Outline-mth314-w19 - Outline of MTH314 PDF

Preview

Summary

Outline of MTH314...

Description

Faculty of Science – Department of Mathematics MTH 314: Discrete Mathematics for Engineers Winter 2019 – Sections 1,2

Instructor: Office: Telephone: Email: 2 Office hours: Course Web Site:

Section 1 Dr. Konstantinos Georgiou 1 ENG250 (416) 979-5000 ext. 7400 [email protected] M 10am-noon my.ryerson.ca (Brightspace)

Section 2 Dr. Alireza Sayyidmousavi VIC703 N/A [email protected] F 11am-1pm my.ryerson.ca (Brightspace)

Course Calendar Description Sets and relations, proposition and predicate logic, functions and sequences, elementary number theory, mathematical reasoning, combinatorics, graphs and trees, finite-state machines, Boolean algebra. Lectures 3 hours per week, Jan. 7 - Apr. 11, 2019 Section 1: Mondays 8-10am (DSQ24) & Wednesdays noon-1pm (DSQ24) Section 2: Mondays 8-10am (DSQ03) & Tuesdays 2-3pm (DSQ13)

Textbook (Recommended) Discrete Mathematics with Applications (4th Ed.), by Susanna S. Epp, 2011, ISBN 0-495-39132-8 Open Source Textbooks

(Recommended)

• Discrete Mathematics: An Open Introduction, by O. Levin http://discretetext.oscarlevin.com/home.php • Applied Discrete Structures, by A. Doerr and K. Levasseur http://faculty.uml.edu/klevasseur/ads-latex/ads-3a.pdf • A Course in Discrete Structures, by R. Pass http://www.cs.cornell.edu/~rafael/discmath.pdf 1 2

Course Coordinator Please add MTH314 in subject

1

• A Spiral Workbook for Discrete Mathematics, by H. Kwong http://textbooks.opensuny.org/download/swdm-pdf/ • Discrete Math for Computer Science Students, by K. Bogart and C. Stein https://math.dartmouth.edu/archive/m19f03/public_html/ Other Course Specifics Prerequisites: MTH 141 and MTH 240 Course Weight: 1.00 Billing Units: 1 Learning Objectives - Applying mathematical algorithms to solve problems - Assessing the reliability of conclusions - Formulating mathematical models using scientific principles - Justifying model assumptions and understanding their limitations - Applying mathematical and scientific principles to predict behaviour of processes - Constructing mathematical models consistent with the available information - Selecting and using an appropriate method for problem definition and problem solution Evaluation Assignments Midterm Exam #1 Midterm Exam #2 Final Exam

10% Weekly, not marked, but graded for completeness 20% 1hr & 30 mins, on February 11, at 8am, during class time. 20% 1hr & 30 mins, on March 18, at 8am, during class time. 50% During Undergrad Examination Period; Details TBA

Online Resources Students are expected to monitor both the official webpage on Brightspace as well as the course discussion forum on piazza on a very regular basis. Official Webpage: Ryerson’s Brightspace site found at https://my.ryerson.ca/ is where the official website for this course is found. All students registered for this course are subscribed automatically to this site and may access its contents by logging in. At this location can be found all documents relating to this course as well as any announcements. In particular, announcements regarding test dates and locations can be found here. Discussion Forum: Our discussion forum will be hosted by https://piazza.com/. Students will receive an invitation by e-mail (contact your instructor if you have not received such an email). Students are expected to monitor reasonably often our online discussion forum on piazza. Questions pertaining to the material or the logistics of the course need to be posted on piazza and should not be directed to your instructor by email.

Topics/Material Coverage This is a tentative schedule with the topics that will be discussed throughout the term. Out of the 39 hours (13 weeks of classes), 4hrs are reserved for the in-class midterms. For every topic discussed in class, you can find below specific references to the recommended textbook (Discrete Mathematics with Applications (4th Ed.), by Susanna S. Epp). You are highly encouraged to try all exercises from these sections (they will be different from the weekly assignments).

