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Tag Archives: Math
Sum of two metrics is a metric
It is quite straightforward to prove or verify that the sum of two metrics (distance functions) is still a metric. Suppose and are metrics. Define . Positivedefinite . . Symmetry . Triangle Inequality Note that it follows by induction that … Continue reading
IP Math Syllabus (Integrated Programme Mathematics)
Students and parents new to IP (Integrated Programme) may be confused on what is the Mathematics syllabus of IP Math. Indeed, it is very confusing as every school has its own syllabus. In general, the syllabus as a whole is … Continue reading
Sellfy free account to be discontinued
Just received some news from Sellfy: Hi there, We have important news about your Sellfy account and your store https://sellfy.com/mathtuition88 You have been on our transaction fee only plan (Legacy plan) since you signed up for Sellfy. We are truly thankful for being with us … Continue reading
Formula for 3×3 Matrix Inverse
Let Then, This method is about the same speed as the GaussianElimination method. However, if you have already calculated det(A), using the formula may be slightly faster. The formula provides an insight on why A is singular (not invertible) if … Continue reading
Superposition Principle of Linear Algebra
Superposition Principle If is a solution to , and is a solution to , then is a solution to . Proof: Properties of Matrix Transpose 1) 2) 3) 4)
RIP Sir Michael Atiyah
Rest in peace, Sir Michael Atiyah. Many scientists have called Atiyah the best mathematician in Britain since Isaac Newton. Read also our previous posts: Sir Michael Atiyah to reveal his awesome proof of the Riemann Hypothesis Interview of Michael Atiyah … Continue reading
Chinese High School Student “Proves” Goldbach Conjecture
URL: https://bbs.hupu.com/24931041.html According to popular Chinese Social Media, a Chinese teenager from high school has purportedly proven the difficult Goldbach Conjecture, which is that every even integer greater than two is the sum of two prime numbers. Update: He has recently … Continue reading
Preschool Math Tuition Books and Toys
There seems to be an increasing demand for kindergarten Maths tuition for children of ages 26. (I have received many such requests lately.) Many parents are worried that their child may lose at the “starting line” which is Primary 1, … Continue reading
The Hardest H3 Math Question (Combinatorics)
I think this may be one of the hardest H3 Math Questions in history. It is taken from RI H3 Prelim 2018. It seems that even in top schools like RI, there are less than 50 people taking H3 Maths … Continue reading
Varignon’s Theorem (Surprising Geometry Theorem)
I first learnt it from Quora: “Take any quadrilateral. It doesn’t have to be any special kind of a quadrilateral. Then connect the midpoints of its sides. Surprisingly, you will always get a parallelogram!” Quite a nice result. Some googling … Continue reading
RI vs HCI vs NUSH
Many excellent P6 students will be spoilt for choice at this stage, as they have been accepted by multiple schools under the DSA. Here are some views on RI versus HCI versus NUS High, which are the top 3 choices … Continue reading
Sir Michael Atiyah to reveal his awesome proof of the Riemann Hypothesis
Source: https://twitter.com/HLForum/status/1042670700652318720 According to the official twitter account of the Heidelberg Laureate Forum, Sir Michael Atiyah will prove the Riemann Hypothesis during the talk on Monday Sept. 25. According to him, it is a “simple” proof, based on previous work by von Neumann, … Continue reading
Amazon Founder Jeff Bezos Originally Wanted to be a Theoretical Physicist
The world’s richest man is currently Jeff Bezos, founder of Amazon. Few people know that he was an undergraduate at Princeton with the goal of becoming a theoretical physicist! What made him change his mind? Watch the video below. Summary: … Continue reading
Morse Inequalities
Let be a CW complex (with a fixed CW decomposition) with cells of dimension . Let be a field and let . (i) (The Weak Morse Inequalities) For each , (ii) , where denotes the Euler characteristic of . Proof: … Continue reading
Challenging P6 Math Question (Cycling)
One afternoon, 5 friends rented 3 bicycles from 5.00 p.m. to 6.30 p.m. and took turns to ride on them. At any time, 3 of them cycled while the other 2 friends rested. If each of them had the same … Continue reading
Basics of Partial Differential Equations Summary
PDE: Separation of Variables 1) Let . 2) Note that , , , , . 3) Rearrange the equation such that LHS is a function of only, RHS is a function of only. 4) Thus, LHS=RHS=some constant . 5) Solve … Continue reading
Linear First Order ODE, Bernoulli Equations and Applications
Linear First Order ODE DE of the form: . Integrating factor: . (Remember to have a constant when integrating the numerator .) Integration by parts Acronym: LIATE (Log, Inverse Trig., Algebraic, Trig., Exponential), where L is the best choice for … Continue reading
Happy Pi Day!
