1st Year Math Notes Chapter 1
Important Complete 1st Year Math Notes Chapter 1 of Number Systems written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of What are Number Systems for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Our comprehensive 1st Year Math Notes Chapter 1 will ensure you're fully prepared for your exams.
- History of number systems
- Number system in civilization
- What is Civilizations
- Chinese number system
- Egypt civilization
- Mayan number system
- Babylon number system
- Greek number system
- Roman number system
- Indian number system
- Type of numbers
- Natural numbers
- Whole numbers integers
- Odd integers even integers
- Rational numbers
- Irrational numbers
- Terminating decimals
- Recurring decimals
- History of Pi and its formula and value
- History and definition of complex number
- Applications of complex numbers
- Mobile communication
- Complex number in AC circuits
- Complex numbers are rotating the numbers
- Complex numbers on number line
- History of logarithm
- Definition of logarithm and its applications and explanations of types of Logarithm (i) Basic Logs (ii) Weirder logs (iii) Natural logs (iv) Even Weirder logs
- Properties of logarithms: (i) equality property (ii) product property (iii) power property (iv) quotient property
- Definition of real numbers, rational numbers with examples irrational numbers with examples, terminating decimals with examples.
- Complete solutions of each question of exercise 1.1
- Complete solutions of each question of exercise 1.2
- Complete solutions of each question of exercise 1.3
- What is modulus of a complex number
- De Moivre's Theorem.
- In the very beginning, human life was simple. An early ancient herdsman compared sheep (or cattle) of his herd with a pile of stones when the herd left for grazing and again on its return for missing animals. In the earliest systems probably the vertical strokes or bars such as I, II, III, llll etc.. were used for the numbers 1, 2, 3, 4 etc. The symbol “lllll” was used by many people including the ancient Egyptians for the number of ingers of one hand. Around 5000 B.C, the Egyptians had a number system based on 10. The symbol for 10 and for 100 were used by them. A symbol was repeated as many times as it was needed. For example, the numbers 13 and 324 were symbolized as and respectively. The symbol was interpreted as 100 + 100 +100+10+10+1+1+1+1. Diferent people invented their own symbols for numbers. But these systems of notations proved to be inadequate with advancement of societies and were discarded. Ultimately the set {1, 2, 3, 4, ...} with base 10 was adopted as the counting set (also called the set of natural numbers). The solution of the equation x + 2 = 2 was not possible in the set of natural numbers, So the natural number system was extended to the set of whole numbers. No number in the set of whole numbers W could satisfy the equation x + 4 = 2 or x + a = b , if a > b, and a, b, UW. The negative integers -1, -2, -3, ... were introduced to form the set of integers Z = {0, ±1, ±2 ,...). Again the equation of the type 2x = 3 or bx = a where a,b,UZ and b ≠ 0 had no solution in the set Z, so the numbers of the form where a,b,UZ and b ≠ 0, were invented to remove such diiculties. The set I a,b,UZ / b ≠ 0} was named as the set of rational numbers. Still the solution of equations such as x = a (where a is not a perfect square) was not possible in the set Q. So the irrational numbers of the type ± 2 or ± a where a is not a perfect square were introduced. This process of enlargement of the number system ultimately led to the set of real numbers = Q~Q’ (Q’ is the set of irrational numbers) which is used most frequently in everyday life.