Basic Number Theory

If I show you the following list: 2, 4, 6, 8, 10,..., you may immediately conclude that the next number after 10 is 12. Exploring number patterns can really help you develop a strong understanding of math concepts. It is my desire that you develop a love for this topic and others to come.

Ratios

Things are not always the same size. Thus, a natural need arises to compare quantities, using division to see how much bigger a quantity is when compared to another.

Proportions

Simply put, whenever we put an equal sign between two ratios and the ratio on the left is equal to the ratio on the right, we say that they form a proportion.

Linear Equations

System of linear equations can arise naturally from many real-life examples. Generally speaking, those problems come up when there are two unknown or variables to solve. Moreover, a system of equations is a set of two or more equations that must be solved at the same time. For this reason, a system could also be called simultaneous equations.

Proof By Mathematical Induction

Proof by mathematical induction is a powerful method that is used to prove that a conjecture (theory, proposition, speculation, belief, statement, formula, etc...) is true for all cases. Just because conjecture is true for many examples does not mean it will be for all cases. In order to show that the conjecture is true for all cases, we can prove it by mathematical induction.