# Mathematics

MATH 155: Mathematics, A Wayof Thinking
Spring 2007, 4 Credits, MWF 1:10 pm. R 1:00 pm, MRC 346

Instructor: Dr Michael Wodzak, Associate Professor of Mathematics
Office: MC 530, 796-3659;
Email: mawodzak@viterbo.edu
Hours: MWF 9 --  10, WF 11 – 12,R 9—11, and by appointment
Final Exam: Monday 7th May 3:005:00

Course Description: An investigation of topics, including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree.

TextMathematics in Our World, by Bluman  (McGraw-Hill, 2005)

CORE SKILL OBJECTIVES:
These skills are related to the General Education core abilities document. They are also written to refer to the various INTASC standards for the purposes of the Elementary Education program.

Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking.
Students will
(a)     ... explore writing numbers and performing calculations in various numeration systems. (INTASC 1)
(b)    ... solve simple linear algebraic equations. (INTASC 1)
(c)     ... explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models. (INTASC 1)
(d)     ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system. (INTASC 1)
(e)      ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms. (INTASC 1)
(f)      ... explore the basics of probability. (INTASC 1)
(g)      ... learn descriptive statistics, including making the connection between probability and the normal distribution table. (INTASC 1)
(h)     ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations. (INTASC 1)
(i)      ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course. (INTASC 1)

Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
Students will
(a)     ... develop an appreciation for the intellectual honesty of deductive reasoning. (INTASC 9)
(b)    ... understand the need to do one's own work, to honestly challenge oneself to master the material. (INTASC 1)

Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally.
Student will
(a)     ... write a mathematical autobiography. (INTASC 9)
(b)    ... do group work (labs and practice exams), involving both written and oral communication. (INTASC 4)
(c)     ... turn in written solutions to occasional problems. (INTASC 1)

Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience.
Student will
(a)     ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples. (INTASC 1)
(b)   ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages". (INTASC 1)
(c)     ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry. (INTASC 1)

It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course:
The students shall develop an appreciation of mathematics, its history and its applications.
The students shall become confident in their own ability to do mathematics.
The students shall become mathematical problem solvers.
The students shall learn to communicate mathematical content.
The students shall learn to reason mathematically.

FURTHER COURSE NOTES:
This course is aimed at the needs of elementary education majors and as such is the first part of a three-course, 12-credit sequence (MATH 155-255-355). This is a "content" course rather than a "methods" course (teaching methods are addressed in the latter two courses in the above sequence). This is what people generally call a "Liberal Arts Mathematics Course", meaning that it covers a wide variety of topics, has an emphasis on problem solving, and uses a historical and humanistic approach. Consequently, the course is considered appropriate for the general education requirements and is open to all students.

Assessment Procedures:

Semester grades in this course will be awarded according to a standard scale:
(90% and above) = A
(80%--89%)       = B
(70%--79%)       = C
(60%--69%)       = D
(Below 60%)      = F

Semester grades are calculated purely on a points basis, that is, the letter grades you earn on individual exams are purely guidelines for you to gauge your progress.  For example, if you miss a particular grade on an exam by a certain number of points, it is still possible to make up those points (and get into that grade bracket) in other parts of the course, perhaps on the next exam.  On the other hand, just because you got a good grade on one test, you should realize that you can lose enough points to get into a lower grade bracket by doing poorly in another area of the course.  Once again: it is points that count.

Homework questions                            100 pts.

(Full credit is given for each completed assignment)
Homework will be due one class week after it has been assigned.  Any questions regarding how to do particular homework problems will be welcomed in the intervening class meetings or in my office but not in class on the day that the homework is due.  Late homework will be penalized by a deduction of 20% of the assigned grade for each schoolday -- including schooldays on which class does not meet – that the work is late, so that, if the work is one week late, it will not receive any points.  You may, however, still hand the work in so that you can benefit from corrections and be certain you know how to do a question that could well appear on an exam

Examinations                                           400 pts
There will be four in class exams worth 100 pts apiece, and lasting 50 minutes each.

Participation                                              50 pts
Participation points are easy to acquire and you probably already know how to get them; don’t chat to your neighbors when I’m lecturing (asking a neighbor to help if you didn’t understand what I said is, however, always acceptable).  General politeness counts.  Cheerfulness, engagement, willingness to push buttons on your calculator, asking me to clarify if you are stuck, taking advantage of my office hours, these are all, to quote the Sound of Music, a few of my favorite things.

Labs                                                         150 pts

Cumulative Final Examination
200 pts

Total                                                        900 pts

Attendance Policy:
You can afford to miss no more than the equivalent of one week of class.  Any more absences are a dangerous loss of classtime percentage. Once you have had 3 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score.
Make up exams situations will be considered on a case-by-case basis, but invariably they require as much forewarning as possible -- and documentation.  You know when the exams are; please do not book flights home, or your wedding, etc, etc on those dates.  If your, or your best friend's, or your uncle's hairdresser's poodle's (if you're from the Coast) wedding is already booked for any of those dates, please let me know ASAP. I will not give make up tests without good reason, and if you should miss a test that is not made up, your score for that test will be zero.
The sad fact is that it is a rare semester when some student doesn't have to rush home to tend a family crisis, or bury a loved one.  Often this interferes with exams.  Should such sadness happen to you, I will need to ask you for some sort of verification (obituary, hospital record, etc) and then we will try to get your semester moving again.

