Tag Archives: Math

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

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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

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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^Pi-Pi … Continue reading

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Stephen Hawking dies aged 76

RIP Stephen Hawking. Source: http://www.bbc.com/news/uk-43396008 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

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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

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No homework, full-day school curriculum to help level playing field (Proposal, not implemented yet)

Full-day school is quite a drastic measure to combat tuition. Also, unless full-day 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

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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

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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

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The results of the 2017 Singapore-Cambridge General Certificate of Education Advanced Level (GCE A-Level) 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 Singapore-Cambridge General Certificate of Education Advanced Level … Continue reading

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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/article-5399143/Heroic-teacher-saved-students-Florida-shooting.html#ixzz57i0Hcvi9 Heroic math teacher saved her students from Florida … Continue reading

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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/article-5400399/Facebook-users-stumped-simple-math-riddle.html#ixzz57ZL1KUHY Follow us: @MailOnline on Twitter | DailyMail on Facebook

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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

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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

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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

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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

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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

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Gaussian Elimination Summary

Row echelon form (REF) For each non-zero 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

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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.

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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

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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

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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 Christmas-themed Math book is the perfect gift for your child. According to Amazon, it … Continue reading

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America’s Lost Einsteins

Source: https://www.theatlantic.com/business/archive/2017/12/innovation-income-chetty/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

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From Medical Doctor to Math Professor

Just read about this rather amazing biography: https://today.duke.edu/2017/10/hau-tieng-wu-vital-signs. From a medical doctor, Hau-tieng 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

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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.

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Kids struggling in math? Try this “magic” method from Japan (VIDEO)

URL: Aleteia It’s an Asian-style 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

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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/us-students-arent-bad-at-math-theyre-just-not-motivated/ It’s … Continue reading

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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

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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 well-known, John Wallis was a talented individual as can … Continue reading

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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

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Union-closed sets conjecture

Just read about this conjecture: Union-closed sets conjecture. The conjecture states that for any finite union-closed 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

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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

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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

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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

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Note on p-divisibility 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 .

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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

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“Actual” GEP Questions 2017 (from Forum)

Since the actual GEP papers are never released, the next best source is from those who have actually taken it and post on forums like Kiasuparents. Some Maths questions my girl remembers. “ In a fishing competition, five kids caught … Continue reading

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Why do people get so anxious about math? – Orly Rubinsten

View full lesson: http://ed.ted.com/lessons/why-do-peop… Have you ever sat down to take a math test and immediately felt your heart beat faster and your palms start to sweat? This is called math anxiety, and if it happens to you, you’re not … Continue reading

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Free Math Games For Everyone

Free Math Games For Everyone Multiplication of big numbers, complex mathematical problems – there are so many issues that people can face not only at school but also in their everyday lives! People need math everywhere and always! That is … Continue reading

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Recommended Books for Spectral Sequences

Best Spectral Sequence Book So far the most comprehensive book looks like McCleary’s book: A User’s Guide to Spectral Sequences. It is also suitable for those interested in the algebraic viewpoint. W.S. Massey wrote a very positive review to this … Continue reading

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Interesting Facts about Green’s Theorem

Firstly, Green’s Theorem is named after the mathematician George Green (14 July 1793 – 31 May 1841). Something remarkable about George Green is that he is almost entirely self-taught. He only went to school for one year (when he was 8 years … Continue reading

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Pierre-Simon de Laplace; French Newton

To increase your interest in mathematics, let me introduce the French mathematician Pierre-Simon de Laplace, also known as the “French Newton” or “Newton of France”. He helped to calculate projectile motion for Napoleon’s artillery. Laplace was also the examiner for Napoleon when … Continue reading

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5 Skills Students Need To Cope With School Pressures

According to an article published by the American Psychological Association (APA), many teenagers in the USA say they experience stress in patterns comparable to what adults go through. Teenagers also report higher stress levels than adults during the school year. … Continue reading

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Best Online Resources to Improve Your Math Skills

Best Online Resources to Improve Your Math Skills Although Maths is a compulsory subject in all the educational institutions all over the world, many students consider it as a complete waste of time and skip this issue, claiming that they … Continue reading

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An ancient Babylonian tablet known as Plimpton 322

Source: NY Times One of my favorite YouTube Math Professors, Norman Wildberger, has made a historical math discovery: that the ancient Babylonian tablet known as Plimpton 322 is actually a trigonometric table. “It’s a trigonometric table, which is 3,000 years … Continue reading

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Education and the Blockchain – Should We be Teaching Blockchain in Schools?

Source: https://preply.com/ It goes without saying that tech progress is moving at a rapid pace. Futurists point to Moore’s law – the idea that tech capabilities double every two years – as evidence for tech’s expansion into nearly every facet of … Continue reading

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The scientist nuns: In pursuit of faith and reason

Source: Aleteia Making a career out of science, just like joining a religious order, requires dedication and discipline. Some tireless souls have managed to do both. In 1965, Mary Kenneth Keller became the first woman to obtain a PhD in … Continue reading

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Theorem of the Day

Just to recommend this excellent website: Theoremoftheday where they feature one mathematical theorem each day. The nice thing is that each theorem is a one-page summary, good for getting acquainted with the theorem, and subsequently you may read it up in more … Continue reading

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Topology application to Physics

Source: https://www.scientificamerican.com/article/the-strange-topology-that-is-reshaping-physics/?W The Strange Topology That Is Reshaping Physics Topological effects might be hiding inside perfectly ordinary materials, waiting to reveal bizarre new particles or bolster quantum computing Charles Kane never thought he would be cavorting with topologists. “I don’t think … Continue reading

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How to do Proof by Cases in LaTeX

If one searches online, one will find many different methods to do “proof by cases” in LaTeX. The most simple and convenient method in my opinion is to use the description environment. Something like this: \begin{proof} Proceed by cases. \begin{description} … Continue reading

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(Important Changes) PSLE Math: Arrow -> vs Equal=

Source: Facebook For those taking PSLE, please take note of this important update regarding the difference between arrow and equal sign. Forward this to your friends taking PSLE! Basically, I think MOE is trying to instill students to be mathematically … Continue reading

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