<p>I am going to be double majoring in both physics and mathematics, but I am not sure whether applied or pure would be better for a physicist. Is it beneficial for a physicist to know how to write proofs? Or would the algorithms I learn in applied mathematics be a more useful tool to a physicist?</p>
<p>An applied math major will still need to take the proof-heavy upper division math courses that a pure math major will take. Some of them are considered especially applicable to physics anyway (e.g. real analysis, complex analysis, abstract algebra (group theory), partial differential equations).</p>
<p>Here are the pure and applied math majors at Berkeley:</p>
<p>[Course</a> Requirements: Pure Mathematics - UC Berkeley Department of Mathematics](<a href=“http://math.berkeley.edu/undergraduate_major_require_pure.html]Course”>Fall 2006 | Department of Mathematics at University of California Berkeley)
[Course</a> Requirements: Applied Mathematics - UC Berkeley Department of Mathematics](<a href=“http://math.berkeley.edu/undergraduate_major_require_applied.html]Course”>http://math.berkeley.edu/undergraduate_major_require_applied.html)</p>
<p>Note that four upper division required courses are the same, and one more for applied is the same as one semi-elective for pure. So it is entirely possible to take a selection of math courses that would effectively do both pure and applied math without too many extra courses (though it is unlikely that they will let you double major in pure and applied math).</p>
<p>Hey, thanks for the quick response. </p>
<p>I just looked at the upper-division classes in both streams at my school, and the pure math classes are only restricted to those who took pure math classes in first and second year and vice-versa with applied math. If I don’t take analysis I in first year, I can’t take abstract algebra, real analysis, topology, complex analysis, or any of the “proof-y” upper year classes because those are prerequisites and the regular calculus sequence are “exclusions” to the analysis sequence, meaning I can’t take analysis after having taken the calculus sequence (calc I and II). Only the analysis sequence will give me the prerequisites needed to take the proof-heavy classes. This is the problem. Should I just stick with the regular calculus sequence and then take applied mathematics or take the analysis sequence and stick with pure mathematics? </p>
<p>Unless, classes such as partial differential equations and fluid mechanics are proof-heavy classes?</p>
<p>For most B.S. math programs (pure or applied), you have to take at least one semester or Abstract Algebra and one semester of Real Analysis, both will have proofs. Now as far as “analysis”, some schools will call it Analysis, some Real Analysis and some will call it Advanced Calculus. Some schools (bigger ones) will have all three and for the most theoretical, you want Real Analysis. Algebra may also be called Abstract Algebra or even Ring Theory.</p>
<p>Usually applied math programs only require Analysis I/Real Analysis I and Algebra I/Abstract Algebra I along with a Complex Analysis course (residues, etc) with the pure math majors usually requiring Real Analysis II and Abstract Algebra II.</p>
<p>If your school offers it, they may offer a course in Mathematical Physics (or Mathematics Methods in Physics).</p>
<p>What school? If I understand you correctly, the analysis course you are referring to is what is often called honors freshman calculus elsewhere, with more proofs and theory than regular freshman calculus, and that having taken that course instead of regular freshman calculus is a prerequisite to core pure math upper division courses.</p>
<p>Why not just take analysis / honors freshman calculus so that you have the option of doing pure or applied later? It does seem hard to imagine majoring in applied math without taking upper division courses like real analysis, abstract algebra, and complex analysis. Group theory from abstract algebra is used in quantum mechanics in physics.</p>
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The only real analysis class that I may have to take is intro to real analysis I, and its optional according to the credit requirements along with many other classes. As for abstract algebra, that can fall under the many other optional classes (intro to Number Theory, Chaos, Fractals and Dynamics, intro to Mathematical Logic, and intro to Combinatorics) along with a 400 level course (either Polynomial Equations and Fields or Classical Geometries) are my program requirements. </p>
<p>The analysis sequence at my school is definitely not real analysis, as real analysis is taken in upper years. It definitely seems like “advanced calculus” as you noted. Here’s the syllabi for analysis I: “A theoretical course in calculus; emphasizing proofs and techniques, as well as geometric and physical understanding. Trigonometric identities. Limits and continuity; least upper bounds, intermediate and extreme value theorems. Derivatives, mean value and inverse function theorems. Integrals; fundamental theorem; elementary transcendental functions. Taylors theorem; sequences and series; uniform convergence and power series.”</p>
