UReddit Courses:
Modern Algebra (Abstract Algebra) Made Easy –
Part 0: Binary Operations
Part 1: Group
Part 2: Subgroup
Part 3: Cyclic Group & its Generator
Part 4: Permutations
Part 5: Orbits & Cycles
Part 6 : Cosets & Lagrange’s Theorem
Part 7 : Direct Products / Finite generated Abelian groups
Part 8: Group Homomorphism
Part 9: Quotient Groups
Part 10: Rings & Fields
Part 11: Integral Domain
Source: http://mathace2012.wiki.hci.edu.sg/
Check out these Formulas for:
at http://mathace2012.wiki.hci.edu.sg/
Featured book: The Ultimate book of Formulas (2000+ Formulas!)
Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 4th Edition: 2,400 Formulas + Tables (Schaum’s Outline Series)
This Schaum’s Outline gives you
Monster Group (code name “Moonshine”) is the largest group, discovered by two Cambridge Mathematicians John Conway and Simon Norton.
Monster Group – (1)
Monster Group (2):
John Conway: Life, Death and the Monster (3)
Ref:
1. Simon Norton (1952 -) – an eccentric mathematician who collects all British Railway Train Time Tables.
http://catalogue.nlb.gov.sg/cgi-bin/spydus.exe/ENQ/EXPNOS/BIBENQ?ENTRY=The%20genius%20in%20my%20basement&ENTRY_NAME=BS&ENTRY_TYPE=K&SORTS=DTE.DATE1.DESC%5DHBT.SOVR
2.
Finding Moonshine: A Mathematician’s Journey Through Symmetry by Marcus Du Sautoy
http://catalogue.nlb.gov.sg/cgi-bin/spydus.exe/FULL/EXPNOS/BIBENQ/6345422/5640834,2
8 and 6 are lucky but 4 is unlucky… if you’re Chinese!
Featuring Xiaohui Yuan from the University of Nottingham.
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Videos by Brady Haran
Brady John Haran is an Australian independent film-maker and video journalist who is known for his educational videos and documentary films produced for BBC News and for his YouTube channels. (http://en.wikipedia.org/wiki/Brady_Haran)
Highly recommended to subscribe to Numberphile on Youtube for fun and interesting Math videos!
Featured book:
Number: The Language of Science
Number is an eloquent, accessible tour de force that reveals how the concept of number evolved from prehistoric times through the twentieth century. Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.
– Rated 4.5/5 on Amazon
| Math, reading performance is stagnant among US 12th-graders, assessment finds Washington Post The nation’s high school seniors have shown no improvement in math and reading performance since 2009, and large racial achievement gaps … |
| Math, reading performance stagnates among US 12th-graders, assessment finds Business Mirror WASHINGTON—The United States’s high-school seniors have shown no improvement in math and reading performance since 2009, and large racial … |
| Social Math: Why Learning Math Involves More Than Writing Numbers Huffington Post My lifelong passion for creating better ways to learn math got its start in a school not unlike the Israeli one I visited — and at the very same age. |
| Math games aim to keep kids sharp over summer Scranton Times-Tribune JAKE DANNA STEVENS / STAFF PHOTOGRAPHER Kaylynn Howe, 8, left, and her sister, Destine Howey, play a math game at Bancroft Elementary … |
| Common Core math gains are worth the pain New York Daily News As more than a million New York students in grades 3-8 took the state math exams last week, a small but vocal cadre of parents railed at the new … |
| Lindblom Math and Science principal among Golden Apple winners Chicago Tribune The organization quickly realized that Mather, principal of Lindblom Math and Science Academy In Chicago’s West Englewood neighborhood was the … |
| Math Learning – A Universal Language? Huffington Post Fifth-grade students at Woodward Elementary School had an interesting math assignment this fall: watching college football games. Though … |
| US students’ reading, math show no progress TheChronicleHerald.ca WASHINGTON — In an abysmal showing, only about one-quarter of U.S. high school seniors performed solidly in math in a major assessment known … |
| Using math in the fight against cancer WNYT But a local college professor says many people don’t like math because they don’t see a connection to it. In this Friday’s STEM 13 report, learn how the … |
| Math Day at Molly Stark honors memory of Gail Harwood Bennington Banner BENNINGTON — The Molly Stark School honored a longtime teacher on Monday with “Gail Harwood Math Day.” Harwood passed away in January … |
| Singapore takes third spot in global education rankings Straits Times Teacher Anthony Tan conducting an English lesson with a class of Primary 6 pupils at Woodlands Primary School. Singapore’s education system has … |
| Singapore offers Saudi Arabia help in education Arab News PROPOSAL: Singapore Senior Minister of State Lee Yi Shyan with Mazen Batterjee, vice chairman of the JCCI, on Wednesday. (AN photo by Irfan … |
| In Singapore, Training Teachers for the ‘Classroom of the Future’ Education Week News Welcome to the Classroom of the Future—a mock-up housed by Singapore’s National Institute of Education (NIE) to demonstrate what learning might … |
| Singapore Polytechnic Assists CDIO Implementation At Malaysia’s Polytechnic Bernama PUTRAJAYA, May 6 (Bernama) — Singapore Polytechnic is assisting Malaysia on the implemention of innovative engineering education framework … |
| Lift education standards: Linfox boss The Australian “Most of our graduates are now coming out of Thailand, Vietnam, Singapore and China because they are just so well educated,” he said. “I can get … |
| In search of education The News International Unless we start investing massively in education, science, technology and innovation, as was done by Singapore, Korea, Malaysia, China and others, … |
| Sultanate, Singapore and the Indian Ocean Oman Daily Observer These are thoughtful words from your education minister (Heng Swee Keat), … a pragmatism which incidentally I believe we share with Singapore. |
| Direct School Admission not meant to lower academic standards TODAYonline In Singapore, there is no compromising a good education. Having a talent does not give a student the licence not to pursue academic excellence. |
| NAFA inspires The Hindu The safe and comfortable cosmopolitan environment Nanyang Academy of Fine Arts, Singapore makes it the perfect destination for education abroad. |
| Japan’s Education Minister visits SMU Perspectives@SMU Singapore Management University (SMU) received a special guest on its campus on 3 May 2014 – Japan’s Minister of Education, Culture, Sports, … |
Check out this Youtube video on the Monster Group (related to Group Theory, a branch in Mathematics)
In the mathematical field of group theory, the monster group M or F1 (also known as the Fischer–Griess monster, or the Friendly Giant) is a group of finite order. (See Wikipedia: http://en.wikipedia.org/wiki/Monster_group)
Featured book:
The Symmetries of Things
This book is written by John Conway, one of the mathematicians who worked on the Monster Group. Rated highly on Amazon.
Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry.
Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments.
This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.
Check out the US “Common Core” Math syllabus, where students need Six Steps just to add 14 and 4!
Sounds unbelievable but true!
A rational number is a number that can be expressed in a fraction with integers as numerators and denominators.
Some examples of rational numbers are 1/3, 0, -1/2, etc. Now, we know that 
Is the square root of 2 rational? Or is it irrational (the opposite of rational)? How do we prove it? It turns out we can prove that the square root of two is irrational using a technique called proof by contradiction. (One of the earlier posts on this blog also used proof by contradiction to show that there are infinitely many prime numbers.)
First, we suppose that 
Next, we square both sides to get 
Hence, 
Thus, we can write 
Hence, 
But if both
Thus, the only possible conclusion is that the square root of two is not a rational number to begin with!
Featured book:
Math Jokes 4 Mathy Folks
Who says math can’t be funny? In Math Jokes 4 Mathy Folks, Patrick Vennebush dispels the myth of the humorless mathematician. His quick wit comes through in this incredible compilation of jokes and stories. Intended for all math types, Math Jokes 4 Mathy Folks provides a comprehensive collection of math humor, containing over 400 jokes.
– Highly rated on Amazon.com
Proof:
in Math logic,
$latex God subset Jesus text{ and}$
$latex Jesus subset God$
$latex implies $
$latex boxed {Jesus = God} $
[QED]
Source: http://news.asiaone.com/News/Education/Story/A1Story20080601-68205.html
When the Mid Year Exams are over, students will receive their results nervously. What to do if one fails the Mid Year Exams?
In many schools, it is common to have a significant portion of the school actually failing the Mid Term exam. “40 per cent of his school cohort failed Social Studies and 30 per cent English.” in the school mentioned in the above article.
“Such significant failure rates have become common in schools here when mid-year or preliminary exams roll around, especially for those with a big national exam – PSLE, O or A levels – at the year-end.”
Here are 5 tips on what are the best actions to take for one who fails the Mid Year Exams, especially for Mathematics:
There are usually two types of students, the ones who are more playful and laidback, and the very perfectionistic student but is prone to stress. For the more playful students, the tough Mid Year exams are actually meant as a wake up call to start studying before it is too late. “‘Papers must be a bit challenging so that they can shake one out of complacency and make one study harder,’ said Mr Lak Pati Singh, 56, principal of St Patrick’s School.”
For students who are too stressed up and already trying their best, the way to improve may be to study more efficiently using the right methods (especially for Maths, the right way to study is practice with understanding). A healthy lifestyle balance may also be very helpful. Again, seeking help from Math tutors may be a choice to be considered, which can alleviate stress from not understanding the subject material.
Read more at: http://news.asiaone.com/News/Education/Story/A1Story20080601-68205.html
Tsung-tung Chang[張聰東] 1988:
“Indo-European vocabulary in Old Chinese: A new thesis on the emergence of Chinese language and civilization in the Late Neolithic Age”, Sino-Platonic Papers 7, Philadelphia.
This Chinese scholar wrote the 1988 paper on the Chinese language origin with the proto-Indo-European (proto IE).
Interestingly very similar ‘coincidence’ occurs in 1500 words between Chinese and proto IE:
Take -> 得 tek (ancient Chinese sound as in Fujian dialect today)
Mort -> 殁 mo
See -> 视 see
Cow -> 牛 gu
…
Click to access spp007_old_chinese.pdf
After the Tower of Babel, God confused the human into different languages, but by the linguistic ‘archaeology’ ‘Half Life’ Theory, we can deduce ~ 4,900 years ago the Chinese and the Germanic (English, Denmark, German …) shared the same common linguistic root.
The ancient Chinese scholar Xu Shen许慎(东汉 : 58 CE…
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Einstein showed by Mathematics (the Riemann Geometry) to explain Space-Time curvature and the Gravity. It was later proved by the astrological discovery in Solar Eclipse.
