<p>I was wondering because I am interested in a phsyics major and then going to grad school. Could you guys tell me the top 10 math courses beyond Calc 2 that someone who wants to go to physics grad school should take?</p>
<p>From what I've researched, every major is required to take Calc 1-3 and Elem Diff Eq, but afterwards, programs vary in what they require. It looks like good courses to take include: Math Methods for Physics, Linear Algebra, Analysis (Real & Complex), Partial Diff Eqs, Vector Calculus, Abstract Algebra, but I want a more definitive list. Also, could you take into consideration that I love algebraic style math but I am not a fan of geometric math (I never enjoyed the idea of being told a bunch of rules for rote memorization instead of learning why those rules exist)</p>
<p>I'm currently a high school junior who has taken AP Physics B (useless for credit, but great for a knowledge base) and will be taking AP Calc BC and AP Chemistry next year. Hopefully I will get a 4 or 5 in BC Calc and get credit for Calc 1 & 2 in college.</p>
<p>On a side note, which is easier to take first, Calc 3 or Elementary Differential Equations? I ask because both can be taken after Calc 2, and I would like to take the easier one my 1st semester in college.</p>
<p>This is what I’ve taken so far in my physics degree in this order: Cal I, Cal II, Cal III, Linear Algebra, Differential Equations, and I just finished Vector Analysis. These were all required in my degree. There is only one more math course left that is required and that’s Intro. to Partial Differential Equations - a pretty difficult course from what I’m told. Since I’m minoring in math, I only need a senior-level math course to complete the minor given that the physics major requires so many math courses. I’m probably going to take Advanced Linear Algebra I when I get around to it.</p>
<p>Take an advanced course in linear algebra–one that discusses linear algebra in the abstract and not just matrices and column vectors. Quantum mechanics becomes a lot easier after taking this course.</p>
<p>Oh. Well, I just finished Modern Physics I. We did special relativity, early quantum, and got into the first parts of modern quantum. I’m taking MP II (QM undergrad) in the fall. I hope I’m not at too much of a disadvantage having only taken the sophomore-level Linear Algebra.</p>
<p>You’ll be fine. A lot of the course is just learning stuff about linear algebra. </p>
<p>In my opinion, though, there will be things that won’t make a lot of sense until you step back a bit and look at lin. algebra a lil more abstractly.</p>
<p>I think the problem with higher-up math classes is that they are geared towards math majors as opposed to Physics majors. So, there will be a different focus than one you probably want. Take things like ODEs and PDEs. Math people don’t care so much about the solution, but more about whether it exists, whether its unique or not, and other properties. </p>
<p>As far as classes you should take, some advanced Linear Algebra would help a lot. Some Complex Analysis/Variables (hopefully geared towards physicists and engineers) would also be nice. </p>
<p>However, you are probably better off asking actual physics majors or at least people in physics.</p>
<p>Thanks for the advise so far, it all seems really helpful.</p>
<p>Another question, how do math courses designed for engineers compare to those that are not, in relation to studying physics?</p>
<p>For example, @ UF they have a course called Advanced Calculus for Engineers 1 vs Advanced Calculus 1, and you can only take credit for one of the two (thus, they are equivalent). Which would be more beneficial for a physics major?</p>
<p>Additionally, should I take a course in Statistics course during undergrad? Due to scheduling issues both junior and senior year I was not able to take AP Stat during high school. Is statistics so important that I should consider taking Statistics at the community college (an undesirable choice since it would result in 5 AP classes + 1 college class at the same time, too much work since at that point it can’t help for college admissions) or simply wait until possibly my sophomore or junior year in college?</p>
<p>A lot depends on the kind of physics you want to do.</p>
<p>I would say linear algebra, calculus 1-3, ODEs, PDEs, probability+statistics, numerical analysis, applied mathematics, vector analysis, Fourier analysis, anything with ‘methods’ or ‘for engineers’ or ‘for scientists’… These are things to consider taking.</p>
<p>Then again, physicists just do whatever they want to math, so why bother?</p>
<p>I agree with the above posters who said that the abstract math classes may have a different flavor from what you want for physics. Your primary focus as an undergraduate should be on the computational math and math methods courses. However, once you know what area of physics you are the most interest in, you should talk to professors and find out what additional math classes might be useful to you. For example, Hodge Theory is essential for plasma physics and electrodynamics, and requires a background in algebraic topology to understand. That does not mean that every physics major needs learn algebraic topology though (in fact, most physics majors would be pretty miserable in that class).</p>
<p>A book that may be useful to look at is “All the Mathematics You Missed [But Need to Know for Graduate School]” by Thomas A. Garrity (2002, Cambridge University Press).</p>
<p>From the book description: “Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge, but few have such a background. This book will help students see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential geometry, real analysis, point-set topology, differential equations, probability theory, complex analysis, abstract algebra, and more. An annotated bibliography offers a guide to further reading and more rigorous foundations.” </p>
<p>Clearly it’s not a substitute for course work. In the preface the author says “This book is far from a rigorous treatment of any topic. There is a deliberate looseness in style and rigor. I am trying to get the point across and to write in the way that most mathematicians talk to each other. The level of rigor in this book would be totally inappropriate in a research paper”. However, I’ve found the book useful for quick reviews of long-forgotten courses. For at least some newcomers, I think it may give a nice 2,000 ft overview of the mathematics you might expect to encounter, but I also think this is a book whose usefulness will be a strong function of the particulars of your situation so, perhaps more so than usual, YMMV…</p>
<p>You may take some solace from the following, also from the preface: “The goal of this book is to give people at least a rough idea of the many topics that beginning graduate students at the best graduate schools are assumed to know. Since there is unfortunately far more that is needed to be known for graduate school and for research that it is possible to learn in a mere four years of college, few beginning students know all of these topics, but hopefully all will know at least some. Different people will know different topics…” </p>
<p>Major chapter headings are:
Preface
On the Structure of Mathematics
Brief Summaries of Topics
Linear Algebra
epsilon and delta Real Analysis
Calculus for Vector-Valued Functions
Point Set Topology
Classical Stokes’ Theorems
Differential Forms and Stokes’ Thm.
Curvature for Curves and Surfaces
Geometry
Complex Analysis
Countability and the Axiom of Choice
Algebra
Lebesgue Integration
Fourier Analysis
Differential Equations
Combinatorics and Probability
Algorithms</p>
<p>In my experience as I just completed my physics and applied math major, I can say that you don’t really need ANY upper-div math classes. Your physics dept should have a class titled Mathematical Methods for Physics, Mathematical Physics, etc. The class should use the book by Arfken or Boas that covers all the necessary math you need for your upper-div physics. </p>
<p>Now if you want to go into industry after your BS in physics, taking more math classes isn’t necessary but it helps. The most useful ones are numerical analysis, fourier analysis, and probability/stats</p>
<p>If you want to go into theoretical physics for grad school, then the following upper-div math classes are useful: linear algebra, topology, differential geometry, real analysis, complex analysis, and abstract algebra/group theory</p>