In the Internet age, there is a general demand that any question we have, there is an answer for. This convenience in some ways has corrupted our education. If there is a problem we don't know the answer to, it is extremely tempting to just Google the problem to find the solution. We have lost touch with the idea that discovery requires struggle, effort. This is a huge problem in mathematics. From arithmetic through things like the first calculus series, differential equations and linear algebra it is mostly possible to type verbatim a problem in a textbook and find an answer for it online. I myself have done this many times. My justification, and the justification I have heard for other people is.. I had no idea how to start and I just needed some direction. We feel like it is no different than going to office hours, or asking in class how it is done. The main difference here is, the teacher had no say about how much of the problem you saw, and if you did see the problem completed in completion, there is no possible way for the work to be your own anymore. I came to this realization during my Linear Algebra class, where half the class was accused of cheating by coping a written proof that used information that was not within the bounds of what we learned in this class. She did not say who in the class it was, but I think some people came to her office, possibly even ones that didn't cheat, with guilty consciences about to what extent they were using "outside resources." My professor's point of view? She viewed using any answer that she did not give cheating. She truly saw homework as a line of communication between herself and the students. That circumventing her and consulting the Internet with your problems was not admitting that you were having difficulty with the subject. She also felt it cheated you out of genuinely struggling to find the answer on your own. She felt that this struggle was paramount to actually understanding what was going on.
This is the purpose of this blog. This blog is a journal of my struggle to understand mathematics in a truly meaningful way. This doesn't mean I need to understand the application of everything. I just want to be able to demonstrate true understanding of what I am learning about, and I want to start using the Internet in a new way. I want to share how I came to understand the things in math in my own language. By posting it on the Internet, I want to open up my work and my wording for the world to criticize. This blog may contain mathematically incorrect information for this reason. What this math blog does contain is mathematics to the best of my knowledge.
One of the roadblocks to starting this blog was actually quite silly. I wanted a clever name for it. Instead of struggling with this issue, I outsourced the problem to my overly clever friends, who came up with a fairly sizable list of good ideas, such as...
- Sum Blog
- Off on a Tangent
- Different(ial) Strokes
- Road Sines
- The Right (Angle) Stuff
- Integrated Education
- Linear Algeblog
- Fractions of a Thought
- Actue Math Blog
- You Can Count on Me
- Parabloggic Curve
- Complex Roots
I ended up choosing Complex Roots for its multiple meanings.
First of all for it's mathematical meaning (which will be given in the next post).
Secondly, I like the imagery that the word "roots" brings. Roots in a more poetic sense can refer to a foundation. I think many people have complex roots in mathematics. For some people, at some point in their life, they got convinced that they were "bad" at mathematics. Or weren't a "math person." These people may not have been bad at math their whole life, but the just hit a wall at some topic and never broke through it. Some other people want to enter into a science or engineering career and see upper level mathematics as this huge roadblock to getting there. People's emotional foundations with math can be very complex.
Third, in a more academic sense, mathematics is an extremely cumulative subject. Rarely do we learn something in mathematics that is not a precursor for something to come. At some point, a class may have moved to fast for us, or we skipped a class, or we got sick and there ended up just being a hole in our mathematical education. There is an assumption as we progress through mathematics that we have perfect understanding of all the mathematics that came before that class. There is an assumption we all have the same mathematical foundation, the same mathematical roots. But this is not true. Some of our roots may be more developed than others. Even if we never missed a class, got a 4.0, over time we forget things that we don't use that much.
As I've progressed through upper level math (I am in Linear Analysis right now, which is the last class in the Linear Algebra, Differential Equations series. This series usually comes after the first calculus series). I have found some of the questions that take the most time in class do with a gap in understanding from something much more basic. In my Linear Analysis class the teacher spent 20 minutes explaining how to factor a polynomial of degree 3, then how to divide polynomials, both topics covered in Algebra.
No matter what your mathematical roots are, I hope that you find this blog insightful in some way. I plan on most of my posts being about explaining a mathematical topic that I am currently working on. I also plan on returning to topics where my own roots are not well developed. Since one of my goals in life is to become a math teacher, I may also write my thoughts and research about mathematical education. I am also willing to write posts on roots you want to develop. In fact, I hope to be able to respond to any and all questions and criticism I receive. I want to live in a world where failure and mistakes in mathematics are completely fine. Where it is totally fine to not understand something at the same rate as someone else, or to understand math at the rate your school wants you. I will never insult *anybody's* question, no matter how basic they are. Nobody is ever stupid for not knowing a piece of mathematical knowledge. It is just simply where you are in mathematics.