Here, this professor made an experiment to demonstrate Einstein’s theory.
Gravity Visualized:
How did the NSA hack our emails?
Using Math in Elliptic curve…
NSA Surveillance (an extra bit) – Numberphile:
Natural Numbers (N) = {1,2,3, 4…}
1-dimension: a Line
2-dimension: a plane
n-dimensional flat space: a Vector Space
Now imagine in a world where we replace every natural number by vector space:
1 by a Line
2 by a Plane
n by a flat space Vector Space
Sum of numbers = Direct sum of vector space.
E.g. Add a 1-D Line to a 2-D Plane = 3-D Space
Product of numbers = Tensor Product (of two vector spaces of respective dimension m & n) with dimension m.n
This new world would be much interesting and richer than the Natural Number world: vector spaces have symmetries, whereas numbers are just numbers with no symmetries.
(Interesting): we can add 1 to 2 in only ONE way (1+2), but there are many ways to embed (add) a Line in a Plane (perpendicular, slanting in any angle, etc).
(Richer): the Lie Group SO(3)…
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Source: http://www.quora.com/Studies-and-Studying/How-do-top-students-study/answer/Qiaochu-Yuan-1
Check out this post by MIT almost perfect-scorer, on how to study. His secret is to study the material in advance, before the lessons even start! This is really a useful strategy, if implemented correctly. Imagine being in Primary 3 and already knowing the Primary 4 syllabus! Primary 3 Math will be a breeze then. This is one of the reasons why China students are so good at Math – they have already studied it back in China, where the Math syllabus is more advanced!
Do try out this strategy if you are really motivated to improve in your studies. The prime time to do this is during the June and December holidays – take some time to read ahead what is going to be learnt during the next semester.
This is an excerpt of the thread:
I graduated from MIT with a GPA of 4.8 (out of 5.0) in mathematics. I had two non-As, both of which were non-math classes.
That doesn’t imply that I have good study methods, but anyway, here’s how I studied at MIT. My main study method as an undergraduate, for math classes, was knowing a sizable chunk of the material in advance.
This isn’t a method that will work for everybody. I did a lot of mathematics outside of the classroom both in high school and at MIT, and I often saw a substantial portion of the material in a given class before I took it. I can’t emphasize enough how much easier this makes a class, and not just for the reasons you might expect: one of the most valuable things you get out of knowing a lot of the material already is just not being intimidated by it. (And you can get this benefit even if you’ve only seen some of the material before and possibly forgotten some of it too.) You’re much more relaxed, and that makes it easier to process the part of the material that you don’t know.
What that translates to in terms of practical advice is this:
- cultivate a sense of curiosity,
- don’t restrict your learning to the classroom,
- only take classes that actually seem really interesting to you, and
- try to learn something related to those classes the semester before.
None of this is advice for studying for a class you’re taking now, but it’s advice for reducing the extent to which you will need to study for classes you’ll take in the future.
– Qiaochu Yuan
Is it safe to log in through well known sites such as Facebook and Google? Think again, for Wang Jing, a PhD student in mathematics at the Nanyang Technological University in Singapore, has detected critical security vulnerabilities in the OAuth, OpenID security protocols. (Source: http://phys.org/news/2014-05-math-student-oauth-openid-vulnerability.html) [Second article in the list below]
Forward this information to your friends via the Tweet button below to warn them of the potential danger!
| Unique Math Learning Center Opens in Lake Forest: Local After-School Program to Provide … Chicago Tribune Mathnasium – The Math Learning Center opened its doors in Lake Forest in March to students looking for math help and math enrichment. The new … |
| Math student detects OAuth, OpenID security vulnerability Phys.Org (Phys.org) —To get right to the point, a doctoral candidate in math has discovered two holes in OAuth and OpenID that could leak data and redirect … |
| A math lesson for city: Teachers’ contract likely to cost billions SILive.com Mayor Bill de Blasio, who visited Staten Island Wednesday evening to speak at an SIEDC cocktail reception at the Hilton Garden Inn, has cleared his … |
| Math error halts Bank of America’s stock buy back and dividend increase UPI.com WILMINGTON, Del., April 28 (UPI) — Bank of America has had to halt its proposed stock buy back and dividend increase because of a math error in its … |
| Philadelphia girl makes math a game – and excels Philly.com Josephine Nyugen, a sixth-grader at St. Cecelia, right, with her father, Joseph, left, plays the math game ‘Into the Vortex’ on the First in Math website. |
| Math for public works borrowing bill proves tough St. Cloud Times Lawmakers from the Minnesota House Capital Investment Committee look around the prison yard near the loading dock inside the Minnesota … |
| Houghton Mifflin Harcourt takes Go Math! Academy into the home market Boston Globe Houghton Mifflin Harcourt, a Boston-based education company, developed the program for students in kindergarten to sixth grade to learn basic math … |
| Steve Ballmer’s math on Apple innovation doesn’t add up ZDNet His math of Apple innovation appears lacking to this longtime Mac user. Let me add a few more of his “tricks” to the list: The Apple II platform. Ballmer … |
| Math class helps special needs student try to win a wheelchair van KOB.com There’s a lot more going on than just addition and subtraction in Mr. Green’s math class. “We just want to help out this family,” Said Cody Green. |
| Budget math takes a U-turn: Christie blames federal tax law that brought windfall last year NorthJersey.com The same federal tax policy that Governor Christie is now blaming for New Jersey’s $807 million budget shortfall helped save his budget last year … |
The young Russian doctor Sergei Arutyunyan was working with patients whose immune systems were rejecting transplanted kidneys.
