This syllabus is subject to change based on specific class needs, especially the schedule. Significant deviations will be discussed in class. Individual exceptions to the policies and schedule are granted only in cases of true emergency. Please make arrangements with me if an emergency arises.
An introduction to proof-based mathematics through the study of key areas of discrete mathematics. This course serves as an introduction to higher-level mathematics and advanced coursework in math. Students will hone their mathematical reasoning skills, learning to express and work with precise mathematical definitions. A strong emphasis is placed on developing the skills necessary to communicate mathematical results.
Topics covered in this course include the the core definitions and theorems from set theory, mathematical logic, and combinatorics. In this context students will explore ideas such as mathematical induction, functions, and relations and the proof techniques of direct proof, contrapositive proof, proof by contradiction, and disproof.
The course textbook will be:
The weekly workload for this course will vary by student and by week but should be about 12 hours per week on average. The following table provides a rough estimate of the distribution of time over different course components for a 16 week semester, as well as detailing the type, amount, and relative value of all assignments.
| Category | Amount | Final Grade Weight | Time/Week (Hours) |
|---|---|---|---|
| Lectures | 41 | 10% (Participation) | 2.5 |
| Problem Sets | 35–45 | 35% | 6 |
| Reading/Study | - | - | 3.5 |
| Exams | 5–8 | 55% | - |
| 12 |
Much of the material builds on previous material; hence, exams are naturally cumulative. Each exam is weighted equally.
Your lowest 3 problem set scores will be dropped, i.e., your final problem set grade is the average of all except the two smallest. Your lowest exam score is also dropped.
Your participation grade is based on a variety of activities. During class I will often make use of the Socrative app, so you’ll need to install this on your phones. Participating in Socrative questions and with in-class group activities is required for a decent participation grade; an A includes asking questions either in class or in office hours.
An additional portion of your participation grade is based on your problem set presentations. Every day that a problem set is due, one or more students will be randomly selected to present their solution to a portion of the assignment. You will be graded based on preparation and the thoroughness of your explanations, NOT on correctness, although you should of course strive for correctness. Students taking late days will be required to leave the classroom during these presentations. You must inform me BEFORE class if you are taking late days to avoid being randomly selected to present. Otherwise, if you are randomly selected to present but have not done the assignment, you will receive a 0.
Your final grade is based on a weighted average of particular assignment categories. You can estimate your current grade based on your scores and these weights. You may always visit the instructor outside of class to discuss your current standing. Assignments and final grades use a standard grading scale shown below and will not be curved except in rare cases when deemed necessary by the instructor.
This courses uses a standard grading scale. Assignments and final grades will not be curved except in rare cases when its deemed necessary by the instructor. Percentage grades translate to letter grades as follows:
| Score | Grade |
|---|---|
| 94–100 | A |
| 90–93 | A- |
| 88–89 | B+ |
| 82–87 | B |
| 80–81 | B- |
| 78–79 | C+ |
| 72–77 | C |
| 70–71 | C- |
| 68–69 | D+ |
| 62–67 | D |
| 60–61 | D- |
| 0–59 | F |
You are always welcome to challenge a grade that you feel is unfair or calculated incorrectly. Mistakes made in your favor will never be corrected to lower your grade. Mistakes made not in your favor will be corrected. Basically, after the initial grading your score can only go up as the result of a challenge*.
You are always welcome to challenge a grade that you feel is unfair or calculated incorrectly. Mistakes made in your favor will never be corrected to lower your grade. Mistakes made not in your favor will be corrected. Basically, after the initial grading your score can only go up as the result of a challenge.
Late Assignments: You have each been allotted a total of 5 late days. You may apply these to any homework or programming assignment (NOT exams, labs, or reading assignments) you see fit and turn in your solutions with no penalty. Each late days gives you exactly 24 extra hours from the original due date and time. However, you may use at most 2 late days on any individual assignment. The whole point here is to give you some flexibility that allows for things like illnesses, long trips, and the like. I am unlikely to grant further extensions. You must notify me if you will use late days, and how many, BEFORE the assignment is due. Late assignments (beyond any applied late days) will be subject to a grade reduction at my discretion. While you should expect a reasonable penalty for late work, know that I will NEVER give you a 0 for late work as long as it is turned in before the final exam.
