Mike Pierce

Math5 – Precalculus Syllabus

I’m trying out a few atypical teaching techniques for this class due to the pandemic, and so I need to reserve the right to change things in this syllabus in case things go horribly awry. But assuredly, you’ll find any changes that I decide we have to make to be agreeable.


Purpose & Goals

The purpose of this class is to prepare you to learn calculus. Just like learning math in high school required you to be adept at arithmetic, it’s much easier to understand calculus if you are fluent in the mathematical language of functions, coordinate geometry, trigonometry, and modelling. In this class we’ll work towards developing that fluency.

In particular, after this course is complete you will be familiar with a library of common transcendental functions, including exponential functions, logarithms, and trigonometric functions. You will be skillful in algebraically manipulating these functions, and you will understand what those manipulations mean in terms of the geometry of the graphs of those functions. You will have developed fluency in trigonometry, and practiced the skill of using mathematics to model concrete situations. You will be able to write about mathematics, having a better understanding of the grammar and syntax of mathematical notation, and having developed skills in technical writing.

Logistics & Organization

The course starts on July 27. I’ll curate a list of readings, videos, and other resources to guide you through learning the course material. Each week there will be a page of homework posted that you should write up responses to and upload to Gradescope before 8am the following Monday:

I’ll be basing some of each week’s lecture sessions on what I read in your previous week’s write-ups. All the materials and links for the course will be posted at:


In discussion you will literally learn to develop your fluency in the topics of this class by learning to write about them.

Mike Pierce
Jonathan Alcaraz
Lecture Tues & Thurs, 8–10am
Discussion Tues & Thurs, 1–2:20pm
Mike’s Office Hours by Appointment
Jonathan’s Office Hours
Final Exam Saturday September 12, 1–3pm

If you cannot take the final at this data/time due to religious reasons, medical reasons, or a sudden emergency, just let me know before the scheduled final time and we’ll figure something out.

Homework & Grades

It’s an unfortunate thing that I, as your instructor, don’t get to simply teach you. As an employee of UC Riverside I’m also supposed to judge you and assign you a letter-grade for the university. But grades aren’t conducive to learning (see here and here), and it’d be a pain to fairly grade you during the pandemic anyways. So instead, throughout this course I’ll be providing you with qualitative feedback to your homework instead of letter grades or numerical scores, and you’ll be actively reflecting on your own learning and understanding. The buzzword to Google is “ungrading” in case you’d like to learn more about what I’m thinking. Then at the end of the term, I’ll glance over your reflections and we’ll have a conversation about what letter-grade I should submit to UCR for you. Note that since the purpose of this course is to prepare you to learn calculus, so long as I’m confident you’ll succeed taking a calculus class next term, you will pass this class.

If at any point during the term you are curious or concerned whether or not I think you’re making sufficient progress in this course, please talk to me. Since I’m not ranking you with scores to communicate your progress, it’s more important that maintain communication with me than if this were a more typical course.

And we’ll have a final for the course. I’ll read it, but the final will not be graded either. I figure since the pandemic will persist into the school year it’d be good practice for you to take a final exam proctored via Zoom like you’ll have to in future classes; remember the purpose here is to prepare you to take calculus.

Books & Resources

University of Washington’s Math120

This is a wonderful textbook by Collingwood, Prince, and Conroy, and huge collection of past quizzes, midterms, and finals. I will certainly be referencing this for the course and assigning you reading from this book.

OpenStax Precalculus by Jay Abramson, et alia

Among the countless 1000+ page precalculus textbooks in the world, I declare this one to be the best. It’s free and Creative Commons licensed, and it’s typeset very nicely. I’ll likely assign computational drills from this book.

Paul’s Online Algebra Notes

Paul Dawkins has worked out tons of examples, and I think he explains concepts really well. There’s also an algebra and trigonometry cheat sheet you might appreciate, and Paul has written notes for calculus and differential equations that you can reference in your later classes if you find you like his style.


Really, there are tons of great lectures and tutorials on every topic imaginable on YouTube. I’m trying to build a curated list of good ones, so if you find any videos that are particularly helpful for this course, please send me a link to them!

Desmos and WolframAlpha

Desmos is nicest online graphing calculator for visualizing real-valued functions. And WolframAlpha is a powerful online “calculator” that might be helpful now, but you should certainly be aware of for future math classes.

Online Etiquette & Tech Tips


All the homework for the course will be uploaded to Gradescope. You can upload either images or PDFs. I imagine the most convenient workflow for you would be to write-up your homework on paper and upload photos of that. But some of the homework has writing components you may prefer to type. You could submit a mix of images and PDFs. Whatever works best for you. A couple technical requests about uploading photos to Gradescope:

  1. Make sure your photos are oriented the same way as your writing. Like, when you take the photo, don’t point your phone straight down at your writing, but make sure to tilt it a little bit so the phone doesn’t change the orientation of the photo. My neck will thank you for this. I’m curious how many students bother to read this section, so if you’ve read this, please (but don’t tell anyone).
  2. Please don’t take high-definition quality photos of your responses. This creates a large file that takes awhile to upload for you, and takes a while to load for me when I’m reading. Smaller, standard quality photos are much better. Just check real quick that your writing is still legible.
  3. Try to make sure your response begins at the top of the photo so I don’t have to scroll down to see your writing.


Most every online class meeting everywhere is being conducted using Zoom. I recommend using their desktop app or phone app over using Zoom in your web browser.

