"PREPARING
FOR THE
POSSIBILITIES"

Fall Semester, 2007

Discrete Mathematics Office Hours: MW 9:30 a.m.-10:15 a.m.

Mathematics 111 T 8:30 a.m. - 11:30 a.m.

3 Credit Hours W 11:45 a.m. – 12:45 p.m.

MWF 2:00 – 2:50 p.m. R 12:30 p.m.-1:00 p.m.

“Heyugotaminute”

Instructor: Al Niemier Phone: 219-239-8381

Office: 179 Vincent E-mail: aniemier@hcc-nd.edu

PERQUISITES: It is presumed that students have taken at least one year of high school algebra. A year of geometry is preferred, but not presumed.

TEXTBOOKS AND/OR EQUIPMENT/SUPPLIES: Purchased by student

SUPPLEMENTS: Video Tutor: See Math Resource Center for complete listing

REQUIRED TEXTBOOK: MATHEMATICS ALL AROUND 3rd Edition, by Thomas L. Pirnot, published by Addison Wesley, Copyright: 2007, ISBN# 0-321-35686-1

REQUIRED CALCULATOR: Each student is required to have a scientific or graphing calculator. In class, the instructor will be using the TEXAS INSTRUMENT TI-89 graphing calculator. Explanations about the various graphs will be tied to keying the TI-89. If a student already has a different calculator, or intends to purchase a different brand, it will be that student’s responsibility to learn how to use that calculator.

COURSE DESCRIPTION: This is a college level mathematics course intended for those students who are taking mathematics for liberal arts or general education purposes, including quantitative literacy and mathematics competency. The topics to be covered include: set theory, problem solving, logic, geometry, statistics and consumer math. The course begins with geometry including line, angles, circles, polygons, perimeter, area, volume, surface area, geometric symmetry, tessellations and fractals. Set theory and problem solving will be followed by a study of logic. The terminology and notation of logical statements and the determination of the validity of statements and arguments are introduced. Students will also be introduced to a unit on consumer mathematics, e.g., interest, consumer loans, annuities, and amortization. The course concludes with a unit on statistics that includes surveys, organizing data, visualizing data, measures of central tendency, measures of dispersion, and normal distribution. Topics include (but not limited to) selected sections from the following chapters: Chapter 1 - Set theory, Chapter 2 – Logic, Chapter 8 – Geometry, Chapter 11 – Consumer Mathematics, and Chapter 14 – Descriptive Statistics.

GOALS AND OBJECTIVES:

CONTENT GOAL: The Discrete Mathematics course is intended to prepare the student mathematically for liberal arts or general education purposes, including quantitative literacy and mathematics competency.

COURSE GOALS:

Chapter 1 – Set Theory

1. To define a set.

2. To compare sets.

3. To perform set operations.

4. To use some common strategies for problem solving.

5. To solve survey problems.

Chapter 2 - Logic

1. To give an example of a statement and, given a phrase or sentence, to tell whether or not it is a statement.

2. Given a statement, to write it in symbolic form.

3. To write an English translation of a symbolic statement.

4. To consider conjunction, disjunction, and negation as operations on statements, and to relate these to operations to the set operations of intersection, union, and complementation.

5. To construct a truth table for a statement composed of one, two, or three simple statements and the connectives.

6. To construct a truth table for a statement composed of two simple statements and connectives.

7. To work with conditional sentences.

8. To work with biconditional sentences.

9. To know the relations among a statement, its converse, its inverse, and its contrapositive.

10. To define a syllogism.

11. To recognize and know the validity of reasoning by the converse, the inverse, or the contrapositive.

12. To use DeMorgan's laws to write a statement in an alternate form.

Chapter 8 – Geometry

1. To work with lines, rays, and line segments.

2. To describe an angle as the union of two rays.

3. To know conditions that describes a plane.

4. To describe half-planes, parallel lines, and intersections of planes.

5. To understand the following terms: vertex, sides, interior, exterior, vertical, adjacent, acute, obtuse, right, complement, supplement, transversal, alternate interior, alternate exterior, and corresponding angles.

6. To use terms applying to polygons in general and to triangles and quadrilaterals in particular.

7. To know and use the Pythagorean theorem and work with Pythagorean triples.

8. To work with similar triangles.

9. To find the perimeter and area of polygons.

10. To find the circumference and area of circles.

11. To find volume and surface area of a rectangular solid, cylinder, and cone.

12. To understand geometric symmetry, tessellations, and fractals.

Chapter 11 – Consumer Math

1. To calculate simple interest or amount, principal, or time.

2. To calculate compound amount.

3. To calculate present value.

4. To determine the monthly payment of an Installment Loan.

Chapter 14 – Descriptive Statistics

1. To work with histograms and stem-and-leaf displays.

2. To calculate the mean, median, and mode of a set of data.

3. To work with quartiles and percentiles.

4. To calculate and interpret the range.

5. To work with box plots (5 – number summary).

6. To work with the variance and standard deviation.

7. To calculate probabilities for a standard normal random variable.

OBJECTIVE GOALS: Holy Cross College graduates should possess certain skills necessary

for transfer to a senior institution. This class requires students to practice the following transferable skills:

1. Technology: Students will use technology to manipulate, operated, and utilize a graphing calculator to analyze and describe function behavior.

