What is Mathematics?
Mathematics is the fragment of our Imagination, which let us understand both the physical and abstract realities using Logic, Numbers and Geometry.
In Galilio's words,
The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in MATHEMATICAL LANGUAGE...
Because of this without maths we cannot learn physics and vice-versa.
To learn mathematics, we need only one thing...
An Open Mind which is capable of Imagination
That's all we need. But for learning, It always helps to see examples and applications. As a result we will use a bit of coding (Mostly Python or Julia).
We will sometimes use codes for solving problems. As an example, consider the birthday problem (see detailed discussion)
arr = [2,6,2,10]
arr.==2
sum(arr.==2)
begin
function prob(n::Int)
favour = 0
for ex_num=1:n
months = rand(1:12,20)
nums = [sum(months.==i) for i=1:12]
if sum(nums.==3)==4 && sum(nums.==2)==4
favour += 1
end
end
probability = favour/n
end
end
println("The output, probability is = ",prob(10_000_000))The output is:
The output, probability is = 0.0010518
