mindmap
root((CSCI 0200))
)**Module 1**(
(Logic)
(Propositional logic)
(Boolean algebra)
(Circuit design)
(Sets)
(Set Operations)
(Logical quantifiers)
)**Module 2**(
(Relations)
(Functions)
(Equivalence Relations)
(Proof Techniques)
(Direct)
(Indirect)
(Contradiction)
(Induction)
(Weak)
(Strong)
)**Module 3**(
(Counting)
(Sum and product principles)
(Permutations and combinations)
(Combinatorial proofs)
(Recurrence Relations)
(Asymptotics)
(Divide and combine)
)**Module 4**(
(Probability)
(Distributions)
(Conditioning)
(Random variables)
(Expectation)
(Graphs)
(Special graphs)
(Trees )
(Cycles)
(Algorithms)
Syllabus
Welcome to CSCI 0200: Math Foundations of Computing! In this course, we’ll study how to think about computation using mathematics. Historically, computer science emerged as a subfield of mathematics before “growing up” into its own discipline. Math remains one of the fundamental tools we use to solve advanced problems. You might know to expect mathematical reasoning in core theory courses like Theory of Computation (CSCI 0301) and Algorithms and Complexity (CSCI 0302), but you’ll also draw on mathematical thinking in courses like Artificial Intelligence (CSCI 0311), Programming Languages (CSCI 0313), Network Science (CSCI 0442), Machine Learning (CSCI 0451), and Computer Graphics (CSCI 0461).
Core Learning Objectives
- You will solve problems using logic, set theory, recurrence relations, combinatorics (counting), graphs, and discrete probability.
- You will apply the above topics to complex problems in computer science and beyond.
- You will write mathematical proofs that allow you to be certain of a mathematical fact or a statement about an algorithm.
- You will perform computational experiments and contextualize your findings against mathematical theory.
- You will develop habits of reflection, collaboration, and persistence for learning theoretical topics.
Tentative Sequence of Topics
Weeks 1-3: Course introduction, logic, set theory
Weeks 4-6: Proof techniques, induction, functions, relations
Weeks 7-9: Counting, recursion, analysis of algorithms
Weeks 10-13: Graphs, probability
Our detailed schedule includes prep, warmup problems, and due dates for assignments. I commit to ensuring that this schedule is always up to date at least two weeks ahead of the present day.
Logistics and Key Highlights
| Scheduled Class Periods |
Mondays, Wednesdays, and Fridays 75 Shannon Street, Room 203 Section A: 8:40am-9:30pm Section B: 9:45pm-10:35pm |
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| Instructor |
Phil Chodrow
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| Assistant Laboratory Instructor |
Smith Gakuya
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| Course Assistants (schedule) |
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| Key Highlights |
Our detailed course schedule contains information on required readings, warmup problems, and other assignments. I encourage you to call me “Prof. Phil” or “Phil.” “Professor Chodrow” is also fine if that’s what’s most comfortable for you. This is a flipped class. This means that we’ll introduce new content with videos, readings, and warmup problems ahead of class time. During class time, we’ll discuss questions, work complex examples, and try some practice problems. It’s very important for you to budget 1.5-2 hours for prep before each class. This class uses standards-based-grading. You don’t have an “average” in this class, just a series of checkboxes you can tick off as you complete and receive feedback on assignments. The boxes you tick off determine your final grade. I anticipate that 9-12 hours of total effort each week (including class time) will be sufficient for most students to earn a B or above. Our classroom is a screen free zone except during Lab activities that involve coding. You are very welcome to email me about matters related to your experience in the course, but please do not email me math questions. Instead, post your questions on EdStem. Student Hours are your time to come chat with me about course content. I want to see you in Student Hours. Attendance and participation are required aspects of this course which have an impact on your grade. |
Class Format
Flipped Class
CSCI 0200 is a flipped classroom. This means that our scheduled class periods will primarily be time for you to actively practice and get feedback. Your first introduction to new material will be through assigned readings, videos, and warmup problems.
- On Mondays and Wednesdays, you will watch videos, complete readings, and do warmup problems before class. In class, we’ll discuss some of your questions from the warmups and work together on practice problems.
