MMW L#3

mathematics language and symbol

Mathematics is written in a symbolic Language that is designed to express Mathematical thoughts.

schiro 1997

“one very important element in a student’s mathematical success is his competence to communicate mathematically.”

Language

is defined as a systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings.

1489, German arithmetic handbook

The familiar sign (+) for addition and the (–) sign for subtraction first appeared in

1557, Robert Recorded

equal sign

1631, William Ought Red

x sign

Johann Heinrich Rahn

division sign

Number system

is a way to represent numbers. We are used to using the base – 10 number system, which is called decimal. Other common number systems include base – 16 (hexadecimal), base – 8 (octal), and base – 2 (binary).

decimal

counting using fingers, Base 10 systems (0-9)

Binary

for computers, base 2 (0,1)

Octal

to shorten, base 8 (0-7)

Hexadecimal

bytes, base 16 (0-9, A-F)

Numbers

are fundamental concepts in mathematics that represent quantity. They are used for counting objects, measuring quantities, and performing calculations.

Natural numbers

fundamental numbers we use for counting (1)

Whole numbers

all natural numbers and the zero

integers

encompasses all whole numbers

rational numbers

fractions

irrational numbers

cannot be expressed as simple fraction

real numbers

set of all rational and irrational numbers

prime numbers

natural number greater than 1

composite number

number greater than 1 that is not prime

consecutive numbers

sequence of number that follow each other in order

variable

any letter or symbol that represents value

Co-efficient

a number of its own is called constant

precise

concise

powerful

characteristics of language of mathematics

nouns

are used to name things we want to talk about (like people, places, and things); whereas sentences are used to state complete thoughts.

Sentence

has at least one noun, and at least one verb. For example, consider the sentence: Ivana loves mathematics.

expression (noun)

a name given to a mathematical object of interest. Whereas in English we need to talk people, places, and things, we’ll see that mathematics has much different ‘objects of interest’.

mathematical sentence

just as an English sentence, must state a complete thought.

Grouping symbols

Exponents

Multiplication

Division

Addition

Subtraction

GEMDAS

variable

is a symbol that can be replaced by any number from a specified set of number.