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main.tex
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main.tex
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% Document type
\documentclass[]{amsbook}
%----------------------------------------------------------
% Packages
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{mathrsfs}
\usepackage{mathtools}
\usepackage[pdftex, bookmarks, colorlinks=true]{hyperref}
\usepackage{tikz-cd}
\usepackage{bbm}
%----------------------------------------------------------
% User-defined environments
\theoremstyle{plain}
\newtheorem{acknowledgement}{Acknowledgement}
\newtheorem{algorithm}{Algorithm}[section]
\newtheorem{axiom}{Axiom}[section]
\newtheorem{case}{Case}[section]
\newtheorem{claim}{Claim}[section]
\newtheorem{conclusion}{Conclusion}[section]
\newtheorem{condition}{Condition}[section]
\newtheorem{conjecture}{Conjecture}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{criterion}{Criterion}
\newtheorem{definition}{Definition}[section]
\newtheorem{example}{Example}[section]
\newtheorem{exercise}{Exercise}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{notation}{Notation}[section]
\newtheorem{problem}{Problem}[section]
\newtheorem{proposition}{Proposition}
\newtheorem{remark}{Remark}[section]
\newtheorem{solution}{Solution}[section]
\newtheorem{summary}{Summary}[section]
\newtheorem{theorem}{Theorem}[section]
\numberwithin{equation}{section}
\theoremstyle{definition}
\newtheorem{xca}{Exercise}[section]
%-----------------------------------------------------------
% User-defined commands
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\dps}{\displaystyle}
\newcommand{\mb}[1]{\mathbf{#1}}
\newcommand{\mbb}[1]{\mathbb{#1}}
\newcommand{\mf}[1]{\mathfrak{#1}}
\newcommand{\mc}[1]{\mathcal{#1}}
\newcommand{\opn}[1]{\operatorname{#1}}
\newcommand{\tb}[1]{\textbf{#1}}
\newcommand{\catname}[1]{\mathbf{#1}}
\newcommand{\0}{\mathbf{0}}
\newcommand{\1}{\mathbf{1}}
\newcommand{\la}{\langle}
\newcommand{\ra}{\rangle}
\newcommand{\q}{\quad}
\newcommand{\qq}{\quad \quad}
\newcommand{\qqq}{\quad \quad \quad}
\newcommand{\oldemptyset}{\emptyset}
\renewcommand{\emptyset}{\varnothing}
%-----------------------------------------------------------
% Math operators
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\lcm}{lcm}
%-----------------------------------------------------------
\begin{document}
\frontmatter
\title[`Algebra: Chapter 0']{Solutions to Exercises from `Algebra: Chapter 0'}
\begin{abstract}
Solutions to exercises from the book `Algebra: Chapter 0' by Paolo Aluffi.
\end{abstract}
\maketitle
\tableofcontents
\chapter*{Preface}
\markboth{PREFACE}{PREFACE} This document contains my attempt at writing
(hopefully correct!) solutions to exercises from Aluffi's book, while engaging
in some self-study of modern abstract algebra with the ultimate aim of teaching
myself some modern algebraic geometry.
\mainmatter
\include{chapters/set-theory-and-categories}
\include{chapters/groups-first-encounter}
\end{document}