- On most Fridays, you will watch videos, complete readings, and do warmup problems before class. During class, you’ll work in groups on Lab assignments. You’ll complete the Lab assignments outside of class and turn them in.
- On four Fridays during the semester, you will complete a quiz in which you demonstrate your understanding of our Learning Targets.
Course Activities
CSCI 0200 is divided into four “modules,” each of which is three weeks long. Here’s the rough schedule that you can expect from a module:
gantt
title A CSCI 0200 Module
axisFormat %A
tickInterval 1day
section Week A
Prep, warmup :active, a1, 2014-01-06, 1d
Class :2014-01-06, 1d
Prep, warmup :active, a2, 2014-01-08, 1d
Class :2014-01-08, 1d
Prep, warmup :active, a1, 2014-01-10, 1d
Lab A :a3, 2014-01-10, 1d
section Week B
Prep, warmup :active, a1, 2014-01-06, 1d
Class :2014-01-06, 1d
Prep, warmup :active, a2, 2014-01-08, 1d
Class :2014-01-08, 1d
Prep, warmup :active, a1, 2014-01-10, 1d
Lab B :a3, 2014-01-10, 1d
Lab A due :done, b3, 2014-01-10, 1d
section Week C
Prep, warmup :active, b1, 2014-01-06, 1d
Class :2014-01-06, 1d
Prep, warmup :active, b2, 2014-01-08, 1d
Class :2014-01-08, 1d
Lab B due :done, b3, 2014-01-10, 1d
Quiz :crit, done, c3, 2014-01-10, 1d
Most days, you’ll prepare with videos and readings, and then complete warmup activities. These activities will prepare you for either class (practice, discussion), or lab. We’ll have our quiz roughly every third Friday.
Rationale
The overall format of CSCI 0200 is designed to help you apply the ideas and skills of the course to progressively higher stages of Bloom’s taxonomy of cognition (Anderson and Krathwohl (2001)).
Anderson, Lorin W, and David R Krathwohl. 2001. A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives: Complete Edition. Addison Wesley Longman, Inc.
Before Class: Warmups
Warmups are here to help you remember and understand new material. Each day, you’ll prepare for class by watching videos, completing readings, and solving a small number of relatively short warmup problems. You’ll then submit your solutions on Gradescope. You’ll get feedback on your solutions from our graders. Your warmup solutions are expected to show effort but are not graded for correctness.
Class on Mondays and Wednesdays: Questions, Activities, and Discussion
By the time you’ve completed the warmups and made it to class, I’m expecting that you have already made some effort to remember and understand the new material for that day. During class time on Mondays and Wednesdays, we’ll usually start with some time to discuss questions you might have from the day’s readings, videos, or warmups, to help build your understanding. Then, we’ll usually have time to work on problems in groups, or to further discuss topics. These activities will help you build your abilities to apply the material and use it to analyze more complicated problems.
Classes are Screen Free Zones
There is now a considerable amount of research showing that the use of screens (laptops, tablets, and especially phones) in learning environments is overall detrimental to classroom community engagement and retention of learning. I encourage you to take notes in class by hand, on paper—this is known to be better for you (Van Der Weel and Van Der Meer 2024)!
If you like digital notes, take a photo of your handwritten notes and include it in your digital notebook. Yes, even writing with a stylus on a tablet is not as good as writing with a pencil and paper (Umejima et al. 2021).
Umejima, Keita, Takuya Ibaraki, Takahiro Yamazaki, and Kuniyoshi L. Sakai. 2021. “Paper Notebooks Vs. Mobile Devices: Brain Activation Differences During Memory Retrieval.” Frontiers in Behavioral Neuroscience 15 (March): 634158. https://doi.org/10.3389/fnbeh.2021.634158.
Van Der Weel, F. R. (Ruud), and Audrey L. H. Van Der Meer. 2024. “Handwriting but Not Typewriting Leads to Widespread Brain Connectivity: A High-Density EEG Study with Implications for the Classroom.” Frontiers in Psychology 14 (January): 1219945. https://doi.org/10.3389/fpsyg.2023.1219945.
Students whose LOAs specify the use of devices for note-taking are exempt from this policy.
