Viterbo University - La Crosse, WI

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.

For some of you this course might serve to satisfy the math competency requirement, for others this will be just one of the mathematics courses required by your major/minor program. In any case, the main goal of this course is to expose you to a variety of areas of mathematics and thus give you an idea of the importance of mathematics in today’s world and a multitude of ways it is being used in practice. We will learn some elements of mathematical logic, set theory, geometry, statistics, probability, consumers mathematics, and some basic algebra.

The content and the methods of this course are designed in accordance with general education objectives and the work in this course should help you in developing a number of skills included in the NCTM (National Council of Teachers of Mathematics) ‘standards” for mathematics education, and also being among the general education objectives at Viterbo. The main emphasis throughout the course will be on problem solving and developing thinking skills. This includes: (a) writing numbers and performing calculations in various numeration system, (b) solving simple linear equations, (c) exploring the mathematical model of simple and compounded interest rates, and learning how to use those ideas in solving the problems of loan payments, (d) exploring a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system, including a variety of different proofs of the Pythagorean Theorem, (e) develop an ability to use deductive reasoning, in the context of the rules 1 2 MATH 155 WAY OF THINKING SYLLABUS - FALL 2002 of logic and syllogisms, i.e., learn how to make/recognize a valid argument, (f) some basics of probability and statistics . . . Mastering this material requires to learn how to reason mathematically, and also how to communicate mathematics. In learning how to do so (on exams, essays, portfolio, and in oral presentations), you will also develop a confidence in your ability to do mathematics.

Other benefits of this course include: cultural skills (appreciation of the history of mathematics and its role in today’s world, learning how to handle simple loans, learning how to reason correctly and make a valid argument), appreciate the beauty and intellectual honesty of deductive reasoning, thereby adding to life value and aesthetic skills.

I encourage you to read the text at: http://www.viterbo.edu/personalpages/faculty/RRuppel/CritThink.html- the Viterbo critical thinking web page

Text: Robert Blitzer, Thinking Mathematically, Prentice-Hall, 2000.

Format: Class sessions will consist of lectures, work in small groups, exams, and individual presentations. I expect students to work out the recommended practice problems and ask for help whenever needed.

Resources: Please do not hesitate to contact me for any question you might have; do not let a feeling such as “I am lost . . . ” to last.

• Internet and the blackboard software. There is a lot of material on my web page. I will use the Blackboard to communicate with you, so please check your e-mail regularly. I would also like to encourage you to explore, and use numerous capabilities of that (Blackboard) software.

• Learning center.

• Library. Note that both a video set and a CD set that covers your textbook exists.

You can use either of these to hear a lecture again, or just to see/hear another explanation of a particular topic.

Grading: The final grade is based on homework, exams, presentations, portfolio, and a (cumulative) final exam. There will be opportunities for a small amount of extra credit.

The following grading scale applies to individual exams, and to the overall grade as well:

A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.

The following exceptions to that scale are possible:

• An A on the final exam (more than 180/200 points) will raise your grade up, one letter, i.e., a B will turn into an A, a BC will become AB, . . . .

• An outstanding presentation, or an outstanding portfolio can raise your grade up a half letter, i.e., a C will turn into a BC, . . . .

• If one is failing the course by the end of the semester, but has over 40% average on exams, and earns at least 55% points on the final, he/she can get a D for the final grade.

• If one is passing the course by the time of the final exam, but earns less than 30% points (a score less than 60/200), that will result in an F for the final grade.

MATH 155 WAY OF THINKING SYLLABUS - FALL 2002 3 Assignments: • Recommended practice: First 10, middle 5 and the last 5 problems from each Practice Exercises set in each section that we cover; at least one or two of the Application Exercises, at least one of the Writing in Mathematics Exercise, and at least two of the Critical

Thinking Exercises. These practice problems will not be graded. However, fell free to ask me for help with any difficulty you might have with those problems.

• Two essays, 20 points each:

(1) Autobiography: Introduce yourself to me in a 2-3 pages essay. State your name, and where (city/state) you are coming from.

The reason you are taking this course, and what mathematics courses you have had before. What was your experience from those courses and what are your expectations, if any, from this course?

This assignment is due Friday, January 18.

(2) World without mathematics: another 2-3 pages 20 points essay.

Try to imagine, and describe, a world without mathematics.

Due: Friday, January 25.

Homework At the end of each chapter, there is a Chapter Test. Each one of those tests will be due second class period after the corresponding chapter is covered, and each problem on the “test”is worth 1 point.

Exams There will be three in-class exams, worth 100 points each. An exam will typically cover three chapters worth of material. The exams will be closed notes, closed book. However, a calculator and a formula sheet (but not any worked out problem) is allowed.

Before each exam, I will give you a take-home practice exam, which will be very much like the actual exam coming. I will grade (25 points) the first one of those, i.e., the “Exam 1 - Practice”, but not the others. I will also allow a makeup (up to 50%) of the lost credit for the exam 2. This makeup will be oral, and will apply to those under 90/100 points on the test, and is to be done within two weeks after the exam.

Final Exam Final exam is a 2-hour, cumulative exam, and is worth 200 points.

Portfolio It should consist of 5 problems, but no two problems should be of the same type (from the same section).

Format: You state a problem, write a complete/correct solution to it, and then write a paragraph (or more) explaining why did you choose that particular problem, what did you learn from it, etc..

The portfolio will be worth 50 points.

The problems you choose for the portfolio should illustrate the progress in learning mathematics, the change of the perception (if any) of what mathematics is about, the change (if any) in your perception about your abilities to do mathematics.

• In-class Presentation: The presentation of a proof of the Pythagorean Theorem found on the Internet. Typically, the explanations you will find on the Internet are a bit sketchy. So part of your job will be to make sure you really understand the proof you are going to present (including filling in the gaps, i.e., the reasons not entirely spelled out in the Internet write-up), and then 4 MATH 155 WAY OF THINKING SYLLABUS - FALL 2002 to clearly explain that proof to your class mates. Sometimes, some people, may find this part quite difficult. Of course, I am here to help you understand and overcome those difficulties, and so please do not hesitate to ask me for help. You should also be prepared for the questions from the audience (myself and/or other students), and it is expected that you listen closely to other presentations and ask any question you might have. The presentation will be worth 35 points. In addition to that, one certain problem for one of the exams, and for the final exam is going to be:

State and prove the Pythagorean Theorem.

Important University Policies: The links:

• Plagiarism:

http://www.viterbo.edu/personalpages/faculty/GSmith/plagiarism.html

- Viterbo policy statement on plagiarism, see also Student Planner and

Handbook, pages 128 through 131.