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. 

Town halls for calculus courses will be scheduled via zoom for early August: times will be listed below. The town halls are run by two of the course instructors, who will talk about how the course runs, its pre-requisites and what it covers, they will give tips that can help students succeed in the course, and answer questions from the audience. The schedule will be posted here.

For now, here is information from sessions in 2022:

• Math 110
  Slides and recording are available on course Canvas syllabus page. 
• Math 112
  Slides from 112 presentation
  Recording is available on course Canvas syllabus page.
• Math 115
  Slides from 115 presentation
• Math 120
  Slides from Math 120 presentation 
  Recording is available on course Canvas syllabus page
• Math major sequence / Math 225
  Slides from math major presentation
  Slides from 225 presentation

Individual calculus placement advising session schedule will be below - zoom links will be posted by 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 math major town hall, or 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 town halls and 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. The necessary background is 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 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. The necessary background is differential calculus (equivalent to Math 112 or 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. The necessary background is integral calculus (such as Math 115 or 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.

We recommend taking linear algebra first, because it is more universally applicable, and because it is a more gentle introduction to proofs – but it is completely fine to take analysis first.

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. 

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.

• 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 j.barnes@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.

1. Take the placement exam on Canvas.
2. If you have questions about the calculus courses or placement exam, check the calculus and placement exam FAQ.
3. 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. 
4. 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.
5. 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 completed some part of the sequence during high school, please visit the Math Major FAQ for information about the options. You should then consult the DUS, who will evaluate your previous coursework, see if an exception could be granted from the requirements, and help you select the best class to continue. 

For advice about the mathematics major or courses, visit our Math Major FAQ, attend our Academic Fair in August, or contact the Math DUS. 

If you are thinking about the math major, we encourage you to sign up for our Math DUS mailing list, to get news from the math department. You can also take a look at our Math community page!