it is difficult to keep track of the new gadgets and equipment that is being invented.
Should be an "are" here because of the word "and".
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The formal education or education that takes place in schools and classrooms is like the working of the computer.
I would suggest including commas to make it a parenthesis so as to avoid looking too messy.
The formal education, education that takes place in schools and classrooms, is like the working of the computer.
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tables of 13 and 23 and such
I actually didn't know what you were talking about. Then eventually I figured out that you probably were refering to the "multiplication table" or "time table". I might still be wrong, but I think you know what I'm implying.
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Or why we have to learn the long and winding lines of a poet, long dead and perhaps forgotten. But when it comes to the "real world", we may need the same tables to see if we can buy groceries from our daily allowance. Or win the heart of a lovely maiden using those very long and winding lines!
Starting a sentence with a conjunction like "or" often draws a little attention. Although it is widely acceptable to start a sentence with a conjunction, I think starting TWO sentences with "or" so close together might be a little uncalled-for.
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However, more importantly, we should go to school for our advance studies.
Can I suggest removing the word "However"? It seems a little redundant and, infact, the clause that follows seems to support the previous sentence rather then contradict it.
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It is important to learn the basics of any profession, be it Accounts, Architecture, Engineering or even Medicine, in the environment of a school or a college.
The study of accounts is known as accountancy. I would suggest that you change "Accounts" with the word "Accountancy". I'm not sure if you should be capitalizing all the initial letters of each field of study as they are established words. I don't think you should.