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1 General Course Information

Course Title & Number MATH 1240: Elementary Discrete Mathematics

Number of Credit Hours 3

Prerequisites 60% in Pre-calculus Mathematics 40S or the former Mathematics

40S (300) or a “C” in MSKL 0100.

Term Winter 2021

Course website UM Learn:

MATH-1240-A01/A02/A03 - Elementary Discrete Mathematics

Textbook Definitions and Theorems for MATH 1240 Winter 2020

by M. Davidson and R. Craigen

Required Resource Discrete and Combinatorial Mathematics: An Applied Introduction

by Ralph P. Gimaldi (Fifth Edition)

Selections will be available on digital reserve (see course website).

Recommended Resources MATH 1240 - Elementary Discrete Mathematics

Final and Midterm Exams with Complete Solutions

Calendar Description The course is intended for students in mathematically rich disciplines including those planning to enter an Honours or Major program in Mathematics or Statistics. An introduction to mathematical ideas, proof, techniques, and mathematical writing, explored through topics in discrete mathematics.

MATH 1240 is an introduction to appropriate mathematical practice in preparation for courses in which mathematical maturity is an expectation. Material in this course is focused on definitions, theorems and proofs. Students will be expected to display mathematics with precision in their writing. We will cover a variety of topics including mathematical induction, modular arithmetic, basic propositional logic, elementary set theory and functional notation, partial orders, basic graph theory, and basic counting. Working with these topics necessitates a deep familiarity with a large list of definitions, theorems, and proof techniques.

There are three different sections of MATH 1240 being run in parallel this winter. Each lecturer will be running their section independently though the course websites have been merged. Your lecturer will create a self-contained collection of modules with the material specific to their section. You are encouraged to start there but you are welcome to read and watch material from other sections, if you find them helpful for your studies

On the “Content Browser” in our on UM Learn page, you will see the following modules (and more):

• Course documents: This syllabus will be there, along with any other documents relevant to all sections.

• Three modules – A01 materials/A02 materials/A03 materials: Will contain all material produced and organized for each section.

This document contains the information that is relevant to all sections. Your instructor will post a separate document with their information about contact information, office hours, and lecture format information.

2 Course Topics

The document Definitions and Theorems for MATH 1240 Winter 2020 (may sometime be referred to as the Local Notes) will indicate which concepts will be covered from within these sections in the Grimaldi textbook, as well as the recommended exercises. Students are expected to come to class having familiarized themselves with the definitions for the week.

Definitions are of key importance in this course, and students are expected to know the definitions verbatim. Students are encouraged to think of this as developing deep familiarity and understanding of all things within a definition rather than a task of memorization.

The following table will provide a rough estimate of the pacing of the course. We will not necessarily cover all parts of each of these sections from the Grimaldi textbook. Some sections will not be completely covered in the week they appear.

Week	Topics	Sections in Resource (Grimaldi)
1	Intro Basic connectives and truth tables Laws of logic	2.1 2.2
2	Logical implication Quantifiers Definitions and proofs	2.3 2.4 2.5
3	Sets and subsets Set operations and laws Rules of sum and product Permutations Combinations: binomial theorem Counting and Venn diagrams	3.1 3.2 1.1 1.2 1.3 3.3
4	Mathematical induction	4.1
5	Recursive definitions Division algorithm and prime numbers	4.2 4.3
6	Euclidean algorithm Fundamental theorem of arithmetic	4.4 4.5
7	Cartesian products and relations Functions: plain and one to one Onto functions, Stirling numbers Special functions	5.1 5.2 5.3 5.4
8	Pigeonhole principle Function composition and inverses	5.5 5.6
9	Countable and uncountable sets Properties of relations Digraphs	Appendix 3 7.1 7.2
10	Partial Orders and Hasse diagrams Equivalence relations and partitions Integers mod n Graph theory definitions	7.3 7.4 14.3 11.1
11	Subgraphs, complements, isomorphism Degree, Eulerian trails and circuits Planar graphs Hamiltonian graphs and cycles	11.2 11.3 11.4 11.5
Time Permitting	Graph Colouring Trees Rooted trees	11.6 12.1 12.2

3 Lab Schedule

Labs are 50 minutes long and students are expected to attend every week in the section in which they are registered. On non-test days, students are expected to spend some time working individually or in small groups on the worksheet using their tutorial’s discussion forum. The Lab Demonstrator will be available in a WebEx meeting to guide the discussion, provide feedback and go over some selected solutions.

