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Math 1
Nature of Mathematics
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What is Mathematics?
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.As a language, mathematics uses symbols, operations and
relations.
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.As a language, mathematics uses symbols, operations and
relations.
There are four basic orprimitivemathematical objects:
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.As a language, mathematics uses symbols, operations and
relations.
There are four basic orprimitivemathematical objects:
1 numbers
Math 1 Nature of Mathematics
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.As a language, mathematics uses symbols, operations and
relations.
There are four basic orprimitivemathematical objects:
1 numbers
2 sets
Math 1 Nature of Mathematics
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.As a language, mathematics uses symbols, operations and
relations.
There are four basic orprimitivemathematical objects:
1 numbers
2 sets
3 statements
Math 1 Nature of Mathematics
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What is Mathematics?
Definition
Mathematics came from the Greek wordmathematawhich literally
means things learned.
Mathematics is also described as a language.As a language, mathematics uses symbols, operations and
relations.
There are four basic orprimitivemathematical objects:
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
1 Hindu-Arabic Numerals:
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
1 Hindu-Arabic Numerals:
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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Rules on operations: PEMDAS
Examples:
1 1 + 2 3 4
1 + 2 3 4
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Rules on operations: PEMDAS
Examples:
1 1 + 2 3 4
1 + 2 3 4 = 1 + 6 4
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Rules on operations: PEMDAS
Examples:
1 1 + 2 3 4
1 + 2 3 4 = 1 + 6 4
= 1 +3
2
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Rules on operations: PEMDAS
Examples:
1 1 + 2 3 4
1 + 2 3 4 = 1 + 6 4
= 1 +3
2
= 2 12
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Rules on operations: PEMDAS
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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Rules on operations: PEMDAS
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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Rules on operations: PEMDAS
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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Rules on operations: PEMDAS
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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Rules on operations: PEMDAS
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
Given any two real numbers a and b, only one of the following is true:
1 a = b
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Numbers
Relations
Theorem
Given any two real numbers a and b, only one of the following is true:
1 a = b
2 a > b
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Numbers
Relations
Theorem
Given any two real numbers a and b, only one of the following is true:
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
Math 1 Nature of Mathematics
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