- Undergraduate Math Courses
- Major and Minor Programs
- Research and Career Opportunities
- Awards, Scholarships, and Prizes
- Extracurricular Activities
- Frequently Asked Questions
- Transfer Credit
It can be helpful for students who intend to take mathematics courses in the Fall to speak with a mathematics advisor regarding course placement. This is particularly true if a student intends to ignore the advice of the placement exam or would like to explore honors math options.
Students who took the BC exam during COVID-19 and received a 5 are highly recommended to speak with a math advisor prior to enrolling in math courses.
Transfer credit: Before meeting with an advisor, students with transfer credit should first check the Math Transfer Credit Database to see if their prior courses will transfer. If not, they should submit any evaluation requests through that site prior to their math advising appointment.
Please schedule any math advising appointment for after meeting with your general advisor. They may be able to answer any math-related questions you have, making a math appointment unnecessary. Many of your quastions may also be answered by the questions and videos that you will find towards the bottom of this page. Please take a look at all of the materials prior to attending your appointment.
To shedule with a mathematics advisor, click on the appropriate link below:
Should I take a math course.......?
College works differently from high school, where you likely took a math course every semester. The advice outlined below will often recommend you talk to your general advisor or a Math advisor, because figuring out what’s best for you will often depend heavily on your individual situation. To make an appointment with a Math advisor using the links provided above.
Am I required to take a math course?
- That will depend on your background, program (college, major, minor) and future plans, and should be discussed with your general advisor, who will best be able answer your questions about what different programs require.
- LSA has a Quantitative Reasoning requirement that is fulfilled by many math courses, but can also be fulfilled with a number of courses in other departments. You should discuss your options with your general advisor.
How should I decide between Calculus and Statistics?
- At the University of Michigan, Math and Statistics are two separate departments. Many students are well-served by statistics courses, and they serve as a prerequisites for many majors. You can learn more about the Statistics Department from their website: https://lsa.umich.edu/stats. Your general advisor can also help you choose your stats course.
Do I have to take a math course this semester, or can I wait?
- Some math courses (especially honors courses) are only offered in the Fall semester, and some (like Math 175) are really intended for first-year students. But many others are offered every semester.
- Because math courses build on one another, it can be helpful to take your math courses sooner rather than later. That being said, “sooner” might mean Winter for you. And there are cases where taking it much later is also fine. A Math advisor can help you figure out this delicate timing.
- Certain math courses are prerequisites for many majors and courses in other departments, which means you’ll need to take the math course before you can declare your major. In that case, you’ll want to take the math course soon. Your general advisor, or an advisor in the program you’re interested in, will have the best information about whether this applies in your case.
Why should I take a math class?
- Math courses help you develop many important skills: logical reasoning, problem-solving, precision with language, and more. And as many of our courses are taught using a lot of groupwork in and out of class, they can also help you build robust communication and teamwork skills. All of these skills will serve you well in whatever you end up doing in college and later in life.
- You might take a math class to fill requirements, such as prerequisites for a major or minor.
- You will definitely take a math course (lots of them!) if you are interested in majoring in mathematics or other math-heavy fields like statistics, economics, physics, or computer science.
- Even in less math-heavy fields, a solid math background can be very beneficial. For example, math majors tend to do extremely well on the LSAT test for law school.
- And, of course, you may just want to take math because you enjoy it!
After this semester, which math course do I take next??
- Once you’ve taken your first math course, your instructor, general advisor, or an advisor from your intended major will be able to discuss future courses with you.
- If you’re interested in advanced math courses--for example, considering majoring or minoring in math--you can make an appointment with a Math Department faculty advisor in the Fall.
- Registration for Winter opens in mid-November, so you should try to have these conversations towards the end of October.
I want to major in math! What course should I start in?
- Great! We’d love to have you!
- There’s no one “right path” for being a math major. In fact, there are several different submajors with different requirements. Students who like applying math to other fields should consider one of the Mathematical Sciences options, which are designed to make it easy for students to double-major in math and related fields, such as computer science, economics, statistics, biology, and more.
- Some math majors start in Math 105, 115, or 116; others in the honors courses like 185, 175, or 295.
- Students starting in 115 who are interested in a math major may be interested in the Douglass Houghton Scholars Program.
- Even if you’re just curious, we would love to talk to you more about a math major. You can make a 20-minute 1-on-1 appointment with one of our Math faculty advisors in the Fall.
Since there are so many math offerings, answering the following questions can help you navigate our courses and identify the right math course for YOU.
What is your math placement recommendation?
