Why Advanced Mathematics is Hard

If you are wondering why you have trouble understanding the likes of advanced mathematics, you might consider that the writing and teaching quality in this field is abysmal at best. As someone who has studied mathematics at the graduate level and beyond, I can say without reservation that there are very few books, and indeed, even fewer teachers, who can convey an understanding of this subject at the higher reaches. Mathematics is a wonderful tool which permits us to understand our world; however, the latent complexities of the subject start to manifest as we try to use this tool to understand the likes of black holes, antimatter, and genomic transcription. Yet understand mathematics we must, as we progress and problem solve in direct proportion to our decoding of this wonderful discipline.

Download Exam Drill of Mathematics for Senior High School Complete with Good Solutions

For many algebra and pre-calculus set the limits of their mathematical understanding. Moreover, to understand the nature of the universe and the myriad mysteries of life, we need much more advanced tools: topological spaces, advanced number theory, chaos theory, and partial differential calculus. The lower branches of mathematics provide the raw tools to unravel the mysteries of these higher branches, yet these higher realms once entered, mystification rules and most quit before they even have the chance to start unraveling the fascinating mysteries of mathematics.
As I see it, the main problem in understanding more advanced mathematics boils down to patience on both the teachers and writers who try to promulgate this material. Many professors and teachers will argue that there is not enough room in a text to break down the subject matter too much, that there would be too many breaks in continuity to proceed in this manner. Yet by not providing adequate exposition, these very same "promoters" of the subject are actually losing their audience to obfuscation.
Personally, I enjoy shedding light on the mysteries of mathematics. Granted I am human and subject to the same limitation of comprehension that everyone else is. Thus I find it daunting when I cannot make heads or tails out of the more advanced reaches of this subject. People interested in mathematics want to be able to understand the likes of partial differential equations, abstract algebra, and their underlying theories. Many individuals (talented at that and potential mathematicians) could understand advanced mathematics if we had better writers and educators. Alas, it seems that many who have finally understood the more advanced reaches of the subject insist on keeping such arcana "secret" and only allow certain chosen ones to enter the circle of understanding. Only then can we propagate mathematical education efficiently and thus create more scientists and mathematicians who will at least give us a chance eventually to help solve the many problems confronting us in the world today.

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