Category Archives: Uncategorized

Powerpac Ceramic Cooker Review

This should be the cheapest ceramic cooker on the market. PowerPac is a reliable Singaporean brand that has been on the market for quite some time. At the price of $29.90, the Ceramic Cooker even comes with a free stainless … Continue reading

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Free Philips Air Fryer (Enfagrow Promo)

Official URL: Enfagrow Homepage

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Group Theorems: Lagrange, Sylow, Cauchy

Originally posted on Math Online Tom Circle:
1. Lagrange Theorem: Order of subgroup H divides order of Group G Converse false: having h | g does not imply there exists a subgroup H of order h. Example: Z3 = {0,1,2}…

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陈省身 SS Chern – “The 2nd Gauss”

Originally posted on Math Online Tom Circle:
陈省身香港科技大学 演讲经典 (Highly Recommended – spoken in English & Chinese) http://www.bilibili.com/video/av5473133 他的女婿是香港科大校长。现任校长是 Prof 陈繁星 Tony F. Chan , the ‘Search Algorithm Thesis’ supervising Prof of the 2 Google founders in Stanford University, Applied…

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70-million Bounded Gap Between Primes

Originally posted on Math Online Tom Circle:
Since Ancient Greek : Euclid had proved there are infinite primes. Sieve of Eratosthenes to enumerate the primes. Recent time 3 Mathematicians GPY attempted another Sieve method to find the bounded gap (N)…

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Betta Fish Tricks

Betta fish are quite intelligent and curious. I trained my Betta fish to do some simple tricks. I bought my 5 Gallon tank on Qoo10: Betta Fish Tank. The modern viewpoint is that Betta should not be kept in small bowls … Continue reading

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小算盘 大乾坤 Abacus

Originally posted on Math Online Tom Circle:
浙江临海市 算盘博物管主人 雷国华 收藏算盘20年,散尽储蓄,感慨涕下不已。 https://youtu.be/d3ua6tz4Gos 中国的算盘上面2珠 (2×5),下面5珠(5), 共15,加1 = 16 进位。古代是16位 (Hexadecimal) 制, 半斤 八两 (= 1/2 斤 x 16 两 = 8 两)。 日本改良成10位制: 上面1珠 (1×5),下面4珠(4), 共9,加1 = 10 进位。 https://youtu.be/DiHfHJAjAlk

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3D Rotation Matrices and Examples

The following rotation matrices rotate vectors by an angle in an anticlockwise direction about the -, -, or -axis respectively (the rotated axis points towards the observer). Example 1 Rotating anticlockwise about -axis: Example 2 Rotating anticlockwise about -axis:

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十二平均律 12-tone Equal Temperament

Originally posted on Math Online Tom Circle:
《十二平均律》 是明朝 "布衣王子" 朱载堉 (1536年-1610年) 发明的,由当时在中国传教的意大利人 利马窦 (Matteo Ricci, 1552 – 1610), 传给欧洲的法国数学家 Marin Mersenne (Mersenne Prime ) 。现代音乐之父 巴哈 Bach 第一个采用,制作世界第一架钢琴有12黑白键,并作曲 《Bach 12-tone Equal Temperament》。 朱载堉把 “1” 到 “i” 的八度 (Octave) 分为等比…

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Richard Dedekind

Originally posted on Math Online Tom Circle:
Julius Wilhelmina Richard Dedekind (6 Oct 1831 – 12 Feb 1916) – Last student of Gauss at Göttingen – Student and closed friend of Dirichlet who influenced his Mathematical education – Introduced the…

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HDB Low Water Pressure: Phone Hotline

For those living near the top floor of HDB blocks, you may experience low water pressure since the water tanks are typically built at the rooftop of HDB flats. The pressure exerted by a column of liquid of height h … Continue reading

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Dedekind Cut : “Prove 0.9999… = 1”

Originally posted on Math Online Tom Circle:
Key Notes: Rational Numbers Q eg. 1/2, … Complete but non Continuous. Irrational numbers eg. Real number is Complete and Continuous Dedekind Cut The Proof of “0.999… = 1” by using Set Theory…

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Bit Coin and Block Chain

Originally posted on Math Online Tom Circle:
Bit Coin is only one application of Block Chain. https://youtu.be/g_fSistU3MQ

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Happy Chinese New Year

Happy Chinese New Year to all readers of Mathtuition88.com! Do check out and follow my Facebook page, where I post interesting news on Math/Education.