Quizzes (Every Third Friday)
On quizzes, you’ll demonstrate your ability to remember, understand, and apply key ideas and skills. We’ll have four quizzes throughout the semester. On each quiz, there will be one problem related to each of the learning targets that we have introduced in the course so far. We’ll introduce new Learning Targets on each quiz. There will be a total of 20 Learning Targets throughout the semester.
You are not expected to complete every problem on every quiz. Correctly completing 3-4 problems on each quiz is a good pace and positions you well for the final exam.
Labs (Every Other Friday)
In labs, you’ll build your abilities to analyze , evaluate, and create using the tools and topics from this class. We’ll have lab assignments in 7 weeks (skipping the weeks in which we have quizzes). You’ll start on lab assignments in groups in class on Fridays. You’ll complete the remaining problems and prepare your report, submitting the entire result as a typed PDF.
Labs are due one week after the day we start them in class.
You may continue to work on your report with classmates, but your report should be written by you and reflect your own understanding of the material. A good heuristic: discussion and work at the whiteboard is great to share, but typed solutions or code should not be shared.
Labs are assessed on a 4-point rubric. After receiving your assessment on your lab report, you may revise and resubmit your report for a higher assessment.
Assessment and Grades
Your Final Grade
Your final grade in the course is primarily determined by the bundle of Learning Targets and Lab assessments you achieve by the end of the course, according to the following table. Learning Targets are graded on a Satisfactory/Not Yet Satisfactory (S/NS) rubric, while Labs are graded are graded on an Excellent, Satisfactory, Revise, or No Learning Shown (EMRN) rubric.
To earn the given grade, you need to meet all requirements for both Learning Targets and Labs.
| Tier | Learning Targets (out of 20) |
Labs (out of 7) |
|---|---|---|
| A | At least 18 |
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| B | At least 14 |
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| C | At least 12 |
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| D | At least 10 |
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I reserve the right to modify this table, but only in ways that make it easier to achieve each grade tier.
Partial Completion
When you completely meet both requirements for one tier and completely meet one requirement for a higher tier, you earn the “+” version of the lower tier grade. For example, you may completely meet the requirements of a B on Learning Targets and completely meet the requirements of an A on Labs. In this case, the lower tier is a B and you earn the “+” version, so: a B+.
Warmups
Warmups are not graded for correctness. The two grades you can receive are “Complete” or “Incomplete/Missing.” A grade of Complete means that you made good effort on the problems and that your attempt demonstrates at least partial understanding of the reading and videos. Most days, 1.5-2 hours of prep time will usually be sufficient for you to complete the readings, videos, and warmups.
Yes, I know, this is a lot of prep. On the other hand, the lab reports are your only homework assignments.
Quizzes
Quiz problems are assessed as Satisfactory (S) or Not Yet Satisfactory/Incomplete (NS). To earn an S on a quiz problem, you must complete the entire problem correctly, modulo minor errors unrelated to the learning goals of the course (like arithmetic typos).
There is no partial credit given on quiz problems. Solutions with minor errors that are otherwise demonstrate learning earn an S, while solutions that demonstrate important misunderstandings (or are not attempted) earn an NS.
Once you have earned an S on a quiz problem, you have completed the corresponding Learning Target. You never need to attempt another quiz problem corresponding to that target. So, if you earn an S on an L3 problem on Quiz 1, you should not try an L3 problem on Quiz 2. Although you are going to have many more than this number of problems placed in front of you, it is sufficient to earn an S on a total of 18 problems in order to earn an A in the course.
Labs
Submitted lab reports can receive one of four assessments:
Here is some more detail on lab grades.
- Excellent (E): the lab exhibits complete understanding of the material and meets all requirements for mathematical content, coding, and expository writing. This report could serve as an exemplary solution for the assignment.
- Meets Expectations (M): the lab exhibits almost complete understanding of the material and meets most technical requirements. This report suggests that you have room to improve, but you understand the material well enough that you may potentially find it a better use of your time to move on.
- Needs Revision (R): The lab exhibits some understanding of the material, but there are major issues that should be fixed before moving on.
- Not Completed (N): The lab isn’t really complete enough to demonstrate understanding of the material.
