**MTH100: General Mathematics**

A set is a mathematical model for a collection of different objects; A set contains elements or elements, which can be mathematical objects of any kind: numbers, symbols, space points, lines, other geometric shapes, variables, or other sets. MTH100 Handouts pdf

## MTH100 Handouts pdf

**Course Category: Mathematics **MTH100 Handouts pdf

**Course Outline**

Sets, Real Numbers, Complex Numbers, Functions, Quadratic Functions, Matrices, Inverse of a Matrix, Determinants, Arithmetic Progression and Arithmetic Series, Geometric progression and Geometric Series, Permutations and Combinations, Binomial theorem, Graphs and Functions, Straight Lines and Circles, Trigonometry, Statistics Introduction, Introduction to data, Frequency Distributions, Graphical representation of data, Measures Of Central Tendency, Range, inter quartile deviation mean deviation, Moments, Skewness and kurtosis. MTH100 Handouts pdf

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### MTH100 HANDOUTS

**MTH100: General Mathematics**

**Sets and Numbering Systems**

Mathematical research begins with the study of sets and the development of number systems. The whole mathematical system can be represented as a “set”; therefore, it is important for us to understand the meanings, notes, and structures of the “sets”.

#### Set

Set is a random collection of unique items. Items in a collection are called set elements.

Examples:

1-A group of people living in Lahore set.

Every person living in Lahore is part of the set.

2-A set of counting numbers is a set.

Each calculation number is an element of the set.

The listing specification set consists of rotating a set of objects with

instruments. For example, a set of counting numbers from 1 to 5 will be written as

{1, 2, 3, 4, 5}.

• The builder set notification has a standard {variable | descriptive statement}.

The straight bar (builder notification) is always read as “always”. Setting builder notes is often used if the list method is invalid or inadequate.

#### Universal Set

A universal set Is a set of all objects related to a specific conversation and is designated with the symbol U For example when working with all students enrolled in Virtual University, the Universal set will be

U = {all Virtual University students}

Some of the sets that remain in this universal set are:

A = {all Computer Technology students}

B = {first year students}

C = {second year students}

**Numbering Systems:**

Counting numbers are called natural numbers and a set of **natural** numbers is defined as N = {1,2,3 …}

• **Integers** are natural numbers, their fractions, and zero. The set of whole values is defined as Z = {…-3, -2, -1, 0,1,2,3 …}

• **Rational** numbers such as 2/3, -31/ 2, 0.3333, numbers that can be written as the ratio of two whole numbers. A set of Rational numbers is denoted by Q. This set includes

o Repeating decimals, terminating decimals and fractions

o integers are also Rational numbers as each number a can be written as a fraction a/1

• Irrational numbers are numbers that cannot be written as fractions.

o 3. 45455455545555 … has a pattern but does not repeat. It doesn’t make sense. It cannot be written as a fraction.

o 2 square root, π (Pi), and e are also irrational.

• The union of a set of rational numbers and a set of odd numbers is a set of real numbers, defined by R.

**Cardinality**

Cardinality refers to the number of elements of a set. The cardinality of a set A is denoted by |A|.

- A finite set contains a fair number of items.
- An infinite set has at least as many features as a set of natural numbers.

**History**: Numbers were originally used for calculations and natural numbers did the job well. However, there are no mathematical solutions of x + 4 = 0. To solve this, natural numbers are multiplied by the addition of negative numbers. This is done by attaching the “-” symbol (which we now call the minus sign) to each natural number and calling the new number “negative” of the first number. This was extended to all real numbers.

Now people had the mathematical solutions of x + 4 = 0, but the x2 + 4 = 0 form math had no solutions. No real number is a square of 4. The number system had to be extended to accommodate the square root of negative numbers. The symbol,, was coined and referred to as the “mental unit”. Real numbers are multiplied by attaching the imaginary unit to each number and calling it the “imaginary copy” of real numbers.