http://www.math.uri.edu/~eaton/MTH307S08.htm
MTH 307 
Spring 2008
Introduction to Mathematical Rigor
Instructor: Dr. Nancy Eaton
Email me: mailto:eaton@math.uri.edu
Phone: 8744439
Office: Rm. 208, Tyler Hall
Office hours: Mon, Tues, Fri: 2:002:30
Visit my web page: http://math.uri.edu/~eaton/
Students who require
accommodations and who have documentation from
Disability Services (8742098) should make arrangements with me as soon as
possible.


Provides a bridge
between lower level and upper level mathematics courses, where proofs of
mathematical statements are discussed.
The emphasis is on basic structures, logic, the structure of
mathematical statements, and proof techniques. Theorems and problems from many areas of
mathematics serve as motivation and come from a wide range of topics including
set theory, number theory, abstract algebra, geometry, discrete math, and
continuous math.
1. Become familiar with and correctly use the basic structures
of mathematics.
2. Learn the many
aspects of logic and correct reasoning to both understand and prove theorems.
3. Additionally, topics from the following list will be covered
in the course.
Texts:
A Discrete Transition to Advanced Mathematics, by Bettina Richmond and
Thomas Richmond, Thomson Brooks/Cole Pubs
Student Solutions
Manual for A Discrete Transition to Advanced
Mathematics, by Bettina Richmond and Thomas Richmond, Thomson Brooks/Cole
Pubs
Homework Assignments  25%
Portfolio  15%
Worksheets
– 10%
Three 1hour exams  30%
Final  20%
o
In order to achieve the most from this course you are expected
to do the following:
o
Read Text.
o
Take notes in class.
o
Do the Suggested Exercises. These are not to be handed in. Check answers in the back of the text
and/or Solutions Manual. Ask about those
you do not understand.
o
Complete the Homework assignments that are to be handed in,
including worksheets.
o
It is recommended that you ask questions during my office hours
about the assignments BEFORE handing them in.
o
Study all of the above for exams. But if you keep up with at least 4 hours
of working the above steps each week, outside of class, studying for an exam
should consist of going over what you have learned, versus learning it for the
first time.
Homework Assignments:
(25% of your grade)
There will be 40 exercises, selected from out text, to hand
in. These will be graded and comments will be given. Each is worth up to 4 HkPts. (See the grading rubrik.) See the guide below.
Earning extra HkPts:
During the semester, each student will be asked to present
solutions to exercises on the board.
These will be chosen from those that you do not hand in. You will
always be given a chance to prepare your presentation. This will serve to
improve your verbal communication skills. You will be graded on your
presentation and earn up to 4 HkPts for each
solution. A formally written, typed
solution must be handed in at the time of your presentation. Sign up sheets will be given in class. I will post your solution for the rest
of the class to download if they like. Solutions posted here. 2.1(2) 2.2(4) 2.2(14a)
At any time during the semester, you may resubmit (once) an
exercise that has been returned to you with a grade of 0, 1, or 2 pts, provided
that you originally handed it in by its due date. You must resubmit the entire question
and answer. No more than one
exercise per sheet of paper. Proper
identification of the problem must be given at the top of the page.
Computation of this portion of your
grade: Total HkPts
divided by 160, or 100%, which ever is smaller.
Guide: You must do the following for full credit on the assignments
that you hand in.
A) Write out the entire question._{}
B)
Write neatly or type your assignment. Do not use torn paper.
C)
The format should be single column.
D) Use only one side of the paper.
E)
Clearly mark the section number and due date on the top of the front page.
F) Arrange
the exercises in order by problem number. Attach pages together.
G) One
point will be deducted from the assignment for each class day that it is late.
In the case that it is late, you must put the date that you handed the
assignment in, or no credit will be given.
I) Explain carefully, using proper mathematical logic.
J) Use
complete sentences.
Portfolio: (15% of your
grade)
I will assign 10 exercises similar to ones that you have worked
on all semester for you to hand in as a portfolio of work, representing what
you learned in this course. This is intended to be a collection of your
best work. This will be due on Monday April 28th. You will have
two weeks advance notice as to which problems will be included in the
portfolio. The problems will be listed on this web page by Friday April 11th.
Portfolio Problems:
1.
Extra credit problem
from Exam 2
2.
2.2 (2f)
3.
4.4 (14)
4.
6.1 (12)
5.
6.1 (6a)
6.
6.1 (19. Do part b 2 ways.)
7.
6.2 (14)
8.
6.2 (5b,d)
9.
6.3 (3c)
10.
6.3 (6)
Extra Credit: 8.3 (2), 8.3(4) Earn up to 2% out of
100% of your grade.
Write out the entire statement of the exercises. Write the
solution as formally as you can. Use complete sentences. Write it
as if it would be published. This MUST BE TYPED. If you have access
to an equation editor, that would be best.
See: link.
Worksheets: (10% of
your grade)
Three worksheets will be given during the semester. These will contain exercises that are
not covered in the book. You should
complete the problems on the worksheets and hand them in by their due dates.
There will
be three 45minute exams. The dates for these are Monday Feb 18th, Wed
Mar 26th, and Monday Apr 21st. The final exam is will be given
during the scheduled time on Monday May 12th from 11:30 – 2:30 PM.
The exams will be taken from material that we covered in class, exercises in
the book, and worksheet problems.
Take careful notes and study them for the exams. No PDAs, cell phones, laptops, or calculators will be allowed
on your desk during exams.
Exam 1: Feb 18; Exam 2: Mar 26; Exam 3: Apr 21
Portfolio: Apr 11 (problems announced), Apr 28 (portfolio due)
Final Exam: May 12 (11:30 – 2:30 PM)
In the following syllabus, approximate dates are given for
starting each section of the text that we will cover. Exact due dates for Homework assignments
and worksheets will be given in advance of each assignment. I suggest that you read ahead in the
book and start working on exercises from the book as soon as we start each
section.
Week of 
Introduce
Section/Topic 
Exams 
Wed
1/23 
1.1 

