# Mathematics

## MATH 155: Mathematics, A Way of Thinking

Fall 2003, MWRF, 10:00-10:50 am, NC 211

Instructor: Rich Maresh, Associate Professor of Mathematics

Office: MC 522, (608)-796-3655    (Home: 526-4988)

Office Hours: R 9-10, MWR 1-2   Email:  rjmaresh@viterbo.edu

Final Exam: Tuesday, 9 Dec 2003, 3:00-5:00 pm

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.

TextThinking Mathematically, 2nd edition, by Robert Blitzer  (Prentice-Hall, 2000)

CORE SKILL OBJECTIVES:

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.

(b)    ... solve simple linear algebraic equations.

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

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

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

(f)      ... explore the basics of probability.

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

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

(i)      ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course.

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.

(b)    ... understand the need to do one's own work, to honestly challenge oneself to master the material.

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.

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

(c)     ... turn in written solutions to occasional problems.

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.

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

(c)     ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry.

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.

There will be a few assignments not generally included in a mathematics course, but which will, I hope, make your experience in this class more well-rounded than in a typical algebra course. These include the following:

MATHEMATICAL AUTOBIOGRAPHY: Due: Monday, September 15. Point value: 25.This will be a 3-page paper in which you explore your life as a math student. I think it is especially appropriate for education majors to reflect on your past mathematical life, and to consider what methods and styles worked for you in the classrooms throughout your K-12 career. Try to be specific and try not to make this a "blame the teacher" paper.

GRADING PROCEDURES: The grading procedure is quite straight-forward. "A" = 90% or more of total possible points, "AB" = 87% or more, "B" = 80% or more, "BC" = 77% or more, "C" = 70% or more, "CD" = 67% or more, and "D" = 60% or more. We will probably end up with about 800 possible points. My advice is simple: if you wish to earn a decent grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. I find that the surest way to receive less than a "C" is to make sure you miss some classes and fail to turn in all your work!

ATTENDANCE POLICIES: Attendance is important in this class. There is really never a "good day" to miss because we will either be covering new material or working in groups on some problems. I will not formally reduce your grade for poor attendance, but you should understand that one good way to lower your grade is to miss out on what we do in class.

LATE ASSIGNMENTS: Turning in assignments late is also something you should avoid. For one thing, if I am going to be able to get your work graded in a timely fashion so that it will do you some good for study purposes, you need to get it turned in on time. Another reason is that since we will be moving from one topic to the next, it is important that you are not spending your time doing work you should have done a week or two earlier instead of focusing on what we are doing at the moment. Therefore, I have a rule on late assignments: 10% of the total point value of a given assignment will be subtracted from your score for each of the first 3 days past the due date. Beyond 3 class periods, I will no longer accept late work. In general it is better to turn in work even if it is not entirely finished than to hold on to it.

RESOURCES: Tutoring is available in the LearningCenter  -third floor, MurphyCenter. The book publisher, Prentice-Hall, has provided a set of CDs that contain lectures for each chapter in the text, covering the main key ideas in that chapter. I will put this set of CDs on reserve in the library; you might want to consider watching some of these lectures, especially if you are having trouble with some material. These CDs should run in the CD-drive of any computer.

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.

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.

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.

Fall 2003 Math 155Course Schedule

### 25 Aug    <1.1> Inductive and Deductive Reasoning                             p 10 # 1-21 odd, 27-33 odd

27 Aug    <1.2> Estimation and Graphs                                                p 20 # 1-49 odd

28 Aug    <1.3> Problem Solving                                                           p 32 # 1-49 odd

30 Aug    Lab #1

1 Sep       - L a b o r   D a y  -

3 Sep       <3.1> Statements, Negations, Quantifiers                              p 97 # 1-37 odd

4 Sep       <3.2> Compound Statements                                                 p 107 # 1-65 odd

5 Sep       <3.3> Truth Tables                                                                p 119 # 1-55 odd

8 Sep       Lab #2

10 Sep     <3.4> Truth Tables for Conditional Statements                    p 131 # 1-53 odd

11 Sep     <3.5> Equivalent Statements, De Morgan’s Laws                 p 142 # 1-53 odd

12 Sep     <3.6> Arguments and Truth Tables: Syllogisms                    p 152 # 1-45 odd

15 Sep     <3.7> Arguments and Euler Diagrams                                    p 163 # 1-23 odd

17 Sep     Lewis Carroll Logic Problems

18 Sep     Lab #3

19 Sep     Group Practice Exam #1  [20 points]

22 Sep     EXAM #1  [80 points]

24 Sep     <4.1> Hindu-Arabic System, Early Positional Systems        p 176 # 1-51 odd

25 Sep     <4.2> Number Bases, Place Value                                          p 183 # 1-53 odd

26 Sep     <4.3> Computation in Number Bases                                    p 189 # 1-37 odd

29 Sep     <4.4> Early Numeration Systems                                          p 196 # 1-55 odd

1 Oct       Lab #4

2 Oct       <6.2> Solving Linear Equations                                              p 295 # 1-63 odd

3 Oct       <6.3> Applications of Linear Equations                                p 304 # 25-45 odd

6 Oct       <8.2> Interest                                                                         p 439 # 1-47 odd

8 Oct       <8.3> Installment Buying                                                       p 450 # 1-19 odd

9 Oct       <8.4> Home Ownership                                                         p 460 # 1-13 odd

10 Oct     Lab #5

13 Oct     Review …

15 Oct     Group Practice Exam #2  [20 points]

16 Oct     EXAM #2  [80 points]

17 Oct     - Mid-semester Break -

20 Oct     <10.1> Points, Lines, Planes, and Angles                              p 513 # 1-41 odd

22 Oct     <10.2> Triangles                                                                     p 523 # 1-35 odd

23 Oct     <10.3> Polygons and Perimeter                                             p 529 # 1-43 odd

24 Oct     <10.4> Area, Circumference                                                   p 540 # 1-35 odd

27 Oct     <10.5> Volume                                                                       p 549 # 1-35 odd

29 Oct     Lab #6

30 Oct     <11.1> Counting Principles                                                    p 585 # 1-19 odd

31 Oct     <11.2> Permutations                                                              p 592 # 1-47 odd

3 Nov      <11.3> Combinations                                                             p 599 # 1-39 odd

5 Nov      <11.4> Fundamentals of Probability                                      p 607 # 1-61 odd

6 Nov      Lab #7

7 Nov      <11.5> Probability and Counting Rules                                 p 615 # 1-17 odd

10 Nov    <11.6> Probability of (A or B)                                              p 625 # 1-63 odd

12 Nov    <11.7> Conditional Probability, P(A and B)                         p 637 # 1-63 odd

13 Nov    Lab #8

14 Nov    Group Practice Exam #3  [20 points]

17 Nov    EXAM #3  [80 points]

19 Nov    <12.1> Sampling, Frequency Distribution, Graphs               p 665 # 1-21 odd

20 Nov    <12.2> Measures of Central Tendency                                  p 681 # 1-55 odd

21 Nov    <12.3> Measures of Dispersion                                             p 691 # 1-35 odd

24 Nov    Lab #9

26 Nov      - T h a n k s g i v i n g –

27 Nov        z z z z z z

28 Nov               - B r e a k –

1 Dec       <12.4> The Normal Distribution                                           p 708 # 1-97 odd

3 Dec       Lab #10

4 Dec       Review …

5 Dec       Group Practice Final Exam  [25 Points]

FINAL EXAM:  Tuesday, 9 Dec 2003, 3:00 – 5:00  [125 Points]