1 -Nature of Mathematics

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Math 1

Nature of Mathematics

Math 1 Nature of Mathematics
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What is Mathematics?

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Definition

Mathematics came from the Greek wordmathematawhich literally

means things learned.

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Definition



Mathematics is also described as a language.

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Definition



Mathematics is also described as a language.As a language, mathematics uses symbols, operations and

relations.

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Definition




relations.

There are four basic orprimitivemathematical objects:

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Definition




relations.


1 numbers

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Definition




relations.


1 numbers

2 sets

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Definition




relations.


1 numbers

2 sets

3 statements

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Definition




relations.


1 numbers

2 sets

3 statements

4 forms

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NumbersSYMBOLS

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NumbersSYMBOLS

1 Hindu-Arabic Numerals:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

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NumbersSYMBOLS


0, 1, 2, 3, 4, 5, 6, 7, 8, 9

2 Roman numerals:

I, V, X, L, C, D, M

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NumbersSYMBOLS


0, 1, 2, 3, 4, 5, 6, 7, 8, 9

2 Roman numerals:

I, V, X, L, C, D, M

3

Egyptian Numerals:

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Roman Numerals

Roman Hindu-Arabic

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Roman Numerals

Roman Hindu-Arabic

I 1



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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

X 10



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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

X 10L 50

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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

X 10L 50

C 100

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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

X 10L 50

C 100

D 500

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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

X 10L 50

C 100

D 500

M 1,000

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Roman Numerals

Roman Hindu-Arabic

I 1

V 5

X 10L 50

C 100

D 500

M 1,000

Example: MCMXCVIII - 1998

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Egyptian Numerals



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Numbers

OPERATIONS

1 Addition (+)

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

3

Multiplication (

)

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

3

Multiplication (

)4 Division ( )

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

3

Multiplication (

)4 Division ( )

5 Exponentiation

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

3

Multiplication (

)4 Division ( )

5 Exponentiation

6 Extracting a root

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

3

Multiplication (

)4 Division ( )

5 Exponentiation

6 Extracting a root

Operations (1)-(4) are calledbinary operations

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Numbers

OPERATIONS

1 Addition (+)

2 Subtraction (-)

3

Multiplication (

)4 Division ( )

5 Exponentiation

6 Extracting a root

Operations (1)-(4) are calledbinary operationswhile operations (5)and (6) are calledunary operations

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Rules on operations: PEMDAS

Examples:

1 1 + 2 3 4



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Examples:

1 1 + 2 3 4

1 + 2 3 4

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

= 2 12

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

= 2 12

2 40 10 3 8 + 5

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

= 2 12

2 40 10 3 8 + 5

40 10 3 8 + 5

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

= 2 12

2 40 10 3 8 + 5

40 10 3 8 + 5 = 4 3 8 + 5

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

= 2 12

2 40 10 3 8 + 5

40 10 3 8 + 5 = 4 3 8 + 5

= 12 8 + 5

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Examples:

1 1 + 2 3 4

1 + 2 3 4 = 1 + 6 4

= 1 +3

2

= 2 12

2 40 10 3 8 + 5

40 10 3 8 + 5 = 4 3 8 + 5

= 12 8 + 5

= 9

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Numbers

Relations

Theorem

Given any two real numbers a and b, only one of the following is true:

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Numbers

Relations

Theorem


1 a = b

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Numbers

Relations

Theorem


1 a = b

2 a > b

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Numbers

Relations

Theorem


1 a = b

2 a > b

3 a < b

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Exercises

1 Convert the following numbers to the indicated system.

a. 1983 to Egyptian hieroglyphicsb. 1987 to Roman numerals

c. 1991 to Egyptian hieroglyphics

d. 2003 to Roman numerals

e. 2008 to Egyptian hieroglyphics

2 Convert the following to Hindu-Arabic numerals.a. CLVI

b. DCCLVI

c. MDCCLXV

d. XCIV

e. CMXCIX3 Perform the indicated operations.

a. 28 14 7 4 + 2

b. 35 2 5 + 7 23

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Documents

1 -Nature of Mathematics