Mon
1/28 
1.2,
1.3, 1.4 

Mon
2/4 
1.5,
1.6, Logarithms 

Mon
2/11 
2.1,
Fields 

Mon
2/18 
2.2 
Exam
1 2/18 
Mon
2/25 
2.3,
3.1 

Mon
3/3 
4.1,
4.2, 4.3 

Mon
3/10 
4.4,
5.1, 5.2 

Mon
3/17 
Spring
Break 

Mon
3/24 
5.3 
Exam
2  3/26 
Mon
3/31 
6.1,
6.2 

Mon
4/7 
6.3,
7.1 

Mon
4/14 
8.1,
8.3 

Mon
4/21 
8.5 
Exam
3 – 4/21 
Mon
4/28 
Game 

Mon
5/12 

Final
Exam 
Section/Topic 
Suggested
Exercises 
Present
In Class 
Hand
In 
HK# 
Due 
1.1 
1, 2, 3, 4,
5, 8 
9 
 
 
 
1.2 
2, 4, 5, 9,
10, 15 
1,
6, 7 
 
 
 
1.3 
5, 9 
3,
8, 11 
6,
10 
1 
2/11 
Set
theory 
 
 
 
1/30 

1.4 
1, 3, 7, 10,
12, 14 
2 
8a,
9 
1 
2/11 
1.5 
1, 2, 4 
3,
6 
5 
2 
2/15 
1.6 
1, 3, 6, 9,
11 
2,
7 
10 
2 
2/15 
Logarithms 
 
 
 
2/29 

2.1 
5, 8, 12, 27 
2,
9a, 25 
4,
7, 11, 14 
3 
3/5 
FieldsWorksheet3 

 

 

2, 3,
6, 8 (8pts) 

2, 4, 5, 11 (8pts) 

5, 8 (4pts) 

2 

3(a, b) 

3 
7(a,b) 

5 

10, 13 
4/16 

 

3a, 6 

☼
I
encourage you to work together under the following circumstances.
☼
Begin
the problem on your own and do as much as you can.
☼
Ask
someone from the class to explain the basic outline of a solution.
☼
Take
what you learned and write out the solution on your own, using your own
words.
The
following is an excerpt from the University Manual.
Solutions to selected homework problems
and examples: