Math major

College Majors Science Majors
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<p>Do you need to be a Math savant in order to do well in the math classes at Top universities? I like numbers and calculus and algebra, but I don't like statistics. What courses would be required in order to be a math major? If I don't get into med school, what Jon opportunities are available for math majors at the undergrad level? What about if you graduate from a graduate school? I also hear that many math majors also minor in computer science. I personally am not a geek with computers and software so I'm guessing I wouldn't be able to do that?</p>

<p>I would appreciate any information revolving math majors. I am currently taking AP Calc BC and it is really easy. I also got a 36 on the math ACT section, though it isn't very hard lol. Thanks for any input!</p>

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<p>Definitely need calculus for math; usually calc1-3 for math, cs/engineering. Job opportunities include working for companies that hire mathematicians, actuary, and teaching. Though actuary deals a lot with probability and statistics than applied math. </p>

<p>Graduate school usually helps get a higher starting salary, may give you better shot at starting a career if not recruited during undergraduate studies. People who do CS take Discrete Math after Calc.1 or 3; but if you don’t enjoy coding and learning computer languages than maybe engineering or taking the engineering and science classes required for med school is best. Math and Science or engineering is another popular combo.</p>

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<p>Maybe you know this already, but if not it’s important to know that university-level math is VERY different from the stuff you learn in high school. It’s infinitely more interesting (well, in my opinion), but if you’re not prepared the transition might be jarring. It’s also not unheard of for people who think they like math to find out that they really don’t, once they encounter the “real thing”. Do you have any experience with writing proofs? </p>

<p>The standard “core” math courses are Real/Complex Analysis, Abstract Algebra, theoretical Linear Algebra (sometimes lumped in with abstract algebra), and Topology. There are also plenty of cool electives you might take, such as number theory, combinatorics, logic, etc. </p>

<p>Doing a CS minor or at least learning how to program is really good idea, since a lot of jobs that hire math majors involve computers in some way (certainly not all of them, though). In addition, theoretical computer science is basically a branch of math, but if you only do a minor you might not take those types of classes.</p>

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<p>At the junior and senior level in college, you will have to do more mathematical proofs in courses like real analysis, complex analysis, abstract algebra, proof-oriented linear algebra, etc…</p>

<p>Many math departments try to prepare students for these courses with:

  • a specific proof techniques course at the freshman or sophomore level
  • bundling the proof techniques practice with a sophomore level course, such as a discrete math course
  • offering honors freshman and sophomore level math courses with more proofs</p>

<p>Math majors’ job prospects tend to lean heavily toward finance and computers. Obviously, taking some applicable electives in statistics, finance, economics, and/or computer science can help here.</p>

5

<p>Yeah, the “mathematical analysis” part is almost mandatory for any math program. At some schools, there may be an “applied mathematics” or “mathematical science” major where you can get away with just one semester of mathematical analysis…which may be called advanced calculus but I don’t know any schools that will let you graduate without some analysis/real analysis/advanced calculus.</p>

<p>Now some schools will let you skate without abstract algebra but that usually means that the math major has NO intentions of doing a graduate math program. Graduate math programs usually want 1 whole year of analysis and 1 whole year of abstract algebra.</p>

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<p>^Yeah, I should probably mention that my post was more oriented towards the pure math side of things. Linear algebra and real/complex analysis are important for any type of math major, but abstract algebra and topology are much more on the “pure” side. In addition, differential equations would definitely be a core class for an applied math degree.</p>

<p>If you decide to do any type of math major, though, I don’t think it’s a good idea to wait to learn how to write proofs. While getting skilled at and comfortable with proofs takes time and practice, learning the basics of how to write them is pretty trivial. If you’re thinking about a math degree and don’t have any experience with proofs, now’s a good time to at least get acquainted with them. In any case, it’ll help you figure out if a math degree is right for you.</p>

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<p>FutureDoc, you don’t need to be a math savant to do well in math in college. I was a math major and yes I was very decent in math in high school but no savant. And I graduated with a GPA above 3.5 in my math courses. So i think I did fairly well and I wasn’t a savant. </p>

<p>You do need to have good to very good mathematical ability to succeed. Math in university as many people before have said or alluded to is quite different (harder) from math in high school. In college, you can get through freshman year and MAYBE 1 semester of your sophomore by relying on the advanced high school math you are taking. Beyond those years math gets REAL. Linear Algebra, Differential Equations (ordinary and Partial), Abstract Algebra/Algebraic structures are no cake walk. You really need to study do well in these classes. Real Analysis is the killer. That’s the hardest thing I have ever taken in my life. I still don’t understand many of the topics covered in Real Analysis. So no you don’t have to be a math savant to do well studying math in university, but you need to have at the very least, good mathematical ability.</p>

