Australia: University of Sydney
Canada: University of Toronto
China: 北京大学
Japan: Tokyo University
Hong Kong: 香港大学
France: Ecole Normale Supérieure, Paris
India: Indian Institute of Technology, Delhi
Taiwan: 国立台湾大学
UK: Cambridge University
USA: Harvard University
Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature’s shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.
Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.
From search engines to big data and cloud services, math plays a key role in IT applications. Read on to know more about the opportunities math has to offer.
In this increasingly digital world, mathematics is everywhere. It is wise to keep track of the myriad opportunities that would be laid open by mathematics education.
“The advancement and perfection of mathematics are intimately connected with the prosperity of the state,” said Napolean Bonaparte. While there may be several opinions regarding Napolean as a leader, this statement holds indisputably true even today.
Read more at: http://www.thehindu.com/features/education/careers/stay-ahead-with-math/article6252546.ece
More than 80 or 90 per cent of students on four-year direct honours programmes at publicly-funded universities here graduate with honours or the equivalent. But only 60 per cent of those in the three-year arts and social sciences, business and science degree courses at the National University of Singapore (NUS) qualify for the fourth year of study, which allows them to graduate with honours.
To close the gap, NUS is lowering the grade to qualify for the honours year in these three schools, which are among the larger faculties in the university and take in some 3,600 students a year. This means another 10 to 15 per cent – 400 to 500 students- from these three faculties can move on to the fourth year to study for their honours.
Previously, students in the three faculties require a Cumulative Average Point (CAP) of 3.5 and above to qualify for honours study. With the change, they need only 3.2. NUS, though, will stick to its policy of keeping the the three plus one structure. Students who fail to notch up a score of at least 3.2 will have to exit the course.
NUS Provost Tan Eng Chye said the university decided to lower the requirement as the quality of students has gone up over the years. Students need As and Bs to enter most of the courses now. Last year, for example, students needed a ABB to enter the arts and social sciences course and those entering business needed triple As.
With more than five million copies in print all around the world, The 7 Habits of Highly Effective Teens is the ultimate teenage success guide—now updated for the digital age.
Imagine you had a roadmap—a step-by-step guide to help you get from where you are now, to where you want to be in the future. Your goals, your dreams, your plans…they are all within reach. You just need the tools to help you get there.
That’s what Sean Covey’s landmark book, The 7 Habits of Highly Effective Teens, has been to millions of teens: a handbook to self-esteem and success. Now updated for the digital age, this classic book applies the timeless principles of the 7 Habits to the tough issues and life-changing decisions teens face. In an entertaining style, Covey provides a simple approach to help teens improve self-image, build friendships, resist peer pressure, achieve their goals, and get along with their parents, as well as tackle the new challenges of our time, like cyberbullying and social media. In addition, this book is stuffed with cartoons, clever ideas, great quotes, and incredible stories about real teens from all over the world.
An indispensable book for teens, as well as parents, teachers, counselors, or any adult who works with teens, The 7 Habits of Highly Effective Teenshas become the last word on surviving and thriving as a teen and beyond.
“If The 7 Habits of Highly Effective Teens doesn’t help you, then you must have a perfect life already.”–Jordan McLaughlin, Age 17
Prodded by several comments, I have finally decided to write up some my thoughts on time management here. I actually have been drafting something about this subject for a while, but I soon realised that my own experience with time management is still very much a work in progress (you should see my backlog of papers that need writing up) and I don’t yet have a coherent or definitive philosophy on this topic (other than my advice on writing papers, for instance my page on rapid prototyping). Also, I can only talk about my own personal experiences, which probably do not generalise to all personality types or work situations, though perhaps readers may wish to contribute their own thoughts, experiences, or suggestions in the comments here. [I should also add that I don’t always follow my own advice on these matters, often to my own regret.]
Excellent and educational post by famous Mathematician Timothy Gowers on how to solve Math (Olympiad) problems.
(Post is at the bottom of this article)
Many students often give up immediately when facing a difficult maths problem. However, if students persist on for some time, usually they can come up with a solution or at least an idea on how to solve the problem. That is a great achievement already!
Never give up, even when your Maths question looks like this!