2. Oral Communication: Students will listen effectively in class and learn to speak on mathematical topics and ideas using proper terminology.

3. Writing: Students will write all homework assignments. Written work for each problem will include as a minimum the set-up and key steps in the problem leading to the final result. Students will not plagiarize, but will develop their own written assignments.

4. Quantitative Reasoning: Students will develop a quantitative reasoning process for the topics listed in the course description.

5. Critical Thinking: Students will be able to ask relevant questions related to course topics, recognize the connections between the mathematical information presented and real life situations, and apply mathematical concepts to real life situations.

6. Creative Thinking: Students should be able to develop and ask alternative questions to some or similar mathematical concepts.

7. Reading: Students will learn how to read a mathematics textbook, and how to understand/analyze mathematical concepts and problems while reading mathematical topics.

COURSE PHILOSOPHY: Learning mathematics depends more on hard work than on any other

factor. Your success is dependent upon your willingness to exert sufficient effort. To succeed in this course your must:

1. Devote minimum of two hours of outside of class study for every one-hour of actual class.

2. Attend every class.

3. Come to class prepared and willing to help your classmates.

4. Seek help from me or another person as soon as the need arises.

5. Be an enthusiastic group participant.

GRADING CRITERIA AND REQUIREMENTS:

EXAMS: There will be five scheduled full period exams during the semester. The dates of

these exams are indicated on the ASSIGNMENT SCHEDULE. Since these dates of the scheduled exams are stipulated at the start of the semester, it is expected that each student will make every effort to be present for each exam. MAKE-UP EXAMS WILL NOT BE GIVEN!! The Registrar’s Office schedules the final exam.

ASSIGNMENTS: There is a large body of educational research which supports that active

involvement with the material is the only way to gain a true understanding of mathematical concepts. Hence, you are encouraged and expected to “dig in” and learn through active involvement with the subject matter and your classmates. You are expected to read the textbook, and it will be necessary for you to read the text in order to complete assignments. Sometimes it will be necessary to look back or forward in the text to find information and definitions that you need. You are responsible for your own learning. I am eager to assist you in every way that I can. It is important for you to realize that it is not possible to receive answers to all questions during class time. You are responsible for finding answers to your questions, from me during office hours, from the Learning Resource Center, or from your classmates.

HOMEWORK: Homework will be assigned as per the ASSIGNMENT SCHEDULE.

Homework is a key to success in this course. Perform each assignment and conscientiously attempt each and every problem in every assignment. Do not allow yourself to fall behind. Leaving a section without mastering it undermines your chances for success with subsequent sections. Mathematics cannot be “put off and crammed” in a couple of days before an exam. Problems on the exams will be similar to the homework problems.

Use a three-ring binder for your class notes and homework papers rather than a spiral notebook. If you use a binder, you can remove and add pages as needed and keep our homework well organized. Your notebook will be a valuable reference and study resource.

READING ASSIGNMENTS that are listed on the ASSIGNMENT SCHEDULE refer to those sections of your text that you should read PRIOR to coming to class. They contain the bulk of the material that will be presented in class that day. References will be made to the material in the assigned sections during class presentation.

WRITTEN ASSIGNMENTS are problems that should be done before coming to class. They are based on material that already has been presented and explained. These problems are also listed on the ASSIGNMENT SCHEDULE. Most of these problems have the answers in the back of the book, which will allow you to check your answer. You should do enough of these problems to be completely familiar with the material covered. Hopefully, you would do some of the problems which do not have answers, and also some of the problems that are not assigned. I may also assign additional problems not listed on the ASSIGNMENT SCHEDULE. These problems will also be expected to be completed for the next class. It is suggested that you keep your problems neatly together in a three ring binder.

Homework will be assigned each class period as per the ASSIGNMENT SCHEDULE and the following assumptions are made.

1. You are completing your homework assignments between class meetings.

2. You are studying and practicing discrete mathematics a minimum of two hours of outside of class study for every one-hour of actual class. Also, understand that more time should be allotted when preparing for exams.

3. You are studying individually and working regularly with classmates.

4. You are responsible for your own learning, and so you will ask questions in class discussions, in my office, at the Learning Resource Center, of your classmates--about problems hat have are troublesome for you.