Academic Dishonesty: Monmouth College’s official policy on academic dishonesty can be found here. You are responsible for reading and complying with that policy.
In this course, any violation of the academic honesty policy will have varying consequences depending on the severity of the infraction as judged by the instructor. Minimally, a violation will result in an “F” or 0 points on the assignment in question. Additionally, the student’s course grade may be lowered by one letter grade. In severe cases, the student will be assigned a course grade of “F” and dismissed from the class. All cases of academic dishonesty must be reported to the Associate Dean who may decide to recommend further action to the Admissions and Academic Status Committee, including suspension or dismissal. It is assumed that students will educate themselves regarding what is considered to be academic dishonesty, so excuses or claims of ignorance will not mitigate the consequences of any violations
Collaboration: We encourage you to make use of the resources available to you – it is fine to seek help from a friend, tutor, instructor, internet, etc. However, copying of answers and any act worthy of the label of “cheating” is never permissible! It is understandable that when you work with a partner or a group that the resultant product is often extremely similar. This is acceptable but be prepared to be asked to defend your collaborations to the instructor. You should always be able to reproduce an answer on your own, and if you cannot you likely do not really know the material.
One way to collaborate effectively is to avoid taking careful notes during a collaboration session. Discuss the material and sketch out possible solutions on a whiteboard. When you have finished, take a break and then write up your solutions without any help from notes or pictures from the study session. This not only helps avoid violations of academic dishonesty, it also improves your retention of the material!
When assignments are meant to be done in groups, you will be directed to turn in one set of solutions per group. Otherwise, each student must turn in an assignment representing their own work.
Electronic Devices: Do not use your phone or other devices in class except where necessary. Any computer or tablet usage should be related to the course. If a device is not being used for Zoom or Socrative it should be put away and turned on silent. Other usage is rude and distracting to others.
General Expectations: In short, I expect you to be respectful of others and take responsibility for your own learning. You are here to learn, so work hard and be professional.
Just attending class is not sufficient to truly learn the material. Read the text, use the resources available at Monmouth College, and go beyond the material.
If you miss class, you are responsible for everything covered on that day. College is, in some sense, your job. Take pride in creating quality work. Staple your assignments, label problems, and present your answers neatly and orderly.
Your job is to convince me that you have learned the material – show your work! Even if you do not know a particular answer, guide me through your thought process.
The following tentative calendar should give you a feel for how work is distributed throughout the semester. Assignments and events are listed in the week they are due or when they occur. This calendar is subject to change based on the circumstances of the course.
