First year student resources

This year’s calculus placement exam will be open in July - exact dates will be announced here. Details about the placement test can be found below. 

At the beginning of August,  each calculus course will post a short video with basic information about the class, tips for success in the course, and other relevant information. 

Individual calculus placement advising session schedule will be below - zoom links will be posted at the beginning of August. If you need placement advice, wait to submit your preference selection entry until after the advising session (you will have several more days to submit, and the timing of your entry does not affect your chances in any way). 

Please note that to receive advice, you must first complete the placement exam - advisers cannot give you placement without it. (Note that these sessions are for level 100 courses only - if you would like advice about higher level courses, please attend the academic fair.)

(Schedule will be posted here.)

The sessions tend to be crowded at the beginning; to decrease your wait time, try joining a little later. 

If you missed the advising sessions and need advice about your placement, please reach out to the course director of the class that you placed into on the exam. If your result was to consult in person, please reach out to math.dus@yale.edu. The list of course director is on the bottom of this page. 

The academic fair will be scheduled by the administration, to take place in August. 

Preference selection will be scheduled by the adminitration, typically in early to mid-August. Please note that the timing of your entry is not taken into account in any way. In particular, you will not be disadvantaged if you submit your entry after the advising sessions. (You may not enter preference selection for two different levels of calculus, so it is important to settle on your placement in advance.)

Math 112 focuses on differential calculus, where the goal is to measure a function’s instantaneous rate of change (the derivative). First, we define limits, which allow us to talk rigorously about instantaneous changes. Then, we define the derivative and find many rules that simplify its computation. Next, we apply the derivative to better understand function behavior (allowing us to minimize cost or maximize profit in economic models). Finally, we develop strategies for reversing the derivative process to find antiderivative functions. These antiderivatives have surprising applications, like computing areas and modeling population growth.

Math 112 requires the placement exam. Students typically take the course after completing pre-calculus.  

Another option is the Math 110/111 sequence, a two-semester course that integrates pre-calculus and differential calculus topics. Successful completion of Math 110 and 111 is equivalent to Math 112 in that it satisfies the same major and professional-school (e.g. pre-med) requirements; however a student completing Math 110 and 111 receives two course credits and two QR credits.  

Math 110/111 requires the placement exam. Some prior knowledge of pre-calculus is helpful. 

Math 115 investigates the mathematics of accumulation. With integral calculus, we use information about instantaneous rates (like the velocity of a moving object) to compute net changes (like change in position). Series convergence tests and Taylor series help us understand how calculators work, and various other topics (solids of revolution, parametric equations, polar coordinates) allow us to apply the tools of single variable calculus in broader contexts. Throughout the semester, we consider both exact and approximate solutions to problems and investigate the role of error.

Math 115 and 116 both cover integral calculus, and both can be used as pre-requisites for any course that requires Math 115. Math 116 places emphasis on applications to biology, and is particularly suitable for biology and pre-medical students.

Math 115 and 116 require the placement exam, or completion of Math 111 or 112 at Yale. Typically, students place into Math 115 after completing a differential calculus course such as AP Calculus AB. 

Math 120 extends skills and knowledge you gain in single variable calculus to two and three variables. We will study how to graph surfaces and solids in three dimensions, differentiate and integrate functions of several variables, optimize functions of several variables (for example when maximizing profit in economics),  we will learn how to integrate along curves and surfaces (for example when calculating how much energy a solar panel will generate while the sun is shining on it), and many other topics.

Math 120 and 121 both cover multivariable calculus, and both can be used as pre-requisites for any course that requires Math 120. Math 121 places emphasis on applications to biology, and is particularly suitable for biology and pre-medical students.

Math 120 and 121 require the placement exam or completion of Math 115 or 116 at Yale. Typically, students place into Math 120 after completing an integral calculus course, such as AP Calculus BC. 

Math 225 is a linear algebra course, and a part of our introductory sequence into the math major. In linear algebra, you will learn key language and concepts used throughout pure mathematics as well as in a wide variety of applications.  Linear algebra starts by studying systems of equations with many variables, and it builds a detailed understanding of how to work in abstract n-dimensional space. This version of linear algebra focuses on concepts, and provides an introduction to writing mathematical proofs.

