Math 290                       Mathematical Reasoning                         Fall 2007

Instructor
Office
Phone
Hours
E-mail
Web Page

John J. Currano
Auditorium Building, Room 418
(312) 341-3773
Monday & Tuesday 4:30-5:45
jcurrano@roosevelt.edu
http://faculty.roosevelt.edu/currano/
Location & Time. Auditorium Building, Room 414; Tuesday 6:00 - 8:30.

Prerequisite: MATH 232, Calculus II; it may be taken concurrently.

Text:  Mathematical Reasoning: Writing and Proof, Second Edition, by Ted Sundstrom,
         Prentice Hall, 2007, ISBN 0131877186.

Additional Course Documents (on the faculty web and RU Online)
Syllabus (this page in pdf)
Schedule (pdf - revised 09/03/07)
Assignments
Solutions (on RU Online)
Portfolio Guidelines (pdf - 09/02/07)
Portfolio Problems (pdf - 09/02/07)

Using the MS Word Equation Editor (by S. Simonds - link)
Using the MS Word Equation Editor (by S. Simonds - pdf)
Proof Guidelines (by T. Sundstrom - pdf)

Comments on Portfolio Problem 3 (pdf)

Course Content. Elementary logic, sets, elementary number theory, relations, functions, and methods of mathematical proof including direct proofs, indirect proofs, mathematical induction, case analysis, and counterexamples.

Course Objectives. The objectives for this course include the following:
1. To develop the ability to read and understand written mathematical proofs.
2. To develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, mathematical induction, case analysis, and counterexamples.
3. To develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting.
4. To develop talents for creative thinking and problem solving.
5. To improve the quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics.
6. To explore and understand the concepts described in the course content above.

Course Materials will available on the course site on RU Online; much will also be available on the Roosevelt Faculty Web at http://faculty.roosevelt.edu/currano/m290/. Some items, including solutions to Preview Activities and homework exercises, will only be posted on RU Online.  Check these sites frequently since the course materials posted there will reflect all changes.

Communication. RU Online has a threaded Discussion Board where you can post comments, ask questions, reply to the comments and questions of others, etc.; I will be an active participant. There is also a Digital Drop Box for submitting assignments on RU Online and facilities for emailing the instructor and your classmates and for checking your grades. Email sent via RU Online is sent to the recipient's Roosevelt email address and I will be using this to email the class, so please check your Roosevelt email regularly. Logon to RU Online and check it out.

Due Dates. All due dates for the course will be strictly enforced. It is expected that all assignments will be turned in by the due date. No late work will be accepted without prior approval from the instructor.

Participation.  Class will consist of discussion and problem solving with very little lecture.  Everyone is expected to participate:
         ■ by asking and answering questions;
         ■ by working on exercises and activities, sometimes in groups; and
         ■ by presenting and discussing solutions to exercises, activities, and homework problems.
In order to participate effectively, you must be prepared and up-to-date.  Attendance in class is critical to your success in this course, and it is imperative that you work on a consistent basis. You should plan to spend 6-9 hours per week outside of class studying for this course; a great deal of your learning in this course must be on your own. It is your responsibility to
         ■ do the
Preview Activities and the Assigned Reading before class,
         ■ do the Homework problems after class, and
         ■ seek help as needed.
A portion of your grade will be for class participation.

Preparation. Each section in the text is preceded by several Preview Activities, whose purpose is to prepare you for the readings and discussion of the section. Ideally you should attempt the Preview Activities before reading the section; after completing them, read the section and modify your solutions if necessary. You may work in groups on the Preview Activities, but each person must write up his or her own solutions. Before the classroom discussion of a section, one of the Preview Activities for that section will be collected for grading. I expect that mistakes will be made on the Preview Activities and that you will learn from these mistakes, so grading will not be based on whether or not everything is correct, but rather on whether or not a serious and substantial effort was made to complete the activity (with scores of 4, 2, or 0 on the graded Preview Activities). After class, do the assigned homework problems; these will not be collected but will be reviewed at the next class upon request.