On test days, students will be required to join the WebEx meeting with their TA and write their test, with their webcam on. Students will be able to use the chat feature to ask the TA questions.

Mondays (A02)	Tuesdays (A03)	Wednesdays (A01)	Scheduled Activity
25 Jan	26 Jan	27 Jan	Lab Worksheet 1
1 Feb	2 Feb	3 Feb	Lab Worksheet 2
8 Feb	9 Feb	10 Feb	Test 1
22 Feb	23 Feb	24 Feb	Lab Worksheet 3
1 Mar	2 Mar	3 Mar	Test 2
8 Mar	9 Mar	10 Mar	Lab Worksheet 4
15 Mar	16 Mar	17 Mar	Test 3
22 Mar	23 Mar	24 Mar	Lab Worksheet 5
29 Mar	30 Mar	31 Mar	Test 4
5 Apr	6 Apr	7 Apr	Lab Worksheet 6
12 Apr	13 Apr	14 Apr	Test 5

4 Course Evaluation

Students in this course will be evaluated according to the following table. The final exam will be scheduled by the registrar.

Assessment	Value of Final Grade
Quizzes	30%
Tests	40%
Final Exam	30%

Students will be given a letter grade using the following table as guaranteed minimums for achieving a particular grade.

Grade	A+	A	B+	B	C+	C	D
Percentage	92	85	78	71	65	58	50

5 Assessment Descriptions

5.1 Honesty Declaration

There will be a compulsory assessment in Crowdmark that will contain an Honesty Declaration which covers all assessments written in this course. It will be due on January 22nd, however students will be given opportunities to resubmit until it is done correctly. Once correct, students will be given one bonus point on their Final Exam.

5.2 Quizzes

There will be 11 quizzes administered using the UM Learn Quiz tool. Instructions will be posted in the course announcements. There will be a practice quiz, not worth marks, that students can complete to see how the procedure will work. The deadlines are as follows (all due at 11:59pm).

Quiz #1 29 Jan

Quiz #2 5 Feb

Quiz #3 12 Feb

Quiz #4 26 Feb

Quiz #5 5 Mar

Quiz #6 12 Mar

Quiz #7 19 Mar

Quiz #8 26 Mar

Quiz #9 1 Apr

Quiz #10 9 Apr

Quiz #11 16 Apr

Quizzes will become available two days before the deadline and can be completed at any time within the availability window. The quiz questions are randomized. Once the quiz is started, you will have 10 minutes to complete the quiz. Students who miss a quiz will be given a grade of zero on that quiz.

Your final quiz grade will be calculated with the lowest two quiz scores dropped.

You must complete each quiz on your own, following the guidelines for academic integrity in Section 7.

5.3 Tests

Each of the five (5) tests will be written during the lab time. The tests will be administered via Crowdmark and when the test begins, you will receive an email from Crowdmark with the test questions. Your solutions are to be handwritten and then scanned or written by hand on electronic paper. Using the link provided by Crowdmark you will be able to submit the scans of your work. The time limit for the test will be 30 minutes to complete your solutions with an additional period of 10 minutes to scan and submit your work. Failure to submit your work before the deadline may result in a grade of zero on the test.

You must join the WebEx meeting for your tutorial with your webcam on and write the test in front of your webcam. This meeting may be recorded. Failure to join the WebEx meeting for invigilation or failure to follow the test guidelines may result in a grade of zero on the test. If you lose the connection to the meeting, rejoin as soon as possible and contact your TA and instructor immediately after the test. If you have any questions during the test, you may ask the TA using the private chat feature of WebEx.