We also offer an intensive version of this course, Math 226, for students who are looking for an extra challenge. Math 226 will teach the same main topics as Math 225, but it may go into more depth, ask more challenging problems on homework and exams, or cover optional side topics. 

If you start in Math 226, and find that it is too time consuming, you can move to Math 225 until Midterm. You can read more about how moving between courses work in our Calculus FAQ. 

Math 222 is a linear algebra course best suited for students who wish to focus on applications and practical solving problem practice, rather than abstract mathematics and mathematical proofs. It is often taken by students majoring in engineering, technology, science, social sciences, and economics. Mathematics majors need to complete Math 225 or 226, rather than 222. 

Math 222, 225, and 226 do not require the placement exam. If you have completed an integral calculus course, you can simply enroll. 

Math 255 is an introduction to real analysis, and a part of our introductory sequence into the math major. The topics are similar to differential and integral calculus, but it’s done in a rigorous way that focuses on proofs and details of the concepts that happen behind the scenes in calculus.  Said differently, our calculus sequence teaches you how to use the tools of limits, derivatives, and integrals to solve a variety of problems, whereas this course teaches you how to build all of those tools from scratch.

We also offer an intensive version of this course, Math 256, for students who are looking for an extra challenge. Math 256 will teach the same main topics as Math 255, but it may go into more depth, ask more challenging problems on homework and exams, or cover some optional side topics.

Math 255 and 256 require prior completion of Math 225 or 226.

Math 255 and 256 do not use the placement exam or preference selection. 

Math 302 is a rigorous and exciting course that explores some of the beautiful connections between linear algebra and real analysis. For this reason, it is intended to be taken after completing 225/226 and 255/256. 

This course is an introduction to manifolds, which are low-dimensional shapes living in a higher dimensional universe (e.g., a one-dimensional coat hanger or a two-dimensional eggshell each living in a three-dimensional world), and it teaches how to do calculus in this abstract setting.  Although the focus of this course will be on abstract mathematical objects and their properties, the material in this course also has applications to a broad range of topics including theoretical physics and machine learning.

Many students who have not completed multivariable calculus in high school would benefit from taking Math 120. However, prospective math majors, and students excited about rigorous proof-based math should consider taking Math 225/226, Math 255/256 and Math 302 instead.  Math 302 is also appropriate for students who have already completed Math 120 and are curious to learn more.

Math 302 does not use the placement exam or preference selection. 

Math 118 teaches a combination of multivariable calculus and linear algebra. It is suited for students majoring in Economics or Social sciences who wish to learn the most relevant mathematics in one semester.  Students intending to take further courses in mathematics should take multivariable calculus (Math 120) and linear algebra (Math 222, 225, or 226) instead. Pre-requisite for Math 118 is differential calculus (such as Math 112 or AP Calculus AB). Knowledge of integral calculus is recommended. 

The math department offers three Quantitative Reasoning (QR) courses that assume no calculus experience:

Math 106 (The shape of space) provides an introduction to mathematical thinking through ideas in geometry and graph theory. The course follows a historical narrative starting from antiquity, and builds mathematical and geometric intuition through problem solving and other activities. 

In Math 107 (Mathematics in the real world), students use mathematical ideas to solve real world problems. Topics include compound interest, population growth, probability and its applications to games of chance, mortgage payments, false positives in drug testing, computer security, and other questions. 

Math 108 (Estimation and error) leads students through a problem-based investigation of basic mathematical principles and techniques that help make sense of the world. Applications include geology, ecology, finance, and other fields. 

Math 241 and 242: probability and statistics teach us how to collect, analyze, and interpret data. That being so, it is directly useful in almost any field where experiments, surveys, or other means for data collection are employed.

Math 244: discrete mathematics includes many topics of interest in computer science.

Math 246: differential equations can be used for modeling complex systems in biology, physics, economics, and other fields. 

Math 270: set theory is at the foundation of mathematics and often taken by philosophy students.

