math paper using latex

\documentclass[12pt]{article} % This file is a modified version of a tex file by Professor Ed Scheiermann from the Department of Applied Mathematics and % Statistics at Johns Hopkins University in Baltimore, Maryland. Many thanks for letting us use it. % This first part of the file is called the PREAMBLE. It includes % customizations and command definitions. The preamble is everything % between \documentclass and \begin{document}. \usepackage[margin=1in]{geometry} % set the margins to 1in on all sides \usepackage{graphicx} % to include figures \usepackage{amsmath} % great math stuff \usepackage{amsfonts} % for blackboard bold, etc \usepackage{amsthm} % better theorem environments % various theorems, numbered by section \newtheorem{thm}{Theorem}[section] \newtheorem{lem}[thm]{Lemma} \newtheorem{prop}[thm]{Proposition} \newtheorem{cor}[thm]{Corollary} \newtheorem{conj}[thm]{Conjecture} \newtheorem{mydef}[thm]{Definition} \begin{document} \title{Instructions Paper 1} \author{Dr. Frank B\"{a}uerle \\ Math 100 Spring 2019\\ University of California at Santa Cruz} \maketitle \begin{abstract} This note will contain the assignment details for your first paper as part of the writing requirement in Math 100. \end{abstract} \section{Introduction} This paper is designed to allow you to get familiar with \LaTeX. The mathematics is from calculus and should be pretty straightforward for you. The paper you need to submit should be one to two pages in length, with the spacing approximately as it is in this paper. If you haven't installed \LaTeX \ on your computer yet, you need to do this asap. See the Writing Assignment Instructions page in the Writing module in Canvas for details. \section{The Details for Paper 1} In this section we describe the problem that you need to present as well as give you some general instructions and guidelines for writing and submitting your paper. \subsection{The Problem} This is taken from first quarter calculus. Assume that $f$ is a real-valued function and let $a$ be a real number. Do the following: \begin{enumerate} \item Give the proper limit definition of what it means for $f$ to be continuous at $x=a$. \item Give the proper limit definition of what it means for $f$ to be differentiable at $x=a$. \item Properly state and give the proof of the fact that differentiabilty at $x=a$ implies continuity at $x=a$. \item Give a counter-example that shows that the converse is not true. You do not need to prove why $f$ is not differentiable at the $a$ you selected. \end{enumerate} If you don't remember this (or even if you do), you can look up the definitions and this theorem in any standard calculus text. \subsection{Writing Guidelines} \vskip .1truein \begin{enumerate} \item Follow all the writing guidelines from your textbook and those discussed in class. \item You can include graphics (see Ed Scheinermann's sample Mathematics paper at \linebreak http://www.ams.jhu.edu/~ers/learn-latex/ for how to do this) \item Your paper will be graded for the correctness of the mathematics that you present, the clarity and quality of your exposition and the overall structure of the paper. Give careful thought to the order in which the parts of your paper appear. \item Try hard to eliminate typos. To that end, do not rely solely on your spell checker; a sentence can be spelled correctly yet still be incorrect grammatically or have a different meaning than you intend. For instance, ``Hear is were they maid there mistake.'' has typos that a spell checker won't catch. \end{enumerate} \subsection{Collaboration: YES Plagiarism: NO} You are allowed (in fact encouraged) to collaborate on this assignment. BUT you need to write your own paper. And YOU need to write it. See here for UCSC's policy on academic integrity. Here is the library's primer on plagiarism and how to avoid it : https://guides.library.ucsc.edu/citesources/plagiarism \subsection{Deadline} The deadline to hand in your paper is Sunday 5/5/2019, 11:59pm. You need to turn in your paper in Canvas, and the same late policies as for homework apply. \section{Closing Remarks} Remember that your TA's Matthew and Mita and I are available in office hours and section for questions. See the Canvas site for office hour details as well as for additional resources for using \LaTeX \ and writing Mathematics papers. \end{document}