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Machine Learning is Just Mathematics! Free Machine Learning Resources

Originally posted on Math Online Tom Circle:
https://youtu.be/tGyfmzuR4d4

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Learn NUMPY in 5 minutes – BEST Python Library!

Originally posted on Math Online Tom Circle:
https://youtu.be/xECXZ3tyONo

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Formula for 3×3 Matrix Inverse

Let Then, This method is about the same speed as the Gaussian-Elimination 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

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Men’s wallet with coin compartment Singapore

Despite many cashless initiatives like PayLah, Singapore is not yet a truly cashless country. Coins are still needed to buy coffee or tea at the “Kopitiam”, or to put a $1 coin for pushing a trolley at supermarkets. Even if … Continue reading

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Horned Nerite Snails

Some video footage of my new Horned Nerite Snails in the Betta Tank. Really amazing and bright colors. Taken using Canon PowerShot: Canon Camera and Camera Case Singapore The fish tank is 5 Gallon: Betta Fish Tank

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Imaginary Numbers

Originally posted on Math Online Tom Circle:
FINAL EPISODE – Riemann Complex Plane : 4 dimension but viewed in 3 dimensions Episode 1 – 9 : History Episode 10: Complex function Function : 1 input mapped to 1 output Multi-function…

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Math for AI : Gradient Descent

Originally posted on Math Online Tom Circle:
Simplest explanation by Cheh Wu: (4 Parts Video : auto-play after each part) Revision: Dot Product of Vectors https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length Gradient Descent (opposite = Ascent) https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/gradient-and-directional-derivatives/v/why-the-gradient-is-the-direction-of-steepest-ascent

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Video on Computing Homology Groups

Originally posted on Singapore Maths Tuition:
This video follows after the previous video on Simplicial Complexes. If you are looking for quality Math textbooks to study from (including Linear Algebra and Calculus, the two most popular Math courses), check out…

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Group Theory in Rubik’s Cube & Music

Originally posted on Math Online Tom Circle:
https://youtu.be/FW2Hvs5WaRY

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Mathematician’s life begins at 40

Originally posted on Math Online Tom Circle:
André Weil told the Japanese professor Goro Shimura that Prof GH Hardy talked nonsense, mathematics is not necessary for young men below 35. Recent math breakthroughs are accomplished by men above 40, because…

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Twin Prime Hero

Originally posted on Math Online Tom Circle:
http://simonsfoundation.org/features/science-news/unheralded-mathematician-bridges-the-prime-gap/ On April 17, 2013, a paper arrived in the inbox of Annals of Mathematics, one of the discipline’s preeminent journals. Written by a mathematician virtually unknown to the experts in his field…

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Cut a cake 1/5

Originally posted on Math Online Tom Circle:
Visually cut a cake 1/5 portions of equal size: 1) divide into half: 2) divide 1/5 of the right half: 3) divide half, obtain 1/5 = right of (3) 4) By symmetry another…

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Quick verify multiplication

Originally posted on Math Online Tom Circle:
Verify: 2,578,314  x 6,321,737 = 16,299,423,011,418 ? 2,578,314  => (2+5+7+8+3+1+4)) =30 => (3+0) = 3 6,321,737 => (6+3+2+1+7+3+7)=29 => 2+9 = 11 => (1+1) = 2 3 x 2 = 6  16,299,423,011,418 => (1+6+2+9+9+4+2+3+0+1+1+4+1+8) = 51 => (5+1) =…

