IT Application’s 5 Evolution Stages

From Mainframe/Mini Server-based Monolithic Application since 80s, to
Browser-based thin-client-thick-Server Application from mid-90s, to
MicroServices-based Applications in 2018’s…

Small is beautiful !!

“Dinausaur” Monolithic Applications give way to Microservice-based Application.

Microservice is a realisation of “mini”-SAAS (Software As A Service).

Component-based Software a la hardware components VLSI is becoming a reality.

https://dzone.com/articles/convert-legacy-applications-into-future-proof-appl

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

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.
  • Princeton Mathematicians applied it to self-driving cars.

https://www.wired.com/story/a-classical-math-problem-gets-pulled-into-self-driving-cars/amp

Explain:

Sum of 2 Squares <=> always non-negative ( 0)

13 = 4 + 9 = 2^{2} + 3^{2}

P (x) = 5x^2+16x+13 = (x+2)^{2} + (2x+3)^{2} \geq 0

Self-driving Car: Trajectory = P (x)

P(x) < 0 where the car’s position in the trajectory;

Obstacles are positions where P (x) 0.

This is one of the many cases of Pure Math turned to be Applied Math in last few decades. Other examples:

Is Applied Math => Pure Math ?
Yes!

School System Video (Do not make a fish climb trees)

Singapore Maths Tuition

Singapore is being mentioned around 4:54. Very nice video. The truth is that the classroom of today is still nearly the same as the classroom of 150 years ago. There needs to be a “Educational Revolution” parallel to that of the Industrial Revolution. Many children cannot fit into the single classroom model, leading to growth in diagnosis of behavioral “problems” such as ADHD in developed nations.

Americans who are tired of “Common Core” may want to check out Singapore Math for their kids, which is highly acclaimed in the educational realm.

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Population Differential Equations and Laplace Transform

Singapore Maths Tuition

Malthus Model
$latex displaystyle frac{dN}{dt}=BN-DN=kN$

$latex N$: Total population

$latex B$: Birth-rate per capita

$latex D$: Death-rate per capita

$latex k=B-D$

Solution to D.E.:
$latex displaystyle boxed{N(t)=widehat{N}e^{kt}},$

where $latex widehat{N}=N(0)$.

Logistic Equation
$latex begin{aligned}
D&=sN
frac{dN}{dt}&=BN-sN^2
widehat{N}&=N(0)
N_infty&=B/s
end{aligned}$

Logistic Case 1: Increasing population ($latex widehat{N}<N_infty$)
$latex begin{aligned}
N(t)&=frac{B}{s+(frac{B}{widehat{N}}-s)e^{-Bt}}
&=frac{N_infty}{1+(frac{N_infty}{widehat{N}}-1)e^{-Bt}}
end{aligned}$

The second expression can be derived from the first: divide by $latex s$ in both the numerator and denominator.

Logistic Case 2: Decreasing population ($latex widehat{N}>N_infty$)
$latex begin{aligned}
N(t)&=frac{B}{s-(s-frac{B}{widehat{N}})e^{-Bt}}
&=frac{N_infty}{1-(1-frac{N_infty}{widehat{N}})e^{-Bt}}
end{aligned}$

Logistic Case 3: Constant population ($latex widehat{N}=N_infty$)
$latex displaystyle N(t)=N_infty$

Harvesting
Basic Harvesting Model: $latex displaystyle boxed{frac{dN}{dt}=(B-sN)N-E}.$

$latex E$: Harvest rate (Amount harvested per unit time)

Maximum harvest rate without causing extinction: $latex boxed{dfrac{B^2}{4s}}$.

$latex displaystyle boxed{beta_1,beta_2=frac{Bmpsqrt{B^2-4Es}}{2s}}.$

$latex beta_1$: Unstable equilibrium population

$latex beta_2$: Stable equilibrium population

Extinction Time: $latex displaystyle boxed{T=int_{widehat{N}}^0frac{dN}{N(B-sN)-E}}.$

Laplace transform of $latex f$
$latex displaystyle F(s)=L(f)=int_0^infty e^{-st}f(t),dt$

Tip: Use this equation when the questions…

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11-year old math and chess prodigy in Singapore

Singapore Maths Tuition

Source: Channel News Asia

Aarushi Maheshwari solved the famous “Cheryl’s Birthday Problem” when she was only 9. She is also a chess champion and can play blindfold chess.

Watch the video below to learn more!

Also read our previous post on The Most Accomplished 10-Year-Old (Gifted pupil).

For those who want to learn more about Olympiad Math and International Chess, check out the previous two links. Math and Chess are two of the most intellectually challenging activities that can develop the intelligence of kids.

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The Inventors of the 10 Computer languages

  1. Python (Dutch Guido van Rossum, 1956)
  2. Java (Canadian James Gosling 1955)
  3. Javascript (USA Brendan Eich, 1961)
  4. C (USA Dennis Ritchie, 1941 – 2011 )
  5. C++ (Denmark Bjarne Stroustrup, 1950)
  6. Ruby (JAPAN Yukihiro “Matz” Matsumoto, 1965)
  7. Perl (USA Larry Wall, 1954)
  8. Pascal (Switzerland Niklaus Wirth, 1934)
  9. Lisp (USA John McCarthy, 1927 – 2011)
  10. PHP (Denmark Rasmus Lerdorf, 1968)

https://www.technotification.com/2018/04/programming-languages-creators.html

Below the 3 hotest Functional Programming language influenced by Lisp:

11. Kotlin(Russia Andrey Breslav)

12. Scala (USA Martin Odersky)

13. Haskell (USA)

14. Clojure (USA Rich Hickey)

How to help gifted children deal with hyper-sensitivity

Singapore Maths Tuition

This should be useful for parents of gifted kids.

Also read:

Books for Gifted Children

Book by Truly Gifted Kid (GEP Book)

Source: Aleteia

Gifted children can be challenging and exhausting: unable to handle frustration, finding it difficult to accept boundaries, talking endlessly, negotiating the slightest rule or order … However, according to Jeanne Siaud-Facchin, a psychologist who is a specialist in gifted children (see our previous article in which she explains what makes a child gifted), creating boundaries and setting limits is a vital necessity for their emotional development, and the only way to avoid the creation of permanent and escalating conflicts. How should we respond to these tantrums due to a child’s heightened emotional state? We’ve spoken to some experienced moms who share what to do to calm and reassure our sensitive children.

Why are many gifted children challenging and exhausting?

Of course, not all gifted children…

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