2

Week 1: Propositional Logic Truth tables, compound statements tautologies, valid arguments. • Sections 2.1-2.3. Week 02: Predicate Logic Predicates, quantifiers, tautologies. • Sections 3.1-3.4. Week 03: Mathematical Inductions & Sequences Principle of Mathematical Induction, Principle of Strong Mathematical Induction, recurrence relations, pigeonhole principle (time permitting). • Sections 5.1-5.4, 5.6-5.8. Week 04: Rational Numbers & Reasoning Rational Numbers, proof by induction and by contraposition, proof by construction, exhaustive proof. • Sections 4.1-4.7 (combined with week 05) Week 05: Elementary Number Theory Divisibility, Euclidean algorithm, gcd’s, primes, coprimes, congruences, modular arithmetic. • Sections 4.1-4.7 (combined with week 04) Week 06: Midterm #1 Week 07: Reading week Week 08: Elementary Set Theory Sets, powersets, cartesian products, set operations, set identities. • Sections 6.1-6.3 Week 09: Relations Relations, equivalence relations, partial and total orders. • Sections 8.1-8.5. Week 10: Functions Functions and function properties, 1-1, onto, inverses, bijections. • Sections 7.1-7.3. Week 11: Midterm #2 Week 12: Combinatorics Permutations, subsets, sequences, multisets. • Sections 9.2,9.3, 9.5-9.7. 3

Week 13: Graph Theory - part 1 Basic definitions and graph types, graph isomorphism, graph traversals, • Sections 10.1-10.5. Week 14: Graph Theory - part 2 Directed graphs, planarity, colouring. • Material not covered in textbook.

General Policies & Regulations Lectures Students are expected to attend all lectures. There is no substitution for missing a lecture. It should be everybody’s priority to insure an atmosphere conducive to learning. As such, students are expected to comply with the following rules: It is important that the lecture hall is quiet so that the instructor may be heard by all people at all times. To avoid unnecessary distractions, students who arrive late to a lecture should wait until the intermission in the middle to enter the lecture hall. As a rule, all cell phones are turned off. If you must receive a call, your phone should be set to vibrate, and you should politely leave the lecture hall to take your call. After, do not re-enter the lecture hall unless it is the intermission. Laptop computers are turned off and put away. Only if you have the permission of your instructor may you use a laptop during lecture. It is considered rude to leave a lecture early. If you must leave early, kindly inform the instructor beforehand. As with any rules of etiquette minor infractions may be tolerated, but continued ignorance of these rules can be treated as academic misconduct. Accommodations due of illness: A missed deadline will be treated the same as a mark of zero unless the cause is some serious circumstance, e.g. illness, in which case appropriate documentation has to be provided complying with the RyersonU regulations. Copyright All material you will have access to, including slides, assignment questions, solutions to exams, are copyrighted by Ryerson University and your instructors. You are not allowed to share any of this material with anyone not enrolled in the course. In particular you are not allowed to share or post this material or parts of it online. Evaluation Guidelines Exams will contain analytic questions (and possible a few multiple choice questions). Apart from solving problems, you are expected to be able to restate and reproduce from scratch all theorems/propositions/lemmas discussed in class. Exam questions will be very similar to the material discussed in class and to the assignment questions. Exams will be closed-book. No calculators will be allowed. Academic Integrity, Misconduct & Penalties Students are expected to maintain high standards when it comes to fairness, transparency, and academic integrity, and to comply with all RU regulations and all course’s guidelines. Explicit (additional) guidelines regarding each assessment will be communicated to you in time. There will be zero tolerance regarding academic misconduct. In case of academic misconduct, an official report will be filed with the Academic Integrity Office. Incurred penalties include, a zero for the subject work, final grade reduction (up to 10%), and in some cases an F in the course or expulsion from the University.