<p>As for mathematical physics, unfortunately, my school does not offer it.</p>
<p>
[URL=<a href=“http://www.artsandscience.utoronto.ca/ofr/calendar/prg_mat.htm]This[/URL”>http://www.artsandscience.utoronto.ca/ofr/calendar/prg_mat.htm]This[/URL</a>] school. It’s a Canadian school, and has one of the strongest, if not the strongest, math departments in the country. I won’t be doing any of the specialists, just a major. </p>
<p>And yes, you are correct in your assumption. The entire class is all proofs, no computation. Problem is, the class is a well-known GPA killer, has a high dropout rate (and bear in mind, it is only taken by math majors/specialists), and the class average cannot be more than a D according to the department. If the class average surpasses a D, the professor is investigated and must submit a letter to the department (all of this information confirmed by a TA and other students who have taken the class). </p>
<p>However, I did contact the department and inquired about this dilemma about taking upper year classes that require the analysis sequence with only taking the regular calculus sequence. They told me that they are currently developing a “bridging” course for students with the regular calculus sequence. With that credit, those students can then take complex analysis, topology, set theory, etc.</p>
<p>If I understand correctly, you have a choice of:</p>
<p>MAT135Y1 = regular calculus
MAT137Y1 = calculus (looks like honors compared to MAT135Y1)
MAT157Y1 = analysis (calculus with lots of proofs and theory, highest honors level)</p>
<p>?</p>
<p>It does seem odd that they do not want the class average in MAT157Y1 to be higher than a D, since it is probably a course with a relatively small number of students whose actual ability and performance could fluctuate significantly from year to year. You may want to ask the department specifically what the grading policy in that course and other math courses is, rather than relying on secondhand information.</p>
<p>Perhaps the course home pages have some more information:</p>
<p><a href=“Department of Mathematics | University of Toronto”>Department of Mathematics | University of Toronto;
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</p>
<p>Yes, you are correct. I will be taking MAT135, as that leaves the option of possibly taking MAT157Y1 by itself in the summer (I can probably get a good mark then), as they are not exclusions of one another. </p>
<p>As for asking the department, I did that. They seemed awfully sketchy and told me they are not allowed to give averages of a class to a student that has not taken it yet, so the only available information is second-hand. The class is also quite large, due to it being an requirement to the actuarial science program (one of the strongest in the country).</p>
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I wouldn’t be so sure about that. Toronto has more math majors than my college has students in total.</p>
<p>I know that it’s probably too early for you to make a decision on these matters, but the ideal math preparation depends on the specialty you want to pursue within physics and your post-graduation plans.</p>
<p>I would go for pure math if you might study theoretical physics at the graduate level. For everything else, applied might be the better option and would also make you more employable outside of academia.</p>
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<p>On the other hand, it does appear that choosing MAT157Y1 will allow the OP to defer the decision until later, without having to take additional course(s) (assuming s/he gets a grade higher than a D).</p>
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You are absolutely right. Now that I have actually looked at the courses, it does appear that MAT157 is accepted everywhere that the other two calculus options are accepted.</p>
<p>Actually, until you have a reason to deviate from that course, you could follow the math courses for the combined math and physics specialist. It too starts off with MAT157, so that’s probably the best calculus course for you to take.</p>
<p>Personally, I’m more interested in experimental and computational physics rather than theoretical and mathematical physics. So, would taking all these proof classes, which will be a great detriment to my GPA, be of any benefit to me at all? It would be ridiculous for me to take classes that will negatively affect my chances of getting into graduate school and won’t be of any benefit in my future career. </p>
<p>Thanks for all the help and advice thus far, both of you.</p>
<p>If you want to get into computational physics, you probably want to look into computational science/engineering coursework OR (if that is not available) look into computational math or Math/CS or Physics/CS as majors.</p>