The doctor has to decide whether to keep or remove it. If they kept the kidney, the patient could die, but if they remove it, the patient would need another long wait (or never) for another kidney.
The mathematician Edward Frankel helped him to analyze the collected data with ‘expert rules’ in a decision tree. (Note: this is like the Artificial Intelligence Rule-based Expert System, except no fuzzy math).
Love and Math by Edward Frenkel http://www.amazon.co.uk/dp/0465050743/ref=cm_sw_r_udp_awd_53swtb16779PY
| The Straits Times holds its first Education Forum on Sunday Straits Times The Straits Times’ first Education Forum on May 4, 2014, held at the Singapore Management University’s Mochtar Riady Auditorium. — ST PHOTO: … |
| All 300 places at The Straits Times’ first education forum this Sunday taken up Straits Times Mr David Hoe, an undergraduate at the National University of Singapore (NUS), is one of the speakers at the inaugural The Straits Times Education … |
| Many turn up at E Plus International Education fair The Hindu The aspirants evinced keen interest in countries like Holland, Singapore, New … Official boards of all the countries presented seminars on education … |
| Tuition and divorce The Independent Singapore News In September 2013, The Independent Singapore reported on Senior Minister of State for Education Ms Indranee Rajah’s observation on the perceived … |
| NS committee may propose changes to IPPT management TODAYonline SINGAPORE — Suggestions to improve the management of the Individual … Veterans’ League, which was founded to promote National Education. |
| Should India Embrace Socialism, Singapore Style? Businessinsider India This is because the Singapore government only borrows to develop a … What offers a ray of hope to Indian educators is that Singapore’s education … |
| How does one of the top-performing countries in the world think about technology? The Hechinger Report SINGAPORE—Forty students in bright yellow shirts hunched over their … Investments in education technology have been a key part of Singapore’s … |
| Why Indonesian education is in crisis Jakarta Post Does anyone seriously believe “education” in Indonesia is on par with the west, or even Asian countries like Japan, Korea or Singapore? Ask the … |
| Are you getting a little crazy in your classroom? T.H.E. Journal We have asked Dr. Zachary Walker, an assistant professor at the National Institute of Education, Singapore, an American who is traveling the world … |
| GEMS Education eyes expansion in the region Business Times (subscription) GEMS Education, the world’s largest operator of private schools, aims to … from kindergarten to pre-university, will open in Singapore later this year. |
“…There’s a long history of high caliber mathematicians finding their experiences with school mathematics alienating or irrelevant. “
Read here:
http://lesswrong.com/r/discussion/lw/2uz/fields_medalists_on_school_mathematics/
In Récoltes et Semailles Fields Medalist Alexander Grothendieck describes an experience of the type that Alain Connes mentions:
I can still recall the first “mathematics essay” (math test, or Composition Mathématique) , and that the teacher gave it a bad mark. It was to be a proof of “three cases in which triangles were congruent.” My proof wasn’t the official one in the textbook he followed religiously. All the same, I already knew that my proof was neither more nor less convincing than the one in the book, and that it was in accord with the traditional spirit of “gliding this figure over that one.” It was self-evident that this man was unable or unwilling to think for himself in judging the worth of a train of…
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This professor criticized the lack of rigor in today’s math education, in particular, there exists universally a prevalent ‘ambiguous’ gap between high school and undergraduate math education.
I admire his great insight which is obvious to those postwar baby boomer generation.
I remember I was the last Singapore batch or so (early 70s) taking the full Euclidean Geometry course at 15 years old, and strangely in that year of Secondary 3 Math (equivalent to 3ème in Baccalaureate) my (Chinese) school had 2 separate math teacher for Geometry and Elementary/Additional (E./A.) Math.
Guess what ? the Geometry teacher was an Art teacher. It turned out it was a blessing in disguise, as my class of average Math students who hated E./A. Maths all scored 90% distinctions in Geometry. We did not treat Geometry like the other boring maths. The lady Art teacher started on the first day from Euclid’s 5 axioms…
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Source: http://arxiv.org/abs/1402.5952
Recently, I saw on Arxiv (an online Math journal) that a professor from South-China Normal University, Mingchun Xu, has proved the notoriously difficult Riemann Hypothesis.
Quote: “By using a theorem of Hurwitz for the analytic functions and a theorem due to T.J.Stieltjes and I. Schur, the Riemann Hypothesis has been proved considering the alternating Riemann zeta function. “
His paper can be downloaded here: http://arxiv.org/pdf/1402.5952v2
More verification is needed to check if it is indeed a proof.
What is the Riemann Hypothesis about? Watch this Youtube Video:
Featured book:
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.
Rated: 4.5 stars on Amazon
3.14159
山顶一寺一壶酒
One fine day when we reach above 80 years old, if the doctor accuses us of having dementia, then prove the doctor wrong by shocking him with 100-digit Pi memory 🙂
With Chinese single-syllable sound for numbers, better still if can sing it as a song, memorizing 100-digit pi is easy!
