First Year Orientation Advising

• 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.

• 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.

• Some math courses (especially honors courses) are only offered in the Fall semester, and some (like Math 275) 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.

• 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!

• 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.

• 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, 275, 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.

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.

• 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.
  

• 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.
  

• 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 after completing a self-paced course called Math 117. Contact math-undergrad-office@umich.edu for more details
    • 6: credit for Math 120 only
    • 5 or lower (or SL Math Exam): no college math credit
• More general information about AP and IB credit at UM is available here.
  

• LSA students get 2 credits for 120, which will increase to 4 each if you take another math course (116, 156, 185, 275, 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.

• 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 275 will not fulfill this requirement. 
• Students with Math 120 credit can also complete the Econ math prerequisite by taking Econ 210.
• 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.

• LSA students get 2 credits for each of these courses, which will increase to 4 each if you take another math course (275, 276, 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.

• 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.

• 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.

• 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.

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/.

• Math 275 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 275 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 275 in place of Math 115, but you should speak with an advisor about this to be sure.
• Math 275 is only offered in the Fall semester, and typically only taken by first-year students. 276 is only offered in Winter.
• A follow-up course, Math 276, provides a bridge into the Honors Calculus sequence for students who want to continue with more math.

• 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.

• 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.

• Students who take one of the three options above (156, 185-186, or 275-276) 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).

• Lecture course.
• 295 is usually accepted in place of 115 requirements. 
• These worksheets are a resource to help you prepare for the mathematical proof-writing in this course. 
• 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.