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18个量子比特纠缠是什么?量子计算机为何如此强大?量子的纠缠态与叠加态

Originally posted on Math Online Tom Circle:
https://youtu.be/BzyOoo4AOxs

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Lambda Calculus – The Math Behind Functional Programming

Originally posted on Math Online Tom Circle:
Functional Programming (FP) Languages : Lisp, Haskell, Scala, Kotlin, etc. Other non-FP influenced by Lambda Calculus: Python, Ruby, Javascript, Java 8, C++ Inventor of Lambda Calculus : Alonzo Church (1903 – 1995), whose…

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How Piano Lessons May Improve Language Learning for Kids | Time

Music => Language => Abstractness (Abstract Mathematics, Advanced Physics), these 3 faculties reside on the same (right) part of our brain., the earlier a kid develops it through music education (piano, violin or any instrument) the better. http://time.com/5322121/music-lessons-language-learning/?utm_source=time.com&utm_medium=email&utm_campaign=the-brief-pm&utm_content=2018070217pm&xid=newsletter-brief&eminfo=%7b%22EMAIL%22%3a%226hTLoMQ3HIhtENFGEFPcksEFAz5azrR8%22%2c%22BRAND%22%3a%22TD%22%2c%22CONTENT%22%3a%22Newsletter%22%2c%22UID%22%3a%22TD_TBP_92EEC7AD-17B1-46E0-BF78-846FB8B42C92%22%2c%22SUBID%22%3a%2284478629%22%2c%22JOBID%22%3a%22807604%22%2c%22NEWSLETTER%22%3a%22THE_BRIEF_PM%22%2c%22ZIP%22%3a%22%22%2c%22COUNTRY%22%3a%22USA%22%7d

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Infinite Cake

Originally posted on Math Online Tom Circle:
The Big Internet Math-Off, Round 1 – James Tanton v Nira Chamberlain | The Aperiodical http://aperiodical.com/2018/07/the-big-internet-math-off-round-1-james-tanton-v-nira-chamberlain/ https://youtu.be/M7e-LByl_68

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Celebrates Mathematician Gottfried Wilhelm Leibniz’s 372nd Birthday

Originally posted on Math Online Tom Circle:
https://www.forbes.com/sites/kionasmith/2018/06/30/sundays-google-doodle-celebrates-mathematician-gottfried-wilhelm-leibniz/ My favorite mathematician is German Leibniz, who co-invented Calculus with Newton. Today we thank Leibniz for his elegant Calculus symbols: Leibniz also invented 01 binary algebra, which he later found it was…

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困扰了人类358年 费马大定理 Fermat’s Last Theorem

Originally posted on Math Online Tom Circle:
https://youtu.be/AoecIZ64sIk Keywords: Fermat’s Last Theorem (FLT): Pierre de Fermat (France 17CE): FLT Conjecture or Prank ? Euler (n= 3) Taniyama-Shimura-Weil Conjecture: Modular Form = Elliptic Curve Galois Group Symmetry Andrew Wiles (UK Cambridge…

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How Abstract Math Can Analyze Social Injustice

Originally posted on Math Online Tom Circle:
Science Friday: How Abstract Math Can Analyze Social Injustice. Dr. Eugenia Cheng https://www.sciencefriday.com/segments/how-abstract-math-can-analyze-social-injustice/ [Sound]: https://m.soundcloud.com/scifri/how-abstract-math-can-analyze-social-injustice Interview: Yoneda Lemma

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Worldcup Math Analysis : Korea vs Germany (2:0)

Originally posted on Math Online Tom Circle:
Worldcup 2018 Surprising Result: World No.1 (Germany) Lost to World No.59 (Korea) – why ? Reason: Math ! For weak Korea to win, the best strategy is to keep the goals number as…

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The Software War : Object-Oriented Programming (OOP) vs Functional Programming (FP)

Originally posted on Math Online Tom Circle:
The “war” of OOP vs FP is akin to Applied Math vs Pure Math. The formers (OOP & Applied Math) are not “rigourous” but practical, compared to the laters (FP & Pure Math)…