22/7 is not an exact value for Pi, but it is a pretty good approximation. 22/7=3.142857143… has just a percentage error of 0.04% compared to the actual value of Pi!
Percentage error is calculated by:
355/113 is an even better approximation for Pi. 355/113=3.14159292… has merely a percentage error of 0.000008%! This is incredibly accurate for a “relatively” simple fraction like 355/113. 355/113 has a cool Chinese name called “Milü” 密率, given by the ancient Chinese Mathematician astronomer Zǔ Chōngzhī (祖沖之) who discovered it.
Using the simple and straightforward 3.14 (0.05% error) may be sufficient for everyday purposes. 🙂
or 2 arcsin(1) (Radian Mode)This relies on the fact that 
We can let n=180 for convenience, and get 
Featured Book:
Pi: A Biography of the World’s Most Mysterious Number
We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren’t told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird.
Best way to study abstract math is to use concrete examples, visualizable 2- or 3- dimensional mathematical ‘objects’.
Groups:
(Do not need to search too far…) Best example is the Integer Group (Z) with + operation, denoted as {Z, +}. (Note: Easy to verify it satisfies the group 4 properties: CAN I“.
It has infinite elements (infinite group)
It is a Discrete Group, because it jumps from one integer to another (1,2,3…, in digital sense).
The group of rotation of a round table, which consists of all points on a circle, is an infinite group. We can change the angle of rotation continously between 0 and 360 degrees, rotating around a geometrical shape – a circle. Such shapes are called Manifolds (流形).
All points of a manifold forms a Lie group.
Example: The group of rotations of a sphere around a central…
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Durian & Group
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Interested to know how Math can be used in Real life? Check out the colorful posters in the post below!
Hi guys here the comes posters of Application of Math in real life .
Source: http://mathigon.org/
If you are wondering which tuition agency is the best, look no further. The best tuition agency in Singapore is without a doubt Startutor.
Startutor is highly recommended by our tutor Mr Wu, and he himself is listed there.
For other subjects besides Mathematics, request for a tutor at Startutor! Startutor is Singapore’s most popular online agency, providing tutors to your home. There are no extra costs for making a request. Tutors’ certificates are carefully vetted by Startutor. (Website: http://startutor.sg/request,wwcsmt)
Startutor is suitable for English Tuition, Social Studies Tuition, Geography Tuition, Physics Tuition, Chemistry Tuition, Biology Tuition, Chinese Tuition, Economics Tuition, GP Tuition, Piano Lessons and more!
(Please use the link above directly, thanks!)
How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up.
EDIT: Could anyone suggest books for someone with a math education that just barely touches on high-school Algebra (got into parabolas, rationalizing, some graphing and functions). This is what I am currently doing: attending high school as a Junior.
Read the answers given by experts at Math Stackexchange!
Some gems of wisdom:
Researchers have shown it takes about ten years to develop expertise in any of a wide variety of areas, including chess playing, music composition, telegraph operation, painting, piano playing, swimming, tennis, and research in neuropsychology and topology.
The key is deliberative practice: not just doing it again and again, but challenging yourself with a task that is just beyond your current ability, trying it, analyzing your performance while and after doing it, and correcting any mistakes. Then repeat. And repeat again.
All the best in your math studies!
Featured book:
Men of Mathematics (Touchstone Book)
Here is the classic, much-read introduction to the craft and history of mathematics by E.T. Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton’s calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians — an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work’s clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.
Prove: Any line L will cut a circle at most 2 points:
Factorize C(x,y) : (x+iy) (x-iy) = 1 in the complex plane.
So C = {L1} U {L2}
where L1 and L2 are two lines
Just to reblog this earlier post on Recommended Singapore Math Books. Ideal for parents living outside Singapore who wish to teach their child the Singapore Math curriculum!
We have compiled a list of Top 5 Best selling and Top rated Singapore Math Books on Amazon. This list is more targeted towards parents and students living outside Singapore, like in the United States. Students in Singapore are already breathing and living Singapore Math!
Hope this list will help you in finding the Best Singapore Math Books for your child. The reviews are from actual customers on Amazon.
1)
This math practice book contains wonderful teaching strategies from the Singapore math program including number bonds and counting on. This would be a good book for homeschooling. We use it as an enrichment tool when we have a little extra time during vacations or on weekends.
I would recommend it to parents who would like to teach their struggling kids math, because it tells you how to teach these concepts.
2)
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Most students will encounter the Maclaurin Series (also known as the Taylor’s Series centered at zero) when they are studying JC H2 or College Maths. The formula looks pretty intimidating at the start:
How on earth does one come up with that formula?
However, it turns out it is not that hard to prove the Maclaurin Series informally, or at least to derive the above formula. (The hard part is related to rigorous proof of convergence, etc.)
The idea is to approximate a function by a power series (a kind of infinite polynomial) and then find out what are the coefficients.
So, we assume we can write the function as such:
We also assume that the above equation holds for all 
Then, letting 
Next, we differentiate the equation 
Letting 
Now, differentiating the above equation one more time gives us:
Letting 
Keep on differentiating, and we will see that 
This is how we get the Maclaurin Series: 🙂
Excellent Video by Khan Academy
Interested to learn more about Calculus? After reading this thick book about Calculus, you will probably know more Calculus than Isaac Newton himself!