Access to a web-cam and microphone are part of the minimum technological requirements for this course (see Section 9). If there is a reason that you will be unable to join a WebEx meeting for remote invigilation, please contact your instructor as soon as possible and at least a week before the test.

Your work on these assignments must be your own and follow the guidelines for academic integrity in Section 7. You are not permitted to discuss the solutions with other students. If you have questions, please ask either the instructor or TA.

Your test grade will be computed by dropping the lowest test score.

5.4 Final Exam

The final exam will be a three (3) hour exam that covers all topics in the course. The exam will consist of three parts:

(i) (1st hour) UM Learn quiz: Once you begin, you will have 30 minutes to complete the quiz and it must be submitted before the end of the hour.

(ii) (2nd hour) Long-answer part 1: Administered via Crowdmark. Once you begin, you will have 40 minutes to complete your solutions and they must be submitted before the end of the hour.

(iii) (3rd hour) Long-answer part 2: Administered via Crowdmark. Once you begin, you will have 40 minutes to complete your solutions and they must be submitted before the end of the hour.

For the duration of the exam, you will be required to join a WebEx meeting with your webcam on and write the test in front of your webcam. This meeting may be recorded. Failure to join the WebEx meeting for invigilation or failure to follow the test guidelines may be grounds for an academic integrity incident. If you lose the connection to the meeting, rejoin as soon as possible and contact your TA and instructor as soon as possible. If you have any questions during the assessment, you may ask the TA using the private chat feature of WebEx.

The day and time of the exam will be scheduled by the registrar’s office.

Final examination and grades policies can be found here: http://umanitoba.ca/admin/governance/governing_documents/academic/1299.html

For more resources about examinations, see: https://www.sci.umanitoba.ca/undergraduate-students/academic-resources/exams-and-appeals/

Students wishing to appeal their term work grade can do so through the Registrar’s Office. A fee is charged for each appeal. More information can be found here: http://umanitoba.ca/student/records/grades/690.html

Any appeal of a final grade is initiated through the Registrar’s office. A fee will be charged for each appeal. For more information, see: http://umanitoba.ca/student/records/

To view your final examination, please check with the department offering the course for policies.

5.5 Missed assessments

Students who are unable to meet a course requirement due to medical circumstances are currently not required to submit medical notes. However, students are required to contact their instructor or academic advisor by email within 48 hours to inform of the missed work and make arrangements.

If you are unable to meet an academic requirement for your courses:

• Contact your instructor for term work such as a class, quiz, midterm/test, assignment, lab.

• Contact an advisor in your faculty of registration for a missed final exam (scheduled in the final examination period).

• Inform your instructor/advisor as soon as possible do not delay. Note for final exams, students must contact their home faculty within 48 hours of the date of the final exam.

• Email your instructor/advisor from a U of M email address, and include your full name, student number, course number, and academic work that was missed.

Failure to initiate contact will result in a grade of zero for the assessment, with no possible alternate arrangements.

The provisions for dropping the lowest scores in assessments when computing the final grades are meant to accommodate the event that a student is unable to complete an assessment due to outside circumstances. Students who miss more assessments need to contact their instructor as soon as possible to discuss possible accommodations.

Please note that circumstances that result in missing multiple course assignments/tests/classes may require medical documentation (e.g., Authorized Withdrawal, Tuition Fee Appeal, Leave of Absence, or accessibility-related accommodations ). Students are advised to speak with an advisor in their faculty/college/school of registration in this case.

6 Expectations: Grading

Assessment results from all tests should available in approximately one week from writing. Final exams will take somewhat longer due to end of term procedures.

Crowdmark is used to grade all tests and the final exam. Results will be returned to the students from Crowdmark by email. In addition to your numerical score, you will receive comments and feedback on your work. You are strongly encouraged to follow up with your instructor or TA about this feedback if you have any questions about it.