Revising Labs
After receiving feedback on your lab report, you may revise it in response to the feedback and resubmit it for a higher assessment. You can do this once for each lab report. The due date for revisions will depend on exactly when our grading time can finalize the first round of assessments, but will usually be about two weeks after you get your first round of feedback.
Participation and Attendance
Participation and attendance are fundamental to the operation of this course and to our success as a learning community. For this reason, participation and attendance are graded components of the course.
Every student begins the class with six tokens. You can use a token to:
- Miss one class period.
- Skip a warmup assignment.
Arriving to class more than 5 minutes late counts as a “missed” class and therefore uses a token.
Note that if you use a token to skip a lab period, you are excused from attendance but still must arrange to complete and submit the lab.
- 7-9 misses: -1/3
- 10-12 misses: -2/3
- 13-15 misses: -1
- etc.
After you have used all your tokens, missed class periods and warmup assignments begin to count against your final grade according to the table on the left. For example, missing a total of 11 warmups or class periods combines would reduce an A to a B+.
Late Work Policies
Warmups
Extensions are never given on warmups unless under guidance from the DRC. Remember that you may use some of your 6 participation passes for warmups.
Labs
For each lab report, you may receive an extension of up to 3 days (72 hours) from the original due date. To do so, you should fill out this modified due date request form. You can count on receiving such an extension without a negotation if you:
- Request the extension at least one day (24 hours) in advance of the original due date.
- Write short but thoughtful responses to the questions posed in the form.
Labs that are turned in after the due date (or possibly the extended due date) will still be accepted and assessed. However, these late lab reports will count as your second submission, and the assessment you receive on that lab report will be final.
Quizzes
You can reschedule quizzes under the following circumstances.
- You have an emergency related to your health, mental health, or wellbeing, or the health, mental health, or wellbeing of your loved ones. A Dean’s Note is usually expected in these cases, but for fast-moving situations you can let me know directly.
- You are traveling for a major athletic event. In this case, you must notify me at least two weeks in advance. Please notify me by email and cc your coach. Usually, athletic conflicts will result in you taking the quiz on the expected day under the proctoring of your coach.
Inclusion, Access, and Participation
I commit to an inclusive, accessible, participatory, and safe classroom for CSCI 0200.
Disabilities and Clearing Barriers
For legal reasons, I am prohibited from offering accommodations to students who do not present letters of accommodation from the DRC. So, get a letter if you need it!
If any aspect of this course raises barriers to your full and equitable participation, it is my job to clear those barriers. A common way in which barriers arise is from unintentional failure to design for all students, including students with disabilities. I’ve done my best, but still may have fallen short! If you have a documented disability, please send me your letter of accommodation from the Disability Resource Center as soon as possible. You do not need to describe your disability or justify your accommodations. I will incorporate your accommodations and work to clear learning barriers to the best of my ability.
If you believe that you may have a disability, please contact the Disability Resource Center as soon as possible. The DRC works with students confidentially and never discloses disability-related information to faculty without your permission.
Academic Support
No matter who you are, it’s normal to feel challenged by your courses. We have many academic resources to support your success in CSCI 0200. I strongly encourage everyone to make use of all of these resources.
- My Student Hours are time for you to come talk with me about any aspect of the course. We’ll usually hold Student Hours in the big lounge outside Room 224 (the one with the windows).
- Experienced CS students hold Peer Help hours some weekday evenings. These sessions are great times for you to work on Warmup problems (before class) and lab reports. You can also ask general questions about course content and connect with other students.
- Our Assistant in Instruction (ASI) is Smith Gakuya. Smith holds regular Student Hours many days, and is prepared to help you in CSCI 0200. Smith can also help you arrange tutoring for long-term academic support.
- EdStem is our online Q&A forum. It’s the best place to ask questions at irregular hours. It’s a good idea to check EdStem frequently, because your question may already have been answered there!
Classroom Environment
Inclusion, access, and participation are collective projects. I expect all students to contribute to a healthy course environment.
We embrace diversity of age, background, beliefs, race, ethnicity, gender, gender identity, gender expression, national origin, religious affiliation, sexual orientation, and other apparent and non-apparent axes of identity. Discrimination is not tolerated in CSCI 0200. Discriminatory speech or acts may lead to engagement with the Community Standards Office.
