# Mathematics

## MATH 155: Mathematics, A Way of Thinking

Fall 2004, MWF, 1:10-2:00 pm, R 1:00-1:50 pm,  MC 406

Instructor: Rich Maresh, Associate Professor of Mathematics

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

Office Hours: MWF 10-11, R 9-10, 2-3

Email:  rjmaresh@viterbo.edu

Final Exam: Tuesday, 14 Dec 2004, 12:50-2:50 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.

TextMathematical Ideas, 10th edition, by Miller, Heeren, and Hornsby  (Pearson/Addison-Wesley, 2004)

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.

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 13. 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 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.

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 2004 Math 155Course Schedule

### 30 Aug    <1.1> Problem Solving and Inductive Reasoning                   p 7 # 15-51 odd

1 Sep       <1.2> Number Patterns                                                          p 17 # 9-47 odd

2 Sep       <1.3> Problem Solving Strategies                                           p 26 # 5-45 odd

3 Sep       <1.4> Calculating, Estimating, Reading Graphs                     p 36 # 19-51 odd

6 Sep       - L a b o r   D a y  -

8 Sep       Lab #1

9 Sep       <2.1> Basic Set Theory                                                          p 54 # 1-45 odd, 53-73 odd

10 Sep     <2.2> Venn Diagrams and Subsets                                         p 61 # 1-51 odd

13 Sep     <2.3> Set Operations                                                             p 73 # 1-53 odd, 81-91 odd

15 Sep     <2.4> Cardinal Numbers and Surveys                                    p 79 # 1-27 odd

16 Sep     Lab #2

17 Sep     <3.1> Statements and Quantifiers                                          p 99 # 1-51 odd, 61-73 odd

20 Sep     <3.2> Truth Tables, Equivalent Statements                           p 111 # 1-49 odd, 61-67 odd, 71

22 Sep     <3.3> The Conditional Statement                                          p 120 # 1-49 odd, 61-69 odd, 79, 81

23 Sep     <3.4> More on the Conditional                                              p 128 # 5-49 odd

24 Sep     <3.5> Arguments and Euler Diagrams                                    p 132 # 1-29 odd

27 Sep     <3.6> Arguments and Truth Tables                                       p 145 # 1-23 odd, 27, 33, 35

29 Sep     Lab #3

30 Sep     Group Practice Exam #1 (20 Points)

1 Oct       EXAM #1 (80 Points)

4 Oct       <4.1> History of Numeration Systems                                  p 158 # 1-29 odd, 35

6 Oct       <4.2> Hindu-Arabic System                                                  p 167 # 1-31 odd, 41-49 odd

7 Oct       <4.3> Number Bases                                                              p 176 # 1-53 odd

8 Oct       Lab #

11 Oct     <5.5> Fibonacci Sequence, Golden Ratio                               p 237 # 1-19 odd, 25-31 odd

13 Oct     <7.1> Linear Equations                                                          p 322 # 1-31 odd, 37-43 odd

14 Oct     <7.2> Applications of Linear Equations                                p 335 # 11-41 odd

15 Oct     Lab #5

18 Oct     Review …

20 Oct     Group Practice Exam #2  (20 points)

21 Oct     EXAM #2  (80 points)

22 Oct     - Mid-semester Break -

25 Oct     <9.1> Points, Lines, Planes, and Angles                                p 499 # 1-65 odd

27 Oct     <9.2> Curves, Polygons, and Circles                                     p 506 # 1-45 odd

28 Oct     <9.3> Perimeter, Area, and Circumference                             p 518 # 1-51 odd, 57-69 odd

29 Oct     <9.4> Triangles: Congruence, Similarity, Pythagoras            p 530 # 1-55 odd

1 Nov      <9.5> Solids: Volume, Surface Area                                       p 542 # 1-33 odd, 43-53 odd

3 Nov      Lab #6

4 Nov      <11.1> Counting Principles                                                    p 635 # 9-55 odd

5 Nov      <11.2> Using the Fundamental Counting Principle               p 644 # 5-49 odd

8 Nov      <11.3> Permutations and Combinations                                p 655 # 15-49 odd

10 Nov    <11.5> Counting Problems Involving “Not” and “Or”          p 699 # 5-37 odd

11 Nov    NCTM Conference in Minneapolis                                         Take-home Lab #7

12 Nov    NCTM Conference in Minneapolis

15 Nov    <12.1> Basics of Probability                                                  p 681 # 5-51 odd

17 Nov    <12.2> Events Involving “Not” and “Or”                              p 689 # 1-33 odd

18 Nov    <12.3> Events Involving “And”                                             p 698 # 1-51 odd

19 Nov    <12.4> Binomial Probability                                                  p 705 # 1-27 odd, 37-45 odd

22 Nov    Lab #8

29 Nov    <14.1> Money and Interest                                                   p 798 # 7-25 odd, 31-43 odd

1 Dec       <14.2> Consumer Credit                                                        p 809 # 1-41 odd

2 Dec       <14.3> Truth in Lending                                                        p 820 # 1-29 odd

3 Dec       <14.4> Purchasing a House                                                    p 829 # 1-31 odd

6 Dec       Group Practice Exam #3  (20 Points)

8 Dec       EXAM #3  (80 Points)

9 Dec       Review …

10 Dec     Group Practice Final Exam  [25 Points]

FINAL EXAM:  Tuesday, 14 Dec 2004 , 12:50 – 2:50  [125 Points]