5. You cannot truly be “stumped” until you have given the problem serious consideration and ample time.

6. You cannot completely understand nor remember a new concept until you have applied it repeatedly to solve problems.

HOMEWORK FORMAT: TO BE OBSERVED ON ALL ASSIGNMENTS:

1. Each day’s homework/written assignment must be on my desk BEFORE the start of class. Homework/assignments will only be accepted if the student is present in class the day the homework/assignment is due. Any homework not turned in by the time the graded homework papers are returned will be considered late and thus will count at 50%. Any homework that is two or more class periods late will not be accepted and will be given a score of zero.

2. Homework must be written in pencil and should NOT be written on spiral paper.

3. Papers should not be folded and, if more than one page, must be stapled in the upper left-hand corner.

4. In the upper right-hand corner PRINT your name, course number, assignment section number, assignment page number, and assignment date due.

5. If you decide to change a problem, erase neatly and thoroughly. “Scratch outs” will not be accepted. In general, any paper bearing the appearance of “scratch work”, or any paper that appears to be list of answers with NO supporting work will NOT be accepted and will be given a grade of zero.

6. I will choose a problem(s) at random to grade. It is essential that you complete each day’s assignment. You cannot be sure you have worked the problem(s) that will be graded unless you have worked all assigned problems.

TUTORING: You are encouraged to make use of the Learning Resource Center (LCR). Hours are posted. Peer tutors, adult tutors, and teachers are available to help you FREE OF CHARGE. Videotapes may be checked out of the library and may be viewed at the LRC or taken back to dorm rooms. Math tutorials corresponding to all sections in the book are accessible in the computer lab and the LRC for extra practice. A CD is included with your text that has a video lesson for each section from the text, along with guided practice problems.

ACADEMIC HONESTY POLICY: Holy Cross College expects honesty from all students in their academic work. Please refer to the student handbook (page 153) for information on the college’s academic honesty policy. Violations of the academic honesty policy include plagiarism or cheating on any examination or assignment. Any student found in violation of the academic honesty policy may be subject to sanctions that could include failure on the assignment or failure in the course, and any finding of violation may be referred to the vice president for academic affairs. Procedures for appealing any sanction can be found in the student handbook (page 153).

GRADING SCALE: Your final grade will be determined from the following:

1. 50%-from the five scheduled period exams. Each scheduled period exam will count 10%.

2. 10%-from the individual project.

3. 20%-from homework and class participation. Each graded homework assignment will

be worth 10 points. The total graded homework/written assignment score will be proportioned to a score based on 100 points.

4. 20%-from the final exam. The final exam will not be returned. If the student has submitted 80% of his/her assignments, AND has at least a 80% average on the total of all assignments, AND has no more than three (3) absences (regardless of the reason), then the student will have the option of having the final exam score replace their lowest regular period exam score. For this purpose two (2) tardies will be the equivalent to one absence.

5. If a student has a grade of “B” or better, AND has never been late to class AND has never been absent from class, AND the student has submitted 80% of his/her assignments, AND has at least a 80% average on the total of all assignments, then the student will be allowed to exercise the option of NOT taking the final exam. If the student meets these qualifications, then the student’s final semester grade will be the grade earned as of the last day of class for the semester.

The semester letter grade will be given based on scheduled period exams, project, homework and class participation, and your final exam. Grading will be done on a point system. The points will be converted to a percentage, and the letter grade will be determined by the following scale:

95-100 = A 87--89.99 = B+ 80-82.99 = B- 70-76.99 = C 60-65.99 = D

90-94.99 = A- 83--86.99 = B 77-79.99 = C+ 66-69.99 = C- 0-59.99 = F

WITHDRAWAL: Holy Cross College policy and regulations on withdrawal are given in the Student Handbook on page 161. All students are expected to know these policies/regulations and to abide by them.

AUDIT: The following are strongly suggested for a student to successfully audit the class:

1. Audit Policy as stated on page 154 of the Student Handbook.

2. Student may take the regularly scheduled period exams (optional).

3. Student may take the final exam (optional).

ATTENDANCE: There is a direct correlation between regular class attendance and student’s success in class. A student will find it very difficult to successfully pass the class if he/she does not attend class regularly. Hence, regular class attendance is highly encouraged. Regular class attendance will affect your final grade in the course in each of the following ways.

1. Each student will begin with 24 extra credit test points. Regardless of the reason, each day a student is absent six points will be deducted. Regardless of the reason, each day the student is less than fifteen minutes late to class (tardy) three points will be deducted. If the student is fifteen or more minutes late to class, the student will be considered absent and six points will be deducted.