Are you looking for a list of A Maths (O Level Additional Maths) Formulae that is not found in the formula list?
Check it out at https://mathtuition88.com/math-notes-worksheets-sale/
The PDF file above contains A Maths Formulae on Algebra, Geometry & Trigonometry, and Calculus (Differentiation and Integration).
We also conduct A Maths Tuition class at Bishan.
If you find this Formula List helpful, feel free to Tweet or share this page on Facebook using the buttons below. 🙂
Examples:
Dim (Circle) in 2-dim plane = 1
As we approach near the neighborhood of the tangential point on the circle, the curvature of the circle disappears, there is no difference between the circle and the tangent line (dim = 1).
Hence, Dim (Circle) = 1
A point on a circle is determined by one independent variable only, which is the polar angle.
Note:
The dimension of the ambient space (2-dim plane) is not relevant to the dimension of the circle itself.
Dim (Sphere) in 3-dim Space = 2
The 2 variables (longitude, latitude) determine a position on the globe. Therefore dimension of a sphere is 2.
Interesting note:
Four Dimension Space (x, y, z, t): what we get if the 4th dimension time is fixed (frozen in time) ? We get a…
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| Saudis learning the Singapore way of teaching Straits Times Since last October, the National Institute of Education (NIE) has taken leadership trainers from the kingdom under its wing, training them in curriculum … |
| All 300 places at The Straits Times’ first education forum this Sunday taken up Straits Times Mr David Hoe, an undergraduate at the National University of Singapore (NUS), is one of the speakers at the inaugural The Straits Times Education … |
| Singapore Plows Ahead of US With Tech in Schools NBCNews.com In the late 1990s, the Singapore Ministry of Education unveiled its master plan for technology. The first phase was spent building up infrastructure and … |
| Govt mulls more recognition for NSmen in housing, health, education Channel News Asia SINGAPORE: More recognition could be given to National Servicemen (NSmen) in areas such as housing, healthcare and education. Defence … |
| Singapore to beef up nuclear technology expertise Channel News Asia Singapore is beefing up its nuclear technology expertise with a newly-announced programme. The 10-year Nuclear Safety Research and Education … |
| Many turn up at E Plus International Education fair The Hindu The aspirants evinced keen interest in countries like Holland, Singapore, New … Official boards of all the countries presented seminars on education … |
| AWARE’s pushback on more benefits for NSmen ignites debate TODAYonline SINGAPORE — The Government’s plan to enhance housing, healthcare and education benefits for operationally ready national servicemen has … |
This is an interesting introduction to some extremely advanced Math: Ricci Flow & Poincare Conjecture!
Ricci Flow was used to finally crack the Poincaré Conjecture. It was devised by Richard Hamilton but famously employed by Grigori Perelman in his acclaimed proof. It is named after mathematician Gregorio Ricci-Curbastro.
In this video it is discussed by James Isenberg from the University of Oregon (filmed here at MSRI).
The famed Poincaré Conjecture – the only Millennium Problem cracked thus far.
Read the below news for the answer and more!
| Math wiz monkeys providing researchers with insights into human brain activity Fox News Monkeys trained to solve math problems are providing researchers with new insights into understanding a human learning disability in which children … |
| Math and Science Pay, But High Schoolers Care Less Wall Street Journal (blog) Math and science are the peas and carrots of the jobs market: great for a career future, but resolutely unpopular with the young. Even amid a relatively … |
| Math wrath in Pincher Creek? Pincher Creek Echo Protesters gather during a rally to support a petition calling for math curriculum reform at the Alberta Legislature Building in Edmonton, Alta., … |
| Monkey Math and Other Number-Crunching Critters Discovery News Rhesus monkeys are able to perform math at an advanced level, reports a study this week from Harvard Medical Medical school. The monkeys were … |
| Math department wins national award for exemplary program The Williams record According to Susan Loepp, professor of mathematics, the College’s department is unique in several regards. “Everyone likes math even if they don’t … |
| From math failure to savant: How a mugging made a numbers whiz CTV News Padgett describes the brutal bar attack and his subsequent transformation into a math savant in his new book, Struck by Genius: How a Brain Injury … |
Here is a compilation of the Formulas needed in GCSE O Levels E Maths Exam.
Includes Formulae on Algebra and Numbers, Geometry and Measurement, Statistics and more!
Check it out at https://mathtuition88.com/math-notes-worksheets-sale/
Students in my Maths Tuition class will be taught how to memorize the formulae with understanding, and how to apply them correctly!
Keep calm, and all the best for your mid-year exams.
Fibonacci Numbers, named after Leonardo Fibonacci, is a sequence of numbers:
with a recurrence relation 
Fibonacci Numbers are linked to the mysterious Golden Ratio,
In fact, the ratio of successive Fibonacci numbers converges to the Golden Ratio! The first person to observe this is Johannes Kepler.
How do we prove it?
Recall the recurrence relation:
Dividing throughout by 
(We will first assume 
Taking limits, we get 
Denoting 
Multiplying by
This is a quadratic equation, solving using the quadratic equation, we get:
Since 
For a complete proof, actually we will need to prove that 
Interested readers can refer to the excellent website at: http://pages.pacificcoast.net/~cazelais/222/fib-limit.pdf
for more details.