Grades from quizzes within UM Learn during the term will be released within two days of the quiz’s deadline. You will receive your numerical score on the test. You are strongly encouraged to follow up with your instructor about questions regarding your responses on these quizzes.

6.1 FIPPA Statement of Purpose - Crowdmark

Your personal information is being collected under the authority of The University of Manitoba Act. It will be used for the purposes of grading papers and providing feedback to students.

Personal information will not be used or disclosed for other purposes, unless permitted by The Freedom of Information and Protection of Privacy Act (FIPPA). The University of Manitoba has taken steps to ensure that its agreement with Crowdmark, Inc. for services provided by the Crowdmark application is in compliance with FIPPA. Please be aware that information held by Crowdmark Inc. may be transmitted to and stored on servers outside of the University of Manitoba, or Canada. The University of Manitoba cannot and does not guarantee protection against the possible disclosure of your data including, without limitation, against possible secret disclosures of data to a foreign authority in accordance with the laws of another jurisdiction. If you have any questions about the collection of personal information, contact the Access and Privacy Office (tel. 204-474-9462), The University of Manitoba, 233 Elizabeth Dafoe Library, Winnipeg, Manitoba, Canada, R3T 2N2.

7 Academic Integrity

The Department of Mathematics, the Faculty of Science and the University of Manitoba all regard acts of academic dishonesty in quizzes, tests, examinations or assignments as serious offences and may assess a variety of penalties depending on the nature of the offence.

Acts of academic dishonesty include bringing unauthorized materials into a test or exam, copying from another student, plagiarism and examination personation. Students are advised to read the sections entitled Academic Integrity and Final Examinations: 4. Personations in the General Academic Regulations of the current Undergraduate Calendar. Note, in particular, that cell phones and pagers are explicitly listed as unauthorized materials, and hence may not be present during tests or examinations.

Penalties for violation include being assigned a grade of zero on a test or assignment, being assigned a grade of “F” in a course, compulsory withdrawal from a course or program, suspension from a course/program/faculty or even expulsion from the University. For specific details about the nature of penalties that may be assessed upon conviction of an act of academic dishonesty, students are referred to University Policy 1202 (Student Discipline Bylaw) and to the Department of Mathematics policy concerning minimum penalties for acts of academic dishonesty.

All students are advised to familiarize themselves with the Student Discipline Bylaw, which is printed in its entirety in the Student Guide; also available on-line or through the Office of the University Secretary. Minimum penalties assessed by the Department of Mathematics for acts of academic dishonesty are available on the Department of Mathematics web-page.

The Student Discipline By-Law may be accessed at: http://umanitoba.ca/admin/governance/governing_documents/students/student_discipline. html

Information from the Faculty of Science regarding Academic Integrity can be found at: http://www.sci.umanitoba.ca/undergraduate-students/academic-resources/academic-integrity-2/

Academic integrity guidelines for this course:

(i) During quizzes, tests, and exams, students may consult their lecture notes, the course textbook, lab worksheets, and their previously completed assessments. No other materials are acceptable. While students may consult the allowed resources, they may not copy from them.

(ii) All work is to be completed independently unless otherwise specified. If you have questions, ask your instructor or the TA.

(iii) Unless otherwise specified, students are not permitted to share questions or answers in whole or in part with others. This includes posting portions of assessments to online forums or websites.

(iv) Students are NOT permitted to allow anyone other person access to their UM Learn account. Doing so is a breach of the University’s Computer Usage Agreements: https://umanitoba.ca/ist/accounts/usage-agreement.html

(v) Any grade of ‘0’ assigned as a penalty for an academic integrity incident will not be dropped in the computation of the final grade.

8 Using Copyrighted Materials

Please respect copyright. We use copyrighted content in this course. We have ensured that the content is appropriately acknowledged and is copied in accordance with copyright laws and University guidelines. Copyrighted works, including those created for this class, are made available for private study and must not be distributed in any format without permission. Do not upload copyrighted works to a learning management system (such as UM Learn), or any website, unless an exception to the Copyright Act applies or written permission has been confirmed.

