Homework
Assignments
Writing
Assignments
Instructor: Karen Mortensen,
247 Illini
Hall, 244-4128, kmortens@math.uiuc.edu
Times: Monday, Tuesday, Wednesday, Friday 10:00-10:50 in 143 Altgeld Hall. All students in this course should plan to attend all class sessions. This course is not suitable for self-study.
Office hours: Thursdays 10-11, Fridays 1-2, in 247
Illini Hall. See me for an appointment if those times are
not convenient.
TA: Ioannis Konstantoulis
Required Text: John P. D'Angelo and
Prerequisites: Calculus II (Math 231 or the equivalent) and
completion of the campus Composition I general education requirement.
Goals: This course prepares students for work in upper division mathematics courses by teaching selected fundamental topics from discrete and continuous mathematics, problem solving, techniques of proof, and clear mathematical exposition. Central goals of the course are to help students learn to read, construct and write mathematical proofs and to help students understand the structure and conventions of written mathematical arguments. Clear mathematical writing and clear mathematical thinking reinforce one another; for this reason, much attention will be given to the writing of mathematics.
Notes: Math 348 does not count towards a Mathematics minor. If you have already succeeded in 400-level courses which require the writing of proofs, then Math 348 is not the course for you! In this case, please choose another course to satisfy the Advanced Composition requirement.
Semester Schedule (subject to change- the chart below gives
as idea of what we'll be covering, but some sections may be omitted):
|
Class Meetings (MWF) |
Topic |
|
|
Part I Elementary Concepts |
|
#1-#3 |
Numbers, Sets, and Functions |
|
#4-#6 |
Language and Proofs |
|
#7-#10 |
Induction |
|
#11-#14 |
Bijections and Cardinality |
|
|
Part II Properties of Numbers |
|
#15-#18 |
Combinatorial Reasoning |
|
#19-#20 |
Divisibility |
|
#21-#23 |
Modular Arithmetic |
|
#24-#26 |
The Rational Numbers |
|
|
Part III Discrete Mathematics |
|
#27-#29 |
Probability |
|
#30-#32 |
Two Principles of Counting |
|
|
Part IV Continuous Mathematics |
|
#33-#35 |
The Real Numbers |
|
#36-#39 |
Sequences and Series |
|
#40-#43 |
Continuous Functions |
Assignments: Homework will be assigned each week in lecture
and will usually
be due on Monday. It will be graded and returned. Homework assignments
will
consist primarily of writing mathematical arguments and proofs; the
validity of
the mathematical reasoning and the quality of the exposition will both
count
toward the grade. You are welcome to use any resources you like,
including
talking to one another. However, the more you can do on your own, the
more you
will learn. I strongly recommend that you put in some real work on a
problem
before consulting with anyone else. Also, each person must write up the
work
independently; doing otherwise will be considered plagiarism.
Additional writing assignments will be assigned in the weekly lab.
See the
summary below and the attached sample writing assignment for more
details.
Topics for Friday Math 348 Mathematical Writing Sessions (subject
to
change, but the schedule should at least give you an idea of the sorts
of things we'll be doing.