Math 105, definite or tentative: we strongly recommend that you take Math 105.
- If your placement test score says: “Math 105, definite or tentative”, we strongly recommend that you take Math 105.
- Your placement result indicates that there are some mathematical topics and/or skills that you need to learn, review, or practice before you will be ready to take other courses in the math department.
- Math 105, along with 115 and 116, is part of the “Intro Program”. See videos about the Intro Program and Math 105 below.
- Math 105 is both a preparation for calculus and a stand-alone course.
- While much of the specific content covered will be familiar to many students, the course covers this material from a perspective, and at a depth, that students still find new and challenging.
- Math 105 is taught in small sections (less than 20) with lots of groupwork, so you get very personalized help from your instructor.
- This placement is based in part on years of data. Students who receive this placement and try to take Math 115 tend to struggle, and frequently end up dropping 115 as a result.
- If unusual circumstances led to your placement score and you think you want to try Math 115, you should definitely speak to a Math advisor (see links above), who can help you determine whether you have the preparation to succeed in Math 105.
- If your placement score says: “Calculus or beyond”: This recommendation means the test has affirmed you have solid pre-calculus skills. It doesn’t actually tell us which course you should take. For that, you should read the information below and, if needed, make an appointment with an advisor.
Do you have college math credit for a course after Calculus II?
- For example, this might be multivariable calculus, differential equations, linear algebra, or an intro to proofs course taken at a university or community college.
- For most students, the answer to this question is no, and you can use the information below to help you think about the appropriate next course.
- If your answer to this question is yes, you should make an appointment with a Math Honors advisor (above), who will be able to talk to you about your specific circumstances and what your best options are.
Students who do not start in 105 or have advanced college credit most commonly take the Mainstream Calculus (115-116-215-216) sequence. These courses focus on the ways that mathematics can be used to model real-life scenarios and understand the world around us.
- Math 115 and 116 (Calculus I and II) are taught in small sections (less than 20) with lots of group work, while 215 (Multivariable Calculus) and 216 (Differential Equations) are taught in large sections (approximately 100 students) with smaller weekly labs.
- Math 115 and 116 are part of the Introductory Program. See videos for the Intro Program, 115, 116, and 215 below.
- Where you start in this sequence will depend on your background (see below for more information).
- A small number of students who are interested in a more intensive, rigorous mathematics experience choose to take one of the Alternative First- and Second-Year Math Sequences. Many of these courses are officially honors courses, but may be taken by other students with permission of a Math Honors advisor. Make an appointment with one if you are interested in one of these courses, even if you’re just curious to know more.
Mainstream Sequence Placement
What course you start in will depend on your previous experience with calculus, such as AP Calculus.
Students with AP or IB math credit
- If you took the AP Calculus exam or IB HL Math course but have not yet received a score, use your best estimation of your score to choose the course you enroll in. You will be able to change to a different course after you receive test results if you need to.
- U of M distinguishes between its own calculus courses and credit earned by AP and IB tests. Math 120 or Math 121 are the course numbers used to represent AP or IB credit, but there are no actual courses at UM bearing those course numbers.
- Based on your scores, you’ll receive the following credits on your transcript:
- Score on the AP Calculus AB Exam:
- 5: credit for Math 120
- 4 or lower: no college math credit
- Score on the AP Calculus BC Exam:
- 5: credit for Math 120 and 121
- 4: credit for Math 120 only
- 3 or lower: no college math credit
- Score on the IB HL Math Exam:
- 7: credit for Math 120 and 121
- 6: credit for Math 120 only
- 5 or lower (or SL Math Exam): no college math credit
- Score on the AP Calculus AB Exam:
- More general information about AP and IB credit at UM is available here.
Students with credit for Math 120 only:
- LSA students get 2 credits for 120, which will increase to 4 each if you take another math course (116, 156, 175, 185, or 295).
- Most programs that require 115 accept 120 in its place (see below for exception).
- Generally, with AP/IB credit for Math 120 will start in Math 116.
- Students interested in applications to engineering or physical sciences may wish instead to take Math 156 (Fall only), Applied Honors Calculus, which focuses specifically on applications relevant to these areas and includes some proofs. (Math 116 also includes applications, but for a wider variety of fields.)
- Students who take Math 105 or 115 will lose 120 credit.
Students Majoring in Economics
- The Economics major requires Math 115 as a prerequisite, but does not accept Math 120 in its place, though it does accept the combination of Math 120 and 121. If you only have credit for Math 120 and intend to major in Econ, then you will need to take an additional math course at UM.
