MATH 247-01 Discrete Mathematics
Syllabus for Spring 2023
Mon, Wed, & Fri, 1:00 – 1:50pm Gildemeister 327
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Instructor: |
Winona
Email: |
Office: |
Office
Hours: |
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Course Texts |
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“Discrete Mathematics” |
“Applied Discrete Structures” |
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1) Sign in or create an account at 2) Use code: WINONAMATH247ErrthumSpring2022 3) Click “Subscribe” to enter
payment info (~$58 and will last until May 2023). |
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A free pdf of the book can be downloaded from: OR ·
An XML version of the book can be found here: |
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Note about
Calculators: You are allowed at most times to use a calculator, but you
must show work. |
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Prerequisite: MATH140 – Applied Calculus or MATH212 – Calculus I. (Though you can probably get by with a strong Pre-Calc background.)
About This Course: This course is designed to inform students about the mathematics that they missed out on as they worked toward calculus. In contrast to Calculus where it is essential that the real numbers have the property of being arbitrarily close, the objects studied in this course – such as integers, sets, graphs, and statements in logic – do not vary smoothly in this way. Instead they have distinct, separated values. Areas of application included digital circuits, design optimization, computer science, general problem solving, etc.
Modality Disclaimer: This course is designed to be an in-person course. For as long as the University allows in-person classes, there is no guarantee that required materials/content/assessments will be available to those who do not attend class in person.
Video
Lectures: Video lectures from the Fall 2020 semester are available on D2L. Feel free
to use these to study from but watching the video does NOT replace
attending lecture. Occasionally you may be referred to a video if we
run out of time during class. NOTE: the videos may make references to
quizzes/exams/due dates/reviews/office hours/etc. that will be different this
semester.
Typical Day in this Course: A complete, detailed schedule can be found on D2L. Most days in this course can be split into 3 parts: Before, During, and After. Make sure you check the schedule frequently and look 2 – 3 days forward and backward each time so that you don’t miss anything.
· Before each class: Read the appropriate sections in the ZyBook and complete all the Participation and Challenge Activities. Occasionally there will be other resources or youtube videos to watch.
· During class: Come to class; listen and ask questions during the lecture. On Homework Days you will be asked to present completed homework problems from the previous class’s material on the board.
· After class: Each class has a collection of problems for you to complete before the next homework day and/or before the next unit.
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Philosophy on Grades[1] · The purpose of being in MATH247 is to learn cool and interesting things, not to score points and get letter grades. If we spend more time thinking about grades than about mathematics, we’ve failed. · Your grades are supposed to serve you, not the other way around. Grades should provide clear, specific, and actionable feedback on what you are doing well and what you need to work on — not just an audit of what you did wrong but a teaching moment for how to improve. · And, you should be given the opportunity to improve your work and learn from your mistakes using the feedback you receive. · Your final course grade should give information about the quantity and quality of evidence you provide during the semester that shows you understand concepts. It should not be based on artificial measurements that can easily be gamed or distorted. · In short -- your individual grades during the course should reflect the result of an iterative process of demonstrating what you know, based on multiple attempts and feedback; and the course grade should indicate all the things you were eventually able to show that you know. The system of assessment and grading that we use in MATH247 is an effort to enact a grading system that does all this — that is accurate, transparent, and fair. It may be somewhat different than you are used to, so read the following carefully. |
Learning Targets: There are 34 learning targets in this class divided (unevenly) into 9 units. Your final grade for the course will be determined by your ability to demonstrate these skills. The complete list of Learning Targets can be found on D2L under “Content >> Course Materials” in the document “MATH247 Learning Targets”.
Active Tasks: These tasks are designed to keep you engaged in the class and on track to achieve success.
· ZyBook Participation and Challenge Activities: The ZyBook text for the course has built in interactive components labelled either “Participation Activity” or “Challenge Activity”. You have unlimited attempts at these activities to get them right. The readings and these activities should be completed before the designated class period on that topic. You have unlimited attempts up to the time they are due.
o Grading: ZyBook activities are assigned a percentage based on correct responses.
· Homework Day: Each lecture has a follow-up set of problems, usually out of the Doerr and Levasseur text. These problems should be completed before the next Homework Day. On Homework Days, problems will be assigned randomly to students to write up their solution on the board.
o Grading: Problems are either “complete” or “incomplete” depending on the student’s work. Ultimately you are assigned a completion percentage.
· Mathematical Virtue Essays: This course does more than aim to give you specific mathematical skills. It also hopes to instill in you the mathematical virtues of Persistence, Curiosity, Imagination, Disposition to Beauty, Creativity, Play/Exploration, and Thinking for Oneself. You will be given the opportunity of demonstrating one or more of these virtues through essay prompts. Prompts can be found on D2L under “Content >> Course Materials” in the “Math Virtues” document.
o Grading: Essays are awarded a “Pass” or an “Incomplete”. An essay earns a “Pass” if it answers all parts of the prompt, communicates well, and truly exhibits the Mathematical Virtue being written about. An essay is “Incomplete” if it does not answer all parts of the prompt and/or fails to communicate in an understandable fashion.
