Definition
Algorithm is a set of sequential steps leading to the solution of a given problem.
If the problem is “ How to bake a cake ? “ then the recipe for a cake is the algorithm.
But the best definition of algorithms would be the one (or many), one may
come up with after studying algorithms for oneself.
History
History is the story of how we got to where we are at any given point of time.
Speaking of history of algorithms .... there is the history of how you in your life have come to know and study algorithms and also why. - This story is important because it will tell us how deeply we are interested in algorithms.
Then there is the history of when how and why algorithms were developed and what impact they had and are having on human society.
History helps us to re examine the path that lead us to the present and if necessary and possible correct our path or change direction and go on a different path.
Algorithms exist in Nature and hence we can say that algorithms are as old as the universe it self. Bio Algorithms or bio inspired algorithms or Neural Network algorithms are examples and proof of algorithms being part of Nature and hence as old as the Universe.
Study and Development of Algorithms and their application is of course unique to human species.
This study began in ancient times -as the human brain developed and civilizations began blooming in different parts of the world long long before the word algorithm was ever coined to refer to the procedures of numerical calculations based on the Indian numerals that were unknown to Europeans until Al Kharzwami wrote a book in Arabic on the Indian Numerals and it was translated into Latin with Al Kharzwami becoming Al Gorismi in Latin.
Eventually the arithmetic procedure of using Hindu or Indian Numerals has come to be known as Algorithm ( Algorismi+Arithemetic ).
Thus algorithm has become synonymous with numerical procedures or calculations and as knowledge of mathematics expanded and became very complex people began thinking of developing mechanical devices that can perform basic if not complex mathematical calculations which needed elaborate detailed instructions to be laid out and written for the mechanical engineers to develop the calculating machines.
With rapid developments in the fields of electrical and electronics the capacity and scope of electro-mechanical and digital calculators expanded vastly and the need for clear elaborate sets of instructions ( Algorithms ) for doing more advanced complicated mathematical operations only increased until computers were invented after which algorithms became all the more important for using the ever increasing computational power of computers.
Thus Algorithms, along with the computers running on algorithms have become extremely important for humans .
Here is an interesting video on history of Algorithms.
Importance
While algorithm is any set of instructions to solve any problem here we refer to only computer and math algorithms whenever we mention the word algorithm.
Giving importance to something or somebody depends on the need.
A computer science student needs Algorithms – So algorithms are important to him/her.
A farmer does not need algorithms – So algorithms are not important to him/her
An athlete does not need algorithms – So algorithms are not important to athletes
A veg/fruit vendor does not need algorithms – So algorithms are not important to them
A housewife does not need algorithms -So algorithms are not important to her
A driver does not need algorithms – So algorithms are not important to him/her
....and so on.
But none of them can live without a phone even for a day and its a fact no one can deny. That's how important mobile phones have become.
These phones come with a variety of apps ( or programs ) that are useful and essential to a farmer/athlete/housewife /driver/student..practically to every humanbeing on earth.
These apps can not function without the right algorithm being used to develop them.
With IOT (internet of things),machine learning and AI set to become an embedded part of tractor , scooter, fan, tap, kettle, cattle, plant, roof, wall, chair.....oven, fridge, stove, schoolbag, desk, cot, mattress, pillow and even our skin, skull, stomach. etc., ...... algorithms will become all pervasive and very invasive.
One can not be blamed for feeling that Its like a Monster being unleashed.
Here are some interesting videos on pros and cons of Algorithms.
Mastery
Mastery of algorithms requires more patience and diligence than intelligence.
If we can write an algorithm to master algorithms it might involve study of the following in the given order more or less.
Definition of algorithms
History of algorithms
Importance of algorithms
Classification of algorithms
Popular algorithms and applications
Analysis of algorithms
Rare and special algorithms
Development of new algorithms
Though not related to Algorithms, here is an interesting video on learning how to learn.