Computational Mathematics

 

https://www.coursera.org/learn/uol-cm1015-computational-mathematics/supplement/Ok8Zg/introduction-to-computational-mathematics-course

handle numbers in any base and perform operations with binary numbers. You will learn about sequences, recursion and series, basic trigonometry and geometry.

You will also be introduced to functions, their different types, how to plot them and how to study their properties through basic calculus, limits and derivatives. You will also be introduced to linear algebra, vector spaces and the basic concepts of combinatorics, statistics and probability.

How to pass?

https://www.coursera.org/learn/uol-cm1015-computational-mathematics/supplement/57Ggy/how-to-pass-the-course

Number Bases

https://www.coursera.org/learn/uol-cm1015-computational-mathematics/lecture/nPHpG/introduction-to-number-bases-conversion-to-decimal

For any number base b, written with positions n such as:

$$ a_n a_{n-1} a_{n-2} ... a_0 $$

the conversion to decimal will be:

$$ a_n * b^n +  a_{n-1}* b^{n-1} + ... +  a_0*b^0 $$

Binary

• 0 - 00000000 
• 1 - 00000001 
• 2 - 00000010 
• 3 - 00000011 
• 4 - 00000100 
• 5 - 00000101 
• 6 - 00000110 
• 7 - 00000111 
• 8 - 00001000

$ 1001_2 \\ = 1*2^3 + 0*2^2 + 0*2^1 + 1*2^0  \\ = 8 + 0 + 0 + 1 \\ =  9_{10} $

$ 100 101 011_2 = \\
= 1*2^8 + 0*2^7 + 0*2^6 + 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = \\
= 1*256 + 0*128 + 0*64 + 1*32 + 0*16 + 1*8 + 0*4 + 1*2 + 1*1 = \\
= 256 + 32 + 8 + 2 +1 = \\ = 299_{10} $

Decimal

count to 9, then zero add 1 in front to make 10. and so on

$ 127_{10} \\ = 100 + 20 + 7 \\ = 1*10^2 + 2*10^1 + 7*10^0 $

Hexadecimal (base 16)

0, 1, 2, ..., 9, A, B, C, D, E, F

$ 1F_{16} =  1*16^1 + 15*16^0 =  16 + 15 =  31_{10} $

Sexagesimal

 - Sumerians, Babylonians, angles, time, etc.


Method of repeated division