Math and Philosophy

First, you will need to complete calculus through the level of Math 1150 (or Calculus BC).

The next course to take would be Math 1200. If you have already seen multivariable calculus, see the FAQ below for information about substituting another course for this requirement. 

After multivariable calculus, there is a variety of options at the 2000 level. Students often enroll in Math 2250, linear algebra that also serves as introduction to proof writing, which is a useful skill for the major (needed in Math 2700, for instance). 

Other courses frequently chosen by Math + Philosophy majors include Math 2410 (probability theory), Math 2440 (discrete math), Math 2460 (differential equations), Math 2550 (analysis 1). Note that Math 2250 is required before Math 2550, and it is strongly recommended before Math 2440. 

We encourage you to consult with your math faculty adviser or with the DUS, to brainstorm about choosing further mathematics courses to take, based on your interests, future plans, etc. We would be happy to help! For assistance on the Philosophy side, please consult with the Philosophy DUS. (For joint majors, each DUS oversees their portion of the requirements.) 

The senior requirement can be completed either with a mathematics seminar (Math 4800 - 4890), or with a philosophy seminar. For a philosophy seminar, extra work must be completed in the course, so you must check in with the Philosophy DUS as well as the instructor before enrolling. 

• Math 4800 is a pure math seminar, and at least two level 3000 courses are recommended as a pre-requisite. 
• Math 4810 is co-taught by the math and economics departments, and has Math 2250 and 2550 as pre-requisite. 
• Math 4820 is focused on math education, and has Math 2250 and 2550 as pre-requisite. 

For details about these courses, as well as seminar topics for the upcoming year, please visit the Math major FAQ. 

If you have not seen multivariable calculus before and need it for your major (e.g. all the combined Math majors), or for other courses you plan to take (e.g. in Economics or Physics), then you should consider taking Math 1200 as soon as you can. 

For the pure math major, you have a choice to complete either Math 1200 or 3020. Most students either complete Math 1200 in their first year (before Math 2250 and 2550), or complete Math 2250 and 2550 first and then take 3020 in their second or third year. 

Yale does not allow transfer credit for courses taken during high school, even if they were taken at a local college. That does not mean you have to repeat material you already know, however. The details depend on why you need Math 1200: 

1. If you need it as a pre-requisite for another Yale course, it should not be an issue: instructors typically accept a high school course in place of Math 1200. If you’re not able to reach the instructor, contact their program’s DUS. 
    
2. If you need it for the pure math major: You can complete the multivariable requirement with Math 3020. This option is available to all students, whether or not they have already completed a course similar to Math 1200. 
    
3. If you need it for a combined math major:  You can send your transcript (unofficial is fine) to math.dus@yale.edu , and request permission to substitute Math 3020 for Math 1200 in requirements of the relevant major (Math + CPSC / Econ / Phil / Phys). Please be sure to specify which major you are interested in. 
   
   If you would like to consider other options for substitutions (i.e. another class in the same area, such as Math 2460 or an analysis course), you can request an evaluation of the course that you have completed. For this evaluation, we would need a copy of your transcript, syllabus for the course, detailed list of topics covered, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .  
    
4. If you need it for another major, please contact the major’s DUS to see what options there may be, as they are in charge of all requirements and exceptions for their major. 

No (but if you passed ENAS 1510 before deciding on the math major, you can complete the multivariable calculus requirement with Math 3020). 

Yale does not allow transfer credit for courses taken during high school, even if they were taken at a local college. Beyond that, the answer and its details depend on why you need linear algebra: 

1. If you need it as a pre-requisite for another Yale course, it should not be an issue: instructors typically accept a high school course, if it is equivalent to the pre-requisite. If you’re not able to reach the instructor, contact their program’s DUS. 
    
2. If you need it for Math + Phil or Math + Phys: These majors recommend taking Math 2250 or 2260, but do not require any linear algebra, so you will not need to get permission to substitute. 
    
