Math 131: Calculus I

Fall 2025

Department of Mathematics and Statistics, Grinnell College

Books and Resources

We will follow a textbook which I am particularly fond of:

(the schedule is based on the 9th edition; it is perfectly fine if you have an earlier edition, though you'll need to adjust the reading schedule accordingly. If you have trouble doing this, talk to me!)

There is an enormous amount of calculus textbooks and online resources out there, each with a slightly different point-of-view. I, for example, like Grant Sanderson's visualization of various ideas in calculus. If you are looking for supplementary resources, talk to me and I will be more than happy to recommend some!

Unsolicited advice: The textbook will be your best resource for this semester. I will assign reading for most class meeting and I strongly encourage you to complete it consistently; you can find the reading schedule here. Spending the time to digest the exposition in the textbook (highly non-trivial!) will help you glimpse the themes of calculus. This, in turn, will be your most reliable problem-solving tool. See, also, the Reading and Engagement section below.

Math Lab. The Math Lab, located in Noyce 2012, is a great place available for you to work with classmates and/or receive calculus help.

Course Goals and Basic Principles

Basic principles. The policies of this course are developed according to the following principles.

Course Goals. Topics covered in Math 131 are listed here. While covering these, I will expect students to meet the following course objectives.

Reading and Engagement

Throughout the semester, you will be assigned reading out of the textbook. Reading this text will better position you to follow, and actively engage with, classroom discussion. The schedule for readings can be found here.

To help you develop a habit of active reading, I will assign short reading assignments on Canvas that are due before most class meetings. Completing these assignments regularly is a necessary (but not sufficient) condition for collecting the reading/engagement part of your grade. Besides reading the text regularly and actively, I will expect you to attend class regularly, contribute to class discussions, and ask questions in office hours or via email.

On reading mathematics. There is a wealth of information and advice on how one might read mathematics out there. This is something many of the greatest mathematicians have written about; see, for example, the end of this blog post, or point 6. in Tim Gower's blog post.

Homework

General information. Homework will be assigned weekly and will be due on Mondays at noon; the schedule for assignments can be found here and on our Canvas page.

Submission. Most, if not all, homework assignments will be administered via WebAssign. The calendar on Canvas shows all the homework assignment deadlines, and you can access our class-specific WebAssign page here and through the navigation links on Canvas.

Expectations. All solutions submitted through WebAssign are expected to be your original work. That is, you did the mathematical work necessary to arrive at the result which you submit using appropriate resources (e.g. textbook, class notes, working with classmates etc. LLMs and online fora are never appropriate resources in our course.). For more on this and related academic honesty matters (e.g. citing collaborations), see the Academic Honesty section below. WebAssign allows you to store your thoughts and work on each question using the Show your Work feature. You are required to cite your collaborations using this features. I strongly encourage you to develop a system for storing your work on homework problems so that you may access it when studying later (e.g. use the "Show your Work" button, a dedicated notebook for problems with a labeling system, etc.).

On writing mathematics. The notion of well-written mathematics is subjective, but you probably have some sense of what you do and do not like to see in mathematical writing (from, say, reading your textbook). Many mathematicians have written on the subject; see these tips, this advice, or this guide, for example. A great source where many such writings are compiled is Terry Tao's blog post. Of course these sources might sometimes disagree, and that is OK. What you should ultimately focus on is the clarity of your argument and reasoning; not only for the benefit of the reader, but also for your own. The mathematical story in your own mind can be greatly clarified with good writing!

Quizzes

Quizzes will be given in class on Wednesdays and will be based on the previous week's material. There will be no make-up quizzes, but the two lowest quiz grades will be dropped.

Quiz corrections. Immediately after each quiz, a PDF of the quiz will be posted on Canvas (under Files). A week after each quiz, solutions will be posted. In the meantime, you will receive a grade for your quiz on Gradescope. Before solutions are posted, and on questions where you did not get all possible points, you may submit your own hand-written solution and a short reflection on how this new solutions compares to the one you initially presented. I will grade your new solution and you will get back up to 50% of the number of points you lost on the relevant question.

Expectations. Quizzes are closed-notes, closed books. No outside resources are permitted. Quiz corrections are expected to be individual; you may consult your textbook and course notes, but no other outside sources (including the Math Lab and sources listed in the Academic Honesty section below). Because solutions to the quiz will be posted on Canvas at that point, no corrections will be accepted any later than a week after the quiz was administered.

Exams

There will be three exams in this course: two midterms and a final. The dates/times are below. If you have a conflict with either one, please let me know as soon as possible.

Grading

Grades will be based on:

Your numerical scores will be used to assign you a letter grade based on a scale at least as generous as the following: [90, 100] earns an A- or better, [80, 90) earns a B- or better, [70, 80) earns a C- or better.

Academic Honesty

All students must adhere to Grinnell's academic honesty policy which can be found here.

Collaboration. You are encouraged to work with your classmates and to consult your textbook while brain-storming solutions and strategies to homework problems. That being said, you are expected to independently write your own solutions in your own words. If you do collaboratively work on a problem, you must indicate this on your solution. You can do this on WebAssign using the Show your Work feature. There are no formatting requirements for this; a simple "I worked on this problem with Omar" will suffice. Similarly, if you received help from a tutor at the Math Lab, you should cite this; something like "I worked with Omar from the Math Lab" will suffice.

Outside resources. It is not my intention that you will need to use outside books/papers or other resources to be able to complete any given assignment. That being said, I encourage you to consult the supplementary references listed above and other online sources (e.g. video lectures, notes, other textbooks, etc.) to help expand your understanding of material presented in class. You may not do any of the following:

Of course these resources are very useful when conducting independent research or study, but do not serve you (or your classmates) in a structured classroom as ours. David Speyer wrote a reasonable explanation of why this policy is in place, which can be found here

Accommodations

Disabilities. I encourage students with documented disabilities, including invisible disabilities such as chronic illness, learning disabilities, and psychiatric disabilities, to discuss appropriate accommodations with me. You will also need to have a conversation about, and provide documentation of, your disability to the Coordinator for Disability Resources, located on the ground level floor of Steiner Hall (641-269-3124).

Medical and counseling services. Grinnell offers an array of services to help support students' physical, mental, and social well-being. If you need help, please do not hesitate to reach out to Student Health and Wellness (SHAW). I am happy to work with you in making resonable accommodations to help you engage with our classroom as fully as possible; just let me know when the need arises.

Religious holidays. If a religious holiday conflicts with assigned class work or class meetings, please let me know as soon as possible and I will be more than happy to work with you to reach a mutual agreement on how to best allow you to attend to your religious responsibility while also meeting class requirements.

Title IX and pregnancy related conditions. Grinnell College is committed to compliance with Title IX and to supporting the academic success of pregnant and parenting students and students with pregnancy related conditions. If you are a pregnant student, have pregnancy related conditions, or are a parenting student who wishes to request reasonable related supportive measures from the College under Title IX, please email the Title IX Coordinator at titleix@grinnell.edu. The Title IX Coordinator will work with Disability Resources and your professors to provide reasonable supportive measures in support of your education while pregnant or as a parent under Title IX.

“The best thing for being sad," replied Merlin, beginning to puff and blow, "is to learn something. That's the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then — to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn.”

― T.H. White, The Once and Future King