If you’re in a Zoom meeting with more than just a couple people, like a full lecture or discussion section for example, you should keep your microphone muted unless you are speaking to reduce the amount of background noise in the meetings. Otherwise in meetings of just a few people with a more personal vibe, you should have you microphone and webcam on to cohere to that vibe. For my class there’s no requirement that you have your webcam on, although I would appreciate it a lot; teaching becomes an depressing experience it I can’t see the class. But, video or not, it would be incredibly helpful if you’d upload a profile pic to Zoom. It doesn’t even have to be a pic of you, but just some photo that I can identify as you.

Any Zoom meetings I host, I have to record for liability purposes.

Learning LaTeX

Did you know that there is a nice way to type math notation? This is based on the document typesetting system LaTeX. To say it simply, LaTeX is a markup language, kinda like a programming language, that makes it super easy to type mathematics. It is the standard tool professional mathematicians and other scientists use to draft papers and notes. Then Overleaf is a website that allows teams to collaborate on documents written with LaTeX, kinda like how Google Docs works with typical documents. Getting started, I’d advise you to use Overleaf. To provide some guidance on how to learn the LaTeX language: the Overleaf website has some nice LaTeX documentation to introduce you to the language. The LaTeX Wikibook is more robust, and the resource I still often reference. Then the website Detexify is invaluable, since it allows you to hand-draw a mathematical symbol to find out the LaTeX command to create that symbol.

A related bit of software that might interest you is TeX for Gmail. This is a chrome browser extension that allows you to type mathematics in an email using LaTeX’s syntax.

Inclusivity & Accessibility

If you anticipate or experience any barriers to learning in this course, please feel welcome to discuss your concerns with me. I’ll do what I can to adapt the class, and adapt my style and demeanor as your teacher, to fit your needs. Due to the sudden shift to remote teaching, it should be pointed out that this includes the technical accessibility of the course too. Remember too that there’s this Google Form to contact me anonymously if you’d ever like to. But if you don’t feel comfortable coming to me to talk to me there are a plethora of resources and communities available on the UCR campus that I urge you to reach out to. Here is a curated list of those resources and communities.


In particular, if you have a disability, or think you may have a disability, you may want to contact the Student Disabilities Resource Center to begin a conversation or request an official accommodation from the university.

Academic Integrity

An assessment is a tool to help me gauge what you know and what you’ve learned, and help me teach you better. Assignments are tasks designed to help you develop and learn. Your homework will serve as both the assessments and assignments in this course. Please don’t do anything to undermine the accuracy of an assessment, or the effectiveness of an assignment, or else it’s UCR’s policy that I inform the administration to get involved. I don’t like the administration. To read over UCR’s academic integrity policies, see:


Advice & FAQs

There are More Important Things that School

Remember that this class, and academics in general, should not be the most important thing to you. Your health and your happiness take precedence over you success in this class. In particular, if you are feeling sick, please take care of yourself instead of coming to class; I can walk you through the lecture you missed in my office hours, and you can request and extension on any assignment if you let me know with enough time before the due date.

Remember that Math is Hard

When learning math your brain is trying to make connections between abstract patterns. But your brain is a squishy meat noodle historically used to find food and recognize danger. It’s not inherently good at dealing with abstract ideas, so it’s perfectly normal to experience a feeling of struggling when learning math. This feeling is just your brain working to make a connection while you work to understand a new idea, and it is through this work that you become better at math. Struggling is not an indicator that you’re bad a math or that you’re just dumb; it’s a normal feeling that comes with actively working to learn.

“So how do I learn math?”

Spend time with it. Immerse yourself in it. Talk to others about it. The proficiency with any skill, math included, is proportional to how much time you spend practicing it.

One important thing to do though specifically to learning math from class lecture is to orient yourself before and after the lecture begins. So when you arrive to class, before the lecturer starts talking, take a few minutes to remind yourself what you learned last time in lecture and why it was important. And after a lecture is over, take a few minutes to think about what the purpose of the lecture was. (and if you’re not sure, then the lecturer did a poor job and you should ask them directly what the purpose was before leaving) Sometimes it helps to do this exercise explicitly in writing

“Do I have to simplify my answer?”

That’s a judgement call you have to make. But generally, remember that you’re writing up your calculation for your instructor or TA to read. I’d hope you want to write it up nicely, and present your answer as cleanly as possible.

Also worth pointing out, the answer is not necessarily the important part of your write-up. When we, your instructors, ask you to calculate something on a quiz/exam/etc, that’s really just a prompt for you to demonstrate your understanding through that calculation. A correct answer alone is not enough to demonstrate understanding, But an “unsimplified” answer will leave us doubting that you understand some basics of arithmetic.

Consciously Reflect on your Progress

You should always take some time to conscientiously reflect on the feedback you got on an exam/assessment/quiz/homework after you receive it. Like literally close your eyes and take a few minutes to ask yourself these questions:
  1. Does this feedback/score make me happy? Am I satisfied with this score?
  2. If I want to do better, how could I have better prepared How can I improve?
  3. Should I talk to the instructor or TA for guidance on how to improve?

The Purpose of Exercises is not to Get Good at Exercises

It's important to remember the goal of doing exercises. Start with an analogy: push-ups. You don't do push-ups to get good at doing push-ups. You do push-ups to get stronger, to develop your chest and arm muscles, and to make tasks that use those muscles easier. Similarly the purpose of doing a mathematical exercise is *not* to get good at doing that exercise. It's to practice applying the thoughts and concepts that go into completing that exercise so that you can apply those same thoughts more broadly and solve a variety of problems. Simply focusing on doing the exercises for their own sake is misguided, and harmful to your growth.