| Week 1 Aug. 28 |
Introduction to Mathematical Writing. Resources, TeX, LaTeX (mathematical word processing programs). |
|
Week 2 Sept. 3 |
Mathematical Writing exercises. |
|
Week 3 Sept. 10 |
Peer review of written work. Students will
work in groups, presenting their mathematical work and giving one
another feedback on written drafts of the work. After the session,
students will revise their drafts before submitting them. |
|
Week 4 Sept. 17 |
"Rules" of mathematical writing. Students
will discuss the conventions of mathematical writing in various
settings and compare these to the conventions of other types of
writing. Mathematical notation. Students will read and compare sample
passages containing mathematical notation. Discussion of how the choice
of mathematical notation affects the clarity of the writing. |
|
Week 5 Sept. 24 |
Peer review of written work. See Week 3. |
|
Week 6 Oct. 1 |
Peer review of written work. See Week
3. |
|
Week 7 Oct. 8 |
Peer review of written work. See Week 3. |
|
Week 8 Oct. 15 |
Audience exercise. Students will compare
several passages, all on a single mathematical topic, written for
different audiences. |
|
Week 9 Oct. 22 |
Peer review. Students will bring to class a
draft of an article written for a general (e.g. newspaper-reading)
audience. In groups, students will discuss the drafts and give one
another feedback. The students will subsequently revise the drafts for
submission. |
|
Week 10 Oct. 29 |
Peer review of written work. See Week 3. |
|
Week 11 Nov. 5 |
Peer review of written work. See Week 3. |
|
Week 12 Nov. 12 |
Peer review of written work. See Week 3. |
|
Week 13 Nov. 19 |
Peer review of written work. See Week 3. |
|
Week 14 Dec. 3 |
Paper-length writing. Students will discuss
the conventions of mathematical writing of article length, having
analyzed several examples in advance. This session will include
practice in writing an abstract. |
|
Week 15 Dec. 10 |
|
|
|
|
Excused Absences: Acceptable reasons for excused absences are
significant illness, family emergency, or University-sponsored travel.
Whenever
possible, you must notify me in advance, preferably in writing (email
is good).
In case of emergency, notify me as soon as possible. The University is
advising students with flu symptoms (fever, cough and body aches) to
stay home until 24 hours after the fever is gone. I encourage all
students in Math 348 to follow this advice. For more information, see http://www.mckinley.illinois.edu/general/news/h1n1_update.htm
For an excused absence, you will be able to either make up the work
or be
excused from it - this is left to the instructor's discretion,
depending on the circumstances. For any
foreseeable absence, the make-up work must be done in advance of the
due date.
Exams: There will be three hour exams (Mondays Sept. 21,
Oct. 19, Nov. 16) and a comprehensive
final exam (Mon. Dec. 14, 8:00-11:00am). Notes and books may not
be used
on exams. You can use a calculator on exams. Because of the nature of
the
material, a calculator is unlikely to be of much use, however. The final exam will cover the entire course.
Please arrange any travel, etc., so that you can take the final on this
date.
Math 348 has a non-combined final exam. There will be no conflict exam
given
except for those few individuals who meet the official university
criteria
given in the student code http://admin.illinois.edu/policy/code/article3_part2_3-201.html
Missed exams: If
you miss an exam, you will receive a 0 for your exam grade. The only
exception
is if you have a valid excuse for missing, such as a significant
illness or a
serious emergency. In this case, you must inform me before the exam,
or, if
this is physically impossible, then as soon as possible afterwards. In
this
situation, you will be given a make-up exam as soon as possible.
Grading: The course grade will be determined by
15% Exam 1
15% Exam 2
15% Exam 3
20% Final Exam
15% Homework
20% Additional Writing Assignments (including participation in the peer review process)
General Education Credit: This course fulfills the Advanced
Composition general education requirement.
Course Information:
LaTeX Example files.
There
are "LaTeX Notes" at the end of most of these:
Skeleton LaTeX file ( you can use
this
for your writing assignments instead of starting from scratch.)
LaTeX
Example #1 (proof that |xy| = |x| |y|
for all
x and y)
Links on the Writing of Mathematics:
Some Notes on Writing Mathematics
by John M. Lee, University of Washington
Common
Errors in Writing Mathematics, by Stephen B. Maurer,
Swarthmore College
Tips on Writing in Mathematics
by Paul Zorn, St. Olaf College
Writing
Mathematics by Eric Behr, Northern Illinois
University
A
Guide to Writing Mathematics, by Kevin P. Lee, Purdue
University Calumet
Announcements
Grades: After the first few weeks of the semester, you will be
able to
check your grades in this class via the Department of Mathematics
gradebook
program. Go to http://www.math.uiuc.edu/Classes
and click on "Score Reports". You will be asked to enter your