- Your First Math Course at UofM: A Guide for Incoming Students
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- Understand your Foundation
- Explore Course Options
- Move Towards a Decision
- Follow-Up
- Undergraduate Math Courses
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- Advising
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- Frequently Asked Questions
- Graduation
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- Student Spotlight
- Transfer Credit
Before choosing a math class, you need to know about what options are out there! There are really two dimensions to understand: What kind of math? How abstract?
For example, most students take a math course in our “Main Sequence” (Precalculus - Calculus I - Calculus II) and need to figure out where in that sequence to start (what kind of math?). But some students may also want a more abstract course and may be deciding between a variety of other math classes (how abstract?).
To help you understand this variety of offerings, we’ve included below:
- course descriptions
- video interviews or written FAQs (with current or recent instructors)
- case studies (describing fictional, but representative, students making course decisions)
- graphics (to understand how certain courses compare)
And you don’t have to make sense of this all alone! Summer math advisors are here to help you understand all these options.
We start with describing the “Main Sequence”, which is what most incoming students pursue.
Main Sequence Coures
Most students take courses in the main calculus sequence:
- Math 105: Data, Functions and Graphs, which prepares students for calculus;
- Math 115: Calculus I
- Math 116: Calculus II
- Math 205/215: Multivariable and Vector Calculus
Students in these courses learn the underlying concepts of the material, and there is a strong focus on modeling content, that is, applications to other areas using this material.
Math 105: Data, Functions, and Graphs
Math 115: Calculus 1
Math 116: Calculus 2
Math 205: Calculus of Several Variables
Math 215: Multivariable and Vector Calculus
Main Sequence Case Studies
Amalgamating the experiences and situations of many different real students over the years, the case studies below illustrate the kinds of considerations that go into selecting a first math course at U-M. As these collectively demonstrate, there are many different factors that go into choosing your first math class! Even if the specifics of these case studies do not resonate with you, giving them a quick read will help you gain familiarity with the way different considerations and factors go into making this important decision.
Jimena went to a high school that did not offer AP Calculus. She received an A in her high school calculus class, but her University of Michigan math placement score comes back with a result of “Math 105, definite.” Jimena wants to major in Biophysics and go to medical school, and is worried that starting in Math 105 (Precalculus: Data, functions, and graphs) in college will set her timeline back. She’s also confused by the “Math 105, definite” placement recommendation, since she already took Calculus in high school. However, after talking to a math advisor and looking through some Math 105 exams together, she realizes she’ll learn a lot by taking Math 105, and understands that taking Math 105 in the fall to prepare for Math 115 (Calculus I) in the winter is a better choice for her than trying to start in Math 115 before she’s ready. Jimena takes Math 105 in the fall, which is challenging for her, but doable. She works with her classmates and attends office hours regularly. She goes on to take Math 115, Math 116 (Calculus II), and Math 215 (Calculus III).
Jay took AB Calculus in high school and received a 3 on the AP Calculus AB exam. Jay’s placement score is “Math 105, tentative”. Jay is deciding between Math 105 (PreCalculus: Datas, Functions, and Graphs) and Math 115 (Calculus I), both of which could be good options for him. Jay knows both courses would be a lot of work, and ultimately decides to take Math 115. The course is challenging, but he puts in a lot of work: Jay goes to all available office hours, spends a lot of time at Math Learning Center (walk-in tutoring service, free to all undergraduates), and forms a regular study group with classmates. Jay ends the semester with a “B” and goes on to major in Cognitive Science.
Chris isn’t sure what they want to major in just yet. Chris took a general calculus course in their final year of high school (not AP) and is thinking about registering for Math 116 (Calculus II) first semester. Prior to the advising session, Chris looked over some old Math 115 (Calculus I) exams from the University of Michigan and felt comfortable with many of the questions, but saw some material they didn’t feel totally confident about. Chris is planning to register for a variety of other courses to see what they might like to focus on in college and decides to register for Math 115 because they want a solid foundation in college-level calculus. (Chris goes on to graduate with a major in Political Science and a minor in Data Science.)