Many incoming students enroll in one of our calculus courses (Math 110, 112, 115, 116, 120, or 121). Within calculus, the sequence of courses is

1. Math 110 + 111 or Math 112 (differential calculus, similar to AP Calculus AB)
2. Math 115 or Math 116 (integral calculus, similar to AP Calculus BC)
3. Math 120 or Math 121 (multivariable calculus)

If you are considering taking calculus, you will need to complete our placement exam, so that we can help you determine the best place to start. We highly recommend taking the test during the summer before you first enroll at Yale. The result will be valid for two years.

• For detailed information about the test, visit our Calculus and placement exam FAQ. 
• The Calculus Placement Exam is typically open in July. All students who wish to take calculus during the upcoming academic year should take the test during the summer, so that they can have the results available, and take advantage of August advising. Toward the end of the Fall semester, there will be a makeup session for Spring registration. The current dates are posted on top of this page, under “News”. 
• All incoming first-year students are automatically enrolled on the Math Placement Exam Canvas course at the end of June. Rising sophomores, juniors, and seniors should contact math.dus@yale.edu to be added to the site. 
• Results of the test are available immediately upon submission, by clicking on the “placement results” tab. (If the tab does not load, try a different browser.) 
• If you would like to take a course that differs from your placement exam result, please attend our calculus advising session in August. The advisers will be happy to help you. Note that you must take the test first - advisers cannot help you without it. Detailed information about the session will be posted on this site by the middle of July. 
• After receiving placement to take your first calculus course, pre-register for the class through Yale’s preference selection website. Preference selection is typically open in August (for the Fall term), in December (for the Spring term), and again in April (for the Fall term, continuing students). 

• The placement exam is NOT required for any math course level 200 or above. In particular, you do not need it in order to enroll in Math 225, 226, 255, or 256.

• Take the placement exam on Canvas.
• If you have questions about the calculus courses or placement exam, check the calculus and placement exam FAQ.
• If you have questions about your placement, attend our calculus advising session in August. Detailed information about the session will be posted on this site by the middle of July. 
• Pre-register for your first calculus course via Preference selection. Note that you must have placement in the course in order to enroll, and you may not enter preference selection for more than one calculus course at the same time.
• If you need help with your placement and missed the advising session, write to the faculty member listed below as a contact for the course into which you were placed. 

Pre-requisite for the mathematics major is integral calculus (for example Math 115, or AP Calculus BC). 

Following the pre-requisite, the introductory sequence includes:

• Linear algebra (Math 225 or 226),
• Real analysis (Math 255 or 256), and
• Multivariable analysis or calculus (Math 302 or 120). 

Most students complete multivariable calculus before enrolling in Math 225 or 226.

Prospective mathematics majors and students with interest in abstract mathematics may consider enrolling in Math 225 (or 226) directly after integral calculus (e.g. Math 115 or AP Caclulus BC), and completing their vector analysis/multivariable calculus requirement with Math 302.  Note that Math 225 does not require the placement exam - if you have completed an integral calculus course, you can just enroll in Math 225. 

If you have not completed a full integral calculus course, including sequences and series, then you will need to complete the calculus placement exam, and start in the calculus sequence. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

If you have completed integral calculus but have not done multivariable calculus, then the best course to start with is either Math 120, or Math 225 or 226. Note that Math 120 will require the placement exam.

Most students with this same background will start with Math 120, to finish the calculus sequence, and gain more experience with mathematics before enrolling in proof-based courses. This choice is recommended particularly if you may need multivariable calculus for another major you are considering, or if it is needed for other courses you might like to take soon (such as in physics or economics). After Math 120, you would move to Math 225 or 226, and Math 255 or 256, which would complete your introductory sequence requirement.

If you are excited to start with proof-based mathematics right away, then Math 225 or 226 may be the best course. For advice choosing between the two, see the above section on “Linear algebra and introduction to proofs”. Your next course would be Math 255 or 256, and you would complete the introductory sequence with Math 302.

If you have completed multivariable calculus but have not taken linear algebra, then the best choice is Math 225 or 226. For advice choosing between the two, see the above section on “Linear algebra and introduction to proofs”. Your next course would be Math 255 or 256, and you would complete the introductory sequence with Math 302.

If you have completed multivariable calculus and have taken linear algebra, then the options are as follows:

First, we need to determine whether your linear algebra course was fully proof-based or not. Most linear algebra courses are not: They may prove some results along the way, but they focus on applications, problem solving, and computations (similarly to a typical calculus course). A proof-based course teaches techniques for writing mathematical proofs (such as induction), and problem sets and exams focus mostly on proving results.

