Columbia College
Evening Campus
1001 Rogers Street
Columbia, MO 65216
(800) 231-2391

### COURSE SYLLABUS

17 / SPRG1 - Early Spring 8-Week Session

## Course Syllabus

Course Syllabus
17 / SPRG1 - Early Spring 8-Week Session
Evening Campus
1001 Rogers Street
Columbia, MO 65216
(800) 231-2391

 Course Prefix and Number: MATH 225 Course Title: Discrete Mathematics I Semester Credit Hours: 3 Class Day and Time: Tue 5:30 PM-9:30 PMAdditional Notes: This course is web-enhanced, taught entirely in a classroom setting using D2L course management software to supplement in-seat content.

#### Catalog Description

This course provides a foundation in formal mathematics and theorem-proving. Topics include functions, relations, sets, simple proof techniques, propositional logic, elementary number theory, the fundamentals of counting, recursion, and an introduction to algorithms. Prerequisite: Grade of C or higher in MATH 201.

#### Prerequisites/Corequisites

Grade of C or higher in MATH 201.

#### Text

Discrete Mathematics and its Applications 7th edition
Author: Rosen ( Science Engineering & Math)
ISBN: 9780073383095

#### Course Learning Outcomes

1. Apply the fundamental laws of logic and rules of inference to form logical arguments.
2. Write mathematical proofs including proofs by contrapositive, contradiction and induction.
3. Demonstrate understanding of the concept of a function including the concepts: range, domain, one-to-one, onto and inverse.
4. Describe and explain basic set theory definitions and operations.
5. Determine the complexity of an algorithm and the growth rates of functions.
6. Employ the basic properties of integers such as divisibility, primes and congruencies to solve basic number theory problems.
7. Calculate numbers of possible outcomes of elementary combinatorial processes using the sum and product rules, permutations and combinations.

#### Special Course Requirements

TI-84 Plus CE - This is the calculator I will use in class. Visualize concepts clearly and makes connections between equations, data, and graphs in full color. But you can use the TI-84 Plus silver edition graphing calculator also.

 Take-home Quizzes 100 Points Description - Homework given for each class session. You will be given homework quizzes each week (over the previous session's homework). It is essential that you attempt all of the exercises in your assignment. Homework problems are chosen to represent the concepts that should be mastered in the course. All Take-Home Quiz questions will be closely modeled on assigned homework problems. Method of Evaluation - There will be 6 Take-Home Quizzes given worth 20 points each. Your lowest Take-Home Quiz score will be dropped, so that your top five Take-Home Quiz scores will be kept. Take-home quizzes are normally due in 1 week. Please, TURN IN ALL TAKE-HOME QUIZZES ON TIME (this includes any absences). Students who fail to turn in a given assignment by the due date will receive the score of 0 points. Midterm Exam 100 Points Description - Midterm Exam is Tuesday of Week Three and incorporates Chapters One, Two, and Three. Method of Evaluation - The exam duration is at least 1.5 hours, with at most 25 problems. Allowed materials on exam: Graphing calculator TI-84 plus CE (or TI-84 Plus silver edition) and 1 hand written (front and back) 3" by 5" note card. Please turn in the note card with the Midterm at the end of the examination. Final Exam 150 Points Description - The Final Exam is Tuesday of Week Eight and incorporates: Comprehensive section which contains material from the Midterm Exam (for 50 points), and New Material which contains material from Chapters Four, Five, Six, and Sections 9.1, 9.5 (for 100 points). Method of Evaluation - The exam duration is at least 2.0 hours, with at most 40 problems. Allowed materials on exam: Graphing calculator TI-84 plus CE (or TI-84 Plus silver edition) and 2 hand written (front and back) 3" by 5" note cards. Please turn in the note cards with the Final Exam at the end of the examination.

 87.5 - 100 A 75 < 87.5 B 62.5 < 75 C 50 < 62.5 D 0 < 50 F

Note on missing or not taking the Midterm Exam: There is no makeup examination for the Midterm Exam. If you miss the Midterm Exam, it will result in a loss of 100 points. The only exception is for unexpected emergencies. These unexpected emergencies need to be brought to my attention as soon as humanly possible. I reserve the right to determine if your excuse is a true emergency or not. If you can verify the emergency and I do agree that you had a true emergency, then I will obtain your missed test score from the final exam.

Late Work:  Any work done outside of class that is turned in for a grade will have a due date. Students who fail to turn in a given assignment by the due date will receive the score of 0 points.

