All students who enter COA with 9 credits or fewer are required to take at least one QR course in order to graduate. QR courses include, but are not limited to, math courses. Most physics classes and some chemistry and economics classes meet the QR requirement.

A QR class is one which students engage meaningfully in mathematics and/or computation. This means that students are doing math or coding. QR classes usually have problem sets and/or coding assignments.

No. Almost all physics classes meet the QR requirement, as do several chemistry and geology/earth science classes. Around half of our economics classes also meet the QR requirement, as do almost all statistics, data science, and programming courses.

Many students delay taking a QR course. This is certainly understandable. However, there are some reasons why I think it's better to take a QR course sooner rather than later: With a solid math and quantitative reasoning background, students will get much more out of some classes, especially science and economics classes.

On the other hand, there may be many other courses that make more sense for you to take, depending on what you're trying to get out of COA. It's usually better to wait and take a math class that is better suited for you than to take a math class right away that isn't a good match. Students sometimes worry that the longer they wait to take a QR course the harder it will be. In my experience, this isn't the case.

The bottom line is that I don't really care when you take a QR course. However, you can box yourself into a corner if you want too long and might end up having to take a course that isn't a good match for you.

Probably. Many math classes essentially have no size limit, so you'll definitely get in. I've never turned anyone away from the Physics and Math of Sustainable Energy. It is rare for first-year students to get into Chaos and Fractals, so you may have to wait a year or two for that class. Over the years I have found that students almost always can get into a course that is a good match for them.

No. AP credits or IB credits do not fulfill the QR requirement.

No. Regardless of whatever math you've had before you came here,you need to take one QR course while at COA (unless you're a transfer student.) The idea is that all students, as part of their interdisciplinary B.A. in human ecology, should take at least one course that requires mathematics or computation.

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Calculus I and II (a standard single-variable calculus sequences) are offered every other year. Calc I and II will be offered in 2024-25, 2026-27, 2028-29, etc. Please plan accordingly.

The most important thing for calculus readiness is that you've seen functions before and have worked with f(x) notation before and been reasonably comfortable with it at some point. If you've forgotten about logs and exponents and trigonometry, that's ok. We review topics as needed.

You do not have to have taken a class called precalculus to be ready for calculus. As noted above, the most important pre-requisite is that you've worked with functions before.

Many students who are good at and/or like math feel they are "supposed to" take calculus. The high school math curriculum is very centered on getting students to reach calculus, so calculus is seen as a goal or a pinnacle. (I don't think this is a great idea, but that's another conversation.) Perhaps your parents or siblings took calculus in college, or maybe you just feel it's next in line. For many, calculus is indeed an appropriate and fun course. Calculus is an incredibly powerful and flexible set of tools and ideas that are used through the mathematical sciences and which help to solidify and synthesize a great deal of mathematics. At the same time, you can live a rich, complete, and happy life without having taken calculus.

Statistics is more important for many areas of study than calculus. And statistics is certainly used more in other classes at COA than calculus. So, don't feel like you "have to" take calculus. Take it if you want to take it.

That said, calculus is required by many graduate schools. So, if you're planning on going to grad school in the sciences or some of the social sciences, you'll probably need to take calculus at some point.

Also, calculus is required for most of advanced math and physics classes offered at COA, including: Differential Equations, Thermodynamics, Calculus III, and Linear Algebra. If you think you might be interested in advanced physics or math, it's a good idea to take calculus sooner rather than later. And calculus is a great deal of fun. It has many applications and it ties together a lot of different things that you learned in previous algebra classes.

Short answer: if you have taken a calculus class before and did reasonably well, you probably should skip Calc I and II. If you have taken AP Calculus (AB or BC) or done an HL maths in IB (AA or AI), then Calc I and II will be almost all review. If you've done SL maths, you can probably skip Calc I and II, but we should talk. (I'm still getting familiar with the new IB maths courses.)

Calc I reviews functions, and then covers differentiation and its applications. Calc II covers integration, applications, and briefly treats infinite sums and series.

If you are at all unsure about whether or not you have the background to skip Calc I and II, please reach out.

Yes! Check out the FAQs for Differential Equations, Linear Algebra, Calculus III, and Thermodynamics.

Physics I and II are offered every other year. Physics I and II will be offered in 2025-26, 2027-2028, 2029-30, and so on. Please plan accordingly.