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Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis? --- Paul R. Halmos |
Targeted Tasks: Each unit will utilize a variety of tasks and assessments to gauge your understanding of 34 specific Learning Targets:
· Written Homework: This is the traditional collection of problems that students will submit individual, written responses/solutions for. These problems can be found in the D2L content and are typically due on the day the next unit begins. Written homework problems earn a single mark per Learning Target. (Note: Written homework is hard. Don’t wait until the last minute to do them. Evidence of Academic Dishonesty will be reported to the appropriate WSU authorities.)
· Exams: We will have 3 traditional, timed exams and comprehensive final. Exam problems earn a double mark per Learning Target. Tentatively exams are scheduled for February 17, March 27, and April 26.
· Post-Exam Opportunities: After the first Exam, you have the opportunity to improve your marks. See “Improving Your Mark” below. Post-Exam Opportunities improve a single mark per Learning Target.
Grading for Targeted Tasks: Each of these items is graded by evaluating the work relative to college-level expectations for quality and one of four marks is given to the work — E, M, R, or N. These marks are explained more in the rubric diagram and table below.
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Mark |
Description |
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E |
Excellent or exemplary. The work has either no errors at all, or only trivial ones. The work shows clear communication and uses correct, well-constructed English along with correct mathematical notation. All work is clearly explained, and detailed justifications are provided. |
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M |
Meets the expectations for the assignment (but is not “excellent”). The solution is complete and reasonably well-communicated and understanding of the concept is evident. There may be some minor, easily correctible mistakes including language or notational errors. Adequate explanations are provided but there are some minor gaps or omissions. |
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R |
Revision needed, due to a serious error or omission. Partial understanding is evident, but there are significant gaps, omissions, or errors. |
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N |
Not assessable, due to major omissions or persistent/systemic major errors. |
Once you have
earned an E (or M) on a Learning Target, it cannot be lost.
Only the top two marks of each Learning Target will be counted.
Improving your Mark: If you want to improve your mark on a Learning Target, there are a variety of ways available to you. See the “Math247 Mark Improvement Options” in D2L. In general, if you want to improve your mark in a LT, email me and/or stop by during office hours. All Mark Improvements must be completed by 3:30pm on Friday, April 30.
Wildcards: Sometimes
written homeworks or exams will contain “Wildcard”
problems that are typically a bit harder than usual and do not fit into one of
the standards. Earning an E or M on a Wildcard will count toward your overall
mark counts but cannot be specifically improved.
Final Exam: The default Final Exam time is Monday (May 1) 1:00-3:00pm. Other time slot options are given below. The final exam will be individualized for each student and only contain problems for LTs that you currently have a second-highest mark of R or N. If you have an LT with EE, EM, or MM, it will not be improved by taking the final exam.
Determination of Course Grade: Your course grade is determined by the number of accomplishments you rack up during the course and the level of skill demonstrated by your work. The Grade Determination Table below shows what accomplishments are required for each basic grade level from A through C. Please note that all the requirements for a grade level must be met in order to earn that grade. The grade awarded will be the highest grade for which all requirements are met. I will try to keep an updated record on D2L, but you can always email me directly if D2L seems to be incorrect and/or out-of-date.
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MATH247 Grade Determination Table |
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to
earn an |
to
earn a |
to
earn a |
to
earn a |
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ZyBook |
≥90% |
≥80% |
≥70% |
Complete
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Homework Day Completions |
≥80% |
≥70% |
≥60% |
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Learning
Targets |
Earn at least 62 Es or Ms including at least 16 LTs with EE |
Earn at least 54 Es or Ms including at least 8 LTs with EE |
Earn at least 48 Es or Ms |
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Mathematical Virtue Essays |
Earn a “Pass” on at least 3 essays |
Earn a “Pass” on at least 2 essays |
Earn a “Pass” on at least 1 essay |
No Essay Requirement |
Academic Dishonesty: Any type of academic dishonesty (cheating, copying, etc.) will result in failure and will be reported to school authorities. This includes access to past quizzes, exams, etc. that have not been handed out to the whole class. This includes posting homework questions to unsanctioned websites. If you are having trouble with the course, please contact the instructor first.
Note: This syllabus is subject to change if deemed necessary by the instructor.