Note on Dropping or Withdrawing from a Course: Once enrolled, a student is considered a member of that class until s/he officially drops or withdraws in accordance with College policy. An official drop/withdrawal takes place only when a student has submitted a Drop/Add/Withdrawal form. A failure to attend class, or advising a fellow student, staff or adjunct faculty member of an intent to withdraw from a class does not constitute official drop/withdrawal. If a student stops attending a class but does not submit the required Drop/Withdrawal form a grade of "F" will be awarded.

This is a preliminary schedule only. The instructor reserves the right to revise the course syllabus and/or tentative schedule as required by either judgment or circumstance. Changes will be announced in class and students are responsible for recording changes as announced.

Note on notation: 1-EOON-25 means work problems 1, 5, 9, 13, 17, 21, 25. Start with problem number 1 work Every Other Odd Number up to problem number 25. Example: 3-EOON-27 means work problems 3,7,11,15,19,23,27.

#### Schedule of Activities and Assignments

 Week 1 The Foundations: Logic and Proofs Assignments: Section 1.1 1-EOON-37 plus 43, Section 1.2 1-EOON-41. Section 1.3 1-EOON-37, Section 1.4 1-EOON-37 plus 39. Examinations: Take-Home Quiz 1 Sections 1.1 through 3.4. Week 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices Assignments: Section 1.6 1-EOON-33, Section 1.7 1-EOON-41. Section 2.1 1-EOON-41, Section 2.2 1-EOON-57. Examinations: Take-Home Quiz 2 Sections 1.6, 1.7, 2.1, and 2.2. Week 3 Algorithms Assignments: Section 2.3 1-EOON-69, Section 2.4 1-EOON-37 plus 39, Section 2.6 1-EOON-33. Section 3.1 1-EOON-53, Section 3.2 1-EOON-61, Sections 3.3 1-EOON-45. Examinations: Take-Home Quiz 3 Sections 2.3, 2.4, 2.6, 3.1, 3.2, and 3.3. Week 4 Review Chapters One, Two, and Three for Midterm Exam Assignments: pages 111-113 Supplementary exercises 1-41 odds, pages 187-188 Supplementary exercises 1-41 odds, and pages 233-234 Supplementary exercises 1-29 odds. Examinations: Midterm Exam over Chapters One, Two, and Three. Additional Notes: The Midterm Exam duration is at least 1.5 hours, with at most 25 problems. Allowed materials on exam: Graphing calculator TI-84 plus CE (or TI-84 Plus silver edition) and 1 hand written (front and back) 3" by 5" note card. Please turn in the note card with the test at the end of the examination. Week 5 Number Theory and Cryptography Assignments: Section 4.1 1-EOON-45, Section 4.2 1-EOON-33. Section 4.3 1-EOON-45 plus 47, Section 5.1 1-EOON-57. Examinations: Take-Home Quiz 4 Chapter Four. Week 6 Induction and Recursion & Counting Assignments: Section 5.2 1-EOON-29, Section 5.3 1-EOON-45. Section 6.1 1-EOON-53 plus 55, Section 6.2 1-EOON-37. Examinations: Take-Home Quiz 5 Chapter Five and Sections 6.1, 6.2. Week 7 Counting & Relations Assignments: Section 6.3 1-EOON-37 plus 39, Section 6.4 1-EOON-33, Section 6.5 1-EOON-45. Section 9.1 1-EOON-45, Section 9.5 1-EOON-45 plus 47. Examinations: Take-Home Quiz 6 Sections 6.3, 6.4, 6.5, 9.1, and 9.5. Week 8 Final Examination Assignments: Pages 307-308 Supplementary exercises 1-41 odds, pages 379-381 Supplementary exercises 1-47 odds, and pages 440-443 Supplementary exercises 1-51 odds, and Section 9.1 1-EOON-45, Section 9.5 1-EOON-45 plus 47. Examinations: The Final Exam is Tuesday of Week Eight and incorporates: Comprehensive section which contains material from the Midterm Exam (for 50 points), and New Material which contains material from Chapters Four, Five, Six, and Sections 9.1, 9.5 (for 100 points). Additional Notes: The Final Exam duration is at least 2.0 hours, with at most 40 problems. Allowed materials on exam: Graphing calculator TI-84 plus CE (or TI-84 Plus silver edition) and 2 hand written (front and back) 3" by 5" note cards. Please turn in the note cards with the Final Exam at the end of the examination.

#### Library Resources

Columbia College Resources - Online databases are available at the Columbia College Stafford Library.  You may access them using your CougarTrack login and password when prompted.

### Course Policies and Procedures

#### Attendance

Columbia College Policy - Columbia College students are expected to attend all classes and laboratory periods for which they are enrolled.  Students are directly responsible to instructors for class attendance and work missed during an absence for any cause.  If absences jeopardize progress in a course, an instructor may withdraw a student from the course with a grade of "F" or "W" at the discretion of the instructor.  For additional information, see the Columbia College policy on Student Attendance.

