% =============================================================================
% VMRC Mentor Proposal — TEMPLATE (2-column HTML-matched, no frame, no cut-off)
% =============================================================================
% -------------------------- INSTRUCTIONS FOR APPLICANTS -----------------------
% • Compile with a modern TeX distribution (TeX Live 2021+). pdflatex works.
% • Submit BOTH your PDF and this .tex source (VMRC prefers LaTeX).
% • Font & size: Times-like via newtxtext/newtxmath; 10pt document class.
% • Two-column look: left column (labels) right-aligned; right column (content)
%   left-aligned—this mirrors the VMRC website sample.
% • Replace the placeholder text ONLY (dates, mentor info, title, topic,
%   Background, Abstract, Outline, References). Do not alter the layout macros.
% • Divider lines: the subtle fade uses TikZ shading. If your TeX install lacks
%   TikZ shadings, a solid rule still appears (graceful fallback).
% • Page break: we use \tcbbreak (inside the tcolorbox) before the Outline section.
%   If your content is shorter/longer, you MAY delete that single \tcbbreak line.
% • Left label column width is set in \newcolumntype{L}{...p{1.35in}} (below).
%   You MAY adjust 1.35in to fit longer labels (e.g., 1.5in) if needed.
% • Bullet indentation under “Outline/Timeline” is controlled in the itemize
%   options (leftmargin=2.6em, labelsep=.8em). You MAY tweak those two values.
% • References numbering and alignment are set to match the website look; don’t
%   change the enumerate options unless spacing truly needs tuning.
% • Italics policy: Only italicize items that are normally italicized:
%   – Project title (right column line “Project title:”)
%   – Each reference’s Title (not authors/publisher/year)
%   Everything else should be in regular (upright) text.
% ------------------------------------------------------------------------------

\documentclass[10pt]{article}

\usepackage[margin=1in]{geometry}
\usepackage{amsmath}                 % load amsmath first if you need it
\usepackage{newtxtext,newtxmath}     % Times-like text + math (includes AMS symbols)
% \usepackage{amssymb}               % ← not needed with newtxmath
\usepackage{enumitem}
\usepackage{xcolor}
\usepackage{hyperref}
\usepackage{array}
\usepackage{tabularx}
\usepackage{microtype}
\usepackage[most]{tcolorbox}
\usepackage{ragged2e}           % better ragged alignment
\usepackage{tikz}               % for the gradient overlay
\usetikzlibrary{shadings}

\definecolor{Muted}{HTML}{5B6470}

% Comfortable paragraph spacing, like the site
\setlength{\parskip}{6pt}
\setlength{\parindent}{0pt}
\setlist[itemize]{topsep=4pt,itemsep=8pt,parsep=0pt}
\raggedbottom

% Column helpers
% NOTE: You may widen 1.35in to accommodate longer labels if absolutely needed.
\newcolumntype{L}{>{\RaggedLeft\arraybackslash\scshape}p{1.35in}}
\newcolumntype{Y}{>{\RaggedRight\arraybackslash}X}

% Spacing knobs for rows
\newcommand{\VMRCrowsep}{10pt}
\newcommand{\VMRCrowsepMentor}{14pt}
\newcommand{\VMRCmentorpad}{\vspace{10pt}}

% Small gap to separate consecutive tabularx blocks (no divider)
\newcommand{\VMRCblockgap}{\vspace{6pt}}

% Date range helpers (raised en-dash rule)
\newcommand{\VMRCdashraise}{0.72ex}
\newcommand{\solidendash}{\rule[\VMRCdashraise]{0.9em}{0.5pt}}
\newcommand{\daterange}[2]{#1~\solidendash~#2}

% --------- Divider (solid rule + gradient overlay for HTML-like fade) ---------
% Do not modify these unless you need a darker/lighter fade.
\newcommand{\VMRCdivht}{1.2pt}     % thickness of the gradient band
\newcommand{\VMRCdivmid}{black!26} % center intensity of the fade

\newcommand{\sectiondivider}{%
  \par\vspace{10pt}%
  % Solid fallback that always shows up
  \noindent{\color{black!26}\rule{\linewidth}{0.6pt}}%
  % Thin gradient band on top (if shadings render)
  \noindent
  \begin{tikzpicture}
    \path[use as bounding box] (0,0) rectangle (\linewidth,\VMRCdivht);
    \shade[shading=axis, left color=white, middle color=\VMRCdivmid, right color=white]
      (0,0) rectangle (\linewidth,\VMRCdivht);
  \end{tikzpicture}%
  \vspace{8pt}\par}