(as of 4/11/23, subject to change)
Things in Yellow can be found in the Zybook.com materials
Things in Blue can be found in the Doerr & Levasseur materials
Things in Grey can
be found on D2L
Things in Green can be found on the web
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Week |
Monday |
Wednesday |
Friday |
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Jan 9 |
Introductions Introduction to Sets |
Before Class
(in zyBook):
After Class (in pdf): Written HW 1: located in D2L |
Before Class:
After Class: Oral HW: (§1.3, pg 12) 2, 4, 6 Oral HW: (§1.4, pg 15) 2, 4, 6, 8 |
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Jan 16 |
NO CLASS |
Before Class: Summation Notation After Class: Oral HW: (§1.5, pg 18) 1, 2bcd, 8, 9, 10 |
Homework Day 1 (§1.1,
1.2, 1.3, 1.4, 1.5) |
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Jan 23 |
Before Class: Written HW 1 Due Logic Propositions and Operations Truth Tables After Class: Written HW 2: located in D2L |
Before Class: Equivalence
and Implication After
Class: |
Homework Day 2 (§3.1, 3.2, 3.3, 3.4) |
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Jan 30 |
Before Class: Written HW 2 Due Digital Logic Gates and Circuits After
Class: Written HW 3: located in D2L |
Before Class:
Watch: "Proof and Problem Solving"
After
Class: |
Before Class:
After Class: Oral HW: Finish Proof Handout |
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Feb 6 |
Homework Day 3 (Circuits, §4.1, Proofs/Examples with Diagrams/Tables) |
Before Class: Written HW 3 Due Propositions over a universe Quantifiers After
Class: Written HW 4: located in D2L |
Before Class: Quantifiers, cont. After
Class: |
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Feb 13 |
Homework
Day 4 |
Written HW 4 Due Review |
Exam I |
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Feb 20 |
Recommended
A Essay Due Date Before Class: Sequences & Recursion After
Class: Written HW 5: located in D2L |
Before Class: Watch: "Finite Differences Tutorial" Finite Difference Methods After
Class: A-Option
Essay |
No In-Person MATH247 Class |
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Feb 27 |
Before Class: Mathematical Induction After
Class: |
Before Class: Mathematical Induction, cont. Solving
Linear Recurrences After
Class: |
Solving Linear Recurrences, cont. After
Class: |
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Mar 6 |
SPRING BREAK |
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Mar 13 |
No In-Person MATH247 Class Before Class: WATCH
VIDEO LECTURES Factorizations After
Class: Written HW 6: located in D2L |
Homework
Day 5.5 |
Before Class: Written HW 5 Due Floor and Ceiling Functions Modular Arithmetic Oral HW: (247OralModularArithHW in D2L) All of them |
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Mar 20 |
Before
Class: Solvability of Systems of Integral Equations Oral HW: (247DiophantineHW in D2L) The ones we didn’t do in class |
Homework
Day 6 |
Written HW 6 Due Review |
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Mar 27 |
Exam II |
Recommended
AB Essay Due Date Before Class: Relations and digraphs After
Class: (§6.2 pg 109) 1-6 |
Before Class: Properties of Relations Closures and Reductions After
Class: Written HW 7: located in D2L |
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Apr 3 |
Before Class: Max-Flow
/ Min Cuts Weighted Graphs Max Flow – Min Cuts / Ford-Fulkerson Algorithm Oral HW:
247MaxFlowMinCut (located in D2L) |
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Before Class: Intro to Graph Theory Graph
Properties After
Class: Written HW 8: located in D2L |
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Apr 10 |
Before Class: Graph Connectedness Paths
and Cycles Graph Coloring After
Class: |
Before Class: Dijkstra's Algorithm: Another example (video) Shortest Paths / Dijkstra’s Algorithm After Class: OralHW 8: 247OralPaths (found in D2L) Written HW 9: located in D2L |
NO CLASS |
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Apr 17 |
Before Class: Trees Applications of Trees Properties of Trees After Class: Oral HW: 247OralTrees (found in D2L) |
NO CLASS |
Homework
Day 8 & 9 |
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Apr 24 |
Before Class: Written HW 8 Due Minimum
Spanning Trees After Class: Oral HW:
247OralHWMinTrees (found in D2L) |
Hand in Paths & MinTrees Review |
Recommended
ABC Essay Due Date Written
HW 9 Due Exam III |
Final Exam Time Options:
Monday
(May 1) 1:00pm – 3:00pm (default)
Tuesday (May 2) 8:00am – 10:00am
Wednesday
(May 3) 8:00am – 10:00am
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Commitment to Inclusive Excellence WSU recognizes that our individual differences can deepen our understanding of one another and the world around us, rather than divide us.
In this class, people of all ethnicities, genders and gender identities, religions, ages, sexual orientations, disabilities, socioeconomic backgrounds, regions, and nationalities are strongly encouraged to share their rich array of perspectives and experiences.
If you feel your differences may in some way isolate you from WSU’s community or if you have a need for any specific accommodations, please speak with the instructor early in the semester about your concerns and what we can do together to help you become an active and engaged member of our class and community.
If you or a friend has been a victim of sexual assault, dating violence, domestic violence, or stalking, you can talk to a trained, confidential advocate by calling 507.457.5610. |
The Standard Disclaimer applies. © Eric Errthum, April 2023, all rights reserved.
[1] Philosophy, following details, and wording heavily borrowed from/influenced by Robert Talbert, GVSU.