http://www.math.uri.edu/~eaton/MTH307S08.htm

 

 

MTH 307 - Spring 2008
Introduction to Mathematical Rigor

Meets MWF:  10:00-10:50

Instructor:  Dr. Nancy Eaton

E-mail me: mailto:eaton@math.uri.edu
Phone:  874-4439
Office:  Rm. 208, Tyler Hall
Office hours:  Mon, Tues, Fri: 2:00-2:30


Visit my web page: http://math.uri.edu/~eaton/

Students who require accommodations and who have documentation from
Disability Services (874-2098) should make arrangements with me as soon as possible

Course Description

Text   Corrections to text

Grade for course

Working with Others

Dates to Remember

 

Other Web Resources

Rubric used for grading

Class Notes

 

Using MS Word equation editor

Keys to Exams

Homework Assignments

Solutions to selected exercises

Practice for Exams

Portfolio assignment

 

Course Description:

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

 

Calculation of Grade:

Homework Assignments - 25%
Portfolio - 15%

Worksheets – 10%
Three 1-hour exams - 30%
Final - 20%

 

Expected work:

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.

Exams: (Exams 30%, Final 20%)

There will be three 45-minute 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.

Dates to remember:

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)

Syllabus:

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

-

-

Worksheet 1

-

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

-

-

Worksheet 2

-

2/29

2.1

5, 8, 12, 27

2, 9a, 25

4, 7, 11, 14

3

3/5

FieldsWorksheet3

-

-

Proposition 1

-

3/10

2.2

23, 9, 15

4, 14a

2c, 2d, 11a

4

3/14

2.3

3, 7, 12

5

-

-

-

3.1

4, 6, 9

-

-

-

-

4.1

4, 6, 8

7

-

-

-

4.2

1, 4, 7

-

2, 3,  6, 8 (8pts)

5

4/2

4.3

1, 3, 7, 9

8

2, 4, 5, 11 (8pts)

5

4/2

4.4

1, 3

-

5, 8 (4pts)

5

4/2

5.1

3, 6, 10, 13

7, 11

2

6

4/9

5.2

2, 5, 8

1

3(a, b)

6

4/9

5.3

5

3

7(a,b)

6

4/9

6.1

2, 4, 10, 17

3, 6, 7, 11, 19,

5

7

4/16

6.2

2, 4, 6, 18

3

10, 13

7

4/16

Functions

-

Worksheet 4

-

-

-

6.3

6, 13

7

3a, 6

8

4/23

7.1

4, 6, 13

11

12

8

4/23

8.1

3, 6, 12

1

1 prob

-

-

8.3

3, 8, 12

5, 14

2 probs

-

-

8.5

2

-

2 probs

-

-

Guide to working with others:


There are benefits to discussing the problems with your classmates.  If you become stuck on a problem, fresh ideas from someone else might provide you with some new angles to try.  In the academic community as well as in business and industry, people often work in teams.  So, it is good to get some practice working with others.  Working with someone from class will help you to improve your math communication skills as well.

       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.

       If working with someone else, sometimes they will also ask you for your understanding of the basic outline.

       Take what you learned and write out the solution on your own, using your own words. 

       Never copy word for word from anyone else’s paper.  In fact it is better not to look at anyone else’s completed written solution or to show yours to anyone else.

       If you still do not completely understand the solution, you can ask your professor to look at what you wrote and try to clear up any parts of the solution that are not completely clear and accurate. 

The following is an excerpt from the University Manual.

8.27.11 A student's name on any written exercise (theme, report, notebook, paper, examination) shall be regarded as assurance that the work is the result of the student's own thought and study, stated in the student's own words and produced without assistance, except as quotation marks, references and footnotes acknowledge the use of other sources of assistance. Occasionally, students may be authorized to work jointly, but such effort must be indicated as joint on the work submitted.  Submitting the same paper for more than one course is considered a breach of academic integrity unless prior approval is given by the instructors.

Class Notes:

Sections 1.1, 1.2     

Sections 1.3, 1.4, 1.5, 1.6

Section 2.1

Fields

Section 2.2

Section 2.3

Binomial Theorem

Section 6.1

Section 6.2

Section 6.3

Solutions to selected homework problems and examples:

Keys to exams:

Key to Exam 2


Practice for exams:

Practice for exam 1

Solutions

Practice for exam 2

Solutions

Some Web Sites:


Proofs in Mathematics

Fermat's Last Theorem
Puzzles - Think.com
Recreational Math

Pythagorean Triples Project