- Either Math 115 or Math 116 will fulfill this requirement. You can also take a calculus course in the honors sequence, such as Math 185 (non-honors students will need to discuss this with a Math Honors advisor), but Math 175 will not fulfill this requirement.
- A competitive application to economics graduate programs will require significantly more mathematics courses, including 217, 316, and 451. Students planning this route may want to consider a math minor or a Mathematical Sciences: Mathematical Economics major, which is designed to work well as a double major with Economics.
Students with credit for both Math 120 & 121:
- LSA students get 2 credits for each of these courses, which will increase to 4 each if you take another math course (175, 176, 185, 215, 216, 285, or 295). Engineering students immediately get 4 credits for each.
- Students who take Math 105 or 115 will lose 120 and 121 credit.
- Most programs accept 120 and 121 in place of any 115 and 116 requirement.
- The next course in the mainstream sequence is Math 215, Multivariable and Vector Calculus.
- Students interested in a more theoretical approach to the material may be interested in taking Math 285, Honors Calculus III. More information about the difference between these courses can be found in the video about 215 and 285. Students who are not in the LSA Honors College can enroll in Math 285, but will first need to meet with a Math Honors advisor to receive permission to enroll. Go to Honors Calculus Sequence below for more information about Math 285.
IMPORTANT for AP Calculus BC tests taken in 2020:
If you received a 5 on the 2020 AP Calculus BC test, you may not have learned some of the topics that are essential for your future studies and covered in Calculus II, such as Taylor series, parametric equations, and polar coordinates.
- These topics are necessary for success in further Math courses (eg 215, 216), and may be important for other fields and courses with a 116 requirement or prerequisite.
- We are offering a 2-credit course, Math 117, to fill in those gaps for you. Students who receive a 5 on the 2020 AP Calculus BC exam will be receiving more information about this course.
- You can also learn that material by taking Math 116 (Calculus II) or Math 156 (Applied Honors Calculus, which focuses specifically on applications relevant to engineering and physical sciences).
Students who have taken a calculus course at another college or university.
- If this course transfers as Mach 115 or 116, you should take the next course in the sequence (116 or 215, respectively).
- If a course you have taken has not been evaluated for transfer credit, you should submit information to have it evaluated.
- Courses must cover certain essential topics in order to transfer.Courses are frequently determined not to transfer as UM courses because they are missing certain topics deemed essential to the course. If you’ve only taken one calculus class that did not transfer, it is likely you will learn a lot in Math 115, which focuses much more on mathematical modeling and conceptual understanding than most calculus courses.
- If you have courses that don’t transfer as UM courses, we strongly recommend meeting with a Math advisor, who can help you decide appropriate placement.
Students who want to take a math course for which they do not have the prerequisites
- You may have taken a calculus course at a different institution that did not transfer as a UM course, or taken the AP test under extenuating circumstances (e.g. a high fever or a family emergency), and received a score that doesn’t represent your understanding.
- If you want to skip ahead to Math 116 without 115 credit, here are two things you need to consider:
- Do you have the mathematical background to be ready to succeed in Math 116? Our courses are very challenging, and you’ll want to take a look at the Math 115 materials (http://www.math.lsa.umich.edu/courses/115/) and speak with a Math advisor to make sure you’ll be ready for Math 116.
- Will your program allow you to skip 115? Some programs will allow students to substitute a more advanced course. For example, students majoring in Computer Science could take 116 and 214 (Applied Linear Algebra) instead of 115 and 116. This is an issue that must be discussed with the department in question, rather than the Math advisor.
- Similarly, if you have credit for a course that does not transfer as Math 116, it is usually wise to take Math 116, but you should meet with a Math advisor to discuss your background and determine whether you would be better off enrolling in a different course, such as Math 215.
Students who do not have college credit for any previous calculus courses.
- You should start in Math 115, unless you’re interested in one of the honors sequences.
- Math 115 contains a mixture of students who have had some calculus before and those who have not. The course covers the material from a substantially different perspective from a typical calculus course.
Douglass Houghton Scholars Program for Math 115 students.
First-year LSA students who are taking Math 115 and 116 and plan to major in math or science might be interested in applying to the Douglass Houghton Scholars Program. This program includes a 2-credit workshop in which students work in small groups to grapple with challenging calculus problems that often go beyond the material covered in 115 and 116. We especially encourage applicants who come from an educational, cultural, geographic, or socioeconomic background that is under-represented in graduate study in math and science. For more information, including information about how to apply, go to https://sites.lsa.umich.edu/dhsp/.
