TABLE OF CONTENT S What is Mathematics 4 Timeline of Mathematics 5 Common Core and STEM 7 Number Systems 8 Counting 11 Addition 13 Subtraction 14 Multiplication 16 Division 19 Sets 22 Finite Sets 23 Infinite Sets 23 Subsets and Supersets 23 Venn Diagrams 24 Ratios 26 Proportions 28 Fractions 28 Decimals 32 Statistics 34 Averages 35 Probability 36 Algebra 37 Variables 37 Exponents 38 Roots 39 Equations 41 Coordinates and Grids 41 Geometry 43 Basic Geometry 43 Advanced Geometry 43 Lines 44 Angles 45 Triangles 46 Rectangles and Squares 48 Circles 51 Curves 53 Measurement 54 Length 55 Mass and Weight 56 Volume 58 Time 60 Temperature 61 Advanced Math 62 Calculus 62 Chaos Theory 62
MATHEMATICS What Is Mathematics When you think of mathematics you probably don’t think of science But mathematics is a science Mathematics is the study of numbers shapes change quantities and patterns It also looks at the relationships between them Math is a short way of saying mathematics Not only is mathematics a science all other scientists use math in their work Can you think of how a chemist biologist or astronomer might use math HOW SCIENTISTS USE MATH Scientists Biologists Chemists Meteorologists Physicists use math to compare microscopic objects sizes and shapes use math to measure chemicals for solutions use math to predict weather patterns use math to estimate lasers power S C I T A M E H T A M S I T A H W 4
MATHEMATICS Timeline of Mathematics 70,000 to 300 BC South Africa ochre rocks adorned with scratched geometric patterns 70,000 BC 35,000 BC to 20,000 BC Africa and France earliest known prehistoric attempts 20,000 BC 3400 BC 3100 BC 2800 BC 2700 BC 2600 BC 1000 BC 400 BC 300 BC 300 BC 300 BC to quantify time Nile Valley the Ishango Bone is possibly the earliest reference to prime numbers and Egyptian multiplication Mesopotamia the Sumerians invent the first numeral system and a system of weights and measures Egypt earliest known decimal system allows indefinite counting by way of introducing new symbols Indus Valley Civilization on the Indian subcontinent earliest use of decimal ratios in a uniform system of ancient weights and measures Egypt precision surveying Indus Valley Civilization objects streets pavements houses and multi-storied buildings are constructed at perfect right angles Egypt use of common fraction by Egyptians India mathematicians write a mathematical text which classifies all numbers into three sets enumerable innumerable and infinite Egypt Euclid proves the infinitude of prime numbers and presents the Euclidean algorithm Mesopotamia the Babylonians invent the earliest calculator the abacus India mathematician Pingala writes the Chhandah Shastra which contains the first Indian use of zero as a digit indicated by a dot and also presents a description of a binary numeral system along with the first use of Fibonacci numbers and Pascal’s triangle W H A T I S M A T H E M A T I C S 5
MATHEMATICS Timeline of Mathematics 260 BC to AD1100s Mexico the Olmecs people were using a true zero a shell glyph several centuries before Ptolemy Greece Eratosthenes uses his sieve algorithm to quickly isolate prime numbers Greece Hipparchus develops the bases of trigonometry India Indian numerals the first positional notation base-10 numeral system begins developing in India Greece Diophantus uses symbols for unknown numbers in terms of the syncopated algebra India the earliest known use of zero as a decimal digit is introduced by Indian mathematicians India Shridhara gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations Europe Al-Khawarizmi is considered father of modern algebra since he was the first to bring Indian mathematics to Europe Iran Ali Ahmad Nasawi divides hours into 60 minutes and minutes into 60 seconds India Indian numerals were modified by Arab mathe maticians to form the modern Hindu-Arabic numeral system used universally in the modern world Europe the Hindu-Arabic numeral system reaches Europe through the Arabs 250 BC 240 BC 140 BC 50 BC AD 250 AD 300 AD 700s AD 750 AD 1030 AD 1100s AD 1100s Like any science mathematics must show us things we didn’t know Proofs and theorems are the basis for math A proof is a mathematical argument that convinces others to believe it is true A theorem is a mathematical statement supported by one or more proofs Mathematicians can prove that theorems are true There are many proofs and theorems in math Mathematics uses reasoning and logic to solve problems In math you solve a problem by thinking Other sciences rely on experiments to solve a problem S C I T A M E H T A M S I T A H W 6
