MAT 477 Template
Author
University of Toronto
License
Creative Commons CC BY 4.0
Abstract
Template for Written Assignments for MAT 477 (Fall 2019)
Template for Written Assignments for MAT 477 (Fall 2019)
\documentclass[10pt]{amsart} %fontsize, article stylte
\usepackage[utf8]{inputenc}
\setlength{\parindent}{0em} %indents to paragraphs
\setlength{\parskip}{1em} %lineskips after paragraph breaks
\usepackage[margin=1.0in]{geometry} %margins
%Standard Packages
\usepackage{bbm}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{enumerate}
\usepackage{mathtools}
\usepackage{amssymb}
%Standard Environments
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{question}{Question}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{remark}[theorem]{Remark}
%Example of a user-made command
\newcommand{\GL}{{\rm GL}}
%Beginning of Document Information
\title{Written Summary \#?}
\author{A MAT 477 Student}
\begin{document}
\maketitle %making the title show in the document
\vspace{-20pt}
{\bf Presentation Date:} September 5, 2019 \\
{\bf Presentation Title:} Overview\\
{\bf Speaker:} Ila Varma
\vspace{-20pt}
\section*{Summary} % '*' suppresses the numbering
The main goal of this lecture was to summarize the presentations for the semester. We begin with Gauss composition of binary quadratic forms as described in \cite{Seguin}.
\begin{definition}
A {\em binary quadratic form} $f(x,y)$ over a ring $R$ is a homogeneous polynomial of degree two in two variables. In other words, $f(x,y)$ is a binary quadratic form if and only if
$$f(x,y) = ax^2 + bxy + cy^2$$ % equation display
where $a,b,c \in R$.
\end{definition}
There is a natural action of $\GL_2(\mathbb{Z})$ on the space of binary quadratic forms over $\mathbb{Z}$...
\newpage
\begin{thebibliography}{12}%Quick Bibliography
\bibitem[HCL1]{HCL}
M.\ Bhargava, ``Higher composition laws I: A new view on Gauss composition and quadratic generalizations,'' {\it Ann.\ of Math.} {\bf 159} (2004), no.\ 1, 217--250.
%\bibitem[BV]{bv1}
%M.\ Bhargava and I.\ Varma, ``The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders,'' {\it Proc. of the London Math Soc.} {\bf 112} (2016), no.\ 2, 235--266.
\bibitem[S]{Seguin}
F.\ Seguin, ``Composition of binary quadratic forms: understanding the approaches of Gauss, Dirichlet, and Bhargava,'' to appear in {\it Resonance Journal}.
\end{thebibliography}
\end{document}