Mathematics and Statistics 280 La Entrada Los Lunas, NM 87031 [email protected] Francesca Bevilacqua, Maths Teacher Rolando da Piazzola High School – Piazzola sul Brenta (Padua) in 2011 Sandro Pertini High School – Camposampiero (Padua) currently in the Province of Padua, Italy [email protected] During the Spring 2011 semester Prof. Elaine Clark from the United States worked with Ms. Francesca Bevilacqua from Piazzola sul Brenta, Italy to create a research project through which college students and high school pupils could learn about some of the history of mathematics. The participants were college students in a second-semester mathematical content course for pre-service teachers at University of New Mexico- Valencia, in Tome, New Mexico, USA and high school pupils from Rolando da Piazzola High School in Piazzola sul Brenta, Italy. As the framework for this project Prof. Clark and Ms. Bevilaqua used portions selected from the first part of the four-part BBC series The Story of Maths hosted by Professor Marcus du Sautoy from the University of Oxford and The Open University (BBC and Open University; 2008). The entire series explores the historical underpinnings of mathematics, beginning with the ancient civilizations of Egypt, Sumeria, and Babylon and working up through more current mathematics. Prof. Clark and Ms. Bevilaqua decided to focus on the beginning, ancient cultures in Part I: The Language of the Universe. This choice was partly because of the learning objectives for the college students, and because they were unsure of possible language barriers with the Italian high school pupils.
    [Show full text]
  • History Can Be a Powerful Ally in Teaching Difficult Mathematical Ideas for the First Time”
    Comment Marcus du Sautoy on… the importance of the history of maths “History can be a powerful ally in teaching difficult mathematical ideas for the first time” hen I learnt my mathematics at gence during the Renaissance. But I discovered how school it was taught in a very much exciting mathematics was being done in India ahistorical manner. The people, the long before Fibonacci (c1175–c1250) kickstarted the cultures, the politics were all mathematical revolution in Europe, and that there W missing. It was the ideas that were inklings of the calculus bubbling away in India counted. I learnt how negative numbers worked. in the 14th century, well before Newton and Leibniz What to do with a sine and a cosine. How to calculate articulated their theory. But these historical vignettes volumes of solids. I knew little of the history of these aren’t just interesting curiosities. ideas. Personally, the abstract ideas were enough to Witnessing the way teachers have used excerpts excite me, but the missing stories of where these ideas from the Story of Maths in the classroom, I’ve seen came from could have engaged so many more in the Marcus du how history can be a powerful ally in teaching wonders of mathematics. Sautoy is the difficult mathematical ideas to those encountering For example, sines and cosines were our best tools Simonyi them for the first time. A historical perspective for navigating the night sky centuries before Galileo Professor for has even helped me in my own journey to create ever had a telescope in his hands.
    [Show full text]
  • An Aesthetic Knowing of Mathematical Identity: Performing Stories of Mathematical
    An Aesthetic Knowing of Mathematical Identity: Performing stories of Mathematical Identity through filmed drama A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy (PhD) in the Faculty of Humanities 10/25/2016 Kelly Pickard-Smith 69960 words School of Environment, Education and Development Table of Contents Abstract .......................................................................................................................... 8 DECLARATION .............................................................................................................. 9 COPYRIGHT STATEMENT ............................................................................................ 9 Acknowledgements ....................................................................................................... 10 Chapter 1. Finding identity and wisdom through the arts ....................................... 11 1.1 Introduction: The background, justification and focus of the thesis .................... 11 1.2 Background to the study .................................................................................... 12 1.2.1 Performing mathematically .......................................................................... 13 1.2.2 A rationale for the research: Personal and professional context .................. 17 1.2.3 A rationale for the research: A previous study on learner experience .......... 20 1.3 Framing the study contribution .......................................................................... 22
    [Show full text]
  • The Role of the History and Epistemology of Mathematics in Teachers Training Panel Discussion
    27 THE ROLE OF THE HISTORY AND EPISTEMOLOGY OF MATHEMATICS IN TEACHERS TRAINING PANEL DISCUSSION INTRODUCTION Evelyne BARBIN IREM and Centre François Viète, University of Nantes, France [email protected] The theme of “History of mathematics in pre and in-service teacher training” has already been established as one of the six topics of the 1st European Summer University in Montpellier (France) where one panel and many workshops were held. The Proceedings of this meeting contain 7 papers on this theme (IREM, 1993, pp.451-496). Five years later, it was also the subject of chapter 4 of the ICMI Study (Fauvel & van Maanen, 2000). The current contribution will offer the possibility to study evolution of ideas on the theme, as well as some institutional changes. If we are not able to give a complete outline of the situation in each country from which our members come, it is clear that the possibility of communication among the participants in our different meetings is important for both encouragement, and as a way of communication, in order to compare and exchange thoughts and information on projects we are involved with. The panel was organized to enable 4 communications concerning 4 countries: Italy, Norway, England and France. In order to have a more fruitful interaction, the four participants had to answer the same 6 questions in total, divided into three groups. The aim of the first group was to situate the purpose of investigation in an institutional frame for each country: 1. How is teacher training conceived in your country (pre and in-service teacher training)? 2.
    [Show full text]
  • January 2009
    THE LONDON MATHEMATICAL SOCIETY NEWSLETTER No. 377 January 2009 Society COUNCIL DIARY visits, they had only reached a very small number (perhaps 400) of the Meetings 21 November 2008 members of the two societies, so and Events The meeting began, under Matters that it was difficult to form any Arising, with an update on the clear idea of members’ views in the 2009 financial situation as it affects the large. The Council rapidly agreed to Wednesday 14 January LMS, which can be summarised as proceed to the next stage, namely Northern Regional ‘gloomy but could be worse’. Under a referendum on the proposal that Meeting, Manchester President’s Business, Brian Davies the Council is commending to the [page 3] recalled that Susan Oakes, the long- LMS members, to combine in a new standing LMS Administrator, was unified mathematics society with Friday 27 February shortly to retire. He noted, moreover, the IMA. Mary Cartwright that Council had been canvassed Penny Davies, in her role as our Lecture, London by email regarding the proposal to representative on the EPSRC liaison [page 5] name the De Morgan House archive group of the Council for the Math- 31 March – 4 April room the Oakes Room in her hon- ematical Sciences, reported on a LMS Invited Lectures our, in recognition of Susan’s contri- recent meeting of the group with Edinburgh [page 9] butions to the Society, particularly David Harman, the Mathematical her work in developing the archives Sciences Programme Head, his team Friday 3 July and preserving the history of the and other EPSRC representatives.
    [Show full text]