RESOURCES: Tutoring is available in the Learning Center  - third floor, Murphy Center. I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don’t resent your coming – it’s part of my job! I want your success as much as you do.

FINAL COMMENTS: I believe firmly that you as the student are the learner, and that "to learn" is an active verb; you must be actively engaged in the learning process, and this is best accomplished by your DOING mathematics. I am not here to show you how much I know - I am here to be "a guide on the side, not a sage on the stage". Please feel free to ask questions in class, either of me or of your group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary. The bottom line is that you must take responsibility for your own learning. Please believe that "Mathematics is not a spectator sport!"

AMERICANS WITH DISABILITY ACT: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski (MC 320, 796-3085) within ten days to discuss your accommodation needs.

Schedule, Spring Semester 2007

15 Jan     Introduction
17 Jan     [1-1] Inductive and Deductive Reasoning                       p7 #1-15 odd
18 Jan     [5-7] Sequences (and Series)                                        p229 #1-31 odd
19 Jan     Continued                                                                     assigned problems

22 Jan     LAB 1 ELEUSIS
24 Jan     LAB 2 POWER SEQENCES
25 Jan     [2-1] Sets                                                                      p41 #1-67 odd
26 Jan     [2-2] Subsets                                                                 p50 #1-63 odd

29 Jan     [2-3] Venn Diagrammes                                                 p58 #1-43 odd
31 Jan     [2-4] Solving Problems Using Sets                                  p63 #1-15 odd, 16
01 Feb    [11-1],[11-2] Intro to Probability                                   p541 #1-15 odd
02 Feb    [11-4],[11-5] Addition  and Multiplication Rules             p556 #1-19 odd , p567 #1-31 odd

05 Feb    [11-6],[11-7] Counting                                                   p576 #1-29 odd, p581 #1-29 odd
07 Feb    [11-8] Wrap-up of  Probability                                       p586 #1-13 odd
08 Feb    REVIEW
09 Feb    EXAM 1

12 Feb    [13-1] Preference Tables and the Plurality Method          p696 #1-11 odd, 17,19
14 Feb    [13-2] Borda Count and Pl w. Elimination                       p705 #1-19 odd
15 Feb    [13-3] Pairwise Comp and Approval                              p715 #1-19 odd
16 Feb    Weighted voting Systems                                                Assigned Problems

19 Feb    Continued                                                                       Assigned Problems
21 Feb    LAB 2 DEMOCRACY
22 Feb    Sharing                                                                           Assigned Problems
23 Feb    Sharing                                                                           Assigned Problems

26 Feb    Sharing                                                                           Assigned Problems
28 Feb    LAB 3  SHARING IN CONGRESS
01 Mar    REVIEW
02 Mar    EXAM 2

05 Mar    Spring Break
07 Mar    Spring Break
08 Mar    Spring Break
09 Mar    Spring Break

12 Mar    [4-1] Numeration Systems                                              p129 #1-81 every other odd
14 Mar    [4-2] Base Numbers                                                       p141 #1-71 every other odd
15 Mar    [5-1] The Natural Numbers                                             p168 #1-69 odds
16 Mar    [5-3] The Rational Numbers                                            p193 #55, 57 and assigned questions

19 Mar    [6-1] Clock Arithmetic                                                    p246 #1-99 every other odd
21 Mar    [6-3] Systems without Numbers                                      p260 #1-37
22 Mar    REVIEW
23 Mar    EXAM 3

26 Mar    LAB 4 BAR CODES
28 Mar    [10-1] Fundamental Geometric Objects                           p466 #1-43 odd, 51
29 Mar    [10-2],[10-3] Polygons                                                   p476 #7-27 odd,p483 #1-5 odd and assigned
30 Mar    [10-6] Trigonometry                                                       p507 #1-31 odd

02 Apr    [10-7] Networks                                                             p513 #1-17 odd
04 Apr    TSPs                                                                               assigned work
05 Apr    Easter Break
06 Apr    Easter Break

09 Apr    Easter Break
11 Apr    Minimal Networks                                                           assigned work
12 Apr    LAB 5 DIGRAPHS
13 Apr    From this point on there will be a number of labs and assigned work on map coloring and tesselation

16 Apr    See above
18 Apr    See above
19 Apr    See above
20 Apr    See above

23 Apr    See above
25 Apr    See above
26 Apr
27 Apr    See above

30 Apr    REVIEW
02 May   EXAM 4
03 May   FINAL REVIEW
04 May   FINAL REVIEW
Final Exam (200 Pts): Monday May 7th 3:005:00