A Friendly Introduction To Abstract Algebra It is safe to say most people are familiar with Algebra from High School which involves solving and manipulating equations where operation(s) is/are defined. In Abstract Algebra ,however, we set out to find the hidden rules or assumptions we make when solving equations. …

Now that we’ve climbed the Olympus of abstractness when we explored what Objects and Operators are, I believe you are ready to put what you know to good use as we now focus our attention on the D-Operator method, an algorithm for getting the particular solution of an Ordinary Differential…

Tricks Of The Trade In Undergraduate Mathematics-Operators Understanding mathematical objects is paramount to problem solving because if you don't even know the players involved you can't understand what the problem is in the first place. In my last post we saw what mathematics objects are and we dealt with two…

Last time we explored the importance of thinking about questions by virtue of two examples; one basic and the other requiring a bit more work. Now in this article we focus on understanding the key players in a mathematical problem. Objects and the operators that act on them. Objects What is…

On Mathematical thinking and philosophical schools of thought. — The foundations of mathematics are inherently philosophical so if we are to fully grasp the subject, we have to grasp its foundations. Now by foundations I do not mean going all out on a crash course in the philosophy of mathematics(it would be nice if you did though). What I…

While Undergraduate mathematics seems to be a taught differently to it’s High School counterpart, it does not imply that the underlying mathematics is different. …