Project Report Guidelines

Douglas B. Meade

Department of Mathematics, University of South Carolina

The purpose of a project report is to present your answer to the project problem(s) and to

communicate the mathematical ideas and methods used to obtain your answer. This information

should be a concisely worded and well-organized paper that is understandable to any other student

in this course.

The format of a typical project report is described below. This format is quite general, but is

not always applicable. If you do not follow this outline, be sure that your report does provide all

of the relevant information. Regardless of the organization you use, your report must

• clearly state the problem

• explain the methods used, including signiﬁcant intermediate results

• answer all questions posed in the problem

The typical report will be at least one (1) page but not more than three (3) pages of a Word

document in 12-point font, including ﬁgures. The report should contain each of the following

elements: Title, Introduction, Analysis and Discussion, and Conclusion. Brief descriptions of what

should be included in each of these sections as well as some guidelines for presenting mathematical

equations and ﬁgures are given below.

Title

The title should summarize, as speciﬁcally as possible, the subject of the project. Your name

should be included here as well. (It is not necessary to put the title on a separate page.)

Introduction

This brief section should include a clear statement of the major objectives of the project.

In particular, clearly identify questions you are going to answer. The problem statement

should also include any background information that may be needed to understand the major

objectives. Lastly, this section should conclude with a brief overview of the mathematics that

will be used to complete the project.

Analysis and Discussion

Provide clear answers to all questions in the project. Explain the methods and intermediate

steps used to obtain the information needed to obtain these answers. Did you encounter

any surprises? Did you try a method that did not work as you expected? This part of the

report should contain enough details for a reader to repeat your analysis for this, or a related,

problem. Include appropriate ﬁgures and equations as needed.

Address any interesting observations you may have had as you were working through the

project. Can you make any generalizations? Why or why not? These comments should be

fairly detailed, but brief.

Equations and Figures

Mathematical expressions should be included in your report when appropriate. Short

expressions should ﬂow with the text. Longer expressions should be presented on a

separate line. For example:

The solutions to the quadratic equation ax

+ bx + c = 0 are

x =

−b ±

√

− 4ac

. (1)

The roots in (1) are real-valued only when the quantity b

− 4ac ≥ 0.

Note that an equation number is included whenever a displayed equation will be refer-

enced elsewhere in the report.

Figures should be included when explicitly requested or when they provide meaningful

information for the report. It is not enough to simply include a ﬁgure. Be sure you ex-

plain, in words, the information obtained from each ﬁgure. As demonstrated in Figure 1,

a caption can be a good way to provide the written description of a ﬁgure.

Figure 1: The equation x = 2 sin(x) has exactly three solutions. This SageMath-generated plot

shows that these solutions are x = 0 (exactly) and x ≈ ±1.89.

Figures and equations do not have to be computer generated. Hand drawn equations

and ﬁgures are acceptable provided they are neat. In many cases it will be easiest to

copy an equation or graph from SageMath directly into a Word document. In general,

you should use the method that is most eﬀective for you.

Conclusion

Summarize your results, the methods used to obtain them, and how they relate to your

stated purpose of the project. To demonstrate the overall signiﬁcance of your ﬁndings and the

concepts you learned, clearly identify connections between the main points of your discussion.

Final Check

After writing — and before turning in — your report, do each of the following:

• Make sure your writing is clear. If you read the report aloud to yourself or a friend, does

it make sense?

• Run the report through a spellchecker. Look for incorrectly spelled words that the

spellcheck misses!

• Check to be sure all of the questions have been answered and all pertinent equations

and ﬁgures are included.

• Staple together all pages of the project report.

Grading Outline for Project and Report

Department of Mathematics, University of South Carolina

Your Name

Category Explanation Score Comments

Analysis

& Discussion

mathematically correct answers

to questions;

supporting mathematical anal-

ysis;

/ 30

Creativeness

& Styling

interesting design;

good visual appearance;

/ 30

Organization

& Structure

appropriate layout of report;

overall appearance

/ 10

Introduction clear statement of problem;

summary of methods to be used

/ 10

Figures

& Equations

clear presentation of mathe-

matical expressions;

inclusion of appropriate ﬁgures,

with clear explanations

/ 10

Conclusion summary of results, including

overall signiﬁcance

/ 10

Writing correct grammar; appropriate

vocabulary;

clear and concise

/ 5

Length at least one page and not more

than three pages

(including graphs and ﬁgures)

/ 5

Total / 110