Mathematics Course - University of El Oued - PDF
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University of El Oued
2024
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This document presents an introduction to mathematics, covering a range of topics such as number sets, including natural, cardinal, ordinal numbers; operations like addition, subtraction, multiplication, division; and geometric shapes.
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# University of El Oued ## Exact Sciences Faculty ## Mathematic Department ### Academic Year 2024/2025 # English for Mathematics Students ## Course I # Numbers Sets - Set of Natural numbers N = {1, 2, 3, 4,...} - Cardinal numbers (Counting numbers) - Table 1: Numbers in letters...
# University of El Oued ## Exact Sciences Faculty ## Mathematic Department ### Academic Year 2024/2025 # English for Mathematics Students ## Course I # Numbers Sets - Set of Natural numbers N = {1, 2, 3, 4,...} - Cardinal numbers (Counting numbers) - Table 1: Numbers in letters | Number | Letter | | --- | --- | | 1 | one | | 2 | two | | 3 | three | | 4 | four | | 5 | five | | 6 | six | | 7 | seven | | 8 | eight | | 9 | nine | | 10 | ten | | 11 | eleven | | 12 | twelve | | 13 | thirteen | | 20 | twenty | | 41 | forty-one | | 100 | one hundred | | 101 | one hundred and one | | 1000 | one thousand | | 1005 | one thousand and five | | 3067 | three thousand and sixty-seven | - Ordinal Numbers (Place Numbers) - Table 2: Numbers in letters | Number | Letter | | --- | --- | | 1st | first | | 2nd | second | | 3rd | third | | 4th | fourth | | 5th | fifth | | 6th | sixth | | 7th | seventh | | 8th | eighth | | 9th | ninth | | 10th | tenth | | 11th | eleventh | | 12th | twelfth | | 21st | twenty first | | 22nd | twenty second | | 23rd | twenty-third | | 30th | thirtieth | | 40th | fortieth | | 100th | hundredth | | 101st | one hundred first | | 1000th | thousandth| - Whole numbers - Set of whole number: NU {0} = {0,1,2,3,...}. - Odd Numbers: 1, 3, 5,... 2n+1,... - Even Numbers: 0, 2, 4,... 2n... - Set of Integers: Z = {, -3, -2, -1, 0, 1, 2, 3,...} - Set of Rational numbers: Q = {; a ∈ Z, n∈N} Example: -3/7 - Set of Real numbers: R Examples: 2, 548. 2, π, exp(1)=e - Set of Complex numbers: C = {z = x + iy; x,y ∈ R, i² = -1} - Examples: 2+3i, √3+1, cos(x)+sin(x).i ## Course II # Operations & Binary Relations ## Operations on Numbers ### Operations List | Operation Name | Operation spelling | |---|---| | Addition | + plus | | Subtraction | - mines | | Multiplication | x times | | Division | ÷ or / divided by | ### Examples | Operation | Example | Written in full | |---|---|---| | two + three = five | 2+3=5 | two plus (or) and three is equal to (or) equals (or) gives five | | five - four = one | 5-4=1 | five mines four is equal to (or) equals one | | two x five=ten | 2×5-10 | two times (or) multiplied by five is equal to ten | | nine ÷ three = three | 9:3-3 | nine divided by (or) over three equals three | ### Comparison | Operation | Operation spelling | |---|---| | < | less than | | ≤ | less than or equal | | > | greater than | | ≥ | greater than or equal | | ≈ | approximately equal | ## 1.2 Fractions, Powers, Roots ### Fractions - consist of a numerator (above the fraction bar) and a denominator (below the fraction bar). - Fractions can be simple (2) or mixed (1 1/2). - You can do arithmetic calculations with fractions, i.e. you can add, subtract, multiply, divide or even cancel fractions. - Example: - 1/2 a half - 1/3 a third - 1/4 a quarter - 2/5 two fifths ### Powers - mean to raise the value of a number to an exponent. - Exponents allow us to write multiplications in short. - Example: a<sup>n</sup> - a is the base - n is the exponent - y is the exponential value - x<sup>2</sup> means x is raised to the power of two, or x is squared - x<sup>3</sup> means x is raised to the power of three, or x is cubed ### Notice! - Numbers with negative exponents can also be written as fractions. The base is then given a positive exponent and is placed as the denominator. - Example: x<sup>-n</sup> ### Roots - are written with a radical sign √. - You can have a square root, a cube root or the nth root of a number. ### Powers of ten - Positive numbers