2009 – 2010 THIS COURSE ADHERES TO ALL COLLEGE POLICIES (See College Calendar) Page No. 1

Please Note: It is the responsibility of students to retain all course outlines for the purpose of applying for transfer of credit to other educational institutions. A fee may be charged for further copies.

COURSE OUTLINE SCHOOL: Engineering Technology and Applied Science

DEPARTMENT: Mathematics

PROGRAMS: Health Informatics Technology Interactive Game Software Development Technology Software Engineering Technician & Technology

COURSE TITLE: Discrete Mathematics

COURSE CODE: Math185

TOTAL COURSE HOURS: 45

PRE-REQUISITES: A score of at least 16 on the Engineering Math assessment

COURSE ELIGIBILITY FOR PRIOR LEARNING ASSESSMENT AND Yes RECOGNITION (PLAR):

ORIGINATED BY: Tapan Rai & Kieh Wong

DATE: June 2002 REVISED: May 2009 (NK)

ACADEMIC YEAR: 2009 – 2010

APPROVED BY:

Donald Wang, Chair, Mathematics & Physics

Course Title: Discrete Mathematics Centennial College Course Code: Math185

2009 – 2010 THIS COURSE ADHERES TO ALL COLLEGE POLICIES (See College Calendar) Page No. 2

Course Description:

This is a first-year mathematics course in discrete mathematics. The course will deal with combinatorics, discrete probability, set theory, logic and Boolean algebra. Properties of finite mathematical systems and elementary number theory will also be covered.

Course Learning Outcomes:

Upon successful completion of the course, the student will have demonstrated the ability to

1. Use the language of set theory in formulating problems and studying mathematical structure.

2. Recognize the structure of modular systems.

3. Solve combinatorial problems using lists, the fundamental counting principle, permutations and combinations.

4. Solve probability problems involving various events.

5. Translate statements and arguments into symbolic logic.

6. Use Truth tables to analyze arguments.

7. Simplify Boolean expressions using the properties of Boolean Algebra and De Morgan’s laws.

Essential Employability Skills:

This course supports the students’ ability to:

Communicate clearly, concisely and correctly in the written and visual form that fulfills the purpose and meets the needs of audiences.

Reframe information, ideas and concepts using written, visual, numerical and symbolic representations, which demonstrate understanding.

Apply a wide variety of mathematical techniques with the degree of accuracy required to solve problems and make decisions.

Evaluate their thinking throughout the steps and processes used in problem solving and decision-making.

Collect, analyze and organize relevant and necessary information from a variety of sources.

Evaluate the validity of arguments based on qualitative and quantitative information in order to accept or challenge the findings of others.

Take responsibility for their actions and decisions.

Prior Learning Assessment and Recognition Process:

Comprehensive Examination to be arranged through the Mathematics Department and the Registrar’s Office. Evaluation and Grading System:

Term 60% Final Examination 40% Total 100%

Course Title: Discrete Mathematics Centennial College Course Code: Math185

2009 – 2010 THIS COURSE ADHERES TO ALL COLLEGE POLICIES (See College Calendar) Page No. 3

Final Grade: Final grades will be assigned according to the following definitions. Grade Description Mark Range A+ Outstanding Achievement 90 - 100 A Excellent Achievement 80 - 89 B+ Very Good Achievement 75 - 79 B Good Achievement 70 - 74 C+ Satisfactory Achievement 65 - 69 C Acceptable Achievement 60 - 64 D+ Pass 55 - 59 *D Pass 50 - 54 F Fail 0 - 49 * Minimum passing-grade required for students in all programs

Student Accommodation:

All students have the right to study and work in an environment that is free from discrimination and/or harassment. It is College Policy to provide accommodation based on grounds defined in the Ontario Human Rights Code. Accommodation may include changes or modifications to standard practices. Students with disabilities who require academic accommodations must register with the Centre for Students with disabilities. Please see the Centre for Students with Disabilities for details. Students requiring accommodation based on Human Rights grounds should talk with their professor(s) as soon as possible. Details are available on the Centennial College website (www.centennialcollege.ca). If students are unable to write an examination due to a medical problem or unforeseen family problems, they should immediately contact their professor or program Chair for advice. In exceptional and well-documented circumstances (e.g. unexpected family problems, serious illness, or death of a close family member), students should be able to write a make-up examination to replace an examination missed. Text and Other Instructional/Learning Materials:

1. Mathematical Ideas, Eleventh Edition, by Miller, Heeren & Hornsby Published by Addison-Wesley 2. Math185 Supplementary Problems Centennial College Mathematics Department (Available on Blackboard) Recommended Calculator: Sharp EL 520 Use of Dictionaries:

Dictionaries are not allowed during any quiz, test or examination.

