Mathematics students: theorems, proofs, and notation that stays consistent

Math papers are notation plus proof structure. LaTeX is the default because both are painful in Word once the argument exceeds a page.

amsthm early

\usepackage{amsthm}
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\theoremstyle{definition}
\newtheorem{definition}{Definition}[section]

Numbering by section keeps references stable when you insert a lemma. Lesson: theorem and proof blocks.

Proofs that end cleanly

Use the proof environment so the QED mark lands correctly. For proofs that end inside an equation, \qedhere avoids a orphaned box on the next line.

Macro hygiene

Define \R, \N, \eps, operator names, and category names once. If two notions share a letter, disambiguate with macros (\VectSpace vs \RandomVar) instead of reusing V with different fonts.

Align for long derivations

align and split keep steps readable. Number only lines you cite. A wall of numbered equations is harder to follow than a short narrative with two tagged lines.

When the PDF is the hand-in

Coursework still needs a clean PDF: margins per the syllabus, page numbers, and a title. The quick reference covers the boring parts so you can spend attention on the proof.