Sections marked with an asterisk (*) may be skimmed.
| Date | Topic/Reading | Assignment |
|---|---|---|
| Wed 08/24 (Week 1) | Logistics, Sets (1.1) | |
| Fri 08/26 | Products (1.2), Subsets (1.3) | PS01: §1.1 (2,6,14,20,26,30,36,48) |
| Mon 08/29 (Week 2) | Set Operations I (1.4-1.5) | PS02: §1.2 (2,4,12,20), §1.3 (6,10,12,14) |
| Tue 08/30 | Presentations/Examples | |
| Wed 08/31 | Set Operations II (1.6-1.7) | PS03: §1.4 (2,8,10,14,18) §1.5 (2,4abcfg,8) |
| Fri 09/02 | Indexed Sets (1.8, 1.9*) | PS04: §1.6 (2,6), §1.7 (4,8) |
| Mon 09/05 (Week 3) | Statements, And,Or,Not (2.1-2.2) | PS05: §1.8 (2,4,6,8) |
| Tue 09/06 | Exam Review | |
| Wed 09/07 | PS06: §2.1 (4,6,8,10), §2.2 (2,4,8,10) | |
| Fri 09/09 | Exam 1 (Ch. 1) | |
| Mon 09/12 (Week 4) | Conditionals (2.3-2.4) | |
| Tue 09/13 | Exam 1 Solutions | |
| Wed 09/14 | Truth Tables, Equivalence (2.5-2.6) | PS07: §2.3 (2,4,6,10), §2.4 (2,4) |
| Fri 09/16 | Quantifiers (2.7) | PS08 |
| Mon 09/19 (Week 5) | English to Logic (2.8-2.9) | PS09: §2.7 (2,6) |
| Tue 09/20 | Exercises | |
| Wed 09/21 | Negation & Inference (2.10-2.12) | PS10: 2.9 (2,6) |
| Fri 09/23 | Multiplication Principle (3.1-3.2) | PS11: §2.10 (2,4) |
| Mon 09/26 (Week 6) | Exam Review | |
| Tue 09/27 | Exam 2 (Ch. 2) | |
| Wed 09/28 | Addition/Subtraction/Permutations (3.3-3.4) | |
| Fri 09/30 | Counting Subsets (3.5-3.6) | PS12: §3.2 (4,6,10), §3.3 (4,8), §3.4 (4,12) |
| Mon 10/03 (Week 7) | Direct Proof (4.1-4.3) | PS13: §3.5 (6,8,12), §3.6 (4,8) |
| Tue 10/04 | Exercises | |
| Wed 10/05 | Cases (4.4-4.5) | |
| Fri 10/07 | Proof by Contrapositive (5.1-5.3) | PS14: §4 (2,6,14) |
| Mon 10/10 (Week 8) | Exam Review | PS15: §5 (8,12,20) |
| Tue 10/11 | Exam 3 (Ch. 3,4,5) | |
| (Wed 10/12) | (Fall Break) | |
| (Fri 10/14) | (Fall Break) | |
| Mon 10/17 (Week 9) | Exam 3 Solutions | |
| Tue 10/18 | Proof by Contradiction (6.1) | |
| Wed 10/19 | More Proofs by Contradiction (6.2-6.4) | |
| Fri 10/21 | Proving Non-Conditional Statements (7.1-7.4) | PS16: §6 (2, 8, 10) |
| Mon 10/24 (Week 10) | Practice Exam Solutions | PS17: §7 (2, 10, 16) |
| Tue 10/25 | Exercises/Review | |
| Wed 10/26 | (No class) | |
| Fri 10/28 | Exam 4 (Ch. 6,7) | |
| Mon 10/31 (Week 11) | Exam 4 Solutions | |
| Tue 11/01 | Proofs with Sets (8.1-8.2) | |
| Wed 11/02 | 8.3-8.4 | |
| Fri 11/04 | 9.1-9.3 | PS18: §8 (4, 20, 28) |
| Mon 11/07 (Week 12) | (no class) | PS19: §9 (2, 6, 30) |
| Tue 11/08 | Review | |
| Wed 11/09 | Exam 5 (Ch. 8,9) | |
| Fri 11/11 | Induction (10.1) | |
| Mon 11/14 (Week 13) | 10.2-10.3 | PS20: §10 (2,10) |
| Tue 11/15 | Exam 5 Solutions | |
| Wed 11/16 | 10.4,10.5 | |
| Fri 11/18 | 11.1-11.2 | PS21: §10 (18, 32) |
| Mon 11/21 (Week 14) | 11.3-11.4 | |
| Tue 11/22 | Practice | PS22: §11.1 (2, 10, 14), §11.2 (2, 6, 8) |
| (Wed 11/23) | (Thanksgiving Break) | |
| (Fri 11/25) | (Thanksgiving Break) | |
| Mon 11/28 (Week 15) | 11.4 (Partitions), 11.5, 12.1 | |
| Tue 11/29 | 12.2 | PS23: §11.3 (2), §11.4 (4, 6) |
| Wed 11/30 | Review | |
| Fri 12/02 | Exam 6 (Ch. 10,11) | |
| Mon 12/05 (Week 16) | 12.4 | PS24: §12.1 (2,4,6,8), §12.2 (4,6) |
| Tue 12/06 | Exam 6 Solutions | PS25: §12.2 (10), §12.4 (4,8,10) |
| Wed 12/07 | Review | |
| Mon 12/12 8:00 AM | Exam 7 (Final) |
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