初等代数学、代数学、幾何学、三角法

If the currently listed section times do not suit you, please contact me to arrange a more suitable time, pending availability. 


PREREQUISITES:
   
Your learner will need to have prior knowledge of the following:

- Basic Arithmetic Skills including Addition, Subtraction, Multiplication, Division
- Fractions and Decimals
- Ratios and Percentages
- Variables
- Inequalities
- Exponents
- Knowledge of basic geometry such as finding the perimeter and area of different shapes
- Recognition of Patterns
- The ability to do word problems
- Different Categories of Shapes
- 2 and 3 dimensional shapes
- Parallel and Perpendicular Lines
- How to Prove Something i.e. Show the Steps to Working Out Mathematic Problems
- Sets
- Logic
- Real Number Systems and Number Theory
- Number Representation and Calculation
- Money Management
- Probability
- Statistics
- Metric Measurement
- Voting and Apportionment
- Graph Theory

If you are unsure as to whether your learner has already covered these pre-requisites, please contact me for further details; I also offer another course which covers these topics, therefore your learner may need to take that course first before enrolling in this course.

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It is often said that mathematics is the language of science. 
If this is true, then an essential part of the language of mathematics is numbers. 
The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. 
Farmers, cattle herders, and traders used tokens, stones, or markers to signify a single quantity; a
sheaf of grain, a head of livestock, or a fixed length of cloth, for example. 
Doing so made commerce possible, leading to improved communications and the spread of civilisation.
Three to four thousand years ago, Egyptians introduced fractions. 
They first used them to show reciprocals. 
Later, they used them to represent the amount when a quantity was divided into equal parts.
But what if there were no cattle to trade, or an entire crop of grain was lost in a flood? 
How could someone indicate the existence of nothing? 
From earliest times, people had thought of a “base state” while counting and used various symbols to represent this null condition. 
                                                                                           
However, it was not until about the fifth century CE in India that zero was added to the number system and used as a numeral in calculations.
Clearly, there was also a need for numbers to represent loss or debt. 
In India, in the seventh century CE, negative numbers were used as solutions to mathematical equations and commercial debts. 
The opposites of the counting numbers expanded the number system even further.
Because of the evolution of the number system, we can now perform complex calculations using these and other categories of real numbers. 
In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
                                                                                                   
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Pre-Algebra:

Day 1: Whole Numbers

Day 2: The Language of Algebra

Day 3: Integers

Day 4: Fractions

Day 5: Decimals

Day 6: Percents

Day 7: The Properties of Real Numbers

Day 8: Solving Linear Equations and Inequalities

Day 9: Models and Geometry

Day 10: Polynomials

Day 11: Graphs
                                        
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Elementary Algebra:

Day 12: Systems of Linear Equations

Day 13: Factoring

Day 14: Rational Expressions and Equations

Day 15: Roots and Radicals

Day 16: Quadratic Equations

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Intermediate Algebra:

Day 17: Graphs and Functions

Day 18: Polynomials and Polynomial Functions

Day 19: Rational Expressions and Functions

Day 20: Quadratic Equations and Functions

Day 21: Exponential and Logarithmic Functions

Day 22: Conics

Day 23: Sequences, Series, and Binomial Theorem

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Algebra and Geometry:

Day 24: Polynomial and Rational Functions

Day 25: Analytic Geometry

Day 26: Sequences, Probability, and Counting Theory

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Algebra and Trigonometry:

Day 27: The Unit Circle - Sine and Cosine Functions

Day 28: Periodic Functions

Day 29: Trigonometric Identities and Equations

Day 30: Further Applications of Trigonometry

Day 31: Systems of Equations and Inequalities

Day 32: Overview of this Course and a Preview of the Precalculus to Calculus Course