Interesting video on Fibonacci numbers!
Fibonacci numbers and the Golden Ratio can also be used for trading stocks.
Shimura and Tanyama are two Japanese mathematicians first put up the conjecture in 1955, later the French mathematician André Weil re-discovered it in 1967.
The British Andrew Wiles proved the conjecture and used this theorem to prove the 380-year-old Fermat’s Last Theorem (FLT) in 1994.
It is concerning the study of these strange curves called Elliptic Curve with 2 variables cubic equation:
Example:
$latex boxed {y^{2} + y = x^{3} – x^{2}
} &fg=aa0000&s=3 $ — (I)
There are many solutions in integers N, real R or complex C numbers, but solutions in modulo N hide the most beautiful gem in Mathematics.
For modulo 5, the above equation has 4 solutions:
(x, y) = (0, 0)
(x, y) = (0, 4)
(x, y) = (1, 0)
(x, y) = (1, 4)
Note: the last solution when y=4,
Left side = 16 + 4 = 20 = 4×5 = 0…
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Do not be discouraged if you find E Maths or A Maths difficult. The main reason why you are finding it to be difficult is that it is new. You have not gotten enough exposure to the type of questions asked. It is like learning to ride a bicycle, at the start it is difficult and you may even fall down. But after you have mastered riding the bicycle, you will be able to ride as fast as you wish. You need to get over the initial difficulty of learning in order to master the art of riding the bicycle.
At our Group Tuition at Bishan, we constantly practice actual exam questions, be it on Trigonometry, Differentiation or Integration (A Maths), or Vectors, Matrices and Probability (E Maths). We learn different methods to check and do the questions. You will find out, at last, that once you master the art of solving O Level questions, all the O Level questions are just repackaging the same questions in different forms. Once you know how to do one question, you will know how to do all similar questions. Expanding your repertoire of questions you know will enable you to get that coveted “A”. Constant practice, as opposed to cramming one month before the O Levels, is absolutely necessary to avoid panic and to consolidate our Mathematical memory.
Some Math formulas like the quotient rule, 
In the end, you may even find that E Maths or A Maths is easy!
(Source: http://www.indianchild.com/inspiring_stories.htm)
THE OBSTACLE IN OUR PATH
In ancient times, a king had a boulder placed on a roadway. Then he hid himself and watched to see if anyone would remove the huge rock. Some of the king’s wealthiest merchants and courtiers came by and simply walked around it.
Many loudly blamed the king for not keeping the roads clear, but none did anything about getting the big stone out of the way. Then a peasant came along carrying a load of vegetables. On approaching the boulder, the peasant laid down his burden and tried to move the stone to the side of the road. After much pushing and straining, he finally succeeded. As the peasant picked up his load of vegetables, he noticed a purse lying in the road where the boulder had been. The purse contained many gold coins and a note from the king indicating that the gold was for the person who removed the boulder from the roadway. The peasant learned what many others never understand.
Every obstacle presents an opportunity to improve one’s condition.
石头的故事
从前有一个国王，他故意派人搬来一块大石头放在道路中间。然后这个国王躲在旁边静静地观察，想知道是否会有人过来把这块大石头搬走。有几个富有的商人经过这块石头，只是直接绕过它。之后又来了几个人，他们只是埋怨国王居然没有找人来清理道路，然后仍然是绕过这块巨石走掉了。又过了一会，一个农夫经过这里，他身上背着沉甸甸的蔬菜。走到巨石的前面，把身上背的蔬菜放下，然后试着去把这块巨大的石头移到道路的旁边。农夫竭尽全力去推那块巨石，终于成功得把石头推到道路的一侧。农夫背起蔬菜准备继续赶路，却发现石头原来所在的地方下面有一个袋子。农夫好奇得打开袋子，里面有许多金币还有一个纸条。纸条是国王留下的，原来金币是用来奖励移走石头的人。
这个小故事讲述了一个简单的道理：困境也有可能是机会。遇到困难的时候，有些人会像商人那样，直接选择放弃。有些人会像那几个埋怨者，只会抱怨却不想着付出行动来改变现状。很少人会像故事中的农夫那样选择迎难而上。然而，最终收获最多的往往就是这部分迎难而上的人。
平常生活中和工作中也是这样，遇到问题，首先要不抛弃不放弃，积极寻求解决方法。无休止的抱怨只会白白错失机会，抱怨多了，好运气也会绕道而行。在困境中寻找机会方法，在挫折中吸取经验教训，那么就会很容易走出困境了，说不定还会有意外的收获哦！
This is the 73rd Edition of the Math Teachers at Play (MTaP) blog carnival!
Some interesting facts about 73 from Wikipedia!:
Math Teachers at Play is a traveling blog carnival. It moves around from month to month but its home base is http://letsplaymath.net/mtap/. From there you can visit the archives, submit your blog post for inclusion in a future edition, and volunteer to host the site. You can also check out the Carnival of Mathematics. Thanks for visiting!
Subscribe to our free newsletter, for updates on Math, Education and other General Knowledge topics!
This is a featured post by Epigami (a tuition agency).