Quote: What I wrote gives some kind of illustration of the twists and turns, many of them fruitless, that people typically take when solving a problem. If I were to draw a moral from it, it would be this: when trying to solve a problem, it is a mistake to expect to take a direct route to the solution. Instead, one formulates subquestions and gradually builds up a useful bank of observations until the direct route becomes clear. Given that we’ve just had the football world cup, I’ll draw an analogy that I find not too bad (though not perfect either): a team plays better if it patiently builds up to an attack on goal than if it hoofs the ball up the pitch or takes shots from a distance. Germany gave an extraordinary illustration of this in their 7-1 defeat of Brazil.
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world’s leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music–and much, much more.
Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
Presents major ideas and branches of pure mathematics in a clear, accessible style
Defines and explains important mathematical concepts, methods, theorems, and open problems
Introduces the language of mathematics and the goals of mathematical research
Covers number theory, algebra, analysis, geometry, logic, probability, and more
Traces the history and development of modern mathematics
Profiles more than ninety-five mathematicians who influenced those working today
Explores the influence of mathematics on other disciplines
Includes bibliographies, cross-references, and a comprehensive index
Contributors incude:
Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger
The title of this post is a nod to Terry Tao’s four mini-polymath discussions, in which IMO questions were solved collaboratively online. As the beginning of what I hope will be a long exercise in gathering data about how humans solve these kinds of problems, I decided to have a go at one of this year’s IMO problems, with the idea of writing down my thoughts as I went along. Because I was doing that (and doing it directly into a LaTeX file rather than using paper and pen), I took quite a long time to solve the problem: it was the first question, and therefore intended to be one of the easier ones, so in a competition one would hope to solve it quickly and move on to the more challenging questions 2 and 3 (particularly 3). You get an average of an hour and a half per…
Professor David Eisenbud gives an excellent explanation of the Fundamental Theorem of Algebra!
In high school, we learnt that some quadratic equations (e.g. ) do not have real roots. However, by the Fundamental Theorem of Algebra, every polynomial equation of degree d has d complex roots! (counting multiplicity)
Learn about the boy who – could read and add numbers when he was three years old, – thwarted his teacher by finding a quick and easy way to sum the numbers 1-100, – attracted the attention of a Duke with his genius, and became the man who… – predicted the reappearance of a lost planet, – discovered basic properties of magnetic forces, – invented a surveying tool used by professionals until the invention of lasers. Based on extensive research of original and secondary sources, this historical narrative will inspire young readers and even curious adults with its touching story of personal achievement.
Most students taking science related courses like Engineering or Physics need to study at least one semester of Calculus. Calculus can be a rather difficult subject, and having a good textbook to learn from is half the battle won! 🙂
We review 3 of the Top Calculus Textbooks on Amazon.com:
The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.
This book by Michael Spivak is strongly recommended for Math Majors, or for students interested in learning the theory behind calculus. Includes the theory of epsilon-delta analysis.
3) Thomas’ Calculus (13th Edition)
Thomas’ Calculus, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded–always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today’s learners.
This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).
If you want your kids to grow up with Math talent, start young in Music, be it playing simple drum or flute, later at age 4 or 5 progressing to piano or violin, along the way pick up musical theory…
Notice that great mathematicians (or Physicists the close cousins of Math) are often music talents, but the converse not true! Einstein performed violin with an orchestra formed by a group of Nobel Prize Physicists; never heard Mozart or any great musicians proofed any Math Conjectures.
Updated to include: Supplementary Angles, Complementary Angles, and Half Angle Formulas for Trigonometry
Remember, memorizing the formula is not enough. We need to know how to apply and use the formula! (The next level is to know how to derive the formulas, but that will not be tested in the exams. 🙂 )
Do you really really hate Math? Is it your most dreaded subject?
Why not learn to love Math as it is pretty much a compulsory subject until high school? Read this book, it may change your mindset about Math. From a well-known actress, math genius and popular contestant on “Dancing With The Stars”—a groundbreaking guide to mathematics for middle school girls, their parents, and educators
Coming across You’re Getting Old, it struck me that the numbers generated by the site would be perfect for standard form exercises; put in a student’s date of birth and even the young ones will have some big numbers reported! For example, for a 12 year old, the following figures are generated, some updated while you watch.
This week’s career memes are an ode to mathematicians, the numerical wizards who use their knowledge to solve practical problems in disciplines such as business, commerce, technology, engineering and the sciences.