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Group is Symmetry

Originally posted on Math Online Tom Circle:
Landau’s book “Symmetry” explains it as follow: Automorphism = Congruence= 叠合 has 1). Proper 真叠合 (symmetry: left= left, right = right) 2). Improper 非真叠合 (non-symmetry: reflection: left changed to right, vice-versa). Congruence => preserve…

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Noether Theorem: Symmetry

Originally posted on Math Online Tom Circle:
Symmetry (hence Group) explains : 1. Conservation of Energy; 2. Conservation of Angular Momentum; 3. Periodic Table; 4. Laws of Thermodynamic. Emmy Noether Theorem (1918): Conservation Laws owes to Symmetry : 1. In…

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Mathematician Emmy Noether changed the face of physics

Originally posted on Math Online Tom Circle:
https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math

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Why do the French excel in maths ?

Originally posted on Math Online Tom Circle:
It is not only owed to the Ecole Normale Superieure where the 11 Fields medalists were educated, but the prominent “Math Culture” in French society. This is similar to the International Math Olympiad…

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Chinese Remainder Theorem 中国剩余定理

Originally posted on Math Online Tom Circle:
中国剩余定理CRT (Chinese Remainder Theorem) X ≡ 2 (mod 3) X ≡ 3 (mod 5) X ≡ 2 (mod 7) Solve X? 明. 程大位 “算法统宗” (1593) 3人同行70稀 5树梅花21支 7子团圆半个月(15) 除百零五(105)便得知 Let remainders: r= 2.70…

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韩信点兵 (中国剩余定理)

Originally posted on Math Online Tom Circle:
Chinese Remainder Theorem (CRT): 韩信点兵 (中国剩余定理) 南北朝 《孙子算经》(4 AD) https://youtu.be/Ope18waS1GU

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《孙子算经》中的鸡兔同笼问题

Originally posted on Math Online Tom Circle:
中国南北朝 : 《孙子算经》(4AD) 鸡兔同笼问题 (Chicken – Rabbits Problem) https://youtu.be/tnKaBeDVFLU

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Yijing & Orchestra Conductor

Originally posted on Math Online Tom Circle:
Problem: The Orchestra conductor has been asked to conduct a series of concert for 2 consecutive months. The Orchestra has to play few pieces of classical music with the following conditions requested by…

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Lavenshtein Distance

Originally posted on Math Online Tom Circle:
https://people.cs.pitt.edu/~kirk/cs1501/Pruhs/Spring2006/assignments/editdistance/Levenshtein%20Distance.htm

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Fix slow iMac annoyed by spinning Beachball

Originally posted on Math Online Tom Circle:
The wonderful iMac is a “long life” machine able to last more than 10 years, but it has an annoying weakness : the frequent spinning “beachball” which slows down or freezes the computer.…

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Pure to Applied Math: Self – driving Cars & “Sum of 2 Squares” Polynomial

Originally posted on Math Online Tom Circle:
Key Points: 1900 Hilbert’s 17th Conjecture: Non-negative Polynomial <=> sum of 2 squares (Proved by Emile Artin in 1927) Computing Math : approximate by optimisation with “Linear Programs” which are faster to compute.…

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Maria Agnesi, the Greatest Female Mathematician You’ve Never Heard of

Originally posted on Math Online Tom Circle:
https://www.scientificamerican.com/article/maria-agnesi-the-greatest-female-mathematician-youve-never-heard-of/ https://www.smithsonianmag.com/science-nature/18th-century-lady-mathematician-who-changed-how-calculus-was-taught-180969078/

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Boolean Algebra

Originally posted on Math Online Tom Circle:
George Boole [2/11/ 1815 – 8/12/ 1864]: 《The Laws of Thought》: symbolic logic representation of thought. Let x = class of sheep’s y = white => white sheep = xy = yx =…