You deserve to be addressed in the manner that reflects who you are. I welcome to tell me your pronouns and/or chosen name at any time, either in person or via email. I expect all students to address each other according to their expressed gender markers, and commit to doing the same.
You deserve to fully and equitably participate in our learning environment. I commit to ensuring that the materials and assessments in this course are accessible to all students, and I welcome feedback on where I can do better. Middlebury’s Disability Resource Center can help you remove barriers to learning in this and other courses.
You deserve a learning environment free from gender-based discrimination, sexual harassment, sexual assault, domestic violence, dating violence, and stalking. If you experience these behaviors or otherwise know of a Title IX violation, you have many options for support and/or reporting. Middlebury’s Civil Rights and Title IX Office (CRTIX) can help you navigate your options. Please be aware that I am a Responsible Employee, which means that I am required by the College to report incidents of sexual harassment or sexual violence to CRTIX. There are resources for emotional and mental health care, advocacy, and academic support listed here, some of which are confidential.
Collaboration and Academic Integrity
The guiding principle of Middlebury’s Honor Code is that work you represent as your own must reflect your learning and understanding. Submission of work that does not reflect your learning and understanding may lead to grade penalties or Honors proceedings.
Collaborating with Integrity
Collaboration is welcome in some settings in this course. In all instances of collaboration, you should acknowledge your collaboration partner(s) and describe their contributions as part of your assignment submission.
- Warmups: collaboration is discouraged because I think warmups are useful as practice for the quizzes. If you do collaborate on warmups, you should acknowledge your collaboration partner in your submission.
- Labs: collaboration is encouraged (and partially mandatory). You’ll start labs in collaboration groups. You’re free to complete the assignment in your groups, or to complete the assignment on your own. All students should turn in an individual submission that reflects their own understanding and which acknowledges the contributions of their collaboration partners.
- Quizzes: collaboration is prohibited.
- In-class activities: collaboration is encouraged (and sometimes mandatory).
- General study: collaboration is encouraged!
Generative Artificial Intelligence
Generative artificial intelligence, especially large language models (LLMs), have rapidly transformed the ways that we write, research, explore, play, and solve problems. The purpose of this course is to support you in deeply learning a topic. Can using LLMs help? We are about three years into the “LLM era,” and there is now an emerging body of evidence about the impact of LLM usage on learning. While the story is incomplete and changing, the evidence available suggests that use of LLMs can be double-edged.
If you are curious about how students at Middlebury are using LLMs, some faculty in our Department of Economics recently conducted a survey analysis with many interesting findings.
LLMs Could (Maybe?) Help Learning
LLMs enable many processes related to learning at an unprecedented level of scale and personalization. With appropriate prompting, LLMs can generate practice problems, offer multiple explanations of concepts, identify and explain errors in your own reasoning, and offer personalized tutor-like experiences. Companies like Khan Academy are racing to develop LLM-powered learning platforms, and some schools are designed with LLMs at the center of the learning experience. It is useful to remember that the primary incentive for many of these efforts is to make money for shareholders rather than the follow the best available evidence or practices in education.
That said, there is very little scholarly evidence that the use of LLMs is ever actually beneficial to learning. It may be that LLMs tend to enable learning the same material while saving time, but evidence here is also lacking.
LLMs Can Harm Learning
We all know that a student using an LLM can generate solutions to math problems faster than a student working purely by hand. However, a recent article suggests that the first student is going to retain less mathematical understanding and ultimately perform worse on tests and other tasks that require them to show their skills unassisted by AI (Bastani et al. 2025). Worse still, that student is unlikely to understand this impact: students who used LLMs and were free to request solutions to problems in the study didn’t believe that they performed worse on assessments, even when they did.
Bastani, Hamsa, Osbert Bastani, Alp Sungu, Haosen Ge, Özge Kabakcı, and Rei Mariman. 2025. “Generative AI Without Guardrails Can Harm Learning: Evidence from High School Mathematics.” Proceedings of the National Academy of Sciences 122 (26): e2422633122. https://doi.org/10.1073/pnas.2422633122.
The authors of this article offer a simple hypothesis:
Asking LLMs for the answer to a problem prevents you from the learning which that problem is intended to offer you.
