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Click here to download the pdf file. The original source code is located here.

This note is an effort to tell the stories in the languages of mathematical concepts mostly used in condensed matter Physics.

I can remember when I found the terminologies used by the mathematicians frightening, as I was more than once deterred by the formidable appearances of Topology, of Abstract Algebra, of Lie Algebra. And I have found the easiest way for me to understand these concepts so that I could see what they have to offer for Physics is via examples and often visualizations. I had to watch hours of open courses and plow through the book just to find a few. That was not a very enjoyable experience, and it can sometimes be infuriating that some perfect examples (perfect that in my opinion would have helped me a lot) are left out. So this is my feat towards the mountain. I will try to cover the fields that I have found useful in my daily applications. These notes are almost bound to be limited, naïve and could be on the edge of misunderstanding by the pure mathematicians. I would love to hear any suggestions.

Much of the materials of this notes came from or inspired by a course taught by Dr. Emil Prodan in Yeshiva University.

This note is to be reorganized. I intended the note to start from sets and go over group and come to algebra. I will also try to add general topology and Lie group if possible. The order of the materials might be changed later.

I only assume the reader have basic knowledge of linear algebra. An introductory level of group theory is appreciated but definitely not required. This note do not require complex analysis.