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Zipf’s Law in Linguistic

Originally posted on Math Online Tom Circle:
https://simple.m.wikipedia.org/wiki/Zipf%27s_law Example: In English, 3 most common words: “the” : occurring 7% of the time; “of” : 3.5% = 7/2 “and” : 2.8% ~ 7/3 => “the” is 2x occurs more often than…

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How Mathematicians Think

Originally posted on Math Online Tom Circle:
Hadamard estimated that : About 90% of mathematicians think visually, 10% think formally. Usually, they think in steps: Get the right idea, often think vaguely about structural issues, leading to some kind of…

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Satz & Theorem

Originally posted on Math Online Tom Circle:
“A mathematician is a machine for turning coffee into theorems.” – Alfréd Rényi It’s a pun in German, where the word Satz means both ‘theorem’ and ‘(coffee) grounds‘ [咖啡渣].

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Quora : How likely is it that a mathematics student can’t solve IMO problems?

Originally posted on Math Online Tom Circle:
How likely is it that a mathematics student can’t solve IMO problems? Is there a fear of embarrassment in being a math Ph.D. who can’t solve problems that high-school students can? by Cornelius…

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Quora: IMO 1988 Question 3

Originally posted on Math Online Tom Circle:
Problem A3 A function f is defined on the positive integers by: for all positive integers n, Determine the number of positive integers n less than or equal to 1988 for which f(n)…

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Blockchains and Application in Bitcoins

Originally posted on Math Online Tom Circle:
Encryption & Decryption: ECC (Elliptic Curve Cryptography): Sending End: Encryption 1) SHA algorithm generates “Digital Signature” ; 2) Generate random “Private Key”. 第3-6步骤: 3) ECC encrypts the text with “Private Key”; 4) From…

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哥德巴赫猜想(2018)

Originally posted on Math Online Tom Circle:
Let N = 2n > 6 哥德巴赫猜想 Conjecture “1+1”: N = p1 + p2 (pj all primes) 陈景润 Chen Theorem “1+2”: N = p1+ p2.p3 https://youtu.be/XkVskCFA8r8

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Seven Fields Medalists

Originally posted on Math Online Tom Circle:
The 7 Fields Medalists are: 2014 – Maryam Mirzakhani (1977-2017) – 1st lady Fields medalist 2010 – Cédric Villani (1973- ) 2006 – Grigori Perelman (1966- ) – 1st declined the award 1998…

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Bill Gates Returns to Harvard to Talk : Math55

Originally posted on Math Online Tom Circle:
http://www.thecrimson.com/article/2018/4/27/bill-gates-event/ Bill Gates, a top Math student at Harvard entrance exams, recalled his first year Harvard “Math55” Course (Advanced Calculus & Linear Algebra) – the toughest at his time because 4 years of…

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Abstract “Nonsenses” in Abstract Math make “Sense”

Originally posted on Math Online Tom Circle:
After 40 years of learning Abstract Algebra (aka Modern Math yet it is a 200-year-old Math since 19CE Galois invented Group Theory), through the axioms and theorems in math textbooks and lectures, then…

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The Modular Form

Originally posted on Math Online Tom Circle:
“Form” : Function with special properties – eg. Space Forms: manifolds with certain shape. Quadratic Forms (of weight 2): Cubic Forms (of weight 3): Automorphic Forms (particular case: Modular Forms): auto (self), morphic…

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爱因斯坦数学差吗?告诉你什么是罗氏几何和黎曼几何

欧氏几何: 第5公理 : 直线上过一点, 只有 n=1 条平行线 非欧几何: 罗氏: n >1 (空间) 黎曼: n = 0 (球体)

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The Inventors of the 10 Computer languages

Originally posted on Math Online Tom Circle:
Python (Dutch Guido van Rossum, 1956) Java (Canadian James Gosling 1955) Javascript (USA Brendan Eich, 1961) C (USA Dennis Ritchie, 1941 – 2011 ) C++ (Denmark Bjarne Stroustrup, 1950) Ruby (JAPAN Yukihiro “Matz”…

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Group Theory Game

Originally posted on Math Online Tom Circle:
https://www.cut-the-knot.org/proofs/PegsAndGroups.shtml