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Proper Way of Cutting Cake

Originally posted on Math Online Tom Circle:
The traditional way of cutting cake a la ‘Camembert Cheese’ is wrong. https://youtu.be/lhJBY84WKUw

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Interview With The Smartest Man In The World

Originally posted on Math Online Tom Circle:
Terence Tao (1975, Adelaide): Chinese-american, with IQ 230-240, full professor at 24. Fields Medalist. https://youtu.be/bUwbO73q0iA

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J.P. Serre: Galois Group (Case Abelian)

Originally posted on Math Online Tom Circle:
(French) Groupes de Galois, le cas abélien Jean Pierre Serre ♢ Youngest Fields Medalist in history at 27. ♢ Wolf Prize in 2000 ♢ 1st person to win Abel Prize in 2003. Listen…

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Introducing WordAds 2.0

Originally posted on WordAds:
Today, we’re excited to introduce you to a new WordAds. On the front end, it’s a simpler and more streamlined experience like never before. On the back-end we have launched a real-time bidding platform to maximize…

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Holder’s Inequality Trick

Click here: Free Career Quiz Holder’s Inequality is a very useful inequality in Functional Analysis, hence many results can be proved by applying Holder’s Inequality. Suppose that and . Prove that if in , then in . Proof: Assume in . … Continue reading

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Abstract Algebra 抽象代数 (石生明教授)

Originally posted on Math Online Tom Circle:
这位石教授的”抽象代数”很棒, 一来是他退休前的最后一课, 二来他总结为何老师教不好, 学生上完课好像听到3个大头”鬼” (群group, 环ring, 域field), 但没实际摸过。 他的第一和第二课很好, 与众不同的花时间讲 “动机”: Motivation – Why study Abstract Algebra ? 抽象代数01: Motivation https://youtu.be/AGd1TZ-IKr0 抽象代数02: 复数扩域 C 扩域 (Extended Field)数学思维 = 人解决问题的思维 例: 国内不可行的问题, 跳出国门, 扩大到世界领域,…

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张益唐: 速食店员竟然是数学天才

Originally posted on Math Online Tom Circle:
【台湾壹週刊】 速食店员竟然是数学天才 张益唐 (1955 – ) : 北京大学 – 美国数学博士。因为执着数学理论的真理, 得罪美国大学台湾籍论文教授, 毕业后找不到大学教职, 在朋友的 Subway 速食店做会计8年, 潜心业余思考世界数学大难题: Twin Primes Gap, 终于攻破。 他的下一个目标是Riemann Hypothesis, 困扰数学家百年的难题: “素数 (Prime numbers)的分布”都集中在 Zeta function complex plane的 实轴(real = 1/2)…

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James H. Simons,  the mathematician who cracked Wallstreet

Originally posted on Math Online Tom Circle:
James H. Simons,  the Jewish mathematician who made $14 billion using Math modelling for Hedge Fund. [Watch from 31:00 mins to 35 mins].  He told the Nobel Physicist Frank Yang (杨振宁) that the…

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Decoding The Universe Great Math Mystery –

Originally posted on Math Online Tom Circle:
Simons Foundation New 2015 Full Documentary #WorldMathsDay” – https://youtu.be/IuGI6pQFZC0 Math Mystery Tour (BBC) https://youtu.be/iQlg86lsy-o

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245A, Notes 4: Modes of convergence

Originally posted on What's new:
If one has a sequence of real numbers , it is unambiguous what it means for that sequence to converge to a limit : it means that for every , there exists an such…

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Measure that is absolutely continuous with respect to mu

Interesting Career Personality Test (Free): https://mathtuition88.com/free-career-quiz/ Let be a measure space, and let be a measurable function. Define the map , , where denotes the characteristic function of . (a) Show that is a measure and that it is absolutely continuous … Continue reading

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Calculus: Difficult Integration

