# Mathematics

## MATH 155: Mathematics, A Wayof Thinking

Fall 2005, 4 Credits, MWF 12:10 pm., R 1:00 pm., MRC 436

Instructor: Dr Michael Wodzak, Associate Professor of Mathematics

Office: MC 530, 796-3659;

Email: mawodzak@viterbo.edu

Hours: MWF 10--11, R 9—11 and by appointment

Final Exam: Friday DEC 16th 9:50--11:50

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.

Text

Mathematics 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

explore writing numbers and performing calculations in various numeration systems. (INTASC 1)

solve simple linear algebraic equations. (INTASC 1)

explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models. (INTASC 1)

explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system. (INTASC 1)

develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms. (INTASC 1)

explore the basics of probability. (INTASC 1)

learn descriptive statistics, including making the connection between probability and the normal distribution table. (INTASC 1)

learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations. (INTASC 1)

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

develop an appreciation for the intellectual honesty of deductive reasoning. (INTASC 9)

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

write a mathematical autobiography. (INTASC 9)

do group work (labs and practice exams), involving both written and oral communication. (INTASC 4)

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

explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples. (INTASC 1)

develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages". (INTASC 1)

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:

729—810pts      (90% and above)    = A

648—728pts      (80%--89%)          = B

567—647pts      (70%--79%)          = C

486—566pts       (60%--69%)        = D

Less than 486pts (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

Practice Exams     100 pts

There will be four group practice exams worth 25 pts apiece before each in class midterm and before the final exam

Examinations   300 pts

There will be three 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  160 pts

There will be eight labs each of which carries 20 pts
Cumulative Final Examination
200 pts

Total 810 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 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 – part of my job! I want your success as much as you do.

BLACKBOARD:

I’m not sure how much I will be using “Blackboard” but I will enter you into the system and it will give us a resource, at least for web sites that might be interesting and useful.

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, Fall Semester 2005

29 Aug   [1-1] Inductive and Deductive Reasoning      p7 #1-15 odd

31 Aug   [1-2] How to Solve It          p15 #1-29 odd

1 Sep    [5-7] Sequences (and Series)     p229 #1-31 odd

2 Sep   assigned problems

This is the last day to add or change sections of a class

5 Sep    Labor Day Break ;-)

7 Sep    Lab #1 (20pts)

8 Sep    [2-1] Sets p41 #1-67 odd

9 Sep    [2-2] Subsets    p50 #1-63 odd

12 Sep    [2-3] Venn  p58 #1-43 odd

(13 Sep: Last day to take a course Credit/No Credit)

14 Sep    [2-4] Solving Problems Using Sets   p63 #1-15 odd, 16

15 Sep    [3-1] Simple and Compound Statements   p80 #1-53 odd

16 Sep    [3-2] Truth Tables   p91 #1-29 odd

19 Sep    [3-3] Statements Revisited       p98 #1-29 odd

21 Sep    Lab #2    (20pts)

22 Sep    [3-4] Arguments  p104 #1-21 odd

23 Sep    [3-5] Euler Circles  p111 #1-29 odd

26 Sep    Lab #3    (20pts)

28 Sep    Group Practice Exam #1 (25pts)

29 Sep    Exam #1 (100pts)

30 Sep    [4-1] Numeration Systems  p129 #1-81 every other odd

3 Oct     [4-2] Base Numbers    p141 #1-71 every other odd

5 Oct     [5-1] The Natural Numbers   p168 #1-69 odds

6 Oct     [5-3] The Rational Numbers   p193 #55, 57 and assigned questions

7 Oct     Lab #4

10 Oct     [6-1] Clock Arithmetic p246 #1-99 every other odd

12 Oct     [6-2] Mathematical Congruencesp254 #1-59 odds

13 Oct     [6-3] Systems without Numbers p260 #1-37

14 Oct     Lab #5 (20pts)

17 Oct     Group Practice Test (25 points)

This is the last day for submitting D/F slips

19 Oct     EXAM #2 (100 points)

20 Oct     [10-1] Fundamental Geometric Objects  p466 #1-43 odd, 51

21 Oct     Mid-Semester Break ;-)

24 Oct     [10-2] Triangles   p475 #1-31 odd

26 Oct     [10-3] Perimeter      p483 #1-35 odd

27 Oct     Lab #6 (20pts)

28 Oct     [10-4] Plane Area    p492 #1-37 odd

31 Oct     [10-5] Surface Area and Volume  p498 #1-27 odd

2 Nov   [10-6] Trigonometry        p507 #1-31 odd

3 Nov   [10-7] Networks        p513 #1-17 odd

4 Nov      assigned pro

7 Nov   Map Colouring

9 Nov   Minimal Networks

10 Nov   Lab #7 (20pts)

11 Nov   (11-1),[11-2] Tree Diagrammes and Tables

14 Nov   [11-4] Addition Rules for Probability

16 Nov   [11-5] Multiplication Rules and Conditional Probability

17 Nov   [11-6] Fundamental Counting Rule, Permutations

18 Nov   [11-7] Combinations

21 Nov   [11-8] Permutations and Combinations

23 Nov   Thanksgiving Break ;-)

24 Nov   Thanksgiving Day ;0)

25 Nov   Thanksgiving Break ;-)

28 Nov   Lab #8 (20pts)

30 Nov   [13-1] Preference Tables, Plurality Method

1 Dec    Other voting methods and Fairness Criteria

2 Dec    Weighted Voting systems

5 Dec    Group Practice Exam (25pts)

7 Dec    Exam 3 (100pts)

8 Dec    REVIEW

(n.b.This is the last day to request a grade of Incomplete)

9 Dec    Group Practice Final (25pts)

Final Exam (200 Pts): FRIDAY DEC 16th 9:50--11:50