Physics I covers mechanics: kinematics, forces and Newton's laws, conservation of energy and momentum. If you've had a good physics class before, you probably don't want to take Physics I -- it might not be challenging. On the other hand, you'll probably find that Physics I covers familiar topics in a different and (hopefully) interesting way. So you might still be interested in Physics I. If you've had AP or IB physics, you should definitely not take Physics I. If you had a non-AP physics class, you probably shouldn't take physics. If in doubt, reach out and we can chat.

Physics I is an excellent course for students who want to improve their quantitative problem solving skills and review algebra. It is taken by some students as their only QR course. It's a great way to get lots of practice solving word problems. Physics I also serves as a pre-calc course of sorts; if you're uncertain of your algebra and trigonometry, taking Physics I can be a good way to improve your skills so you have an easier time with Calculus or other math adventures.

Yes.

Physics II focuses on Einstein's theory of special relativity and some key ideas and phenomena from quantum mechanics. We will cover topics that are not covered in AP or IB (SL or HL) physics. This course does not require any mathematics beyond algebra and functions.

Here is the course description: What are relativity and quantum mechanics, and why were they viewed as revolutionary when they were formulated in the early 1900s? How and why does relativity and quantum mechanics compel us to discard commonsense ideas about the nature of the physical world that are part of classical mechanics? Why is there not agreement on how to interpret quantum mechanics, and why does quantum mechanics even need interpretation? This version of Physics II covers Einstein's theory of special relativity and selected topics in quantum mechanics, and is designed to introduce students to some of the formalism and central results of relativity and quantum mechanics, so that they can formulate scientifically grounded answers to the above questions. Throughout the course we will start with first principles and carefully build toward key results, allowing students to see how relativity and quantum mechanics—two of the pillars of modern physics—were constructed and how they cohere as mathematically consistent and experimentally verified theories. The first half of the course will cover relativity topics including the principle of relativity, spacetime intervals and proper time, coordinate transformations, time dilation and Lorentz contraction, and relativistic energy and momentum. The second half of the course will turn toward the foundations of quantum mechanics, including: spin-1/2 particles, wave-particle duality, and Bell's inequalities and the Einstein-Podolsky-Rosen paradox. If time permits, we may cover additional topics such as blackbody radiation, the photoelectric effect, Bohr's model of the hydrogen atom, and quantum cryptography. To gain a sense of the scientific, social, and material context in which the theories of relativity and quantum mechanics were developed, we will read a number of papers and book chapters by historians and philosophers of science. This course is designed to appeal to a wide range of students—both those whose interests lie outside of science as well as those who are drawn toward the sciences or mathematics. Students who take this course should be comfortable working with mathematical abstraction. Evaluation is based on weekly problem sets, participation in weekly discussion sections, and several short reflection assignments.

No.

Some. In the course description I wrote "Students who take this course should be comfortable working with mathematical abstraction." What does this mean? Good question.

Relativity and quantum mechanics aren't intuitive, in that they are far outside of our everyday experience. So we don't have any experience or intuition about relativistic or quantum mechanical phenomena. So what we have to do is start with some first principles. For example, in relativity, we assume that the speed of light is the same to all observers, regardless of the observer's speed. Then from that starting point, we need to do some math (and geometry) to see where that idea leads us.

In contrast, say, in regular mechanics, we have some intuition that can guide us. E.g., someone running faster has more energy than someone slow. Jumping off a tall tree is more dangerous than jumping off a short tree.

I don't think the level of math in the class is hard, in that there's no advanced algebra, no calculus, etc. It's just that the math is used in a context that isn't relatable, and so takes on a more abstract flavor.

In the past the class has been taken by students with a pretty wide range of math backgrounds and it's been ok. If Quantum and Relativity are topics you're excited about, then I'd encourage you to sign up.

Yes. You should take Physics II.

I'll write something here someday. For now, see the web page from the 2023 edition of the course.

Intro to Chaos and Fractals is an introductory, algebra-based class. It is the most interdisciplinary and least traditional math class that I teach. It is taken by a very wide range of students and is often a particularly good choice for students interested in the humanities, arts, literature, education. In addition to problem sets, students participate in discussions of readings, complete one or two reflection assignments (which could be a paper, poetry, visual art, etc), and do a final project on a topic and in a medium of their choosing. This class tends toward the abstract; we use math to explore the meanings of order, disorder, pattern, simplicity, and complexity. Here is web page for the Fall 2023 Intro to Chaos and Fractals class.

Answer.