Alternative First- and Second-Year Math Sequences
The Math Department offers a number of other sequences available to students. If you’re interested in taking courses listed below other than Math 156, you should meet with a Math Honors Advisor (see links at the top of this page). The goal of this meeting is to make sure you understand the content and expectations of the course, and to discuss how this course might fit into your overall academic plan. Students are required to waitlist for these courses, and will be given permission to enroll upon confirmation that they have met with an advisor.
Introduction to Cryptology (175) and Explorations in Calculus (176):
If you want to try out a rigorous, exciting mathematics course that isn’t calculus, you should consider Math 175, Intro to Cryptology.
- Math 175 is a first-year seminar-style course. Class sections are small (less than 20), and class time is primarily spent with students working on problems in small groups and discussing solutions. Learn more about this course by viewing a short video interview with the instructor, Dr. Anna Weigandt.
- Math 175 is appropriate for motivated students (of any major) interested in deeply exploring rigorous mathematics that really departs from the content of high school math. Completing the whole sequence is an on-ramp to the honors math major.
- This is an honors sequence. Students who are not in the LSA Honors College will need to meet with an Honors Math advisor to receive permission to enroll in one of these courses.
- Many programs will accept Math 175 in place of Math 115, but you should speak with an advisor about this to be sure.
- Math 175 is only offered in the Fall semester, and typically only taken by first-year students. 176 is only offered in Winter.
- A follow-up course, Math 176, provides a bridge into the Honors Calculus sequence for students who want to continue with more math.
Honors Calculus I and II (185-186):
This sequence includes more rigorous mathematical proofs. You’ll learn how mathematicians think about and justify mathematical concepts.
- Students who are not in the LSA Honors College will need to meet with an Honors Math Advisor to receive permission to enroll in one of these courses.
- See the video for Math 185 below. Most programs and majors will accept 185 as fulfilling the 115 requirement.
- Taught in small (less than 30) sections, primarily lecture.
- 185 is only taught in Fall, and 186 only in Winter. New students do not start in 186, even if they have 115 or 120 credit, because 185 teaches proof-writing skills that are necessary to succeed in 186 and not taught in most calculus courses.
Applied Honors Calculus (156):
This course is for students who scored a 4 or 5 on the Calculus AB or BC exam and are specifically interested in applications to Engineering and physical sciences and would like to see some of the proofs of the material being covered.
- Math 156 is only offered in Fall semester, and taught in small sections (less than 20 students).
- See the video interview for Math 156 with Dr. Robert Krasny, the coordinator for Math 156, below.
- 156 and 116 cover similar material. Some differences between the courses:
- 156 has the AP prerequisite
- The applications in 156 are more focused on topics specific to engineering and physical sciences
- 156 shows students some proofs
- 156 is taught as a lecture course while 116 is taught with active learning.
- Students do not need permission from a Math Honors advisor to enroll in Math 156, but they do need to have received a 4 or 5 on the AP Calculus AB or BC exam to take the course.
- Students who pass 156 will be able to enroll in Math 285 without permission from a Math Honors advisor.
Honors Calculus III and IV (285-286)
These courses cover multivariable calculus (285) and differential equations (286) from a more rigorous perspective than the mainstream sequence.
- Students who take one of the three options above (156, 175-176, or 185-186) who wish to take further mathematics frequently take 285 and 286.
- Students can also take 285 without one of those courses, if they wish to take a multivariable calculus course that takes a more rigorous approach than 215.. See the video discussing the differences between 215 and 285.
- 285 and 286 are both offered in both Fall and Winter.
- Section 1 of 285 in the Fall is smaller (less than 20) and taught using IBL methods, which means there will be less lecture and class time will involve students presenting solutions at the board. Other sections of 285 and 286 are taught in a lecture format, but still kept small (less than 30 students).
Honors Math (295-296-395-396):
This sequence is for students who like the idea of an immersive mathematical experience. Students considering this course should be aware that it has a very heavy workload: you should expect 15-20 hours of homework each week.
- Lecture course.
- 295 is usually accepted in place of 115 requirements.
- See the video for 295 below.
- This is an honors sequence. Students who are not in the LSA Honors College will need to meet with a Math Honors advisor to receive permission to enroll in one of these courses.
- Incoming first-year students almost always start this sequence in 295. Students who do not start in this sequence and are interested in joining it later will have an opportunity to do so by taking Math 297 after Math 217.
- Math 295 and 185 are designed to make it easy for a student to switch from 295 to 185 in the first few weeks of the semester. If you are trying to decide which to take, you can try 295, and if the workload is too heavy, switch to 185.