Advanced Mathematics

For those adventurous souls out there who try to plumb the depths of more advanced mathematics, I certainly give you credit for your efforts. Studying advanced mathematics can be very humbling, to say the least. You feel good about yourself because you think you are smart, and then you read something on advanced mathematics and you realize how little you understand. The sad thing is though, it may not be that you and I are not bright enough but that the teachers and writers of this particular subject fail terriby at what they do. Because I love a challenge, I decided to make my major mathematics in college. This was by no means my strongest subject. English and foreign languages certainly came very easily to me and could have been slam-dunk choices as majors.

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I probably would have suffered a lot less than I did from studying things like advanced calculus, real and complex analysis, mathematical statistics and set theory. This study was further compounded by professors who, for the most part, failed to elucidate the subject matter. Consequently, I got my degree, although with not perfect grades, good grades, and am certainly proud of my accomplishment. The irony in all this is that after all that suffering, I now relish the subject and have written extensively on many facets of this discipline.
What I have found in my study of mathematics, particularly advanced mathematics, is that there are so few good teachers of it. When I was a graduate student - yes I actually decided to punish myself more by studying this subject at the graduate level - I remember sitting in my complex analysis course, listening to my Indian professor go off on tangents about exotic realms of this subject. The purpose of going to school and attending lectures or classes is to ask questions and learn. Material should be presented in a way so that students, willing to put in the time and effort, should understand - at least at a superficial level. What I found from most of the lectures I attended and most of the textbooks I used is that I understood very little - if anything. One could say that I could not discern the forest from the trees; but the real truth is that I could not discern even one tree from another. How sad.
When I try to plumb the depths of advanced mathematics I encounter the same outdated, stale, methods of pedagogy that just do not serve. Why can't anyone produce books on advanced mathematics, or even articles on the subject, so that willing learners like me or you, could understand? Certainly the men who understand this subject are smart enough to be able to do this, no? Then again, there might be an agenda: that of not letting too many into this select circle of prominent mystique. This is much like the master karate instructor's inner circle of disciples. These masters are not too quick to teach their secret methods, which took a lifetime to acquire and understand, to some neophyte, until that person has proven his loyalty, and even sanity. Indeed you would not want such killer techniques in the wrong person's hands.
Such easy dissemination of enlightenment might serve a purpose in the martial arts, yet I argue that such in a discipline as advanced mathematics should be freely available. Even with my background and experience, I find it enormously frustrating that I cannot teach myself to master the theory of, let us say, partial differential equations, because there is not one book that tries to teach this subject without quickly throwing the student into the forest without a roadmap. Yes I know that the subject is comprehensive and depends on other branches of mathematics, and that if the author were to break everything down, the book might have to be three thousand pages; yet the alternative is that very little if anything is learned by the student, and thus the realm of advanced mathematics remains untouched but by a select few, leaving out many potential bright students, who perhaps, before being daunted and quitting the pursuit of such subject, would make great contributions to the subject and even world. After all, mathematics is the language of the universe, and a comprehensive understanding of this subject can lead to all kinds of useful applications.
Thus I scream, "Can anyone please help!" I want to be able to learn Einsteinian mathematics and all about tensors. Could someone please break this down so that a person with my intelligence might glimpse this awesome domain. Alas. No one answers; and therefore, I have to be content to trudge through such readings with the labors of childbirth. But I stay hopeful that one day this might change.