What major topics are there in arithmetic and what order to learn them?

[mark2142]

TL;DR Summary: What topics to cover to safely say I know arithmetic ?

I am learning arithmetic from Indian NCERT textbook. Currently I have finished addition ,substraction of 2 digit numbers and divisions, multiplication of 1 digit numbers. I am moving pretty slowly. Can someone tell me what topics to cover first to build a framework and then go on in detail. I want to learn fast. It has taken me a year now learning arithmetic. I want to speed up. Thanks for the help in advance. (I also have a book called arithmetic for the practical man by Thompson.)

 

[fresh_42]

I could be wrong since your description lacks details, so I have to make guesses. This sounds to me as if you were currently studying something like taught in this book:
https://openstax.org/details/books/prealgebra-2e

You could go on from there to the other (free pdf) books on that webpage.

 

[jedishrfu]

Here’s a youtube video called the Map of Mathematics

 

[mark2142]

I could be wrong since your description lacks details, so I have to make guesses. This sounds to me as if you were currently studying something like taught in this book:
https://openstax.org/details/books/prealgebra-2e

You could go on from there to the other (free pdf) books on that webpage.

1. How did indians come up with such positional system ? Even though its simple but Looks mysterious.

2. Why 400 + 20 +3 is written as 423 ? Why have we omitted zeros ?

3. Why four hundred is written as 400 and not as 4 hundred or 4. Similarly why twenty is written as 20 and not as 2 ten or 2 ?

4. What is place value notation ? Is it different from place value ?

 

[WWGD]

1. How did indians come up with such positional system ? Even though its simple but Looks mysterious.

2. Why 400 + 20 +3 is written as 423 ? Why have we omitted zeros ?

3. Why four hundred is written as 400 and not as 4 hundred or 4. Similarly why twenty is written as 20 and not as 2 ten or 2 ?

4. What is place value notation ? Is it different from place value ?

It seems you're looking more for history of Mathematics and Arithmetic than Arithmetic itself.

 

[jedishrfu]

Jan Gullberg's book:

https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X?tag=pfamazon01-20

It's a good place to start, part historical and part tutorial up to first-year college math.

I don't think it has Eskimo math:

https://en.wikipedia.org/wiki/Kaktovik_numerals

Invented by school children in 1994, to go along with their cultural traditions and use of base-20 math in their native language.

 

[fresh_42]

1. How did indians come up with such positional system ? Even though its simple but Looks mysterious.

2. Why 400 + 20 +3 is written as 423 ? Why have we omitted zeros ?

3. Why four hundred is written as 400 and not as 4 hundred or 4. Similarly why twenty is written as 20 and not as 2 ten or 2 ?

4. What is place value notation ? Is it different from place value ?

These are interesting questions and not easy to answer. As far as I know, the Indians were the first culture to give zero a symbol that ended up in our 0. The Babylonians, later, also introduced a symbol for an empty space. Western history writing basically starts with the Sumerians. I had a hard time searching for Indian sources, and it was even harder to figure out what had been migrated from India to Sumer or Babylon. They are not that far away from one another, so there might have been a cultural exchange along trading paths.

I like to consider the finding of zero as the beginning of mathematics: Someone decided to count what wasn’t there! Just brilliant! However, the truth is as often less glamorous. Babylonian accountants needed a placeholder for an empty space for the number system they used in their books. The digits zero to nine have been first introduced in India. In Sanskrit, zero stands for emptiness, or nothingness.

Source: https://www.physicsforums.com/insights/counting-to-p-adic-calculus-all-number-systems-that-we-have/