# Instructions Paper 1 - Mathematics 1-2-3

Instructions Paper 1 - Mathematics 1-2-3

Instructions Paper 1 - Mathematics 1-2-3

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<strong>Instructions</strong> <strong>Paper</strong> 1<br />

Dr. Frank Bäuerle<br />

Math 100 Winter 2012<br />

University of California at Santa Cruz<br />

January 18, 2012<br />

Abstract<br />

This note will contain the assignment details for your first paper as part of the<br />

writing requirement in Math 100.<br />

1 Introduction<br />

This paper is designed to allow you to get familiar with L A TEX. The mathematics is from<br />

calculus and should be pretty straightforward for you. The paper you need to submit<br />

should be one to two pages in length, with the spacing approximately as it is in this paper.<br />

If you haven’t installed L A TEX on your computer yet, you need to do this asap. See<br />

http://slugmath.ucsc.edu/mediawiki/index.php/Skill/Installing and running a Tex package<br />

and follow the instructions.<br />

2 The Details for <strong>Paper</strong> 1<br />

In this section we describe the problem that you need to present as well as give you some<br />

general instructions and guidelines for writing and submitting your paper.<br />

2.1 The Problem<br />

This is taken from first quarter calculus. Assume that f is a real-valued function and let a<br />

be a real number. Do the following:<br />

1. Give the proper limit definition of what it means for f to be continuous at x = a.<br />

2. Give the proper limit definition of what it means for f to be differentiable at x = a.<br />

3. Properly state and give the proof of the fact that differentiabilty at x = a implies<br />

continuity at x = a.<br />

4. Give a counter-example that shows that the converse is not true. You do not need to<br />

prove why f is not differentiable at the a you selected.<br />

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If you don’t remember this (or even if you do), you can look up the definitions and<br />

this theorem in any standard calculus text. The text book for Math 19A (Stewart Early<br />

Transcendentals, 7th ed.) has this and is on reserve at the Science Library.<br />

2.2 Writing Guidelines<br />

1. Follow all the writing guidelines from your textbook and those discussed in class.<br />

2. You can include graphics (see Ed Scheinermann’s sample <strong>Mathematics</strong> paper at<br />

http://www.ams.jhu.edu/ ers/learn-latex/ for how to do this)<br />

3. Your paper will be graded for the correctness of the mathematics that you present,<br />

the clarity and quality of your exposition and the overall structure of the paper. Give<br />

careful thought to the order in which the parts of your paper appear.<br />

4. Try hard to eliminate typos. To that end, do not rely solely on your spell checker; a<br />

sentence can be spelled correctly yet still be incorrect grammatically or have a different<br />

meaning than you intend. For instance,<br />

“Hear is were they maid there mistake.” has typos that a spell checker won’t catch.<br />

2.3 Collaboration: YES Plagiarism: NO<br />

You are allowed (in fact encouraged) to collaborate on this assignment. BUT you need to<br />

write your own paper. And YOU need to write it. See<br />

http://www1.ucsc.edu/academics/academic integrity . . .<br />

. . . /undergraduate students/resources.html<br />

for information about what constitutes cheating/plagiarism. Here is a well-written primer<br />

on plagiarism and how to avoid it written by UCSC faculty Gregory S. Gilbert (Environmental<br />

Studies) and Ingrid M. Parker (Ecology and Evolutionary Biology):<br />

http://scwibles.ucsc.edu/Documents/Avoiding%20Plagiarism.pdf<br />

2.4 Deadline<br />

The deadline to hand in your paper is Monday 1/30/2012, 5pm sharp. You can turn in your<br />

paper in class or in my office at McH 4163.<br />

3 Closing Remarks<br />

Remember that your TA’s Felicia and Liz and I are available in office hours and section for<br />

questions. See the class web site for office hour details as well as for additional resources for<br />

using L A TEX and writing <strong>Mathematics</strong> papers.<br />

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