Columbia College Policy - Columbia College students must fulfill their academic obligations through honest, independent effort.  Dishonesty is considered a serious offense subject to strong disciplinary actions.  Activities which constitute academic dishonesty include plagiarism, unauthorized joint effort on exams or assignments, falsification of forms or records, providing false or misleading information, or aiding another in an act of academic dishonesty.  For more information, see the Columbia College Academic Integrity Policy and Procedures.

#### Class Conduct and Personal Conduct

Columbia College Policy - Students must conduct themselves so others will not be distracted from the pursuit of learning.  Students may be disciplined for any conduct which constitutes a hazard to the health, safety, or well-being of members of the College community or which is deemed detrimental to the College's interests. Discourteous or unseemly conduct may result in a student being asked to leave the classroom.  For more information, see the Columbia College Student Code of Conduct and Student Behavioral Misconduct Policy and Procedures.

#### Cancelled Class Make-Up

Columbia College Policy - Classes cancelled because of inclement weather or other reasons must be rescheduled.  For more information, see the Columbia College Inclement Weather Policy.

#### Make-Up Examinations

Columbia College Policy - Make-up examinations may be authorized for students who miss regularly scheduled examinations due to circumstances beyond their control.  Make-up examinations must be administered as soon as possible after the regularly scheduled examination period and must be administered in a controlled environment.

Campus Policy - Make up examinations are scheduled on designated Saturday mornings 9am in 103 Buchanan. Students must present a picture I.D. in order to be admitted to the testing session. Students must arrange with the instructor to take the exam before or after it is given in class and permission to take a makeup examination (or any graded activity) is granted at the discretion of the instructor.

#### Adding, Dropping, or Withdrawing from a Course

Columbia College Policy - Students may add a course through Wednesday of the first week of the session and drop a course without academic or financial liability through close of business on Monday of the second week of the session.  Once enrolled, a student is considered a member of that class until he or she officially drops or withdraws in accordance with College policy.  An official drop/withdrawal takes place only when a student has submitted a Drop/Add/Withdrawal form.  A failure to attend class, or advising a fellow student, staff or adjunct faculty member of an intent to withdraw from a class does not constitute official drop/withdrawal.  The drop/add/withdrawal periods begin the same day/date the session starts, not the first day a particular class begins. If a student stops attending a class but does not submit the required Drop/Withdrawal form a grade of "F" will be awarded.  For more information, see the Columbia College Registration Policy and Procedures.

#### Withdrawal Excused

Columbia College Policy - A student may request an excused withdrawal (WE) under extraordinary circumstances by submitting a Drop/Withdrawal form accompanied by a complete explanation of the circumstances and supporting documentation to the location director.  The WE request must include all classes in which the student is currently enrolled.  The Vice President for Adult Higher Education is the approving authority for all WE requests.  A student who receives approval of their WE request may still be required to return some or all of the federal financial assistance received for the session.  For more information, see the Columbia College Withdrawal Policy.

#### Incomplete

Columbia College Policy - A student may request that the instructor award a grade of "I" due to extraordinary circumstances (unforeseen or unexpected circumstances beyond the student's control) that prevent a student from completing the requirements of a course by the end of a session.  An "I" will not be given because a student is failing, negligent or not meeting requirements.  If the instructor believes an "I" is appropriate, the instructor will specify the work needed to complete the course and the time allowed to complete the work.  Work missed must be made up within two subsequent sessions unless the instructor specifies an earlier date.  Extensions beyond two sessions must be approved by the Vice President for Adult Higher Education.  If the work is completed during the specified time period, the instructor will change the "I" to the grade earned.  If the work is not completed during the specified time, the instructor may allow the incomplete to remain on the student's permanent record or change it to any other letter grade.  For more information, see the Columbia College Undergraduate Grading Policy.

#### Prerequisites

Columbia College Policy - Course prerequisites are established to ensure that a student has adequate academic preparation to succeed in a particular course.  Staff members will attempt to ensure that students meet prerequisite requirements.  However, it is the student's responsibility to closely examine the course descriptions to determine if prerequisites exist and to enroll in courses in the proper sequence.  In some exceptional cases it may be apparent that the student possesses the required skills and knowledge to succeed in a particular course, even though they have not taken the prerequisite course.  In this case the prerequisite course may be waived by the location director.  Waiver of a course as a prerequisite does not remove the requirement to complete the course if it is a requirement for the student's degree program.

#### CougarTrack

Columbia College Policy - The College provides all students access to CougarMail (the official means of e-mail communication for the College), online resources from the Stafford Library, and their Columbia College records (transcripts, grades, student schedules, etc.) through CougarTrack.

