FOUNDATIONS OF ADVANCED MATHEMATICS  -- MATH 251 – Fall, 2004

 

Time:   M T Th F  10:20 – 11:10 am                  Location:  Collins 306

 

Professor:  Steve Prothero                                Office:  Collins 307

 

Phones:    Office:  370 - 6484                           Home:  (503) 393 - 5143

 

e-mail:  prothero@willamette.edu                      home:  prothero4@comcast.com

                   

Office Hours:    M T Th F  9 – 10:15;   W  8:30 - noon

                                           Afternoons by appointment

                          {In class:   M T Th F  8 – 8:50, 10:20 – 11:10, & 1:50 – 2:50}

 

Text:  Chapter Zero by Carol Schumacher, 2nd edition  

 

The Course:  The purposes of this course are three-fold.

                           

                 1.  to introduce and practice the methods of mathematical proof

                 2.  to become familiar with mathematical tools to be used in other courses

                 3.  to learn to read and write concise mathematics

 

Coverage:   We will discuss set theory, logic, and methods of proof while learning some of the

                   fundamental aspects of higher mathematics.

 

                  We will develop the primary number systems of mathematics (natural numbers,

                  integers, rational, real and complex numbers) from fundamental concepts.

 

                  We will study sequences and series of numbers and functions including power                    series.

 

Journal:    Sometime between the end of one class and the beginning of the next you are to                do the following in your journal.

 

               1.  Indicate the date of your entry.

               2.  Summarize the previous class.

               3.  Indicate what (if anything) was good or bad, easy or hard, interesting or boring.

               4.  Indicate your feelings (hopes, fears, etc.) about what went on in that class                        session or that is going on in the course.

 

               This is informal and primarily for your own personal use.  However, you                should try to use correct grammar, punctuation, and spelling.  The journal will                be handed in on a regular basis (see schedule) and will be graded each time.                 The grade will be based primarily on the whether or not the journal was on time                and complete.   Journals will be due on Fridays by noon, according to the course                schedule.

 

 

Proofs Without Words:  Students will be expected to orally present two “Proofs                                        Without Words” in class.  Each is a highly visual proof of

                                       some mathematical theorem or formula.  The presentation

                                       schedule will be determined by lot.

 

Class Participation:   Students will be called upon to present solutions / proofs of

                                  problems / theorems from the book or from outside sources.

                                  It is expected that the student will be present and will be

                                  prepared to present.

 

Problem Sets:   There will be regularly assigned proofs/problems.  Some will be done in

                         groups; others will be individual assignments.

 

Special Lectures:  There may be special lectures given outside of class time.  If so there will                               be a writing assignment associated with the lecture.

                      

 

Grading:

 

 

 

 

Journal Submissions

4 @ 10 points

40

 

Proofs Without Words

2 @ 20 points

40

 

Class Participation

 

200

 

Special Lecture Assignment

1 @ 20 points

20

 

Mid - Terms

3-4 @ 40 points

120 - 160

 

Final

(may be part take-home)

100

 

 

 

 

 

 

Total

~ 520 - 560

 

                 The total points earned will determine the course grade.  The grade will not be                  based on fixed percentages.   However, 90% guarantees at least an A-, 80%                  guarantees at least a B-, etc.

 

Writing:   Writing for this course will consist of, but may not be limited to, several of the                        following:

 

                       1.  proofs of theorems

                       2.  written discussions of pieces of established mathematics

                       3.  problem solutions

                       4.  your personal journal

                       5.  expository papers relating to mathematics