Assignments. During the semester, there will be several take-home assignments that will be announced in class and be due the following week

Portfolio Project: You will be given ten mathematical problems to complete for a "Proof Portfolio."  You may submit, via the Digital Drop Box on RU Online, each of the Portfolio Problems two times to be critiqued. They will be returned, with comments, via the Digital Drop Box. After each submission, you have the opportunity to rewrite your portfolio proof prior to submission for a final grade. However, no more than four problems may be submitted for review during any given week. Start work on the problems early. Two problems only require Chapter 1 of the text and three others only require portions of Chapter 3 and the earlier chapters. So you can complete, or make significant progress on, half of the problems by the end of the sixth week of the semester - and earn at least 20 bonus points into the bargain.

Graded Work and Use of a Word Processor. I expect your very best on all graded assignments. All solutions for the problems on the Portfolio Project must be written using a word processor capable of producing the appropriate mathematical symbols and equations, and submitted in a form readable by Microsoft Word or Corel WordPerfect. Microsoft Word and its Equation Editor, which is available on all the computers in the Computer Labs, is one such word processor.  The tutorial Using the MS Word Equation Editor by Prof. Steve Simonds of Portland Community College is an excellent introduction to the use of the Equation Editor.

Use a 12 point font (Times New Roman or a similar font) and standard margins. Your papers must be spell-checked and proofread for grammatical correctness as deductions will be made for spelling and grammatical errors. Mathematical Writing. One of the primary objectives of this course is to learn to write mathematics well and, in particular, to learn to write mathematical proofs. Writing is an important part of communicating mathematical results. You will be required to write mathematical proofs and solutions to problems on the tests and assignments. Writing proofs and solutions means more than writing formulas and circling an "answer". Everything you write is your "answer" and it all will be read and evaluated. You must explain all significant steps, using complete sentences with appropriate formulas and graphs included. The grading of the written assignments will be based on the quality of the writing, the quality of the mathematical content, and the logical organization of the writing.
 
You might find the documents ProofGuidelinesSundstrom.pdf, by the author of the text, Ted Sundstrom, and ProofGuidelinesSklar.pdf, by Jessica Sklar of Pacific Lutheran University, interesting and useful. (They are on the faculty web and on RU Online.) They collect and expand on the writing guidelines given in the text and will help you to write in a conventional mathematical style.

Academic Integrity. Some of the work done in this course will be done collaboratively. Collaboration requires you to contribute to the solutions, work through details on your own, and write your own solutions in your own words. This type of collaboration is allowed on the preview activities and assignments. However, copying or rephrasing an answer or a solution to which you have not contributed is plagiarism. The Portfolio Project is to be done entirely on your own, although you may ask questions which may lead to a discussion in class. Collaboration is not allowed on the Portfolio Project or on tests. Plagiarism, unauthorized collaboration, and cheating on tests are forms of Academic Dishonesty and will result in a grade of zero for a first offense and a grade of "F" in the course for a second offense. Second offenses will also be reported to the Assistant Vice President for Student Services. Roosevelt University's policies on Academic Integrity are on the web at http://www.roosevelt.edu/plagiarism/.

Two Mid-Term Tests will be given on October 9 and November 13 (dates subject to change).  Tests will be closed book. No make-ups except for excused absences with advance notice.

The Final Examination will be given on Tuesday, December 18. It will be closed book and comprehensive.  No make-ups except for excused absences with advance notice.

Grades.  Regulations covering grades (especially I and W) are on pages 254-255 of the 2006-2008 Undergraduate Catalog. Incompletes will not be given, except to a student who has done passing work up to the Final Examination but misses the final exam because of an excused absence with advance notice. The last day to drop a class (with a grade of "W") is Friday, November 16, and the drop form must be submitted to the Registrar's Office by that date. Anyone registered after November 16th must be graded solely on her/his performance. The course grade will be determined by the scores on the preview activities, class participation, assignments, portfolio, mid-term tests, and the final examination, according to the following scale:
 

 Item

Points 

 Preview Activities

88 

 Class Participation

42 

 Assignments

125 

 Portfolio

125 

 Mid-Term Test 1

80 

 Mid-Term Test 2

80 

 Final Examination

160 

 Total

700 

 Grade 

 Minimum 
 Score

   A

90%

   A-

87%

   B+

84%

   B

80%

   B-

77%

 Grade 

 Minimum 
 Score

   C+

74%

   C

70%

   C-

67%

   D+

64%

   D

60%

 

 
This page is at http://faculty.roosevelt.edu/currano/m290/Revised: July 08, 2008