### Questions about Math at Yale

*Why is this topic on the Physics site?*Math is the natural language of Physics. If you become fluent, then you can travel far and wide, enjoying the natural beauty of the countryside. On the other hand, if you struggle, then you tend to stay close to the tourist traps, often returning home before your trip was scheduled to end.

Even if you don’t understand my analogy, here is the message: get started on math courses as soon as you arrive, and keep going as far as you can!

*What is a recommended sequence of intro math courses?*A recommended intro math sequence at Yale is:

Math 112- df/dx Math 115- Int (f dx) Math 120- f(x,y,z), partial derivatives & multi-variable integrals Math 225 or 222- Linear Algebra & Matrix Methods Math 250- Vector Analysis (extension of Math 120, where Vector fields like Electric & Magnetic fields (Bi(x,y,z), Bj(x,y,z), Bk(x,y,z)) are considered, using matrix methods, etc.)

Alternatively, for more mathematically inclined students (who like proof-based approaches):

Math 112- df/dx Math 115- Int (f dx) Math 230/230- This year-long course which covers much of the material in 112-250, but more formally…intended for future math majors, many physics majors take as well.

People should start taking the intro math sequence at the level that their background permits (e.g., some people need to start at Math 112). Most physics majors start at Math 120 or at Math 230. A smaller number start at Math 225, some at Math 250.

If your math background allows you to take either Math 225 or Math 230 when you first arrive, then you should probably try Physics 260. If you feel Math 120 is a better fit, then you should probably try Physics 200.

It is always possible to start at one level (of either physics or math), and move up (a rare, but possible occurence) or down (more common) during the semester.

*Is there a “flow diagram” illustrating these intro courses?*Here is one…you want to progress from the upper left corner down to the lower right corner. As you move towards the right, the courses become more “pure”. If you have taken the AP Calculus exam, you can jump into the sequence at several points, depending upon your score (shown in the green boxes):

*What about Differential Equations?*The Physics major explicitly requires certain math courses, both “prereqs” (e.g., Math 120) and one “advanced” course (e.g., Math 310-Complex Analysis).

The Physics major does not explicitly require that you take a Diff. Eqns. course (i.e., Math 246 or ENAS 194). Nevertheless, the material is very important, and you would benefit from taking this “intermediate course”, if you can fit it into your schedule (i.e., without breaking the flow diagram above). Note that these are offered in both the Fall and the Spring.

*How does Physics 301 fit into this?*Physics 301 (Intro to Math Methods of Physics) is another very useful “intermediate” course. It covers most of the book: Basic Training in Mathematics, by R. Shankar.

Physics 301 is designed to provide students with a practical foundation in the Math Methods that they will need to take the “advanced” Physics courses (i.e., Physics 410, 430, 440, 420, etc.). Physics 301 starts with the ideas of Math 112…and goes right up through ideas of Math 250 (including some Diff. Eqns), all in a single semester! The accelerated pace does have two benefits: it is easier to see how the ideas in the various Math courses are inter-related, and an “advanced” foundation in Math is in place before the “advanced” Physics courses begin.

Ordinarily, Physics 301 should not be used to replace a math course…it moves too quickly, and the overlap is incomplete. It is a good fit for people who are taking Math 250 concurrently. It could also be taken by freshman with advanced math backgrounds (e.g., taking Math 230 or Math 225/2 concurrently). This is a Fall only course.

*What does “advanced math” mean for the Physics B.S.?*These are the courses “beyond” Math 250 or Math 230b. Popular examples include: Math 310, Math 350, or the analysis sequence (Math 301, Math 305, Math 310, Math 315). There are a few examples in other departments that would also fit the bill.

For the Physics B.S., you need to take at least one math course at this level…and I would encourage to take more if you have the opportunity!

*How do “intermediate” courses figure into things?*Intermediate courses like Math 246 or ENAS 194 cover material that would be useful to a Physics major.

While they will not fufill the “advanced math” requirement, they would be included in a tally of courses taken for the Physics major (e.g., used for departmental honors, etc.).

*What about Physics 460?*Physics 460 is a graduate class on math methods. This is open to undergrads who have sufficient preparation (e.g., Math 310 would be very helpful).

*Any advice about Fall vs. Spring Math/Physics Courses?*When planning your future schedules, you should think carefully about the ordering, as some of the popular Math/Physics Courses are Fall Only:

Physics 301a, Math 250a, Math 301a, Math 310a, Math 350a, Physics 460a.

Other Math/Physics Courses are Spring Only:

Math 225b (not this year, but in recent years), Math 260b, Math 305b, Physics 430b, ENAS 397b.