4

Assignments Assignment questions will be given on a weekly basis. Assignment will not be marked, but will be graded for completeness. Every homework assignment will be given either 1 mark, if all questions have been answered properly (justifications are present, and not just dry numerical answers), and 0 otherwise. Assignment submissions are accepted exclusively online on d2l by the due dates, which will be usually on Monday at 8am, sharp. Emails and Correspondence Policy 157 http://www.ryerson.ca/senate/policies/pol157. pdf regulates email correspondence between students and instructors. In particular, only Ryerson e-mail accounts are to be used for student communication with faculty. Faculty members will not respond to any other addresses. The policy also states that students are obliged to set up their proper Ryerson e-mail account and regularly attend to it. Messages regarding this course may be sent to you via your Ryerson account; you are responsible for knowing the content of these messages. Concerns and questions regarding personal matters may be addressed to your professor via e-mail. Questions pertaining to the material of the course may only be posted on our discussion forum. Exams You must bring a Ryerson Photo ID to the midterm or the final exam. All tests, exams and quizzes will be written without calculators or any other aids. The use of electronic devices such as (but not limited to) cell phones and mp3 players is strictly prohibited during tests, exams and quizzes. Such devices must be turned off. Food or drink (unless medically necessary) is prohibited during tests, exams and quizzes. All bags, backpacks and other personal items are to be placed out of reach. A missed exam will result in a grade of zero in the exam. Exceptions do apply in extreme circumstances, e.g. ma jor illness. In all cases, accommodations might be considered only if the home department is notified in time and proper and valid documentation is submitted and approved as per RU regulations. In such cases, a make-up exam might be scheduled just once for each midterm exam and once for the final exam (soon after the missed exams, and for all qualifying students at the same time). A missed midterm make-up exam will result in a grade of zero in the midterm, unless there is again some special circumstance which has to be documented similarly, and in which case the the midterm weight will be shifted to the final. A missed final make-up exam will result in zero grade in the final exam. Remarking Requests Results to assessments will become available online soon after each deadline. Students are expected to read and understand the solutions before submitting a remarking request. Any such request has to be submitted in writing, explaining in detail why marking was not done properly, and no later than 10 business days after exams are returned to students. In such a case, the paper will be remarked from scratch, and the grade may either increase or decrease.

University Policies Students are required to inform their instructors of any situation which arises during the semester which may have an adverse effect upon their academic performance, and must request any considerations and accommodations according to the relevant policies and well in advance. Failure to do so will jeopardize any academic appeals. Health certificates If a student misses the deadline for submitting an assignment, or the date of an exam or other evaluation component because of illness, he or she must submit a Ryerson

5

Student Medical Certificate AND an Academic Consideration form within 3 working days of the missed date. Important: 1. The Academic Consideration Request (ACR) online form (https://www.ryerson.ca/ senate/StudentInfo/AcademicConsiderationRequest/) must be used by all undergraduate students in the Faculty of Science, Ted Rogers School of Management (TRSM), Faculty of Engineering & Architectural Science (FEAS), with the exception of the Electrical Engineering program, and Faculty of Arts (FoA). 2. Students in all other Ryerson programs, and students taking courses in the G. Raymond Chang School of Continuing Education, must submit their request for academic consideration on health grounds by completing the Academic Consideration Document Submission Form (https://www.ryerson.ca/content/dam/senate/forms/academic_ consideration_document_submission.pdf), along with a completed Student Health Certificate (or letter from an appropriate regulated health professional), https://www. ryerson.ca/content/dam/senate/forms/medical.pdf. Religious observance If a student needs accommodation because of religious observance, he or she must submit a Request for Accommodation of Student Religious, Aboriginal and Spiritual Observance AND an Academic Consideration form within the first 2 weeks of the class or, for a final examination, within 2 weeks of the posting of the examination schedule. If the required absence occurs within the first 2 weeks of classes, or the dates are not known well in advance as they are linked to other conditions, these forms should be submitted with as much lead time as possible in advance of the required absence. Both documents are available at http://www.ryerson.ca/senate/forms/relobservforminstr.pdf. If you are a full-time or part-time degree student, then you submit the forms to your own program department or school. If you are a certificate or non-certificate student, then you submit the forms to the staff at the front desk of the Chang School. Academic Accommodation Support Students who need academic accommodation support should register with the Academic Accommodation Support office (formerly called the Access Centre). Before the first graded work is due, registered students should inform their instructors through an Accommodation Form for Professors that they are registered with Academic Accommodation Support and what accommodations are required. Ryerson Policies of Interest Ryerson Senate Policies - http://www.ryerson.ca/senate/policies/ Ryerson Academic Integrity - http://www.ryerson.ca/academicintegrity/ Policy 46 - Undergraduate Grading, Promotion and Academic Standing Policy 60 - Student Code of Academic Conduct - http://www.ryerson.ca/content/dam/ senate/policies/pol60.pdf Policy 61 - Student Code of Non-academic Conduct - http://www.ryerson.ca/content/ dam/senate/policies/pol61.pdf Policy 134 - Undergraduate Academic Consideration and Appeals Policy 135 - Examination Policy Policy 150 - Accommodation of Student Religious Observance Obligations Policy 157 - Student Email Accounts for Official University Communication Academic Conduct http://www.ryerson.ca/academicintegrity/ In order to create an environment conducive to learning and respectful of others rights, phones and pagers must be silenced during lectures, lab sessions and evaluations. Students should refrain from disrupting the lectures by arriving late and/or leaving the classroom before the lecture is finished. 6