Introductory statistics is taught yearly by either Susan Letcher or Sean Todd. The class covers some pretty standard topics: measures of central tendency, regression, t-tests, p-values, and so on. Students learn some of the basics of the R programming language. Introductory statistics meets the QR requirement. This is a general introduction to statistics and is appropriate all students, including both those interested in the natural or social sciences.

This is a class taught roughly every other year by Susan Letcher. It covers statistical techniques commonly used in ecology. R programming is emphasized. Intro stats or the equivalent in a pre-req.

I don't know. Best to talk to Sean or Susan.

Yes. Sean Todd, John Anderson, and I have offered tutorials and independent studies on different aspects of intermediate statistics. Susan Letcher facilitates independent studies on biodiversity statistics and robust experimental design for ecological field sampling. Talk to one of us if you think you might be interested. Also, John's Wildlife Ecology class includes a fair amount of statistics and meets the QR requirement.

Calculus III is calculus applied to functions of two and three variables --- surfaces and volumes. We also briefly survey the calculus of vector fields in the last few weeks of the course. Most students find Calc III to be more interesting and somewhat less challenging than Calc I and II. To take this class you should have had integral and differential calculus. AP Calculus at the AB or BC level, or IB math HL or (probably) SL, will prepare you for this class, as would Calculus I and II here or at another college. If you feel you have forgotten a lot of Calculus, that's ok. Calc III reviews Calc I and II topics along the way, so this is a great course to solidify basic calculus knowledge. I typically offer this course only once every 3-4 years. Here is the course website from the last time I taught Calc III.

Although often viewed as a post-calculus class, Linear Algebra is not a continuation of calculus, and prior coursework in calculus is not a pre-requisite.

Linear algebra is an area of mathematics concerned with the generic algebra of linear systems and vector spaces. Linear Algebra is one of the cornerstones of applied and pure mathematics. It is used across the quantitative sciences, including in economics, multivariable statistics, machine learning, physics, and many ecological and epidemiological models.

In the spring 2024 course we will use free, online, interactive textbook Understanding Linear Algebra, by David Austin. I hope to cover most of the topics in the first four chapters.

The spring 2024 course will be similar to the 2013 edition of Linear Algebra.

I teach Linear Algebra roughly once every four years.

Linear Algebra will feel very much a math class: we will be learning mathematical constructions and techniques using mostly pencil and paper. But it will feel very different than calculus and pre-calculus.

Official Course Description: Linear algebra is a foundational area of mathematics, finding widespread application in statistics, machine learning, economics, physics, and across the sciences. The starting point for this course is to consider basic properties of matrices and techniques for solving systems of linear equations. Abstracting and formalizing the process of solving linear equations leads us to the notion of a vector space and related ideas, such as linear independence, dimension, and basis. The course then turns to further properties of matrices and vector spaces, including determinants, eigenvalues and eigenvectors, and linear transformations. As time permits, we will study various applications of linear algebra, such as image compression, dynamical systems (with a focus on ecological applications), Markov chains, and Google's PageRank algorithm. Students who successfully complete this course will gain a solid introduction to the calculational techniques and key constructions and ideas of linear algebra that will prepare them for further work in the sciences and mathematics. Additionally, students will gain experience working at a level of generality and abstraction above that encountered in a typical introductory calculus sequence. Evaluation will be based on weekly problem sets. Students who enroll in this course should have successfully completed a high-school-level algebra class and be motivated to explore a powerful and broadly-used branch of mathematics that for most has a very different feel than the functions-precalculus-calculus sequence. Calculus is not a prerequisite for this class. Level: Introductory/Intermediate. Prerequisites: A high school-level algebra class. Class limit: None. Lab fee: None. Meets the following degree requirements: QR.

No.

Longer answer TBA. In the meantime, here's the course website from the Winter 2020 Differential Equations Course, which was the last time I taught it.

Longer answer TBA. In the meantime, here's the course website from the Spring 2021 Thermodynamics Course, which was the last time I taught it.

Pre-reqs for thermo: Calculus I and II. An introductory chemistry class is strongly recommended.

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COA does not have a math skills center as such. But all math classes (except for a few advanced courses) have multiple peer teaching assistants (TAs). These students hold open sessions to provide help on the weekly homework assignments. In a typical class there will be around six hours of scheduled help sessions weekly -- this includes both the TAs and me. If the scheduled times don't work, you can find an alternative time with me or one of the TAs.

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It depends on the graduate school. Answer TBA.

Yes! Let's chat.

Apparently yes.