3. If you need it for another major, please contact the major’s DUS to see what options there may be. 
    
4. If you need it for the Pure math, Math + Econ or Math + CPSC: These three majors require Math 2250 or 2260, so substitution can only be considered if your course was fully proof-based (e.g. you learned proof techniques such as induction, and most problems on homeworks and exams explicitly asked “prove [something]”). In all three majors, students who completed linear algebra in high school typically still enroll in Math 2250 or 2260. 
   
   If your course was proof-based you can request an evaluation of it. For this evaluation, you will need to reach out to math.dus@yale.edu during the summer before your first semester at Yale. We will need a copy of your transcript, syllabus for the course, detailed list of topics covered, a copy of one or two assignments, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .    
   
   If the course is reasonably equivalent to Math 2250, then you may be granted permission to substitute Math 3400. 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). Please note that this permission has to be granted by the Math DUS - obtaining permission from the Math 255 instructor to enroll will not take care of requirements of the math major. 
   
   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 can try placing out of Math 225 by taking an exam during the summer before your first semester at Yale.  Details are listed in a question just below. 
   
    

First, please note that the test does not award course credit or fulfill any requirements at Yale. It can only grant permission to substitute a higher level course in the same area for Math 225, in requirements of the math and joint math majors. 

The test is available to incoming first-year students who learned the material of a fully proof-based linear algebra course (such as Math 225) prior to enrolling at Yale, but the course was not evaluated as equivalent to Math 225. (See above for how to have a course evaluated.)

The test is only open to students who have had some formal training in proofs and linear algebra, including regular feedback about their work from experienced mathematicians. 

If you wish to take the test, you must first e-mail us the materials from the course you completed, at math.dus@yale.edu. This needs to be done by August 15, during the summer before you first enroll at Yale. (The exam is not available to continuing students.) 

We will offer the test in person, at the end of August, just before classes start (usually that Monday or Tuesday). We will set the time according to everyone’s availability: you will hear from us after August 15 about scheduling, if your name is on our list. 

Students who pass will receive permission to substitute a higher level course in the same area for Math 225, in requirements of the math or combined math major (Math + CPSC, Econ, Phil, Phys)  

If you need linear algebra for another major, please check in with their DUS - our process only works for math majors, we have no say in requirements of other majors (though we would be happy to assist, if the DUS wishes). 

As a rule, the answer is “no”. Courses required for the major must be completed. In rare cases where an incoming student has learned in high school the material and skills taught in a particular required course, the DUS may grant an option to substitute a higher level course in the same area. Please be sure to discuss this with the DUS prior to your first semester at Yale. 

All three courses cover linear algebra. Math 2220 focuses more on computational techniques and applications, while 2250 and 2260 emphasize mathematical proofs and a more conceptual approach.

Math 2250 (linear algebra) or 2260 (intensive linear algebra) is recommended for students who wish to take further proof-based mathematics courses. Students majoring in mathematics, Math + CPSC or Math + Econ are required to complete either Math 2250 or Math 2260. 

 In more detail: For math majors, and students who wish or need to continue with proof-based math courses, the theory and proof writing skills learned in Math 2250 or 2260 provide essential preparation for further study. That is why the math major does not accept Math 2220. 

Outside of the major: generally speaking, proofs are useful in many fields. They help one to become a better problem solver, evaluate different approaches to a question, consider options along the way, keep track of important details, check solutions for correctness, and present them in a way that is accessible to others. These skills are very helpful, in math and outside of it. 

For that reason, many students find it beneficial to take Math 2250 or 2260, even if they do not continue with further math courses. If you try the course and enjoy it, the skills you learn will not be wasted. 

If you enjoy applications more, and want to get lots of practice solving concrete problems, rather then focus on theory, then Math 2220 is a better choice. It provides great preparation on the practical side of linear algebra, and it is preferred by the majority of students in engineering, social sciences, and many other fields. 

Moving from Math 2260 to Math 2250 is permitted until Midterm. Moving from Math 2260 or 2250 to Math 222 is permitted until the end of the third week of classes (this has an earlier deadline because the courses are quite different, and it is too difficult to catch up later on). You can read more about how moving works in our Calculus FAQ.