If you are not sure whether your linear algebra counts as proof-based or not, send a syllabus to math.dus@yale.edu; we will be happy to take a look and advise you.

If the linear algebra course was not proof based, then you will still need to take Math 225 or 226. For advice choosing between the two, see the above section on “Linear algebra and introduction to proofs”. Your next course would be Math 255 or 256, and you would complete the introductory sequence with Math 302.

If the linear algebra course was proof based, then please reach out to the DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but we can evaluate the course you have taken, and if it seems reasonably equivalent to Math 225, we will give you permission to substitute a higher level course in the same area for Math 225. We will also help you find the best starting course (likely Math 255 or 256 – or higher, if you have taken real analysis as well).

If you know proof-based linear algebra but have not taken officially taken a course in it, or if your course is not evaluated as equivalent to Math 225, you will have a chance to place out of Math 225 by taking an exam at the end of August before your first semester at Yale. Please reach out to math.dus@yale.edu during the summer, and we will help you with the arrangements. Note that the test must be taken before you first enroll at Yale, and that it does not grant course credit – it may only allow you to substitute another course in the same area for Math 225.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 120. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

If you have completed a multivariable calculus course equivalent to Math 120, then please reach out to the DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but we can evaluate the course you have taken, and if it seems reasonably equivalent to Math 120, we will give you permission to substitute a higher level course in the same area for Math 120. We will also help you determine the best math course to start with. In most cases, this will be Math 225 or 226; but it could be a higher level course, if you have completed linear algebra already.

To complete the specifically required courses (other than the senior requirement), you will need to complete Math 225 or 226 (proof-based linear algebra), and Math 244 (discrete math). We recommend taking Math 225 or 226 before Math 244, as the former provides a thorough preparation in proof writing, and this is very helpful skill in Math 244.

Other courses frequently taken by Math + CPSC majors include Math 241 (probability theory), Math 246 (ordinary differential equations), Math 255 (analysis 1), Math 270 (set theory), Math 305 (analysis 2), Math 350 (abstract algebra). You can find more information about most of these courses in the above section on “Math introductory courses”.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 120. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

For Math + Econ majors, it is important to take multivariable calculus as soon as possible. We recommend starting with your Yale calculus classes right away, in the Fall of your first year.

If you have completed a multivariable calculus course equivalent to Math 120, then please reach out to the DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but we can evaluate the course you have taken, and if it seems reasonably equivalent to Math 120, we will give you permission to substitute a higher level course in the same area for Math 120. We will also help you determine the best math course to start with. In most cases, this will be Math 225 or 226; but it could be a higher level course, if you have completed linear algebra already.

To complete the specifically required courses (other than the senior requirement), you will need to complete Math 225 or 226, and Math 255. Math 225 or 226 must be taken first.

Other courses frequently taken by Math + Econ majors include Math 244 (discrete math), Math 246 (differential equations), Math 270 (set theory), Math 330 (advanced probability). You can find more information about most of these courses in the above section on “Math introductory courses”.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 120. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

If you have completed a multivariable calculus course equivalent to Math 120, then please reach out to the DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but we can evaluate the course you have taken, and if it seems reasonably equivalent to Math 120, we will give you permission to substitute a higher level course in the same area for Math 120. We will also help you determine the best math course to start with.

While linear algebra is not required for the major, we very much recommend completing Math 225 or 226, partly for the topic they teach, and partly because they provide a thorough preparation with proof writing, which is an essential skill for the major.

To complete the specifically required courses (other than the senior requirement), you will need to complete Math 270. We recommend first completing Math 225 or 226, for the extra proof preparation, but this is not required. 

Other courses frequently taken by Math + Phil majors include Math 241 (probability theory), Math 244 (discrete math), Math 246 (differntial equations), Math 255 (analysis 1).   You can find more information about most of these courses in the above section on “Math introductory courses”.

If you have not completed a multivariable calculus course, then you will need to complete the calculus placement exam, and start in the calculus sequence, through Math 120. For more information, see the above notes about the placement exam, and checklist for enrolling in calculus.

For Math + Phys majors, it is important to take multivariable calculus as soon as possible. We recommend starting with your Yale calculus classes right away, in the Fall of your first year.

If you have completed a multivariable calculus course equivalent to Math 120, then please reach out to the DUS during the summer before your first year, at math.dus@yale.edu . Yale does not permit students to get credit for courses taken during high school, but we can evaluate the course you have taken, and if it seems reasonably equivalent to Math 120, we will give you permission to substitute a higher level course in the same area for Math 120. We will also help you determine the best math course to start with.

While linear algebra is not required for the major, we very much recommend completing Math 222, 225 or 226, as it teaches skills directly relevant to the major, as well as to many of the potential subsequent courses. For students who wish to keep open the possibility of taking proof-based courses in the future, Math 225 or 226 is highly recommended over Math 222, as the former provides a thorough preparation with proof writing.

Other courses frequently taken by Math + Phys majors include Math 241 (probability theory), Math 244 (discrete math), Math 246 (differntial equations), Math 255 (analysis 1). Students interested in theoretical physics and proof-based courses often include some of the level 300 courses, most often Math 305 (analysis 2), Math 310 (complex analysis), or Math 350 (abstract algebra). You can find more information about most of these courses in the above section on “Math introductory courses”.

Most Yale students complete a calculus course at some point during their studies. If you have not yet completed all of calculus, through multivariable, and you either wish to continue with the sequence, or you want to keep your options open as far majors or other courses that require calculus, then one of the courses in the calculus sequence may be a great place to start.

In order to enroll, you will need to complete the placement exam, and then register for a section of your course through preference selection. For details, see the above notes about the calculus sequence, placement exam, and checklist for enrolling in calculus.

If you have never taken calculus, do not expect to need calculus for your major or other classes, and would prefer to take another kind of math course at Yale, then you might enjoy one of our level 100 seminars: these are described above under “Other courses at the 100 level”. The seminars have limited enrollment, and do not expect any prior knowledge of calculus. They teach a combination of math topics and problem solving skills that can be useful for students in any major.

If you have completed a multivariable calculus course, and your major does not require calculus, then you can enroll directly in a higher level math course. Frequent choices for many majors include linear algebra (Math 222, 225, or 226), probability theory (Math 241), discrete mathematics (Math 244), or differential equations (Math 246). You will find these described under “Linear algebra” and “Other courses at the 200 level” above. If you need any help choosing, please don’t hesitate to write to math.dus@yale.edu, stop by one of our office hours, posted on the Math DUS website, or consult the DUS of your major for recommendations.

If you have completed a multivariable calculus course and your major does require calculus, then you should meet with the DUS of your major to discuss what the options may be. (Some majors allow students to substitute a higher level math course, for example.)

With additional questions, a good place to start are our FAQ’s:

• Placement exam and calculus FAQ,  
• Math major and advanced courses FAQ

If your question is not addressed there, please contact the Math DUS at math.dus@yale.edu .  Please allow at least two weekdays for an answer. (During school recess, especially winter and summer break, our response time may be longer.) 

For questions about specific multi-section courses (such as most of calculus and Math 222), please contact the course director listed below. For single-section courses, the best person to contact is the instructor. 

• Math 110 and 111: John Hall
• Math 112: Ian Adelstein (Fall), Andrew Yarmola (Spring)
• Math 115: Meghan Anderson (Fall), Mihai Alboiu (Spring)
• Math 120: Su Ji Hong (Fall), C.J. Argue (Spring)
• Math 222: Brett Smith (Fall), Erik Hiltunen and Hanwen Zhang (Spring)
• For questions about a specific single-section course, the best person to ask is the instructor (listed in Yale Course Search). 
• For other advice (e.g. about course selection or requirements of the major), please don’t hesitate to reach out to math.dus@yale.edu.

The Student Accessibility Services (SAS) Office works with students with ADHD/Autism/learning difficulties, sensory or motor disabilities, mental health concerns, temporary disabilities like concussions and serious injuries, and more. Our peer liaison program is designed so that first-years can connect with someone who has first-hand experience with navigating accommodations at Yale. If you think you could benefit from additional resources in regards to academics and general college life, please don’t hesitate to fill out this form and the PL for your college will reach out ASAP.