![]() ![]() Last week, my monthly domain hosting invoice came in, reminding me that I had a personal website which I built to document cool stuff that I could look back on, and perhaps bring value to some people along the way. (Plus it looks cool and gives me a dopamine kick whenever I review at it!) It was a significant time investment but I think it was well worth it. Once I came across analogies, proofs, derivations and/or example questions that were vital for my personal understanding of a certain topic, I documented them using LaTeX (Had some guidance from Jarell). In attempts to intuitively understand concepts, I explored multiple resources that was within my reach. The purpose is not to memorize algebraic details that you could work out on your own with a strong understanding and sufficient exposure to practice. It requires you to understand Mathematical concepts on a first principle basis, such that you will be able to apply and manipulate these concepts in a valid way in order to solve problems. It requires you to be able to reconstruct certain arguments to prove or disprove a certain statement. Undergrad Mathematics, however, is quite different. In High School and A-Levels, I used to brute force my way through as many questions as possible, identify my mistakes and memorize the correct procedures. That's has worked out well for most of my pre-university Mathematics courses (although I admit there were some huge warning signs). And sure, I've directly replicated every symbol and every word from an example problem into my notebook. Sure, I've copied equations off the whiteboard. I've never properly taken any notes for Mathematics. If that bores you and you want to get to the notes right away, feel free to use the Table of Contents (ToC) below! Preamble I also share certain misconceptions about Mathematics and how I previously appraoched it, the rationale for typing up the notes, how you can benefit from this Study Guide etc. text - text formulas are displayed inline, that is, within the body of text where it is declared, for example, I can say that a + a = 2 a įor more integral symbols, including those not included by default in the Computer Modern font, try the esint package.Hey friends, I spent some time this quarter typing up some notes for Vector Calculus and thought I'd share it on my website.They can be distinguished into two categories depending on how they are presented: Therefore, special environments have been declared for this purpose. This is because LaTeX typesets math notation differently from normal text. LaTeX needs to know when the text is mathematical. 17.3 Write an equation with the align environment.17 Advanced Mathematics: AMS Math package.1.1 Inserting "Displayed" maths inside blocks of text.The mathtools package fixes some amsmath quirks and adds some useful settings, symbols, and environments to amsmath. If you are writing a scientific document that contains numerous complex formulas, the amsmath package introduces several new commands that are more powerful and flexible than the ones provided by basic LaTeX. If your document requires only a few simple mathematical formulas, plain LaTeX has most of the tools that you will ever need. It is also a large topic due to the existence of so much mathematical notation. Typesetting mathematics is one of LaTeX's greatest strengths. The fact that he succeeded was most probably why TeX (and later on, LaTeX) became so popular within the scientific community. ![]() ![]() One of the greatest motivating forces for Donald Knuth when he began developing the original TeX system was to create something that allowed simple construction of mathematical formulae, while looking professional when printed. Collaborative Writing of LaTeX Documents.Scientific Reports (Bachelor Report, Master Thesis, Dissertation). ![]()
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