Students who instead use LLMs in ways that emphasize working through steps, answering questions along the way, and avoiding revealing the full solution appear to have retained mathematics understanding comparably to those who used no LLMs at all. Even here, however, students were misled: students using the LLM with “tutoring guardrails” thought they performed much better than they actually did. So, in this study, even best-case usage of LLMs was neutral for learning and harmful for self-awareness.
Similarly, there is some preliminary evidence that LLMs can make you feel faster at completing tasks (like coding) even when they are actually making you slower (Becker et al. 2025). This is an active area of exploration, with much more research likely to come soon.
Becker, Joel, Nate Rush, Elizabeth Barnes, and David Rein. 2025. “Measuring the Impact of Early-2025 AI on Experienced Open-Source Developer Productivity.” arXiv. https://doi.org/10.48550/arXiv.2507.09089.
In This Class
My thinking about generative AI in this course stems from a simple goal:
I want you to grow in your ability to think mathematically.
This means that I will be encouraging learning practices which help you learn, and giving you feedback and grades based primarily on your learning.
I’m fully supportive of uses of generative AI which promote your practice and learning in mathematical reasoning. I am not supportive of uses of generative AI which outsource your practice and learning to the model; that’s counterproductive to your growth.
The following policies flow from this simple goal.
Policies
Quizzes and the final exam are in-class assessments which allow you to demonstrate your learning of the course material. Since I’m interested in your learning, use of LLMs or any other forms of aid not provided by me is prohibited.
Lab reports are an opportunity for you to demonstrate your ability to write careful mathematical proofs and relate mathematics to computation. Because your ability to write mathematics is a fundamental learning objective of the course, I’m interested in reading your writing. For this reason, you are prohibited from using LLMs to generate or edit text or mathematics for Lab Reports. Representing an LLM’s writing as your own is a violation of academic integrity and a waste of everyone’s time.
You may be tempted to run your proof through an LLM to make it sound “more professional.” Please do not do this! I’d much rather read your own writing even if it’s a smidge less polished.
On the other hand, Lab reports also include some coding problems. Because coding is not a primary learning objective of the course, you are permitted to use LLMs for reasonable assistance with coding problems. I know that not everyone is coming into this class with background in Python programming, and the primary learning objective of the course is not code syntax. That said, you are responsible for what you turn in; if the LLM generates something that’s not functioning correctly, it’s your job to fix it. If you use an LLM in any way as part of your lab report, please cite your source right below your list of coauthors and explain in comments which parts of the code were generated with LLM assistance.
Warmup problems are primarily designed for you to test your understanding of the prep materials for the day and to help you build the skills that you’ll demonstrate on quizzes. Because of this, you are strongly discouraged from using LLMs on warmup problems—I won’t stop you, but you’re likely to harm your performance on the quizzes where it counts.
Remember that warmup problems are graded only for completion, not correctness.
You are encouraged to use LLMs for general studying outside of class. For example, LLMs can be a very helpful way to generate practice problems which are similar to problems I have already supplied you. It can also be helpful to get hints and problem-solving tips from an LLM, keeping in mind that asking for solutions is counterproductive to your learning. You should also keep in mind that all LLM outputs (including problem statements, hints, and solutions) have a chance of being flawed, misleading, or incorrect.
More on LLMs
How Do They Work?
LLMs use next-token prediction to predict the next entries in a sequence of text by using the previous entries. This enables them to mimic human-produced text. So, if you saw the sequence “I love Math Foundations of _____”, you might guess that the next word might be “Computing” and that it’s probably not “Pineapples.”
LLMs are trained using reinforcement learning with human feedback (RLHF) to produce sentences that are not just realistic but also helpful, pleasant, nonoffensive, or accurate. They do this using a multistage training process that involves humans rating the quality of candidate texts. RLHF explains the tendency of many LLMs to be highly positive–even to the point of sycophantic–in how they interact with us.
Beyond This Course
General Advice
I am always happy to talk with you about your future plans, including internships, research opportunities, and graduate school applications. Because I am a creature of the academy, I am less knowledgeable about industry jobs, although you are welcome to ask about those too. You can drop in during Student Hours or email me to make an appointment.
© Phil Chodrow, 2025