Discrete Structures

Course Information

Required Resources

Learning Objectives

In this course, students will:

Course Liturgies

The best way to learn mathematics is to do mathematics. To that end, we’ll regularly engage in the following.

In-Class Explorations

Each class period will start with a short introduction to the topics for the day, and will be followed by examples and explorations for you work in groups in order to gain fluency and practice with new mathematical ideas. Near the end of class, solutions will be solicited from the class. You should be ready to share your thinking, even if it’s incomplete or you’re unsure of your correctness. This exchange of ideas will be crucial for our learning!

This also means that attendance is a must. We’ll learn best from one another and by explaining our thinking to one another. Engaged attendance at one class meeting will earn you one engagement point. Engagement points will be monitored and factored into the final grade.

Quizzes

Most Fridays will conclude with a short 2-engagement point quiz over the week’s big ideas.

Homework

The online homework (done on Edfinity and accessed via Canvas) consists of regular problems due by 11:59pm Central on the listed due dates, typically the class day after we finish covering the relevant section. Your average on all of the homework sets will affect your final grade. You have an unlimited number of attempts on each problem, so your overall homework average should reflect not only your knowledge of the material but also your perseverance and commitment to finishing the work.

Reading Reflections

As we mature in our mathematical studies, we’ll consider the formative nature of mathematical practice. (Former Dordt First Mondays Speaker) Francis Su argues that mathematics can help inculcate certain virtues. We’ll read Su’s book in chunks, complete reflection essays, and discuss them in class. See the schedule and the reflection assignments’ Canvas pages for more details.

Portfolio

One of the ways in which we will grow as mathematical communicators is through careful study of/practice with writing mathematical proofs. We’ll look at techniques, writing style, and, the LaTeX document preparation system (accessed via Overleaf). Periodically you will be assigned Portfolio Problems (see due dates in the schedule below). These must be typed in LaTeX and submitted in PDF form on Canvas. Each problem/proof will be assessed according to Dr. Janssen’s standard proof rubric. You will have the freedom to revise and resubmit your work throughout the semester. New feedback will be given approximately once every two weeks (after the next batch of problems are due; see the schedule). At the end of the semester, your work will be compiled into a single portfolio, along with a short reflection assignment. This is the major summative work of the semester; your final grade will be directly impacted by the cumulative final assessments of each portfolio problem.

For more on the portfolio, see the full assignment description.

Exams

There will be two exams, the first on March 5, and the second on April 30. The first will be cumulative up to that point, while the second will be cumulative from the point at which the first exam ended. The format for the exams will be announced at least three weeks ahead of time. Your exam average will be a major factor in your final grade.

Grading

In general, your final grade will be the highest fully completed row in the following table.

Grade Engagement Points Homework Average Exams Reflections Portfolio M’s Portfolio E’s
A 60 90% 87% 5 9 8
A- 57 88% 85% 5 9 8
B+ 54 85% 81% 5 9 7
B 51 82% 77% 5 9 6
B- 47 78% 75% 5 9 5
C+ 44 75% 70% 5 9 4
C 40 72% 65% 4 8 3
C- 35 65% 60% 4 7 2
D 30 50% 50% 3 6 0

Other Polices and Advice

Additional Information

Dordt University Student’s Right to Accommodations Policy

Any student who needs access to accommodations based on the impact of a documented disability should contact the Coordinator of Services for Students with Disabilities (CSSD): Marliss Van Der Zwaag, Academic Enrichment Center, (712) 722-6490, marliss.vanderzwaag@dordt.edu.

Dordt University Academic Dishonesty Policy

Dordt University is committed to developing a community of Christian scholars where all members accept the responsibility of practicing personal and academic integrity in obedience to biblical teaching. For students, this means not lying, cheating, or stealing others’ work to gain academic advantage; it also means opposing academic dishonesty. Students found to be academically dishonest will receive academic sanctions from their professor (from a failing grade on the particular academic task to a failing grade in the course) and will be reported to the Student Life Committee for possible institutional sanctions (from a warning to dismissal from the university). Appeals in such matters will be handled by the student disciplinary process. For more information, see the Student Handbook.

COVID-19 Classroom Protocols

As we begin the Spring 2021 semester, Dordt is a mask-required environment. While on Dordt’s campus, you will need to wear a mask in all public places or common indoor spaces, which include: classrooms, hallways, laboratories, restrooms, the Hulst Library and all building lobbies.