Happy Pi Day to all readers of Mathtuition88.com! Check out our previous posts on Pi: Did you know, Pi day is also Einstein’s Birthday? How to get Pi on Calculator – Without pressing the Pi Button The Mystery of e^PiPi … Continue reading
Stephen Hawking dies aged 76
RIP Stephen Hawking. Source: http://www.bbc.com/news/uk43396008 The British physicist was known for his work with black holes and relativity, and wrote several popular science books including A Brief History of Time. “We are deeply saddened that our beloved father passed away today,” … Continue reading
The magic (and math) of skating on thin ice without falling in
Very interesting video. Do try to imagine the sound of the ice and check out the video to confirm your guess. Very surprising sound! It is a pity that not many countries have such ice to skate in. The main … Continue reading
No homework, fullday school curriculum to help level playing field (Proposal, not implemented yet)
Fullday school is quite a drastic measure to combat tuition. Also, unless fullday means 7am to 7pm, it is unlikely to be different from the status quo. Any parent with children in secondary school or JC is aware that school … Continue reading
Higher paying job than Doctor / Lawyer
We encourage top students to look beyond the traditional Singaporean jobs of Doctor / Lawyer as there are new emerging jobs that can equal or even surpass the pay of Doctor/Lawyer. At the end of the day, do also consider … Continue reading
GEP Questions
Recently one of our GEP Questions, the Fish Tank Question, was featured in the popular news site Mustsharenews. Do also check out our other equally tough GEP questions: The Worker Question Chicken and Rabbit GEP Question Gauss Sum Question GEP … Continue reading
The results of the 2017 SingaporeCambridge General Certificate of Education Advanced Level (GCE ALevel) examination will be released on Friday, 23 February 2018.
Good luck to all collecting their A Level results today! Check out our post on BMAT Book Recommendations for NTU Medicine, and also Alternate Admission Route to NUS Computing. 1. The results of the 2017 SingaporeCambridge General Certificate of Education Advanced Level … Continue reading
Heroic math teacher saved her students from Florida shooting
Heroic math teacher saved her students from Florida shooting by covering classroom door’s window, ordering kids to the floor and refusing to let anyone in… even the SWAT team. Read more: http://www.dailymail.co.uk/news/article5399143/HeroicteachersavedstudentsFloridashooting.html#ixzz57i0Hcvi9 Heroic math teacher saved her students from Florida … Continue reading
Tricky Riddle involving a horse
Can YOU figure it out? Simple math riddle about a horse leaves social media users totally stumped Read more: http://www.dailymail.co.uk/femail/article5400399/Facebookusersstumpedsimplemathriddle.html#ixzz57ZL1KUHY Follow us: @MailOnline on Twitter  DailyMail on Facebook
Linear System of Differential Equations, Solutions, Phase Portrait Sketching
Solutions of Homogeneous Linear System of DE where and are eigenvalue and eigenvector for respectively. Superposition Principle If and are two solutions to a homogeneous SDE , then is also a solution for any scalars , . Euler’s formula General … Continue reading
Characteristic Polynomial, Eigenvalues, Eigenvectors
Characteristic Polynomial, Eigenspace The solution space of is called the eigenspace of associated with the eigenvalue . The eigenspace is denoted by . Sum/Product of Eigenvalues – The sum of all eigenvalues of (including repeated eigenvalues) is the same as … Continue reading
Finding Least Squares Solution Review and Others
Rotation Matrix The rotation matrix rotates points in the plane counterclockwise through an angle about the origin. For example rotating the vector 45 degrees counterclockwise gives us: Finding Least Squares Solution Given (inconsistent system), solve instead to get a least … Continue reading
5 Ways To Make Math More Fun And Meaningful For Kids
5 Ways To Make Math More Fun And Meaningful For Kids Fun and meaningful – these are two words that children rarely use to describe math. There are several reasons why many kids dislike math, but according to kids and … Continue reading
Dot Product and Span Summary
Dot Product – – Span Subspaces is a subspace of if 1) for some vectors . 2) satisfies the closure properties: (i) for all , we must have . (ii) for all and , we must have . 3) is … Continue reading
Gaussian Elimination Summary
Row echelon form (REF) For each nonzero row, the leading entry is to the right of the leading entry of the row above. E.g. Note that the leading entry 9 of the second row is to the right of the … Continue reading
Happy New Year
Happy New Year to all readers of Mathtuition88.com! Thanks to your support, Mathtuition88.com has reached 885,060 views! We will continue posting Math and Education posts so please continue to visit the website for updates.