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Hans Rosling’s Best TED Talk & Book “Factfulness”

Originally posted on Math Online Tom Circle:
http://time.com/5224618/bill-gates-hans-rosling-factfulness/ https://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen/up-next?referrer=playlist-the_best_hans_rosling_talks_yo

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Why Prime Numbers Still A Mistery

Originally posted on Math Online Tom Circle:
Prime Numbers since Euclid 2300 years ago remains a mystery today… Riemann’s Hypothesis is the Top Conjecture Unsolved in 21st Century. https://theconversation.com/why-prime-numbers-still-fascinate-mathematicians-2-300-years-later-92484

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Joseph Fourier is Still Transforming Science

Originally posted on Math Online Tom Circle:
Key Words: 250 years anniversary Yesterdays: Fourier discovered Heat is a wave , Fourier Series, Fourier Transformation, Signal processing… Today: IT imaging JPEG compression, Wavelets, 3G/4G Telecommunications, Gravitational waves … Friends / bosses:…

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Louis-Le-Grand, un lycée d’élite 法国(巴黎)精英学校: 路易大帝中学

Originally posted on Math Online Tom Circle:
Lycée Louis-Le-Grand is the best high school (lycée) for Math in France – if not in the world – it produced many world-class mathematicians, among them “the Father of Modern Math” in 19th…

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Senior Wrangler: Singapore Prime Minister

Originally posted on Math Online Tom Circle:
Senior Wrangler is the First position in the Math Tripos in Cambridge. Singapore Prime Minister Lee Hsien Loong was the Senior Wrangler in 1973, the first Singaporean student with such great honors, among…

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Topological Data Analysis

Originally posted on Math Online Tom Circle:
Three Key Ideas: Cloud of Points Filter function: f (x,y,z) –> x Cluster: Overlapping bins Draw network: Vertices: clusters Edges: connecting lines between clusters. https://youtu.be/6Hll-SzcrS0

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Crash course in Category Theory

Originally posted on Math Online Tom Circle:
Key Point: Haskell & any FP compiler don’t check the Category Theory proof if your codes (eg. fmap) follow Functor’s Laws (eg. Preserve structure, identity) or Monad’s Laws ! https://youtu.be/iJ7V1KXJpsE

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God’s Book of Perfect Proof

Originally posted on Math Online Tom Circle:
https://www.quantamagazine.org/gunter-ziegler-and-martin-aigner-seek-gods-perfect-math-proofs-20180319/

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Canadian mathematician Langlands wins Abel Prize

Originally posted on Math Online Tom Circle:
http://www.thehindu.com/sci-tech/science/canadian-mathematician-langlands-wins-abel-prize/article23304119.ece/amp/ See also: Langland’s Program

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Michael Bishop’s Science

Originally posted on Math Online Tom Circle:
Michael Bishop (Nobel Medicine 1989) School Science subjects should be taught in this sequence (unless in single ‘Combined Science’): 1st Physics 2nd Chemistry 3rd Biology

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Mind over Matter : Bruce Lipton

Originally posted on Math Online Tom Circle:
Key Points: 1. The Foundation of Science has changed since Newtonian Era, except Biology / Medicine and Psychology which don’t keep up: Math => Fractal Math Newton Physics (Matter)=> Quantum Physics (Energy) (Organic)…

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“Deep Learning” Online Book

Originally posted on Math Online Tom Circle:
Most popular AI Deeplearning Book by MIT : [English] http://www.deeplearningbook.org/ [中文版] https://exacity.github.io/deeplearningbook-chinese/

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Choosing a Programming Language

Originally posted on Math Online Tom Circle:
https://dev.to/drminnaar/choosing-a-programming-language-493h

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Programmers need Advanced Math ?

Originally posted on Math Online Tom Circle:
As software becomes more complicated for high-speed trains, driverless cars, missile weapons. .. and AI deeplearning algorithm, we can’t depend our life safety on the programmers who don’t understand the advanced maths behind…

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