What is Mathematics?
Why is there a 50/50 chance of two people in a room of 20 having their birthday on the same day? What are the odds of getting the winning hand on the "river" in Texas Hold 'Em? How do I calculate a fair tip on my restaurant tab? How many cans of paint do I need to purchase for the rooms I'm painting? How do I know when to leave home for Fort Langley for an 11 AM tee-off time?
- A man has a goat, a wolf, and a head of cabbage. He must cross a river in a boat that will carry him and only one of his possessions at a time. If left alone, the wolf will eat the goat or the goat will eat the cabbage. The river is too wide and cold for swimming or tossing the cabbage across. How does he accomplish his mission?
- Twelve coins are in a bag. They look alike but one is counterfeit and either heavier or lighter than the others. Use a balance scale to find the fake coin in three weightings, and determine if it is lighter or heavier than the others.
- There are two red hats and three blue hats. Three students cover their eyes, their teacher puts a hat on each of their heads, and hides the other two. The students are told that if they guess wrong they will be assigned extra work. One student at a time will uncover their eyes and either provide an answer or pass. Neither can see their own hat. Jane is first. She looks at the other two and does not wish to risk a guess. Bob is next. He looks at the other two and after a moment he also passes. Janice is last. She looks at the other two, thinks of their responses, smiles and gives the correct answer. How does she know, and what colour is her hat?
- Find the missing number in the circle below:
Solving the above four problems requires the application of logical reasoning. Mathematics requires the same basic skills.
Mathematics is the science of structure, order, and relation that has evolved through elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation. Its development has involved an ever increasing degree of idealization and abstraction. While there are records of mathematics in many areas of the world, such as India and China, new developments from the 1500s to the late 1900s have been largely concentrated in Europe and North America.
Mathematics is traditionally categorized under the following branches: arithmetic, algebra, analysis, combinatorics, Euclidean geometry, game theory, number theory, number analysis, optimization, probability theory, set theory, statistics, and trigonometry.
Perhaps the most basic notion in mathematics is the equation, a formal statement that two sides of a mathematical expression are equal (as in the equation x2 – 3 = 13) and that both sides of the equation can be simultaneously manipulated by adding, subtracting, dividing, taking roots, etc. in order to solve the equation. A number of graphical methods have been developed for describing data used in mathematics; a variety of numerical measures are used to summarize data, including proportions, percentages, averages, means, modes, range, percentiles and variance; and the use of angles and angle functions (sine, cosine, tangent, secant, cosecant, cotangent) in relation to right angles are commonly found in mathematical problems of a trigonometric nature.
A strong knowledge base of mathematics is mandatory for the wealth of our nation. Unfortunately, while Canadian youth do relatively well in comparison with youth in many other participating areas of the world, there is a general disassociation and relative phobia of mathematics amongst our youth and society at large. Many teachers teaching mathematics in the developmental years of schooling lack a math background. Many guidance counselors discourage taking the regular stream of math for those with less than stellar achievements. It creates a "can't do it" mindset. Add to that the general lack of parental discomfort with mathematics leading to their restricted ability to offer assistance and less than favourable portrayals of mathematics in the media, comics and movies, and it all threatens to throw our society into a dark age of mathematics at the very time we need mathematics the most.
This is where you can count. Whether you pursue an educational pathway that includes a reasonable amount of mathematics, or follow a pathway that is limited in mathematical contact, you will require at least a working knowledge of mathematics in your daily life. Become math literate and contribute to our nation's economic growth.
Mathematics is offered at Kwantlen at the Surrey and Richmond campuses, with a select offering at the Langley campus. Check out these offerings in the Calendar. If you need Q credits for your degree, or mathematics credit for education, take a look at our Mathematical Explorations (MATH 1116) course. You will find it very entertaining and rewarding. For those with a general interest in mathematics or in teaching in the secondary school system, watch for a future minor in Mathematics for Kwantlen's Bachelor of Arts degree.