Amazing that Terence Tao is doing a Math Masterclass!
In this Masterclass, famous Mathematician Terence Tao is going to teach math problem-solving skills to the general audience. In fact, not much math background is necessary! There is also no homework, just relax and learn from the Mozart of Math!
Professor Terence Tao is a Fields Medallist (Math equivalent of the Nobel Prize). He certainly knows his stuff and is an expert in the field! He also has a knack for explaining abstract mathematical concepts in a very clear and interesting way.
Masterclass Link: Terence Tao Teaches Mathematical Thinking
Masterclass usually chooses top talents in their respective fields to give a lecture. For example, previously Garry Kasparov also gave a Masterclass on chess.
Terence Tao Masterclass Review
Overall, Terence Tao’s masterclass will be great for students, homeschool parents, and even future mathematicians. It will certainly help to inspire them to have a greater passion in mathematics.
Mathematics is more about the mindset and the approach, rather than just the answers. The rote learning techniques of math can be learnt by anyone, but it takes a master like Terence Tao to be able to explain and demonstrate the beauty of mathematics.
If you have any feedback on Terence Tao’s Masterclass, do post it in the comments below!
.
.
if and only if its minimal polynomial is a product of distinct linear factors over 
be an 
matrix. The characteristic polynomial of 
, is the polynomial defined by 
where 
.
and 
are metrics. Define 
.
.
.
.![\begin{aligned} d(x,y) &\leq d_1(x,z)+d_1(z,y)+d_2(x,z)+d_2(z,y)\\ &=[d_1(x,z)+d_2(x,z)]+[d_1(z,y)+d_2(z,y)]\\ &=d(x,z)+d(z,y) \end{aligned}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Baligned%7D++++d%28x%2Cy%29+%26%5Cleq+d_1%28x%2Cz%29%2Bd_1%28z%2Cy%29%2Bd_2%28x%2Cz%29%2Bd_2%28z%2Cy%29%5C%5C++++%26%3D%5Bd_1%28x%2Cz%29%2Bd_2%28x%2Cz%29%5D%2B%5Bd_1%28z%2Cy%29%2Bd_2%28z%2Cy%29%5D%5C%5C++++%26%3Dd%28x%2Cz%29%2Bd%28z%2Cy%29++++%5Cend%7Baligned%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
is a solution to 
, and 
is a solution to 
, then 
is a solution to 
.
be a CW complex (with a fixed CW decomposition) with 
cells of dimension 
. Let 
be a field and let 
.
,
denotes the Euler characteristic of 
.
.
.
.
.
, 
, 
, 
, 
.
only, RHS is a function of 
only.
.
where 
, 
, 
.
where 
![\displaystyle y(t,x)=\frac{1}{2}[f(x+ct)+f(x-ct)].](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+y%28t%2Cx%29%3D%5Cfrac%7B1%7D%7B2%7D%5Bf%28x%2Bct%29%2Bf%28x-ct%29%5D.&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
, 
.
where 
are Fourier sine coefficients of 
.
.
.
when integrating the numerator 
.)
. (This is only a rough guideline.)
.
.
. The given DE becomes
.
![\displaystyle \boxed{\frac{T}{U}=\frac{k_U}{k_T-k_U}[1-e^{(k_U-k_T)t}]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cboxed%7B%5Cfrac%7BT%7D%7BU%7D%3D%5Cfrac%7Bk_U%7D%7Bk_T-k_U%7D%5B1-e%5E%7B%28k_U-k_T%29t%7D%5D%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
and 
respectively.
and 
are two solutions to a homogeneous SDE 
, then 
is also a solution for any scalars 
, 
.
be an eigenvalue corresponding to eigenvector 
. (The eigenvectors are complex conjugates: 
.)
is called the eigenspace of 
. The eigenspace is denoted by 
.
(trace of 
.
-plane counterclockwise through an angle 
about the origin.
45 degrees counterclockwise gives us:
(inconsistent system), solve
instead to get a least squares solution of the original equation.
, we can find the projection 
of 
onto the column space of 
columns, then 
=number of pivot columns,
=number of non-pivot columns.)
from 
to 
is linearly independent in the interval 
if ![\displaystyle W[\vec{f_1}(x),\dots,\vec{f_n}(x)]\neq 0](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+W%5B%5Cvec%7Bf_1%7D%28x%29%2C%5Cdots%2C%5Cvec%7Bf_n%7D%28x%29%5D%5Cneq+0&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
for at least one value of 
is a subspace of 
for some vectors 
.
satisfies the closure properties:
, we must have 
.
and 
, we must have 
.
must be in 
, we have 
.)
has only the trivial solution, i.e. 
.
not zero, then 
Singapore Maths Tuition 