greater than 1 are expressed with a positive exponent and positive numbers less than 1 are expressed with a negative exponent ## 1.3 Geometry - Geometry is a branch of mathematics that is concerned with the properties of angles, shapes, lines, curves, surfaces and solid objects. ### Angles - An angle may be acute, flat, obtuse, reflex or right. ### Task 1 1. An angle of 90º is a right angle 2. An angle which equals 180º is a/an **straight** angle 3. An angle which is less than 90º is a/an **acute** angle 4. An angle which is greater than 180º is a/an **reflex** angle 5. An angle which is between 90º and 180º is a/an **obtuse** angle ### Triangles -Triangles are geometric forms with three angles and three sides. They can be classified according to their sides or angles. -Sides and angles can be calculated using the **Pythagoras' theorem.** - a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> - a = side - b = side - c = hypotenuse ### Task 2 Describe the Pythagorean theorem. *The Pythagorean Theorem states that for right triangles, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.* ### Task 3 Name the triangle types. 1. **Scalene** triangle 2. **Equilateral** triangle 3. **Isosceles** triangle ### Sides or Legs of Triangles - A scalene triangle has three sides all with different lengths. - An isosceles triangle has two sides or legs of equal length. - In an equilateral triangle all sides are equal. ## 2-D and 3-D Shapes - Objects have forms or shapes with different dimensions regarding length, width, height or depth - They can be drawn or presented in two or three dimensions. - Two dimensional shapes (2-D) are flat forms with length and width. - Three dimensional shapes (3-D) additionally have depth or thickness, as they are seen in reality. ### Task 4 Enter the words into the right columns. - cone - cube - cylinder - hexagon - polygon - prism - pyramid - rectangle - sphere - square - triangle | 2-D Shapes | 3-D Shapes | |---|---| | square | cube | | | cylinder | | | sphere | | | prism | | | pyramid | | | cone | | | hexagon | | | rectangle | | | triangle | ## MATH SYMBOLS | Symbol | Description | |---|---| | + | Addition or positive | | - | Subtraction or negative | | x | Multiplication | | ÷ | Division | | = | Is equal to | | √ | Square root | | ≈ | Is approximately equal to | | < | Is less than | | > | Is greater than | | ≤ | Is less than or equal to | | ≥ | Is Greater than or equal to | | ≠ | Is not equal to | | % | Percent | | Δ | Triangle | | ∞ | Infinity | | π | Pi | | |x| | Absolute value of x | | ⇔ | Material equivalence | ## Task 2 Complete the table for these basic mathematical calculations. | Operation | Verb | Example | Written in full | |---|---|---|---| | addition | to add | 5+4=9 | Five plus four equals (or: is equal to) nine. | | subtraction | to subtract | 45-5=40 | Forty five minus five equals (or: is equal to) forty. | | multiplication | to multiply by / times | 50*5=250 | Fifty multiplied by five equals (or: is equal to) two hundred and fifty. | | division | to divide by | 55:5=11 | Fifty five divided by five equals (or: is equal to) eleven. | | fraction | to calculate the fraction | 2 1/2, 4 1/4 | Two and a half, Four and a quarter | | root exctraction | to exctract the root | √4, √27, √16 | The square root of four, the cube root of twenty seven, the square root of sixteen. | | power | to raise to a power | x<sup>2</sup>, x<sup>3</sup>, x<sup>n</sup>, x<sup>m</sup> | x squared, x cubed, x raised to the power of n, x raised to the power of m | ## Signs and Symbols - Using signs and symbols, you can express whether a value is greater than or less than, equal to or only approximately equal to another value. - A value can be written in brackets or can be within the limits of something. ### Mathematical Signs | Symbol | Description | |---|---| | > | greater than | | < | less than | | ≠ | is not equal to, is unequal to | | Σ | sum of | | |x| | the absolute value of x | | n! | factorial n | | % | percentage / per cent | | / | slash | | ∫ | integral of | | ≈ | approximately equal to | | f(x) | the function of x | | x<sub>1</sub> | x sub one | | ( ) | round brackets | | [ ] | square brackets | | { } | braces, curly brackets | | x' | x prime |