A mathematician’s job involves performing computations and analysing and interpreting data, reporting conclusions from a data analysis and using those findings to support or improve business decisions, and developing mathematical or statistical models to analyse data.
Many mathematicians work for governments or for private scientific and R&D companies.
This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
How many marks to get A1 for A Maths / E Maths for O Levels?
The official answer is not released by Cambridge / MOE, but it is definitely not 75 as the papers are subject to the bell curve (using normal distribution).
Hello! Was wondering how much marks do I have to get in order to get A1… Many have been saying you need to get 90%. Is it really 90% for both Maths?
Cambridge has never revealed its score. Was wondering what you hve heard from your teachers or from other reliable sources. Thank you!
Appreciate it very much.
Ans by a forummer: 90 marks for emaths. 80+ for amaths
Now, getting 90 marks for E Maths is no mean feat. But it is possible with practice and the right coaching!
Getting 80+ for A Maths is no joke either. If you have taken A Maths before you know how difficult it is, and usually for any test in school more than half the class will fail.
We must approach the O Levels with the right positive mindset:
1) It is always possible to improve. No matter how weak the student is in Maths, it is always possible to improve. The key thing is to:
2) Start revision and practice early. The earlier you start revision and practicing Maths, the more chance of improvement you have!
3) Learn to love math and appreciate its beauty, or at least try your best not to hate math. Since Math is pretty much compulsory till JC, why not try to like it? Adopt a positive mindset and you will be able to study for longer hours for Maths, which will translate to a better score in the end.
If you are looking to brush up on your A Maths / E Maths skills and learn some tips on scoring during exams, join our weekly group tuition at Bishan!
1. Galois’s mother home-schooling him Latin & other languages before entering Lycée Louis-Le-Grand.
2. William Hamilton: knew 15 languages include Chinese before discovered Quarternions (1,i,j,k) on Monday 16 Oct 1843 walking along Brougham Bridge, Ireland.
3. Pascal, Descartes are philosopher good in writing.
4. Gauss learnt even at old age Russian to read Lobatschefsky’s Non-Euclidean Geometry
5. Cauchy’s father heeded the advice of his neighbour Laplace to teach young Cauchy language before mathematics.
A Southern Song dynasty (南宋) officer. During his 3-yr leaves when his mother died, he generalised 孙子算经 (4th century)’s “Chinese Remainder Theorem” in ‘大衍求一术’. After leaves, he went back to chase money & women, produced no more Maths.
G. Polya / Paul Halmos advocate getting math students to construct not just one but classes of examples to:
1. Extend & enrich own Example Spaces;
2. Develop full appreciation of concepts, definitions, techniques that they are taught.
[Polya, Halmos, Feynman]: they collect and build a personal ‘repertoire’ of “Examples Space” (include counter-examples) for each abstract math idea, which they can relate to a concrete object.
Examples:
Group abelian = (Z,+)
Ring = Z
Principal Ideal = nZ
Equivalence Relation = mod (n)
Cosets = {3Z, 1+3Z, 2+3Z}
…
There is a less well-known proof that is a direct constructive approach to proving that the square root of 2 is irrational!
We consider an arbitrary rational number , and show that the difference between and cannot be zero. Hence, the square root of 2 cannot be rational.
Firstly, we have:
(Rationalizing the numerator)
Now, we analyse the numerator. We can write ,
, where are odd.
Then ,
.
Since the largest power of two dividing is an odd power, whilst for the largest power of two dividing it is an even power, and cannot be the same number. Hence we have .
Now, we analyse the denominator. Firstly, we can consider just the rationals . Because if , it is clear that is not going to be .
Rearranging, we have: .
Multiplying throughout by , .
Going back to the original equation (boxed), we can conclude that:
.
We have shown constructively that is not a rational number!
Every math student needs a tool belt of problem solving strategies to call upon when solving word problems. In addition to many traditional strategies, this book includes new techniques such as Think 1, the 2-10 method, and others developed by math educator Ed Zaccaro. Each unit contains problems at five levels of difficulty to meet the needs of not only the average math student, but also the highly gifted. Answer key and detailed solutions are included. Grades 4-12
You’re getting old! 
Mathtuition88 