Originally posted on Math Online Tom Circle:
Question on @Quora: In the French Classe Préparatoire 1st year “Mathematiques Supérieures”,  we wanted to test our admired Math Prof whom we think was a “super know-all” mathematician. We asked him the above…

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Visual Math

Originally posted on Math Online Tom Circle:
99% of my friends get it wrong,  except a 13-year-old boy who can ‘see’ it. Wrong answer : 25 Answer (below): Try before you scroll down. . . . . . . .…

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Singapore PSLE 2015 Math

Originally posted on Math Online Tom Circle:
PSLE is “Primary School Leaving Exams” for 11~12 year-old children sitting at the end of 6-year primary education. The result is used as selection criteria to enter the secondary school of choice. Hint:…

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εδ Confusion in Limit & Continuity

Originally posted on Math Online Tom Circle:
1. Basic: |y|= 0 or > 0 for all y 2. Limit: ; x≠a |x-a|≠0 and always >0 hence For all ε >0, there exists δ >0 such that 3. Continuity: f(x) continuous at…

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Limit: ε-δ Analysis

Originally posted on Math Online Tom Circle:
For x->0, find limit L of f(x)= (x³+5x)/x 1) guess L: f(x)= x(x²+5)/x= x²+5 => L= 5  when x->0 2) epsilon-delta Proof: find δ in function of ε such that: |f(x)-5| < ε |(x²+5)-5| <ε…

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Newtonian Calculus not rigorous !

Originally posted on Math Online Tom Circle:
Why Newton’s Calculus Not Rigorous? …[1] cancel x (≠0)from upper and below => …[2] In [1]: we assume x ≠ 0, so cancel upper & lower x But In [2]: assume x=0 to get…

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Rigorous Calculus: ε-δ Analysis

Originally posted on Math Online Tom Circle:
Rigorous Analysis epsilon-delta (ε-δ) Cauchy gave epsilon-delta the rigor to Analysis, Weierstrass ‘arithmatized‘ it to become the standard language of modern analysis. 1) Limit was first defined by Cauchy in “Analyse Algébrique” (1821)…

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German Terms

Originally posted on Math Online Tom Circle:
1. The electron orbits: first 4 orbits from atom s, p, d, f s = Sharfe (Sharp) p =prinzipielle (principle) d = diffusiv (diffuse) f= fundamentale (fundamental) 2. eigen (special) eigenvector eigenvalue eigenfunction…

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“Well-defined”( “定义良好”)

Originally posted on Math Online Tom Circle:
万门大学抽象代数7: “定义良好” (Well-defined) 集合: Set (S) 等价关系: Equivalence Relation (~) 商集 : Quotient Set (S/~) 映射 : Mapping (f) Prove : f is well-defined ? https://youtu.be/uFjX6WQ-Us8

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抽象代数 Abstract Algebra

Originally posted on Math Online Tom Circle:
北京航空航天大学:数学大观 第2讲 数学抽象 无招胜有招” 1. Euclid 5条公理 (Axioms) => 全部 几何 (Geometry) 2. Galois 运算律 (Laws of Operations) => 抽象代数 (Abstract Algebra) https://youtu.be/8zsyPCRpjtE

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Abstract Math discomforts

Originally posted on Math Online Tom Circle:
3 Wide Discomforts For Abstract Math Students 1. Group : Coset, Quotient group, morphism… 2. Limit ε-δ: Cauchy 3. Bourbaki Sets: Function f: A-> B is subset of Cartesian Product AxB. Students should…

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Probability: Dice

Originally posted on Math Online Tom Circle:
Throw 2 dies, the sum of points i, j and probability P (i+j): 2(1/36) 3(1/18) 4(1/12) 5(1/9) 6(5/36) 7(1/6) 8(5/36) 9(1/9) 10(1/12) 11(1/18) 12(1/36) => Bell curve symmetric both sides, peak 1/6 (sum 7).

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