Advising
The Peer Advising Program is managed by the College Center for Advising Services (CCAS). As a Peer Adviser in the Department of Physics and Astronomy, I help students:
- Plan their major/minor
- Choose and register for courses
- Find study abroad programs
- Engage in research opportunities
- Work on study strategies
- Develop independent studies
or anything else at all! This page will be dedicated to answering some of the most
common questions and concerns incoming PAS majors have.
Please note that all Major/Minor/Certificate requirements can be found on the department
website.
Which Math Sequence Should I Take?
There are three introductory math sequences, MTH 140s, 160s, and 170s. The 140 sequence of
math is not accepted for the Physics or Physics and Astronomy Major (B.S. or B.A.), so those
intending to major in PHY or PAS should not consider the MTH 140s.
MTH 171/172/173/174: This is the honors math sequence and is intended for those with a strong
background and interest in mathematics, and who are potentially also considering a major in
mathematics. Each course in this sequence is 5.0 credit hours, as opposed to the usual 4.0.
The honors sequence covers all of the same material as the 160s, namely Calc I/II/III
(multivariable), ordinary differential equations and linear algebra. The classes are all
proof-based, which means that students will be rigorously developing and proving mathematical
theorems, starting with the basic axioms of mathematics and building their way all the way
thorugh, for example, the definition of integration in terms of upper and lower (Darboux)
sums, by the end of MTH 171. Lectures and homeworks will both involve writing proofs for
various theorems, with the homeworks building on the definitions and theorems covered in class.
Pros:
- MTH 173 credit may be used to replace taking MTH 235 as a foundational requirement. Thus only two upper level (200+) courses need to be taken, after 171-174, to obtain a math minor. Since the PHY and PAS majors require two upper level math courses anyway, a math minor is automatically obtained for you.
Cons:
- Proof-based math can be a steep learning curve for those who haven't encountered it before. These are not your 9th grade geometry proofs! For an example of an elementary proof, see the proof of commutativity of addition of natural numbers.
- Taking the full 171-174 sequence will take four full semesters, or two years. Alternatively, using AP Calc credit to skip MTH 161 (or skip 162 as well with a 4 or 5 on BC) will put you ahead a semester (or a full year if jumping straight to MTH 164/165). It is very rare, and only in exceptional cases, that one will skip to MTH 173 their first semester. Check out the math placement guide to see what your AP credit can count for.
Depending on who you are, the richness of the material in the 170s may completely outweigh these cons, especially if you are considering a math major.
MTH 161/162/164/165: This is the normal calculus track taken by most students. Often, students with AP credit will skip MTH 161 (Calc I) and start with MTH 162 (Calc II), and occasionally students will skip MTH 162 and start with MTH 164/165 (multivariable/linear algebra and differential equations). While MTH 161/162 are required to be taken first and in sequence, MTH 164/165 may be taken in either order (or simultaneously, and while doable you may discover the final exam for both classes will be on the same day) as they do not depend on each other. The classes are the type of math class you are likely used to, i.e. not proof-based. In lecture you learn new math techniques and methods of solving new and more complicated problems, and for your homework you practice these techniques on many repetitive problems. In my opinion, this is the more practical approach for PHY/PAS majors, as you will mostly be concerned with learning the new techniques, and not necessarily proving their truth.
Pros:
- As a counter to the 170 sequence, with AP credit one can skip one or two semesters ahead by jumping to MTH 162 or 164/165. This will free up one or two course slots that you can use to take something else that interests you (or potentially graduate physics classes later down the road).
Cons:
- If one is pursuing a math minor, then MTH 235 (linear algebra) will need to be taken. However, I would argue that this is actually a pro, as it is only one extra class on top of the PHY/PAS major requirements, and it is an EXTREMELY useful course for physics majors (linear algebra will find its way into EVERY upper level physics course you take, but it is especially useful for quantum mechanics). MTH 235 is proof-based, so that much is unavoidable, however you do not need any previous experience writing proofs to do well in MTH 235. Besides, its a good skill to learn, and you'll write proofs in MTH 282 (complex analysis) which is a PHY/PAS major requirement anyway.
In the end, I'm not here to tell you which classes to take, but I hope that these summaries of the 160 vs 170 sequences will help you decide on where you personally stand as far as which math to take. It is always an option to start with the MTH 170s and drop to the 160s should the material get too difficult. As always, feel free to email me with any other questions you may have.