Source: http://www.epigami.sg/blog/dont-just-learn-understand/
In the last decade, the Singapore educational system has become a global leader in the education field, helping exemplary pupils to be accepted in the worlds best universities. But with the increasing competitiveness of those top tier universities, students are faced with mounting pressure to excel in every aspect which might have an impact on their exams. This has led to the mass implementation of ‘rote learning’ in Asia, where students focus more on memorising knowledge than the full comprehension of the concepts behind it.
From the earliest days of schooling, rote learning is an essential tool to efficiently memorize educational fundamentals. It is a knowledge acquisition process based on repetition. Simply put, make a child say the alphabet every day for 6 months, and they will remember it ‘forever’. This is of course the most obvious way of learning and no other method could be better suited for the developing mind of an infant, as the concepts taught are simple in nature, and do not require a broader knowledge base.
Though, as one progresses through the ranks and gets shifted through the numerous streams put into place by the MOE, new knowledge starts to build upon old concepts, some aspects converging, others diverging, and all of if defining a complex web of knowledge which requires the student to delve into a deeper state understanding if he is to find any further use to it.
How many of us wonder at one point or another: Why am I learning this?
Read more at: http://www.epigami.sg/blog/dont-just-learn-understand/
![In the last decade, the Singapore educational system has become a global leader in the education field...[read more]](https://i0.wp.com/www.epigami.sg/blog/wp-content/uploads/2014/04/rote-learning-820x400.jpg "In the last decade, the Singapore educational system has become a global leader in the education field...[read more]")
Email Correspondence with Epigami Team:
Dear Mr Wu,
Epigami has recently written an article on meaningful learning as compared to rote learning. Once again, we believe that such an article would be useful and beneficial for your students in Singapore, especially in the subject of Mathematics. You can read more about our article at: http://www.epigami.sg/blog/dont-just-learn-understand/ and we hope that you can share it with your readers on your blog.
Thank you and have a great week ahead! 😀
Best regards,
Sandra @ the Epigami Team
Math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)
Dr James Grime on the Pisano Period – a seemingly strange property of the Fibonacci Sequence.
Fibonacci Fun: Fascinating Activities With Intriguing Numbers
From “Raising Rabbits” to “Prickly Pinecones”, 24 easy-to-use, reproducible activities and projects introduce students to Fibonacci numbers and the golden ratio. Grades 4-8
| MOE officers recognised for providing holistic education experience Channel News Asia SINGAPORE: A total of 7,103 Ministry of Education (MOE) officers were promoted this year, with some recognised for their contributions at a promotion … |
| Parents should start saving up early for kids’ education Channel News Asia Nearly all Singaporean parents want their children to get a university education — that is what a recent survey “The Value of Education: Springboard … |
| Education in Singapore: When Number 1 is not enough Asian Correspondent Singapore students pass PISA tests with flying colors, but critics say ‘so what?’, writes Zach Isaiah Chia. “Who says Singaporean’s are rote learners? |
| Singapore to train 3000 Saudi school principals Arab News Singapore’s National Institute of Education (NIE) will train 3,000 Saudi school principals over the next few years, Singapore’s Ambassador Lawrence … |
| CET campuses in full operation by second half of 2014 Channel News Asia SINGAPORE: The two national Continuing Education and Training (CET) campuses will be fully operational by the second half of this year, where they … |
| New school-to-work transition programme to help special needs students Channel News Asia This was announced by Education Minister Heng Swee Keat at the official … Students attend a class at a special education school in Singapore. |
| Lee Kuan Yew Fund for Bilingualism supports 5 more projects Channel News Asia The Ministry of Education (MOE) said the fund is sponsoring another five … Brainchild Pictures, YMCA of Singapore, and Saintly Education Centre. |
| Boy who exposed- and fought- the education monster The Independent Singapore News He is Singapore’s role model. He is the boy who fought his way from Normal (Technical) Stream to a place at the National University of Singapore … |
| GBSN & INSEAD organize Edu Technology Summit in Singapore MBAUniverse.com Eminent leaders in business education and industry participated at INSEAD’s Asia campus in Singapore on April 6, 2014 to participate in a summit on … |
| A lesson learnt from Singapore The Australian (blog) Education authorities should be encouraged that the national executive of the Australian Primary Principals Association was impressed after a briefing … |
Just to share a website on Tuition Agency and Past Year Papers.
Website: http://www.pastyearpaper.com
Past Year Paper is an established Singapore Home Tuition Agency that brings to you quality private tutors and free exam papers for primary, secondary school to junior college level students.
Excellent Fun post about Quadrilaterals
Check out our Free Test Papers site at: https://mathtuition88.com/free-exam-papers/
http://www.ted.com In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He’ll tell you.
TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world’s leading thinkers and doers are invited to give the talk of their lives in 18 minutes — including speakers such as Jill Bolte Taylor, Sir Ken Robinson, Hans Rosling, Al Gore and Arthur Benjamin. TED stands for Technology, Entertainment, and Design, and TEDTalks cover these topics as well as science, business, politics and the arts. Watch the Top 10 TEDTalks on TED.com, at
http://www.ted.com/index.php/talks/top10
Interested to learn more tricks? Check out these two books:
Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks
Mathemagics: How to Look Like a Genius Without Really Trying
These simple math secrets and tricks will forever change how you look at the world of numbers.
Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.
Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
