A Path to Pure Math for High School Students and Anyone in General
“The infinite! No other question has ever moved so profoundly the spirit of man.”- David Hilbert
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ABOUT ME
Hi, my name is Daniel Waters, I am a high school senior from the United States, and I am interested in mathematics and physics. Particularly, I like complex analysis, geometry (in all forms), abstract algebra, quantum mechanics, and topology. I am interested in, but have not yet learned, differential geometry, functional analysis, general relativity, partial differential equations, quantum field theory, algebraic geometry, and non-commutative geometry. I have a long road ahead of me if I am to become a mathematical physicist, but I would like to share the experience and show the wonderful things that I learn along the way. That is what this blog is for!
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(Image belongs to Dover Publications) A Book of Abstract Algebra by Charles Pinter. This book is an excellent way to learn abstract algebra for the first time. The topics covered include: groups, rings, fields, the fundamental homomorphism theorem, Galois theory, and even some number theory. The book is written in a very informal matter, like having a conversation with Pinter, and I think it is a great way to learn a subject like abstract algebra. Some important results are not included in the main text, but in the exercises. These include the Sylow theorems, the first and second isomorphism theorems, Cauchy's theorem, etc. I think this is a wonderful approach, as it allows the learner to work on proof writing, not while doing somewhat meaningless exercises, but while proving important results for themselves. Overall, 5/5!