For more information, see the University’s Copyright Office website at http://umanitoba.ca/copyright/ or contact [email protected].

Posting/uploading course materials to note-sharing sites is prohibited: https://umanitoba.ca/admin/vp_admin/ofp/copyright/media/Note_sharing_Web_sites.pdf

9 Minimum Technological Requirements

The Faculty of Science has indicated that all students enrolled in this course must ensure they have access to the following:

1. a computing device where one can create and edit documents;

2. an internet connection capable of streaming videos and downloading software; and

3. access to a web-cam and microphone.

Additionally, some of the assessments in this course will require students to submit scans (PDFs or JPGs) of their handwritten work, so some form of technology that facilitates submission of document scans is necessary. For this, students will need either a scanner or a document scanner application on a smartphone or tablet (see the course website for some possible options). Use of handwriting with a stylus on electronic paper that can be exported to a PDF/JPG is also acceptable. Instructions on scanning handwritten work will be posted on the course website.

10 Course Technology

• We will post announcements, grades, notes, solutions, and videos on UM Learn. Some parts of your quizzes, tests and exams will be administered through UM Learn. You can access UM Learn at the following address: https://universityofmanitoba.desire2learn.com/d2l/login.

If you cannot access UM Learn, inform your instructor as soon as possible.

Information on accessing and using UM Learn can be found here: https://centre.cc.umanitoba.ca/technology/umlearn/.

• Some sections will be using WebEx for both synchronous lectures and office hours. Information on using WebEx can be found here: https://centre.cc.umanitoba.ca/webex-support/

• Some sections will be using Zoom for both synchronous lectures and office hours.

• Some of your assessments will be submitted using Crowdmark. You can log into Crowdmark using the UM Learn login at: https://app.crowdmark.com/sign-in/umanitoba

Information on using Crowdmark can be found at: https://crowdmark.com/help/categories/support-for-students/

It is the policy of the University of Manitoba policy that all technology resources be used in a responsible, efficient, ethical and legal manner. The student can use all technology in classroom setting only for appropriate educational purposes approved by instructor and/or the University of Manitoba Student Accessibility Services.

11 Recording Class Lectures

The instructors hold copyright over their course materials, presentations, and lectures which form part of this course. No audio or video recording of lectures or presentations is allowed in any format, openly or surreptitiously, in whole or in part without permission of your instructor. Course materials (both paper and digital) are for the student’s private study and research.

In some sections, class lectures will be recorded and will be and these will be available to stream through UM Learn. You may not download and/or repost these recordings without your instructor’s permission.

12 Class Communications

Please note that all communication between myself and you as a student must comply with the electronic communication with student policy—see http://umanitoba.ca/admin/governance/governing_documents/community/electronic_communication_with_students_policy.html You are required to obtain and use your U of M email account for all communication between your-self and the university.

13 Getting Help

• LevelUp

LevelUp is a self-paced program of online modules on UMLearn (instructional videos, exercises, and quizzes) to get students refreshed on basic mathematical skills. Everything from basic number sense and fractions to Trigonometry and Logarithmic functions is covered, and students can do as little or as much as they wish to be prepared for any introductory mathematics course (or other science course requiring basic math skills).

For more information: https://www.math.umanitoba.ca/undergrad-info/level-up/

• Math Bootcamp

Formerly known as ‘PreCalculus Refresher’, the Math Bootcamp reviews high school mate-rial directly relevant to MATH 1500, MATH 1510 or MATH 1520. The Bootcamp is sched-uled on:

THURS 21 JAN 4:30PM to 7:30PM

FRI 22 JAN 4:30PM to 7:30PM

SAT 23 SEPT 10:00AM to 12:00PM

Registration available on the Math Help Centre homepage:

https://server.math.umanitoba.ca/~help/Workshops.html

• Saturday Workshop Series

A series of three 3-hour lectures, scheduled early in the term, to help students review topics that are relevant background knowledge for our first year courses. Students may attend any or all of these sessions. Registration is required, as space is limited.