2. If a student has no more than three (3) absences (regardless of the reason), then the student will have the option of having the final exam score replace their lowest regular period exam score, PROVIDED the student has submitted 80% of his/her assignments, AND has at least a 80% average on the total of all assignments. For this purpose two (2) tardies will be equivalent of one absence. A student who leaves class is also considered absent.

3. If a student has a grade of “B” or better, AND has never late or absent from class, AND the student has submitted 80% of his/her assignments, AND has at least a 80% average on the total of all assignments, then the student will be allowed to exercise the option of NOT taking the final exam. If the student meets these qualifications, then the student’s final semester grade will be the grade earned as of the last day of class for the semester.

This policy on attendance will be effective starting with the first day of class.

REQUESTING ACCOMMODATIONS FOR A DISABILITY: Students requesting accommodations for specific requirements for class and/or testing must have on file, through the office of Brother Christopher J. Dreyer, C.S.C., L.C.S.W., a Request for Accommodations form. Such students are highly encouraged to discuss with me their specific class and/or testing requirements at their earliest convenience. In general, for testing purposes, twice the amount of the regular testing time will be allowed. In this regard, it is the responsibility of the student to request specific testing accommodations 48 hours prior to a scheduled test/exam.

ASSIGNMENT SCHEDULE MATH 111 DISCRETE MATHEMATICS

FALL SEMESTER 2007

Class Number	Day	Date	Reading Assignment	Written Assignment
1	M	8-27	Section 8.1 Lines, Angles, and Circles, pages 426 to 434	Please Come
2	W	8-29	Section 8.1 Lines, Angles, and Circles, pages 426 to 434	Section 8.1, pages 434 to 437: All 9 to 36, Every 3^rd: 39, 42, 45,…,60
3	F	8-31	Section 8.2 Polygons, pages 437 to 444	Section 8.1, pages 434 to 437: All 9 to 36, Every 3^rd: 39, 42, 45,…,60
4	M	9-3	Section 8.3 Perimeter and Area, pages 448 to 455	Section 8.2, pages 444 to 447: All 8 to 26, Even 28 to 42
5	W	9-5	Section 8.4 Volume and Surface Area, pages 461 to 467	Section 8.3, pages 456 to 461: Even 10 to 70, 69
6	F	9-7	Section 8.6 Geometric Symmetry and Tessellations; pages 482 to 492	Section 8.4, pages 468 to 470; Even 8 to 44
7	M	9-10	CATCH-UP AND REVIEW; pages 426 to 495	Section 8.6, pages 492 to 495: Odd 7 to 45
8	W	9-12	TEST ON CHAPTER 8	STUDY FOR TEST ON CHAPTER 8
9	F	9-14	Tessellation Project	Please Come Back J
10	M	9-17	Section 1.3 The Language of Sets, pages 26 to 31	Project Questions
11	W	9-19	Section 1.4 Comparing Sets, pages 34 to 39	Section 1.3, pages 31 to 34: Every 3^rd: 12, 15, 18, … ,87
12	F	9-21	Section 1.5 Set Operations, pages 42 to 50	Section 1.4, pages 38 to 42: Every 3^rd: 12, 15, 18,…,54
13	M	9-17	Section 1.6 Survey Problems, pages 50 to 59	Section 1.5, pages 50 to 54: Every 3^rd: 12, 15, 18,…,75
14	W	9-19	CATCH-UP AND REVIEW; pages 26 to 63	Section 1.6, pages 60 to 63: Every 3^rd: 9, 12, 15,…,36, 26
15	F	9-21	TEST ON CHAPTER 1	STUDY FOR TEST ON CHAPTER 1
16	M	9-24	Section 2.2 Statements, Connectives, and Quantifiers, pages 83 to 90	Nearing The Halfway Point J J
17	W	9-26	Section 2.2 Statements, Connectives, and Quantifiers, pages 83 to 90 and Section 2.3 Truth Tables, pages 93 to 101	Section 2.2, pages 90 to 92: Every 3^rd: 12, 15, 18,…,69; PROJECT DUE
18	F	9-28	Section 2.3 Truth Tables, pages 93 to 101	Section 2.2, pages 90 to 92: Every 3^rd: 12, 15, 18,…,69; and Section 2.3, pages 101 to 104: 9, 12, 15, 18, 20, All 21 to 34, Every 3^rd: 39, 42, 45,…,66, 52, 71
19	M	10-1	CATCH UP AND REVIEW, Pages 83 to 104	Section 2.3, pages 101 to 104: 9, 12, 15, 18, 20, All 21 to 34, Every 3^rd: 39, 42, 45,…,66, 52, 71

Class

Number

Day

Date

Reading Assignment

Written Assignment

10-3

Section 2.4 The Conditional and Biconditional, pages 105 to 111

TBA

10-12

Section 2.5 Verifying Arguments, pages 114 to 120