#### CougarMail

Columbia College Policy - The official student email address (also known as CougarMail) will be used for all official correspondence from faculty and staff.  Students are responsible for the information received and are required to monitor their CougarMail account on a regular basis.  Students may forward their CougarMail to another email account but will be held responsible for the information sent over CougarMail, even if there is a problem with the alternate mail service.

#### Cell Phones

Columbia College Policy - Cell phones can be a distraction to the learning process.  Location directors or course instructors may require that cell phones be turned off or set to vibrate during class periods.  Students requiring special arrangements to receive a cell phone call during class should make prior arrangements with their location director or course instructor.

#### Bookstore Information

Columbia College Policy - As part of Truition, students will receive their course materials automatically as described below.

eText Information

Physical Course Materials Information

Students enrolled in courses that require physical materials will receive these materials automatically at the address on file with Columbia College.  Delivery date of physical materials is dependent on registration date and shipping location.  Please refer to confirmation emails sent from Ed Map for more details on shipping status.

Returns:  Students who drop a course with physical course materials will be responsible for returning those items to Ed Map within 30 days of receipt of the order.  More specific information on how to do so will be included in the package received from Ed Map.  See here for Ed Map's return policy.  Failure to return physical items from a dropped course will result in a charge to the student account for all unreturned items.

Note:
Students who opt-out of having their books provided as part of TruitionSM are responsible for purchasing their own course materials.  Visit https://www.ccis.edu/bookstore.aspx for details.

#### FERPA

Columbia College Policy - The Family Educational Rights and Privacy Act (FERPA) affords students certain rights with respect to their education records.  For more information, see the Columbia College Family Education Rights and Privacy Policy.

#### Student Accessibility Resources

Columbia College Policy - Students with documented disabilities who may need academic services for this course are required to register with the office of Student Accessibility Resources.  Until the student has been cleared through this office, accommodations do not have to be granted.  If you are a student who has a documented disability, it is important for you to read the entire syllabus as soon as possible.  The structure or the content of the course may make an accommodation not feasible.  Student Accessibility Resources is located in Student Affairs in AHSC 215 and can be reached by phone at (573) 875-7626.  For more information, see the Columbia College ADA and Section 504 Policy for Students.

#### Alcohol and Other Drugs: Columbia College Policies & Resources

Columbia College Policy - Columbia College recognizes the negative health effects associated with the use, possession, and distribution of controlled and/or illicit substances, and their detrimental impact on the quality of the educational environment.  Therefore, all members of the College community share in the responsibility of protecting the campus environment by exemplifying high standards of professional and personal conduct.  For more information and resources, see the Columbia College Alcohol and Other Drugs Policy.

#### Tobacco-Free Policy

Columbia College Policy - The following policy goes into effect on August 21, 2017.  Columbia College values and is concerned for the health and well-being of its students, employees and visitors. The College is committed to providing a healthful and productive educational and employment environment for members of the College community. Consistent with this commitment and in the interest of the general health and welfare of the College community, the College prohibits the use of all tobacco products and related devices on all College property and premises.  For more information, see the Columbia College Tobacco-Free Policy.

#### Non-Discrimination

Columbia College Policy - Discrimination, harassment, and retaliation on the basis of protected status (see Notice of Non-Discrimination and Equal Opportunity for a definition of "protected status") are strictly prohibited. Persons who engage in such conduct are subject to discipline up to and including termination or dismissal.  For more information, see the Columbia College Non-Discrimination and Equal Opportunity Policy and Complaint Resolution Procedure.

#### Columbia College Policy Library

Columbia College Policy - The policies set forth in the Online Policy Library are the current official versions of College policies and supersede and replace any other existing or conflicting policies covering the same subject matter.  The Online Policy Library is currently under construction with new policies being added on a frequent basis and the policies currently listed are not comprehensive of every College policy.  Questions regarding the Online Policy Library should be directed to the Office of the General Counsel.  For more information on policies applicable to students, see Student Policies.  For more information on policies applicable to the entire Columbia College community, see College-Wide Policies.

#### Technical Support

Columbia College Policy - If you have problems accessing the course or posting your assignments, contact your instructor, the Columbia College Technology Solutions Center, or the D2L Helpdesk for assistance.  If you have technical problems with the VitalSource eText reader, please contact VitalSource.  Contact information is also available within the online course environment.

- Columbia College Technology Solutions Center:  CCHelpDesk@ccis.edu, 1-800-231-2391 ext. 4357

- D2L Helpdesk:  helpdesk@d2l.com, 1-877-325-7778

- VitalSource:  support@vitalsource.com, 1-855-200-4146