%% Holy Cross Math/CS honors thesis template
%%
%% Version 1.2,  September 01, 2018 
%% Andrew D. Hwang <ahwang -at- holycross -dot- edu>
%%
%% This file contains several useful macros and stylistic suggestions
%% for writing a medium-length scholarly document containing lots of
%% mathematics, such as a department honors thesis. 
%%
%% To use this file, save it in your working directory (or, if you
%% know about shell configuration, in your TEXINPUTS path) as
%% hc_thesis.sty, then put the line
%%
%%    \usepackage{hc_thesis}
%%
%% in your document preamble.
%%
%% The primary purpose of expository writing is to convey ideas
%% clearly. LaTeX provides features that simplify the task of writing,
%% and that facilitate creation of flexible, long-lived files. These
%% include:
%% * A plain-text (human- and machine-readable) file format
%% * High-level formating and cross-referencing capabilities
%% * High-quality, easy-to-use mathematical fonts
%%
%% A well-written LaTeX document can be translated into multiple
%% formats, such as HTML, Postscript, or PDF, without loss of quality,
%% for years into the future, using commonly-available software. The
%% same cannot be said of word-processor files, which become obsolete
%% at each software release (often 1-3 years) and are subject to data
%% corruption, which can make a file unreadable.
%%
%% Ideally, a LaTeX file reflects the logical structure of your
%% document; the appearance of the printed version will be handled in
%% software, and can be changed easily. For the most part, you should
%% not think about how the finished product looks while you're
%% writing.
%%
%% LaTeX accomplishes these tasks by acting as a ``markup language'',
%% using mnemonic, human-readable tags to control the document
%% structure. You may add tags of your own, called ``macros'', that
%% are used to represent concepts that recur frequently in your
%% document. For maximum flexibility and consistency, you should
%% create high-level macros early in the writing process and use them
%% assiduously.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% The ``preamble'' contains commands that determine the appearance of
%% the document, ranging from package inclusion to macro definitions. 
%%
\documentclass[12pt]{article}
\usepackage[leqno]{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}

%% Some graphics inclusion facilities
%% \usepackage{tikz}
%% \usepackage{graphicx} % [sic]

% Specify the size of the text block
\usepackage[body={5.5in,8.8in}]{geometry}

%%%%%%%%%%%%%%%%%%%%%% Item numbering %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% LaTeX can automatically generate numbers for definitions, theorems,
%% equations, etc. Numbering serves a dual purpose: To allow you (the
%% author) to refer back and forward to parts of your document, and to
%% assist the reader in locating said references. However, the default
%% numbering scheme in LaTeX is for each type of ``environment'' to be
%% numbered separately. Experience reveals that separate numbering is
%% unhelpful to the reader. Instead, it's better to number theorems,
%% definitions, lemmas (``lemmata'' for you Latin sticklers), etc.,
%% consecutively within a section.
%%
%% LaTeX also allows equations and ``floating'' environments (tables
%% and figures) to be numbered. A floating environment will be placed
%% according to criteria depending on page composition, rather than
%% the environment's location in the source file. For this reason,
%% tables and figures should be numbered separately. Equations should
%% be numbered separately as well, since gaps in the sequence of
%% equation numbers are jarring to the reader.
%%
%% The next sets of commands cause LaTeX to number environments
%% according to the criteria above.

%% Make LaTeX number equations, figures, and tables consecutively
%% within a section. Without the first three commands below, the first
%% figure in each section would be ``Figure 1''.
%% 
\renewcommand{\theequation}{\arabic{section}.\arabic{equation}}
\renewcommand{\thefigure}{\arabic{section}.\arabic{figure}}
\renewcommand{\thetable}{\arabic{section}.\arabic{table}}

\numberwithin{equation}{section}
\numberwithin{figure}{section}
\numberwithin{table}{section}

%% Number items consecutively within sections, as in Definition 2.1,
%% Lemma 2.2, Theorem 2.3, Corollary 2.4, Remark 2.5. This numbering
%% scheme makes it easier for the reader to locate an item. 

%% These environments are set in italic type
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}

%% These environments are set in Roman (plain) type
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}

%% Don't number \subsubsections
\renewcommand{\thesubsubsection}{\hskip -1em}
%%%%%%%%%%%%%%%%%%% End of numbering commands%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% Font declarations %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% For flexibility, it's best to use two-stage macros: First define a
%% font class for a type of object (e.g., boldface for sets of
%% numbers), then define document macros using the font macro. That
%% way it's easy to decide final notation after the document is
%% written. 
%%
\newcommand{\Number}[1]{\mathbf{#1}}
\newcommand{\Vector}[1]{\mathbf{#1}}
%\newcommand{\Script}[1]{\mathscr{#1}}% Requires the mathrsfs package

%% Document macros (the macros that actually appear in the document)
\newcommand{\C}{\Number{C}}
\newcommand{\N}{\Number{N}}
\newcommand{\R}{\Number{R}}
\newcommand{\Z}{\Number{Z}}
\newcommand{\e}{\Vector{e}}

%%%%%%%%%%%%%%%%%% End of font-specific macros %%%%%%%%%%%%%%%%%%%%%

%% Miscellaneous symbol abbreviations. A macro can accept arguments.
%% For example, \dual{f} typesets f-hat.
%% The \left and \right commands cause delimiters to re-size
%% automatically according to what comes between them.
\newcommand{\abs}[1]{\left\lvert#1\right\rvert}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand{\del}{\partial}
\newcommand{\dual}[1]{\widehat{#1}}
\newcommand{\eps}{\varepsilon}
%% Angle brackets, for inner products. Use like this: \brak{v}{w}. 
%% Less than/greater than symbols are not suitable; LaTeX treats them
%% as binary relations, giving them too much spacing.
\newcommand{\brak}[2]{\left\langle#1,#2\right\rangle}

%% Text operators, which fine-tune their spacing just like \exp,
%% \log, \cos, etc.
\DeclareMathOperator{\re}{Re}
\DeclareMathOperator{\im}{Im}

%% Miscellaneous formatting/spacing commands
\newcommand{\Neg}{\phantom{-}} % Invisible minus sign, for alignment

%% Ordinarily, lined fractions are set in a small font in a paragraph;
%% integrals, sums, and limits have their sub- and super-scripts
%% placed to avoid uneven line spacing. Sometimes you want displayed
%% math notation in paragraph mode. The next command defines a short,
%% useful alias. Use displaystyle sparingly in paragraph mode; uneven
%% line spacing is considered unprofessional.
%%
\newcommand{\dsp}{\displaystyle}

%% End of hc_thesis.sty