% Card container — frame removed (no left/right borders)
\tcbset{
  vmrcbox/.style={
    enhanced, breakable,
    colback=white, colframe=white, boxrule=0pt, arc=0pt,
    left=10pt,right=10pt,top=10pt,bottom=10pt, overlay={}
  }
}

\begin{document}
\begin{tcolorbox}[vmrcbox]

  % ============================== TITLE BLOCK ================================
  % ACTION: Replace the title/subtitle text only. Do not change centering/format.
  \begin{center}
    {\large\bfseries Research Proposal — Virtual Math Research Circle}\\
    {\small\color{Muted} Template for mentor submissions}
  \end{center}
  \vspace{8pt}

  % ============================ METADATA + BACKGROUND ========================
  % ACTION: Replace values on the right (Y column). Keep label wording on the left.
  \begin{tabularx}{\linewidth}{@{} L Y @{}}
    Session: &
      Session name/number: \daterange{Start date}{End date} \\[\VMRCrowsep]

    Mentor: &
      \begin{tabular}[t]{@{}l@{}}
        Full name \\
        Position/Title \\
        Department \\
        Institution\VMRCmentorpad
      \end{tabular}\\[\VMRCrowsepMentor]

    Project title: & \emph{Project title} \\[\VMRCrowsep]
    Topic area:    & Mathematical subject area (e.g., graph theory, probability) \\[\VMRCrowsep]

    Background: &
      Brief prerequisites and assumed background. Indicate whether calculus
      is required or taught as needed. Mention skills/tools students may use. \\
  \end{tabularx}

  \sectiondivider

  % ================================= ABSTRACT ================================
  % ACTION: Replace the abstract body only (right column). Keep "Abstract:" label.
  \begin{tabularx}{\linewidth}{@{} L Y @{}}
    Abstract: &
      $\leq$\,250-word abstract, minimal jargon. State the problem/theme and what
      students will attempt, including any planned proof/computation components. \\
  \end{tabularx}

  % ---- Add a bit of breathing room between Abstract and Possible extension ---
  \VMRCblockgap

  % ============================ POSSIBLE EXTENSION ===========================
  % ACTION: Replace the text after "Possible extension:" with your own (optional).
  \begin{tabularx}{\linewidth}{@{} L Y @{}}
    Possible extension: &
      Optional follow-on directions for students who continue:
      additional conjectures, generalizations, complexity/optimization angles, etc. \\
  \end{tabularx}

% \tcbbreak % ACTION: You may delete this line if you want to avoid a page break here.

  % ============================ OUTLINE / TIMELINE ===========================
  % NOTE: Divider above is intentional; keep it for visual consistency.
    \sectiondivider
\begin{tabularx}{\linewidth}{@{} L Y @{}}
  Outline/Timeline: &
    Brief overview of cadence and expectations for the chosen session format
    (e.g., 3-week intensive vs. semester).
    %
    % IMPORTANT: keep the bullets INSIDE the same right-column cell so they
    % don't slip into the left column. Do NOT end the row before the itemize.
    \par\smallskip
    % ACTION: You may adjust leftmargin (indent) and labelsep (gap after bullet).
    \begin{itemize}[leftmargin=2.6em, labelsep=.8em, itemsep=8pt, topsep=6pt]
      \item \textbf{Week 1 (Focus).}
        Planned readings/topics; definitions/examples; initial experiments;
        scaffolding for proof writing or computation.

      \item \textbf{Week 2 (Focus).}
        Core problem attack; empirical work or conjecture refinement; begin
        formal proofs or algorithm design/analysis.

      \item \textbf{Week 3 (Focus).}
        Finalize results; draft write-up; presentation prep (slides/poster);
        rehearse talk; next-step suggestions.
    \end{itemize} \\
\end{tabularx}


% ================================= REFERENCES =============================
% ACTION: Replace these items with your project’s references (use the same format).
\sectiondivider
\begin{tabularx}{\linewidth}{@{} L Y @{}}
  References: &
    \begin{enumerate}[label={[}\arabic*{]}, leftmargin=*, labelsep=.5em,
      topsep=0pt, partopsep=0pt, parsep=0pt, itemsep=3pt,
      before=\vspace{-\parskip}\vspace{-0.5\baselineskip}] % nudge up to align with "References:"
      \item Author(s), \emph{Title}, Edition, Publisher, Year.
      \item Author(s), \emph{Title}, Edition, Publisher, Year.
      \item Author(s), \emph{Title}, Edition, Publisher, Year.
    \end{enumerate} \\
\end{tabularx}

  
\end{tcolorbox}
\end{document}
