Introduction To Mathematics
Math is the study of the relationships between measurable quantities. It encompasses a wide range of fields and principles that explain how different ways to represent numbers can be connected. There are many connected areas of math: number theory (the study of how numbers behave), algebra (the study of symbolic representations of numbers), geometry (the study of shapes and their interactions), analysis (the study of continuous changes), and set theory (used to definitively explain mathematics). Math involves the manipulation of abstract objects derived from nature and is used to explain the behaviour of the universe. It also involves the use of reason to deduce proofs that are built on to derive new formulas and theorems. In mathematics, all proofs must be strictly rigorous without any unreasonable assumptions. Just like going to the gym to exercise and train your muscles, learning mathematics as a student is useful as training for the brain. Being highly proficient at math can also grant scholarship opportunities. This includes over 100000 dollars worth of scholarships at the University of British Columbia alone.
"Mathematics is the language with which God has written the universe." - Galileo Galilei
Big Ideas
1. Mathematical relationships can be generalized and represented in multiple connected forms. This includes Algebraic, quadratic, rational, trigonometric, and calculus. Algebra, graphs, tables, and symbolic rules all provide models to describe patterns and change.
2. Operations with numbers extend to more abstract structures. Things that apply to whole numbers also apply to rational numbers, powers, radicals, polynomials, and beyond. Fluency with operations grows from arithmetic to symbolic and algebraic manipulation.
3. Proportional reasoning is effective across different sections of mathematics. It involves ratios, rates, fractions, similarity, and trigonometry, enabling indirect measurement and comparison between number.
4. Geometry and measurement describe spatial relationships. Properties such as similarity, surface area, volume, and trigonometric ratios allow us to measure, compare, and reason about shapes in multiple dimensions.
5. Data analysis helps us interpret and make decisions from information. Understanding averages, variability, and their representations helps us evaluate reliability and draw meaningful comparisons.
