A whole new world of mathematics
This site is designed to expose its readers to a world of mathematics that is not covered in middle school or high school math curricula. It is a world of abstraction and logic, and a world without mundane repetition or arbitrary rules. This math is usually not taught before the second or third year of an undergraduate math major’s curriculum, and therefore many people live out their entire lives without being exposed to this incredible side of math. Conventional wisdom says that these ideas are too abstract or too technical to teach at an earlier age, but I could not disagree more whole-heartedly with conventional wisdom in this case. This can be taught, and moreover it should be taught. This is the kind of math that often gets people to fall in love with the subject, and this is the kind of math that can help one to appreciate more thoroughly that which is done in high school. Accordingly, this site attempts to make one small step in the direction that goes against the grain of conventional wisdom.
What You’ll Find Here
The main thrust of this site lies in the series of lessons (found in the creatively titled tab “Lessons”) that will expose the reader to abstract mathematics in a user friendly, light-hearted, and step-by-step way. Although these lessons are completely rigorous and in no way “watered-down”, they are also meant to be accessible and easy to digest. My goal with the lessons is to ensure that the reader never has to pull out pen and paper if he or she doesn’t want to. Accordingly, I tend to lean on the side of “over-explaining”, which is a fault I’m willing to accept. The lessons will prove to you that math is beautiful and profound not merely by philosophizing about math, but rather by directly teaching it to you. This is rigorous, abstract math, whose beauty speaks for itself.
The second part of the site consists of more fluffy, philosophical ramblings about what math is, what it isn’t, and why it’s amazing. This discussion is found in the “Blog” portion of the site, and will hopefully supplement the lessons for those days that you’re not so keen on learning about new logical constructions.
How To Use The Site
There are two different (and not mutually exclusive) ways to approach this site. You can use it in the more casual sense of reading some of the blog posts about the nature and philosophy of mathematics, and participate in those discussions. Or, you can head over to the “Lessons” tab and begin diving into the rich world of mathematics head first. Certain parts of certain blog posts might make references to mathematical ideas that the reader is unfamiliar with, but I guarantee that all such references will have thorough explanations in the lessons and that the reader will be linked to the relevant sections. If I miss such a linking opportunity, please do let me know.
Personally, I’d recommend a healthy mix of the two approaches when perusing this site. There is a lot of good content in the “fluffier” discussions, but to really understand and appreciate math (and to prove my point that ANYONE can do so), you’ll really need to read the lessons. I think you’ll be surprised at how not-scary they turn out to be!
Intended Audience: Everyone
I will remind the reader that this site is not intended solely for experts—or even amateurs—in mathematics . It is geared towards those with all degrees of familiarity with math. The uninitiated reader will find here a wonderful journey into one of the universe’s most beautiful art forms—that of pure logic—and will likely leave with a deeper appreciation of this wonderful subject.
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