Mathematics Today
Mathematics is a human invention–our only perfect invention. It is something that exists only in our minds where only the shadows and projections of it are seen in our world…
There are several subjects in mathematics. These subjects can be categorized into two types: applied and pure. Applied math is stressed heavily, almost exclusively, in western education while pure mathematics is all but forgotten in public school systems. What is applied mathematics? If you have ever solved an equation, found the determinant of a matrix, found the area under a curve, … then you have experience applied mathematics, being very useful in real world situations and computations. We use it every day in figuring out our tips, balancing checkbooks, calculating sales taxes, and sales in general.
Unfortunately, this emphasis on applied mathematics gives the wrong impression of mathematics as a whole in my opinion. Sure, I enjoy computations which you can see in my post Math Web Apps where we play with primes and the geometric distribution. However, someone who is interested in mathematics and wishes to study it fresh out of high school more than likely has the wrong impression of what they will be truly be studying. Upper-undergraduate and graduate students of mathematics study maybe 10% applied mathematics and 90% pure mathematics.
So, what is pure math? Logic. Pure and perfect logic with splashes of creativity. In pure mathematics, a subject has a set of axioms, or definitions, that are assumed to be true. Then with these truths the subject is created. For example, every mathematician agrees that a line is a breadthless length. It was defined that way a long time ago by Euclid where he formed geometry in his book Elements.
Pure mathematics is not hard to learn but it takes a clear and logical mind to master. I have always found that learning is greatly supplemented by examples. But, before we jump into pure mathematics, It may be best for you to learn with something you like or are comfortable with. So, I have made the following quiz below that will help you decide if you are an algebraic person or a geometric person. Your results will then suggest which example to view which will either be geometry or algebra.
Algebraic or Geometric? Quiz
- In high school, did you prefer algebra or geometry? Algebra Geometry Both
- True or False: variables have less meaning to me than shapes. True False There is no difference
- Which of the options more clearly depicts a half? .5 ½
There is no difference. - When I add and subtract time, I think of the times digital representation. For example, if someone says, “meet me in 20 minutes” and it is 5:45, do you add 20 to 45? I think digitally I think of an analog clock I have another way
- Calculating values is more interesting than interpreting objects. True False Both are interesting