Pure Math for Physics Major?

College Majors Science Majors
1

<p>Hi everyone, </p>

<p>I'm a sophomore in astrophysics eventually planning on going to grad school. I've heard that for grad school, it's always better to have taken more math classes than less, but I'm wondering whether pure (heavily proof-based) math classes tend to be useful to physics majors. </p>

<p>So far, the math classes I've taken are vector calc, linear algebra, ODEs, and a "math methods for physics" course that covered some complex analysis and applications of linear algebra to physics. </p>

<p>In physics, I've taken an intro sequence in mechanics and E&M, a semester of "modern physics," and a ton of astro classes. </p>

<p>I the next couple of years, I'll need to take a more advanced mechanics class, a more advanced E&M class, statistical mechanics/thermodynamics, quantum, and GR, as well as some more advanced astro classes for which I'll learn galactic dynamics, fluid dynamics, etc.</p>

<p>I need to decide whether it's worth taking more math classes through the math department or just taking the physics classes and learning any necessary math along the way. Math classes that could potentially be useful are PDEs, vector analysis/advanced calculus, real analysis, group theory, complex analysis (which may or may not require a background in analysis), and differential geometry (which would probably be useful for GR). </p>

<p>The only abstract math class I've taken is linear algebra (it was all about vector and function spaces, often considered infinite dimensions, and involved no applications), and to be honest, I found it very annoying. I don't really like memorizing and writing proofs. </p>

<p>Do people on CC have experience taking higher math classes as physics majors? Is it worth the effort and potential ding to my GPA?</p>

2

<p>You have read your school’s recommendations?
[Undergraduate</a> Studies - Physics FAQs: Math and Physics | Department of Physics](<a href=“http://physics.yale.edu/academics/undergraduate-studies/physics-faqs/undergraduate-studies-physics-faqs-math-and-physics]Undergraduate”>http://physics.yale.edu/academics/undergraduate-studies/physics-faqs/undergraduate-studies-physics-faqs-math-and-physics)</p>

3

<p>In general, applied type courses are going to be more useful than purely theoretical courses as far as math goes. Writing rigorous mathematical proofs and such isn’t really a crucial part of doing physics. It’s definitely good stuff to learn and know how to do, but it isn’t as crucial as actually knowing how to ‘use’ the math. </p>

<p>I’m a physics major myself, and I’m also minoring in math. I’m considering doing a double major. I haven’t gotten to my upper level courses yet, but some of the math courses that I’m planning on taking are PDE’s, differential geometry, an intro topology course, a statistics and probability theory course, all on top of the basic calculus sequence, differential equations, and linear algebra.</p>

<p>More math is always a good thing for physics. You mentioned a math methods for physics course, but are there other upper level courses with a similar structure? Those types of classes will often teach you some of the more crucial aspects of all of these different fields.</p>

4

<p>High school physics is incredibly simple in comparison. It’s a very rudimentary introduction to the entire field, without any real depth. It’s mainly taught like “here’s the equation, here are the numbers, here’s how to plug them in.” There’s no real rigorous development of theory involved. That said, being good at it is certainly a good sign.</p>

<p>Engineering and physics are, individually, two of the most demanding majors in a school. While there is a lot of course overlap at the lower level with calculus, university physics, some general chemistry, linear algebra, diff eq etc., there really isn’t going to be very much course overlap beyond the second year. Both majors on their own tend to require overloading with classes every semester. Personally an engineering/physics double major does not seem all that feasible to me. </p>

<p>That said, it’s not impossible to get a bachelors in engineering, and still go to grad school for physics, or vice versa. Plenty of people have done both.</p>

5

<p>Most of undergraduate physics IS applied mathematics. That being said, if you enjoy the math courses, take them. If you would like to take something else instead do that. Since you plan to go into a graduate program in astrophysics, ask your advisor what courses might be a good preparation for that route. You might find that a better plan is to take an undergraduate research course instead. In my 30 years of advising physics majors at Illinois Tech, I would say that our 4 Calculus classes plus 2 math electives is more than enough to prepare students for a top graduate program.</p>

6

<p>More math is better, but “proof-oriented” theoretical math is not very relevant (unless you plan on doing string theory).</p>

<p>At the undergrad level, you want to take Calculus I, II, III (vector calculus), an intro to linear algebra and linear ordinary differential equations with constant coefficients (often combined as one class).
That is the minimum. </p>

<p>Beyond that, many schools offer a year of applied mathematics for science & engineering… it is called different names at different schools, but it generally covers complex analysis, laplace transforms, applied probability, ordinary differential equations with non-constant coefficients, power series solutions, Fourier series and transforms, partial differential equations and separation of variables, etc.</p>

<p>It would be advisable to take at least 1 programming class, and perhaps a second programming class focussed on numerical methods for science/engineering applications.</p>

<p>For pure math, you may be interested in a class in “Complex Analysis” or “Set Theory”. Proof-driven classes are sort of irrelevant, but if you really want to take them, go for it… not everything you take as an undergrad has to be 100% relevant to your major.</p>