MATH 155: Mathematics, A Wayof Thinking
Fall 2006, 4 Credits, MWRF 8:00 am., MRC 414
Instructor: Dr Michael Wodzak, Associate Professor of Mathematics
Office: MC 530, 796-3659;
Hours: MWF 9 -- 10, WF 11 – 12,R 9—11, and by appointment
Final Exam: Wednesday DEC 13th 7:40—9:40
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.
(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.
(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.
(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.
(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.
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
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, Fall Semester 2006
30 Aug Introduction
31 Aug [1-1] Inductive and Deductive Reasoning p7 #1-15 odd
01 Sept [5-7] Sequences (and Series) p229 #1-31 odd
06 Sept Continued assigned problems
07 Sept LAB 1 ELEUSIS
08 Sept [2-1] Sets p41 #1-67 odd
11 Sept [2-2] Subsets p50 #1-63 odd|
13 Sept [2-3] Venn Diagrammes p58 #1-43 odd
14 Sept [2-4] Solving Problems Using Sets p63 #1-15 odd, 16
15 Sept [11-1],[11-2] Intro to Probability p541 #1-15 odd
18 Sept [11-4],[11-5] Addition and Multiplication Rules p556 #1-19 odd , p567 #1-31 odd
20 Sept [11-6],[11-7] Counting p576 #1-29 odd, p581 #1-29 odd
21 Sept [11-8] Wrap-up of Probability p586 #1-13 odd
22 Sept REVIEW
25 Sept EXAM 1
27 Sept [13-1] Preference Tables and the Plurality Method p696 #1-11 odd, 17,19
28 Sept [13-2] Borda Count and Pl w. Elimination p705 #1-19 odd
29 Sept [13-3] Pairwise Comp and Approval p715 #1-19 odd
02 Oct Weighted voting Systems Assigned Problems
04 Oct Continued Assigned Problems
05 Oct LAB 2 DEMOCRACY
06 Oct Sharing Assigned Problems
09 Oct Sharing Assigned Problems
11 Oct Sharing Assigned Problems
12 Oct LAB 4 SHARING IN CONGRESS
13 Oct REVIEW
16 Oct EXAM 2
18 Oct [4-1] Numeration Systems p129 #1-81 every other odd
19 Oct [4-2] Base Numbers p141 #1-71 every other odd
20 Oct Mid Semester Break
23 Oct [5-1] The Natural Numbers p168 #1-69 odds
25 Oct [5-3] The Rational Numbers p193 #55, 57 and assigned questions
26 Oct [6-1] Clock Arithmetic p246 #1-99 every other odd
27 Oct [6-3] Systems without Numbers p260 #1-37
30 Oct LAB 5 BAR CODES
01 Nov REVIEW
02 Nov EXAM 3
03 Nov [10-1] Fundamental Geometric Objects p466 #1-43 odd, 51
06 Nov [10-2],[10-3] Polygons p476 #7-27 odd,p483 #1-5 odd and assigned
08 Nov [10-6] Trigonometry p507 #1-31 odd
09 Nov [10-7] Networks p513 #1-17 odd
10 Nov TSPs assigned work
13 Nov Minimal Networks assigned work
15 Nov From this point on there will be a number of labs and assigned work on map coloring and tesselation
16 Nov See above
17 Nov See above
20 Nov See above
22 Nov THANKSGIVING
23 Nov THANKSGIVING
24 Nov THANKSGIVING
27 Nov See above
29 Nov See above
30 Nov See above
01 Dec See above
04 Dec REVIEW
06 Dec EXAM 4
07 Dec FINAL REVIEW
08 Dec FINAL REVIEW
Final Exam (200 Pts): Wednesday DEC 13th 7:40—9:40