Should you forget your mask, there may be a disposable paper mask available in the classroom/lab for your use. If not, your instructor will ask you to return to your room to retrieve your mask. Physical distancing practices will also be in effect. Your instructor may also ask for student volunteers who are willing to take a few minutes to spray cleaning solution on classroom surfaces when class concludes. Should you not wear your mask appropriately in class, your instructor will remind you to mask appropriately. Students who do not mask appropriately may be asked to not attend class (and will be counted absent). Multiple absences of this nature may result in an Academic Alert and may impact your grade in the course.

If you are approved by Student Services for accommodations for virtual learning due to COVID-19, your instructor will be notified via the COVID-19 Dashboard, and you will receive information from your instructor about virtual learning during your isolation/quarantine period. Please be patient as there may be some delay between you being notified of quarantine/isolation, placed on the COVID dashboard, and contacted by your instructor about your status. Students not approved (or not awaiting approval) for virtual learning should follow normal class attendance policies.

Major assessments must be completed in-person on the scheduled date unless prior approval for online/remote (or delay) has been approved by Student Services due to isolation, quarantine, or other approved medical reasons.

Tentative Schedule

I aim to build a dynamic classroom; as such, the schedule below may be changed as the semester progresses. Any changes will be reflected here and in the course notes.

Week Day Topic Work Due
1 15-Jan Course intro
2 18-Jan 0.2 Statements and Implications
2 20-Jan 0.2: Predicates and Quantifiers Edfinity Demo assignment
2 22-Jan 0.3: Sets and Relationships Quiz; Edfinity 0.2
3 25-Jan 0.3: Operations on Sets
3 27-Jan Relations and Equivalence Relations Portfolio Problem 0; Edfinity 0.3
3 29-Jan Relations and Equivalence Relations Quiz
4 1-Feb 0.4: Functions M4HF Reflection: Chs. 1-5
4 3-Feb Reading discussion; 0.4: Functions Portfolio Problem I
4 5-Feb 0.4: Functions Quiz
5 8-Feb 1.1: Additive and Multiplicative Principles Edfinity 0.4
5 10-Feb 1.1: Counting with Sets; PIE
5 12-Feb 1.2: Binomial Coefficients I Quiz; Edfinity 1.1
6 15-Feb No class
6 17-Feb 1.2: Binomial Coefficients II Portfolio Problem II
6 19-Feb 1.3: Combinations and Permutations M4HF Reflection: Chs. 6-7; Quiz; Edfinity 1.2
7 22-Feb 1.4: Combinatorial Proofs Edfinity 1.3
7 24-Feb 1.4: Combinatorial Proofs
7 26-Feb 1.5: Stars and Bars Quiz
8 1-Mar 1.6: Advanced Counting with PIE Edfinity 1.5
8 3-Mar Catchup and Review Edfinity 1.6
8 5-Mar Midterm I
9 8-Mar 2.1: Sequences
9 10-Mar 2.2: Arithmetic and Geometric Sequences Portfolio Problem III; Edfinity 2.1
9 12-Mar 2.3: Polynomial Fitting Quiz; Edfinity 2.2
10 15-Mar 2.4: Recurrence relations Edfinity 2.3
10 17-Mar 2.5: Induction I Edfinity 2.4
10 19-Mar 2.5: Induction II Portfolio Problem IV; Quiz
11 22-Mar 3.1: Propositional Logic I M4HF Reflection: Chs. 8-11; 2.5 Homework
11 24-Mar Reading discussion; 3.1: Propositional Logic
11 26-Mar 3.2: Direct Proofs Quiz; Edfinity 3.1
12 29-Mar 3.2: Proofs by Contrapositive/Proofs by Contradiction Portfolio Problem V
12 31-Mar 3.2: Other Proof Techniques
12 2-Apr 4.1: Intro to Graph Theory Quiz; Edfinity 3.2
13 5-Apr 4.1: Intro to Graph Theory Portfolio Problem VI
13 7-Apr No class
13 9-Apr 4.2: Trees I Quiz; Edfinity 4.1
14 12-Apr 4.2: Trees II
14 14-Apr 4.3: Planar graphs Portfolio Problems VII-VIII
14 16-Apr Portfolio work day Edfinity 4.2
15 19-Apr 4.4: Coloring Edfinity 4.3
15 21-Apr 4.5: Euler Paths and Circuits M4HF Reflection: Chs. 12-13, Epilogue; Edfinity 4.4
15 23-Apr 4.6: Matching in Bipartite Graphs Quiz; Edfinity 4.5
16 26-Apr Reading discussion; 5.1: Generating Functions Portfolio Problem IX
16 28-Apr 5.1: Generating Functions
16 30-Apr Midterm II
Finals 6-May, 1:15pm Final Draft of Portfolio