Course Title: Discrete Mathematics Centennial College Course Code: Math185

2009 – 2010 THIS COURSE ADHERES TO ALL COLLEGE POLICIES (See College Calendar) Page No. 4

TOPICAL OUTLINE

Topics Text Reference

Unit Pages

1 Problem Solving Strategies

- Inductive Reasoning - Strategies for Problem Solving

1.1 1.3

2 – 10 20 – 33

2

The Basic Concepts of Set Theory

- Symbols and Terminology - Venn Diagrams and Subsets - Set Operations and Cartesian Products - Cardinal Numbers and Surveys

2.1 2.2 2.3 2.4

52 – 58 58 – 65 65 – 79 79 – 86

3 Mathematical Systems and Number Theory

- Clock Arithmetic and Modular Systems - Finite Mathematical Systems - Prime and Composite Numbers - Greatest Common Factor and Least Common Multiple

- The Fibonacci Sequence and the Golden Ratio*

4.4 4.5 5.1 5.3 5.4

189 – 203 203 – 210 222 – 233 241 – 249 257 – 265

4 Counting Methods

- Counting by Systematic Listing - The Fundamental Counting Principle - Permutations and Combinations - Counting Problems using Not and Or

11.1 11.2 11.3 11.5

672 – 681 681 – 692 692 – 705 712 - 719

5 Discrete Probability

- Basic Concepts - Events Involving Not and Or - Events Involving And - Estimating Probabilities by Simulation

12.1 12.2 12.3 12 Ext.

724 – 735 736 – 743 744 – 755 774 – 778

6 Logic and Boolean Algebra

- Statements and Quantifiers - Truth Tables and Equivalent Statements - The Conditional and Circuits - More on The Conditional - Analyzing Arguments with Truth Tables - De Morgan’s Laws and the properties of Boolean Algebra

3.1 3.2 3.3 3.4 3.6 Supplement

98 – 104 105 – 117 117 – 127 127 – 134 144 – 154

* Optional topic

Course Title: Discrete Mathematics Centennial College Course Code: Math185

2009 – 2010 THIS COURSE ADHERES TO ALL COLLEGE POLICIES (See College Calendar) Page No. 5

POLICY STATEMENTS

College Policies: The following statements are selected from Centennial College policies approved by the Board of Governors. Student Responsibilities Students are expected to know the contents of the course outline and to discuss with the professor any areas where clarification is required. Students should keep the course outlines for all courses taken at Centennial College. These may be used to apply to transfer of credit to other educational institutions. A fee may be charged for additional or replacement copies.

Other Policies:

Students should familiarize themselves with all College Policies that cover students’ rights, responsibilities, and the Academic Appeal process. For further information consult the Academic Matters Section in the Full-Time and Continuing Education Calendars. The Academic Appeal Application form is available from any Enrolment Services (Registrar) Office. Proof of Student Status Students are obliged to produce official photo identification at any time during the semester when requested to do so by any professor. (The official piece is the Centennial Student Card.) Continuing Education students do not have Centennial Student Cards, and so they may use other forms of photo identification, such as a driver’s license, health card, or other government-issued photo identification. Final Examinations When writing a test or examination, students must put their official photo-ID cards in full view, for review by the invigilator. Students who do not have official photo-ID will be permitted to write the examination with a substitute photo-ID, but they will be required to produce photo-ID at the program or department office within 24 hours or the next business day following the examination, or else the examination results will be void. More Final Examination Policies are available at http://my.centennialcollege.ca.

Academic Progression Policy for Diploma and Certificate Programs: College Academic Standings will be applied. Please see Academic Policies and Procedures, Full-Time Calendar.

Faculty Consultation Professors are available to see students outside of class time. Students can contact professors via voice mail, email, or through their program or department office. Information regarding how to contact teachers will be provided at the beginning of the course and is also available in the program or department office.

Human Rights Statement It is the policy of the College that all programs will strive for a learning, teaching, and working environment that promotes inclusion, understanding and respect for all students and employees, consistent with the Ontario Human Rights Code and the Centennial College's Statement of Diversity.

Course Title: Discrete Mathematics Centennial College Course Code: Math185

2009 – 2010 THIS COURSE ADHERES TO ALL COLLEGE POLICIES (See College Calendar) Page No. 6

Course Policies: Testing

a) There will be term tests and a comprehensive final examination.

b) No additional time will be allowed for any student who comes late to any test or the final examination.

c) No student will be allowed to leave during the first half-hour of any test or the final examination.

d) Unless otherwise stated, no written or other aids may be used during the tests or the final examination. Any student who is found using or having used unauthorized aids will be given a mark of zero for that test or final examination. Furthermore, a final grade of “F” may be given in this course. Every incidence of cheating will be reported to the program Chair.

e) There will be no rewrites of term tests.

f) If a particular test cannot be written because of documented medical or compassionate reasons, the weight of the final exam will be proportionally increased. A mark of zero will be recorded in cases where no reason acceptable to the professor is provided. In the case of a missed final exam, the student will be eligible to write a make-up exam if proper documentation is provided; otherwise, a mark of zero will be recorded.

g) All classroom instruction will be based on the Sharp EL-520. During tests and examinations,

students may use an equivalent scientific calculator; however, programmable and/or graphing calculators are prohibited. No other electronic devices will be permitted.

Attendance

The student is expected to attend all classes and be punctual. The student is responsible for all classes missed. In particular, a student who misses a class is responsible for obtaining the notes and any homework assignments from a classmate who was in attendance.