Highly Motivational Math Video (in Chinese)
This is actually one of the best motivational videos on Math I have seen. Unfortunately there is no English translation. It covers how useful Math is, and also some history of Math in ancient China. (It is rarely known, but … Continue reading
Amos Yee Math Talent
Amos Yee (“famous” for posting controversial videos) actually has good talent and aptitude in Mathematics. His mother is a Math secondary teacher with decades of experience. Many people know him for his infamous videos and his “American English” pronunciation, but … Continue reading
Math Books for Christmas
Wishing all readers a joyous Christmas ahead! Here are some ideas for a mathematical Christmas gift for your loved ones who are math lovers: 1) This Christmasthemed Math book is the perfect gift for your child. According to Amazon, it … Continue reading
America’s Lost Einsteins
Source: https://www.theatlantic.com/business/archive/2017/12/innovationincomechetty/547202/ Millions of children from poor families who excel in math and science rarely live up to their potential—and that hurts everyone. Consider two American children, one rich and one poor, both brilliant. The rich one is much more likely … Continue reading
From Medical Doctor to Math Professor
Just read about this rather amazing biography: https://today.duke.edu/2017/10/hautiengwuvitalsigns. From a medical doctor, Hautieng Wu pursued a Ph.D. in math, and is now a math professor at Duke. Quite an interesting transition, that is quite rare, possibly less than 100 such cases … Continue reading
Very nice introduction to Cohomology (8 min)
This is a very nice and concise 8 minute introduction to cohomology. Very clear and tells you the gist of cohomology.
Kids struggling in math? Try this “magic” method from Japan (VIDEO)
URL: Aleteia It’s an Asianstyle mathematics similar to Common Core that’s actually fun to do. Confession time: I’m terrible at math. I don’t just mean like “struggled with calculus” bad, I mean like “had to watch YouTube videos to relearn … Continue reading
US students aren’t bad at math—they’re just not motivated
It turns out that US students aren’t that bad at math, they just have no motivation to do the PISA test properly. (The PISA test is an external test that has no bearing on their school academic results.) Source: https://qz.com/1130505/usstudentsarentbadatmaththeyrejustnotmotivated/ It’s … Continue reading
Hokkaido University Photo Gallery and Trip Guide
These photos are from a trip to Hokkaido University in August 2017. Hokkaido University is just walking distance away from Sapporo station, and is worth spending an afternoon there. Admission is free. Even in the hottest summer, Hokkaido has cool … Continue reading
8 Facts About Infinity That Will Blow Your Mind
Nice article on infinity. Also little known is the fact that the symbol of infinity was introduced by clergyman and mathematician John Wallis, hundreds of years ago in 1655. Although not wellknown, John Wallis was a talented individual as can … Continue reading
Free Math Public Lecture at National Library
Interested students may want to attend. It is at the National Library, on 14th December 2017. The Liar Game: Truths & Proofs from Euclid to Turing Ng Kong Beng Public Lecture Series Mark Wildon, Royal Holloway, University of London, UK … Continue reading
Unionclosed sets conjecture
Just read about this conjecture: Unionclosed sets conjecture. The conjecture states that for any finite unionclosed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the … Continue reading
He who loves learning is better than he who knows how to learn (Confucius)
From Baidu Baike: 知之者不如好之者，好之者不如乐之者: 对于学习，了解怎么学习的人，不如喜爱学习的人；喜爱学习的人，又不如以学习为乐的人。比喻学习知识或本领，知道它的人不如爱好它的人接受得快，爱好它的人不如以此为乐的人接受得更快。 Translation: He who knows how to learn, is not as good as he who likes learning. He who likes learning, is not as good as he who loves learning. (Confucius) I guess this applies to … Continue reading
It’s mathematically impossible to beat aging, scientists say
According to Math, no one can live forever. So far, the only counterexample that I know of is Turritopsis dohrnii, also known as the “immortal jellyfish”. The article doesn’t seem to address this counterexample though. Source: Science Daily Aging is a … Continue reading
Leibniz was a universal genius, but why is Isaac Newton more known? Does it have to do with Newton being British and Leibniz being German?
Answer by Albert Heisenberg, Science Historian M.A. Brown University Leibniz’s formulation of differential and integral calculus was more refined, elegant, and ‘generalizable’ than Newton’s ‘fluxions.’ Leibniz, the natural genius that he was, became interested in mathematics much later in his life … Continue reading
Note on pdivisibility in Bockstein Spectral Sequence
If generates a copy of , then . Write , where , . Note that since , hence does not generate a copy of . The only way that is possible is when , i.e .
Terence Tao Numberphile
Among current mathematicians, many people regard Professor Tao as the world’s finest… Opinions on such things vary, of course. Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers. EXTRA FOOTAGE: https://youtu.be/48Hr3CT5Tpk (and more extras to … Continue reading