Instructions Paper 1 - Mathematics 1-2-3

Instructions Paper 1
Dr. Frank Bäuerle
Math 100 Winter 2012
University of California at Santa Cruz
January 18, 2012
Abstract
This note will contain the assignment details for your first paper as part of the
writing requirement in Math 100.
1 Introduction
This paper is designed to allow you to get familiar with L A TEX. 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 L A TEX on your computer yet, you need to do this asap. See
http://slugmath.ucsc.edu/mediawiki/index.php/Skill/Installing and running a Tex package
and follow the instructions.
2 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.
2.1 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:
1. Give the proper limit definition of what it means for f to be continuous at x = a.
2. Give the proper limit definition of what it means for f to be differentiable at x = a.
3. Properly state and give the proof of the fact that differentiabilty at x = a implies
continuity at x = a.
4. 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.
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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. The text book for Math 19A (Stewart Early
Transcendentals, 7th ed.) has this and is on reserve at the Science Library.
2.2 Writing Guidelines
1. Follow all the writing guidelines from your textbook and those discussed in class.
2. You can include graphics (see Ed Scheinermann’s sample Mathematics paper at
http://www.ams.jhu.edu/ ers/learn-latex/ for how to do this)
3. 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.
4. 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.
2.3 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
http://www1.ucsc.edu/academics/academic integrity . . .
. . . /undergraduate students/resources.html
for information about what constitutes cheating/plagiarism. Here is a well-written primer
on plagiarism and how to avoid it written by UCSC faculty Gregory S. Gilbert (Environmental
Studies) and Ingrid M. Parker (Ecology and Evolutionary Biology):
http://scwibles.ucsc.edu/Documents/Avoiding%20Plagiarism.pdf
2.4 Deadline
The deadline to hand in your paper is Monday 1/30/2012, 5pm sharp. You can turn in your
paper in class or in my office at McH 4163.
3 Closing Remarks
Remember that your TA’s Felicia and Liz and I are available in office hours and section for
questions. See the class web site for office hour details as well as for additional resources for
using L A TEX and writing Mathematics papers.
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