Bea is eager to pursue a pre-medicine course load. Her University of Michigan math placement exam result suggests she’s prepared to enroll in “calculus or beyond, tentative” but Bea is a little wary of this recommendation because she took calculus in an IB program and not a “traditional high school calculus course” as she says. The math advisor notes that math could be quite beneficial to her for a career in medicine, and that the IB curriculum Bea took (Analysis and Approaches HL) actually prepares students well for the expectations of a college calculus course. Bea and the advisor go over some problems from Math 115 final exams, and Bea finds she is able to do them. She leaves the advising session prepared to register for Math 116 (Calculus II).
Alternative Courses (Math 185+)
Overview
While most students take the “Main Sequence” courses described above, there is a variety of alternative course offerings as well. The infographic below depicts how these courses vary from the main sequence courses in terms of abstraction, breadth, and applications. For example: Math 295 is shown below as highly abstract (underground) and also covering a lot of material; in contrast Math 156 is shown to be above ground, meaning it includes many applications.
Important Note: Because of the abstraction in courses like Math 185 and 295, even though one might call them “Calculus I”, they are typically taken after something like AP Calculus. They are intended for students who want a very deep level of abstraction and it is not “going backward” in the curriculum to take these courses after Calculus I, Calculus II, or even Calculus III.
Math 185: Honors Calculus 1
Math 156: Applied Honors Calculus II
Math 295: Honors Mathematics I
Math 215 and 285: Multivariable and Vector Calculus
Math 205: Calculus of Several Variables
Math 216: Introduction to Differential Equations
Math 275: Intro to Cryptology
Math 276: Explorations in Calculus
Math 201 (1 credit): An Introduction to Mathematical Writing
Math 214: Applied Linear Algebra
Math 217: Linear Algebra
Alternative Course Case Studies
Parker is an engineering student who is waiting to receive their AP Exam results, but feels confident they’ll receive a 5 on the AP Calculus BC exam. Parker’s heard different things about whether it would be better to start in Math 116 (Calculus II), to get used to the expectations of a college math course and reinforce Calculus II knowledge, or to start in Math 215 (Calculus III) which will consist entirely of new material. After looking over some Math 116 math problems with a math advisor, Parker decides to start in Math 215, but knows that if they end up with a lower score on the AP exam, or feel overwhelmed by the initial homework assignments in Math 215, then switching into Math 116 is possible.
Parker considered Math 285, but knows that Math 215 is more applied than Math 285, which fits with their goals for Engineering.
Steve really likes math and finds it fun, but has never thought about majoring in math in college. He shares with his advisor that he prefers abstract math over applied, real-world applications and that he took AB Calculus in high school and earned a 5 on the AP AB Calculus exam. Steve shares that he likely wants to major in something in the sciences, maybe physics or biology. At the end of the advising session he is thinking about enrolling in either Math 116 (Calculus II), Math 185 (Honors Calculus I), or Math 275 (Cryptology). Ultimately, Steve registers for Math 275 for the fall with a plan to take Math 276 (Explorations in Calculus) in the winter. He goes on to graduate with a double major in Biochemistry and Mathematical Biology.
Ceecee has always been pretty advanced with math coursework and took Calculus III and Linear Algebra at a local community college during junior year of high school. In her senior year of high school Ceecee didn’t take any math in person, but explored discrete math through online courses. Ceecee is deciding between Math 275 (Cryptology), Math 185 (Honors Calculus I), and Math 295 (Honors Mathematics I). Ceecee ultimately decides that she’s interested in a calculus-based course, but wants to balance her time between multiple interests. Ultimately, she chooses to take Math 185, followed by Math 186 (Honors Calculus II). Ceecee graduates with an Honors Math major.
Dov is in the College of Engineering. Dov took BC Calculus their junior year in high school and received a score of 5 on the AP Calculus BC exam. They know they want to progress quickly through math coursework so that they can focus on engineering coursework, and know they need a multivariable calculus course for their intended Mechanical Engineering major. They’re deciding between Math 215 (Calculus III) and Math 285 (Honors Calculus III). Ultimately, Dov chooses Math 285 because of the smaller class size and active learning format.
