MATH 247-01 Discrete Mathematics
Syllabus for Fall 2020
Mon, Wed, & Fri, 9:00 – 9:50am Gildemeister 325
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Instructor: |
Winona
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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: WINONAMATH247ErrthumFall2021 3) Click “Subscribe” to enter
payment info (~$58 and will last until Jan 2022). |
· 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. Although, at times you will be asked how to demonstrate certain computations without the use of a calculator. |
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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 Disclaimers: (i) 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. (ii) Proper masking is required at all times by all persons until the University Guidelines change. However, I am not able to forcefully enforce this policy on your fellow classmates. Flagrant unmasking will result in being reported to the Dean after class. (iii) If you are unable to regularly attend class in person, I strongly recommend that you either find a synonymous/transferable online course or contact Access Services (access@winona.edu) to apply for special consideration.
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’ 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. |
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· 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. |
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Learning Targets: There are 34 learning targets in this class divided (unevenly) into 8 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 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. (Note: These are hard. Don’t wait until the last minute to do them.)
· Exams: We will have 3 traditional, timed exams and comprehensive final. Tentatively exams are scheduled for October 1, October 29, December 3, with the Final on December 7 at 8am.
· Post-Exam Opportunities: After the first Exam, you have the opportunity to improve your marks. See “Improving Your Mark” below.
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. |
How to earn an E (or M) on a Learning Target: Students will
earn an E or an M mark on a Learning Target in one of the following ways:
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Earn an E (or M) on an exam question |
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Earn an E (or M) on at least 2 of: · A Written HW problem · A Post Exam Opportunity |
Once you have earned an E (or M) on a Learning Target, it cannot be lost.
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. Note: You are only allowed to improve your mark in 1 Learning Target per week (except when using a token). Students have 5 tokens for the semester that allow them to initiate additional mark improvements outside the one per week limitation.
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.
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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Group Collaboration Completions |
≥80% |
≥70% |
≥60% |
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Learning
Targets |
Earn an E or M on at least 31 out of 34 learning targets, including at least 16 E marks |
Earn an E or M on at least 27 out of 34 learning targets, including at least 8 E marks |
Earn an E or M on at least 24 out
of 34 learning targets |
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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 |
Videos: Video lectures from the Fall 2020 semester will be posted
to 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.
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.
Schedule of Events – Math 247
(as of 8/18/21, 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
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Week |
Monday |
Wednesday |
Friday |
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Aug 23 |
Introductions |
Before Class (in
zyBook):
Set operations and Venn Diagrams
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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Aug 30 |
Before Class: Summation Notation
After Class: Oral HW: (§1.5, pg 18) 1, 2bcd, 8, 9, 10 |
Homework Day |
Before Class:
Written HW 1 Due Logic Propositions and Operations Truth Tables
After Class: Written HW 2: located in D2L |
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Sep 6 |
NO CLASS |
Before Class:
Equivalence
and Implication
After
Class: |
Homework Day |
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Sep 13 |
Before Class:
Written HW 2 Due Digital Logic Gates and Circuits
After
Class: Written HW 3: located in D2L |
Before Class:
After
Class: |
Before Class:
After Class: Oral HW: Finish Proof Handout |
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Sep 20 |
Homework Day |
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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Sep 27 |
Online Discussion Session |
Written HW 4 Due
Review |
Exam I |
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Oct 4 |
Before Class:
Sequences & Recursion
After
Class: Written HW 5: located in D2L |
NO CLASS
A-Option
Essay |
Before
Class:
Finite Difference Methods
After
Class: |
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Oct 11 |
Before Class:
Mathematical Induction
After
Class: |
Before Class:
Solving
Linear Recurrences
After
Class: |
Homework Day |
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Oct 18 |
Before Class:
Written HW 5 Due Division Algorithm Factorizations
After
Class: Written HW 6: located in D2L |
Before Class:
Floor and Ceiling Functions Modular Arithmetic
Oral HW: (247OralModularArithHW in D2L) All of them |
Before
Class:
Solvability of Systems of Integral Equations
Oral HW: (247DiophantineHW in D2L) The ones we didn’t do in class |
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Oct 25 |
Homework Day |
Written HW 6 Due
Review |
Exam II |
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Nov 1 |
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 |
Before Class: Max-Flow
/ Min Cuts
Weighted Graphs Max Flow – Min Cuts / Ford-Fulkerson Algorithm
Written HW 7.5: 247MaxFlowMinCut (located in D2L)
AB-Option
Essay |
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Nov 8 |
Homework Day |
Before Class: Intro to Graph Theory Graph
Properties
After
Class: |
Before Class:
Graph Connectedness Paths
and Cycles Graph Coloring
After
Class: |
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Nov 15 |
Homework Day |
Before Class: Dijkstra's Algorithm: Another example (video)
Shortest Paths / Dijkstra’s Algorithm
After Class: Witten HW 8: 247WrittenHWPaths (found in D2L) |
Before Class:
Trees Applications of Trees Properties of Trees
After Class: Oral HW: 247OralTrees (found in D2L) |
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Nov 22 |
Before Class:
Written HW 8 Due Minimum
Spanning Trees
After Class: Written HW 9: 247WrittenHWMinTrees (found in D2L)
ABC-Option
Essay |
NO CLASS |
NO CLASS |
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Nov 29 |
Homework Day |
Written HW 9 Due Review |
Exam III |
Final Exam Time:
Tuesday (Dec 7) 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. |
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The Standard Disclaimer applies. © Eric Errthum, August 2021, all rights reserved. |
[1] Philosophy, following details, and wording heavily borrowed from/influenced by Robert Talbert, GVSU.