Academic Misconduct According to the Ryerson policy 60 (http://www.ryerson.ca/content/ dam/senate/policies/pol60.pdf), academic misconduct includes, but not limited to: • Plagiarism which is the claiming of words, ideas, artistry, drawings or data of another person. This also includes submitting your own work in whole or in part for credit in two or more courses. • Cheating • Misrepresentation of personal identity or performance • Submission of false information • Contributing to academic misconduct • Damaging, tampering, or interfering with the scholarly environment • Unauthorized copying or use of copyrighted materials • Violations of departmental policies or professional behavior • Violations of specific departmental or course requirements Committing academic misconduct will trigger academic penalties, including failing grades, suspension and possibly expulsion from the University. As a Ryerson student, you are responsible for familiarizing yourself with Ryerson conduct policies. Non-Academic Conduct http://www.ryerson.ca/content/dam/senate/policies/pol61.pdf Among many other infractions, the code specifically refers to the following as a violation: Disruption of Learning and Teaching - Students shall not behave in disruptive ways that obstruct the learning and teaching environment. Student Code of Academic Conduct / Academic Integrity Ryersons Policy 60 (the Student Code of Academic Conduct) applies to all students at the University. Forms of academic misconduct include plagiarism, cheating, supplying false information to the University, and other acts. The most common form of academic misconduct is plagiarism a serious academic offence, with potentially severe penalties and other consequences. It is expected, therefore, that all examinations and work submitted for evaluation and course credit will be the product of each students individual effort (or an authorized group of students). Submitting the same work for credit to more than one course, without instructor approval, can also be considered a form of plagiarism. Suspicions of academic misconduct may be referred to the Academic Integrity Office (AIO). Students who are found to have committed academic misconduct will have a Disciplinary Notation (DN) placed on their academic record (not on their transcript) and will normally be assigned one or more of the following penalties: - A grade reduction for the work, ranging up to an including a zero on the work (minimum penalty for graduate work is a zero on the work) - A grade reduction in the course greater than a zero on the work. (Note that this penalty can only be applied to course components worth 10% or less, and any additional penalty cannot exceed 10% of the final course grade. Students must be given prior notice that such a penalty will be assigned (e.g. in the course outline or on the assignment handout) - An F in the course - More serious penalties up to and including expulsion from the University The unauthorized use of intellectual property of others, including your professor, for distribution, sale, or profit is expressly prohibited, in accordance with Policy 60 (Sections 2.8 and 7

2.10). Intellectual property includes, but is not limited to: - Slides - Lecture notes - Presentation materials used in and outside of class - Lab manuals - Course packs - Exams For more detailed information on these issues, please refer to the Academic Integrity policy http://www.ryerson.ca/senate/policies/pol60.pdf and to the Academic Integrity Office website http://www.ryerson.ca/ai. Important Resources Available at Ryerson Use the services of the University (Student Learning Centre) when you are having problems writing, editing or researching papers, or when you need help with course material. There is one general site where you may see and register for all of the workshops offered by all of these areas: http://www.ryerson.ca/ studentlearningsupport/index.html Examples of available resources are: • The Library (LIB 2nd floor) provides research workshops and individual assistance. Enquire at the Reference Desk or at http://library.ryerson.ca/guides/workshops/. • The Writing Centre (LIB 272- B) offers one-on-one tutorial help with writing and workshops http://www.ryerson.ca/studentlearningsupport/writing-support/index.html. • English Language Support offers workshops to improve overall communication skills http://www.ryerson.ca/studentlearningsupport/english-language-support/index. html

8...