<p>As for job opportunities:
you can be high school teacher (who wants to do that right? That’s what I’m doing now) or college teacher (with graduate math studies), an actuary (takes a while to become a full fledged one but it’s worth it), you can work for the department of defense or CIA if you do well at a top university. You can become a lawyer. You can even go into engineering. Graduate engineering programs tend to accept math majors if their grades are good. I am gonna be going to graduate school to study Industrial Engineering.</p>

<p>Good luck!</p>

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<p>Bounce007’s comment about the CIA reminds me of a cool fact: The National Security Agency is the largest single employer of mathematicians in the country (and maybe the world). </p>

<p>[Career</a> Paths at the National Security Agency (NSA) - Mathematics](<a href=“http://www.nsa.gov/careers/career_fields/mathematics.shtml]Career”>National Security Agency Careers | Apply Now)</p>

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<p>The “learn how to write proofs” course is something that I think has only been in effect the last 10 years or so. I know that at Michigan State (late 80’s/early 90’s), we had no such course. You went from Calculus III or Linear Algebra STRAIGHT to Advanced Calculus or Real Analysis and had to learn to write proofs while learning Advanced Calculus. I WISH I had a “writing proofs” course first.</p>

<p>Plus, since I was Computational Math, our Advanced Calculus course was like “Real Analysis Lite”. I shudder to think if I had to take the Real Analysis course with the “Rudin Book” with no prior experience in writing proofs.</p>

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<p>PKD wow, I didn’t know that NSA specifically seek out math majors like that. Just another thing FutureDoc. Algebra in high school is faaaaaaaaarrrrr different from algebra in university. It’s good that you have a back up plan, but if your dream is to become a physician, pursue it with discipline and dedication and never give up on your dream. You can become that future medical doctor!</p>

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<p>@GLOBALTRAVELER</p>

<p>To be honest, I never really understood the point of having an entire class devoted just to proof writing. It seems like massive overkill. Options 2 and 3 in ucbalumnus’s post make a lot more sense to me - introducing proofs in a relatively easy-going math course (meaning NOT real analysis or abstract algebra), or in a course they might have seen before in a non-rigorous context (like calculus or linear algebra). I mean, the only way to get used to proofs is solve problems in a proof-based math course, so why not have this be a course they need to take anyway?</p>

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<p>@PKDFan…</p>

<p>The usual math major sequence is:</p>

<p>Calculus I (Limits, Sequences and all that mess)
Calculus II (Integrals and all that mess)
Calculus III (Vectors, Multiple Integrals, Surface Integrals, Gradients and all that mess)
Linear Algebra (varies by school…some more on Matrix Algebra…others on theory)
Differential Equations (Starting to optional at more and more schools)</p>

<p>After those 5 courses, technically you qualify for Real Analysis and Abstract Algebra. Where should the proof-writing start? What would you name the course. Many schools call it something like “Intro to Higher Mathematics”.</p>

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<p>Well, Linear Algebra is a natural place to introduce proofs. In fact, I think most linear algebra courses require some proofs, although there is a huge variety in how theoretical it could be (a few simple proofs throughout the semester on one end vs. entirely proof based on the other). They could also take two semesters, first one that’s computation based and then another that would proof based.</p>

<p>If someone knows they’re going to be a math major coming into college, then they’d probably want to take an honors version of the Calculus sequence that would be proof based (like linear algebra, this can vary a lot in just how rigorous). Another example would be discrete math. This is where computer science students usually learn about proofs - no reason math majors can’t as well. In any case, there’s a big gap between purely computational intro calculus and Rudin-style real analysis. </p>

<p>I don’t think many (or even any) schools currently do this, but one solution would be to have something like a 1-credit seminar for potential math majors that would introduce them to proofs. The main problem I have with “intro to proofs” classes is that the stuff you need to know in order to write a correct proof can’t possibly fill up a whole course. So these classes usually have a whole bunch of other stuff packed in that, while interesting, are also quite unnecessary. A short seminar would probably still be more than they “need to know”, but it could include stuff like problem-solving strategies and general mathematical information.</p>

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<p>I started learning how to formally write proofs in a course called, “Introduction to Higher Algebra” right after I got done with Differential equations. Then I went on to take Abstract Algebra… You are well learned Global Traveler.</p>

<p>This Higher Algebra class seemed to be somewhere between Discrete math and Abstract Algebra in terms of content and was filled with proofs.</p>

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<p>@Bounce,</p>

<p>You may be on to something. Since I was a Computational Math major who almost doubled with CS, I was able to take both the Discrete Structures sophomore-level course (not required by math majors at the time) and later on a junior/senior course in Combinatorics. Of course those two courses have a lot of overlap but I recall that the junior/senior level Combinatorics course pretty much covered the Discrete Structures topics in like 5 weeks.</p>

<p>That has me thinking, maybe Discrete Structures should be given more meat and throw in more proof-writing and then make ALL the “computational type majors” (comp math and CS, etc) take Combinatorics in junior year. That would allow students to be introduced to proofs very early.</p>

<p>One note about the Advanced Calculus course at MSU during my time there. Very few of us got A’s on our first try. Many of us had to either drop the course and take it the next semester…or eek out a B- or B grade (we had intermediate letter grades).</p>

<p>I myself took two sections of the course at different times of the day and dropped the one with the lowest midterm grade (midterms were usually near when courses could be dropped with only losing 10 or 20% of money).</p>

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<p>I would like to major in Applied Math, but am also interested in econ, cs, and engineering. I have also read that it is a good idea to take some classes in other areas like so that you could qualify for jobs in those areas. Would you be spreading yourself too thin if you did the minimum math req’s and then double minored in cs and econ, or would that just open up more jobs? Also would your math degree be so light in math courses that it could turn off employers?</p>

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<p>I’m an Applied Math major, but I was a transfer student so coming in as a junior things can be a little different. Most linear algebra courses at the community college level are computationally based. Mine wasn’t too much, but I consider that the exception. We were exposed to proof techniques the very first day and had to prove many things throughout the course. It kind of became second-nature. The teacher probably put around 40 computation problems on the test (she referred to this as “pencil whipping”) that we had to zoom through without making any mistakes basically and then tackle 3/4 proofs on each test. If you didn’t make the right insights when you saw it, you’d never get it. But when you did it was very very easy to finish it and was not long at all. I took Applied Probability Theory my first quarter here and we had a proof on each test. They didn’t really prove anything in the book too much, but the teacher picked something like proving that combination formula or whatever. Something you could look up and memorize or just crank through the for the first time on the exam. He assumed most of us had a proofs course already. </p>

<p>I am signed up to begin my “bridging” course MAT 310 before I take Modern Algebra & Real Analysis in the Fall. The course description is: </p>

<p>MAT 310: Basic Set Theory and Logic (4) FSp
Basic set theory and logic, relations, functions, mathematical induction, countable and uncountable sets. Emphasis on how to present and understand mathematical proof. 4 lecture/problems. Prerequisite: C or better in MAT 116, or consent of instructor. </p>

<p>Now I don’t know if set theory needs to be covered over an entire quarter (10 weeks), but this is pretty much the course you have to pass if you wish to take the Real Analysis sequence or Modern Algebra sequence and Complex Variables for our math core or any other proof-oriented class. </p>

<p>For Applied Math electives here it is common to take Operations Research I and II, upper-division Differential Equations (Nonlinear Dynamics & Chaos) and Partial Differential Equations. Then you can either do another sequence in Mathematical Programming or take Graph Theory and Combinatorics. You get a lot of math fulfilling just the “minimum” requirements. I don’t think it’d turn off anyone. Recently they combined the Applied Math & Statistics options into one so that students have more flexibility in picking what classes they want to do that would be more relevant to them. </p>

<p>I think minoring in CS would be a great idea because by gosh my major uses a lot of programming for classes. You’ll encounter programming in Operations Research, Numerical Methods, and a lot of stat classes. I would say programming is a very valuable skillset because it can also let you check your answers! I took two econ classes, which I really thought were just a waste of time and I learned nothing valuable from them. I’d say as long as you have common sense that’d work in most cases in place of those two intro econ classes. Most of the time minoring in something is kind of a useless thing to do. I’m minoring in physics because I intend to become a patent lawyer. Honestly, it is just a few classes away once you finish your lower-divison math classes. I technically have 6 physics classes under my belt and only need two more to finish (and I’m going to do that next year by taking Mathematical Physics I and II). I also like physics more than I like math, but I didn’t find going down that road the best way to make a good living. Although if I didn’t do my physics minor I’d have more room to take math electives like topology. Most people here kind of find what they like (econ, physics, compsci, engineering) and take courses they want when they have space to do so. </p>

<p>The book I used was largely plug and chug for Calculus, but the thing a friend and me used to do was to look at the proofs section at the end of each chapter and see if we could solve the proofs for fun. Sometimes they were putnam challenges. So if we solved that basically we concluded we didn’t really need to mindlessly work through all the computation problems. Even in my summer Calc II class although it was super computation based cause things were going so fast, she’d say prove the taylor series or maclaurain series or all these other things for extra credit. It was a fun thing to do to prove them. I think they need to introduce incentives into lower-divison classes, but I think during lower-divison classes most people are mixed in with other majors from engineering, pre-med, pre-pharm whatever they they probably don’t want to burden people I guess if they’re never going to use it. Well, that was my experience at community college. They do things differently here at my new university where they have engineering majors take the “technical calculus” sequence I think instead of the regular calc sequence where everyone else is lumped in there. They do the Putnam Exam here also.</p>

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<p>Thanks for all the input Caldud, that was good information to think about for sure. My problem is that I am interested in the differences in Keynesian vs. Austrian economics, and the different nuances of economics and government. </p>

<p>I see most people in your school are spending their electives on math. That’s what I was wondering since after the fifteen math classes required and the core classes I would have around 40 credits left to fill.</p>