<p>I just got accepted to the University of Pennsylvania and I plan on majoring in either mathematics or statistics. I really like math and I am pretty good at it (800 on my math level 2 SAT subject test and a 5 on my AP calc exam), but I don't think I would like doing proofs and stuff like that. I like pure math, but I am also interested in applied/practical mathematics. Is becoming a math major as hard as people say it is? And is majoring in statistics any easier and/or more practical?</p>
<p>Pure math can be difficult but some find it naturally easy. In fact, I know many mathematicians who find statistics difficult.</p>
<p>That said, statistics is a highly mathematical field (a subfield of math in many ways) so I would recommend a good dose of pure math courses for those choosing to major in statistics (and don’t leave them at the last minute, they may be a pain to go through, but it’s better to take them early than late). Similarly, unless one wants to stay forever in academia (tough job market), a math major should take a non-negligeable number of applied math and statistics courses. Also, many math programs allow a lot of flexibility in terms of course selection, outside the core courses, try to take a wide variety of courses early on, so you can focus on the area you are most comfortable with later on. I actually started in math thinking I’d do pure and ended up doing statistics, but course-wise I had more applied math (differential equations, numerical analysis) than probability and stats at the end of my BSc. In any case, I also recommend at least 2 CS courses to learn at least basic programming and design of algorithms (many math programs require it now, but it was and is still not always the case; I minored in CS, and even those in pure math doing PhDs and postdocs who didn’t do any CS when they had the chance now regret it).</p>
<p>A healthy combination of solid theoretical background with a good understanding of real world applications is what makes a math or stats major attractive in a wide variety of jobs and work environments.</p>
<p>Thank you very much; that was very helpful.</p>
<p>I am a statistics major, and I am very much like you. Pure math I was decent at, but proofs I was terrified of. All I knew was that statistics was interesting to me, and I loved the visual aspect of it. I’ve always been a visual learner, and it really seemed interesting.</p>
<p>Going through 4 years of statistics, I’ve learned a few things:</p>
<p>1. You’re going to take a lot of math classes.</p>
<p>There is no way around it. You cannot have a statistics degree without at least Calc III and a basic proofs course. Don’t be afraid of proofs! Just don’t go any higher than that (that is, do not take real analysis: it is proving calculus). If you do decide to go higher for, say, some elective, be sure that you feel confident and good. I personally did not, and I know it only gets harder from there.</p>
<p>I got through Calc I-III pretty easily. It was not difficult, and I was someone that was really scared of the word “derivative” and “integral” from hearing my friend talk about his AB calc class in high school. I had three excellent professors: really make sure that you research your professors well. Generally, calculus courses tend to be taught by a lot of professors since so many people need to take it. Research them well. Honestly, some of my best professors have been graduate students. They are nice, understanding, teach extremely well, and give out very fair tests. They know what you went through in undergrad, and they do not want to make anything more stressful than they have to. </p>
<p>I saved my proofs course that I had to take for last. I hated thinking in variables, and I did not know even how to start my first proof. Day 1, he asked us to begin doing a basic proof, and I was just lost. By the end of the semester, I did just fine. I grasped the concepts very well, and pulled out of there with a B. I knew it was going to be difficult for me, but I really tried hard.</p>
<p>When you take proofs, you will ask yourself why it is important to you. Once you get to set theory, you’ll know exactly why. </p>
<p>After proofs, I learned how to think in variables. It completely changed my way of thinking, and I am so happy for it. It makes dealing with large equations much more easily, and in stats, you will encounter some very nasty equations because there really is no better way to write some of these. </p>
<p>2. Probability may or may not be your cup of tea.</p>
<p>Probability is one of the least intuitive areas of math. It’s hard to teach, and even harder to understand. My suggestion? Go get the Actex Probability P/1 exam book, and just crank through it. Some of those problems are disgustingly difficult (skip those if you want: trust me, you’ll know which ones they are), but overall, the way that it teaches you probability is excellent. When I was considering being an actuary, I studied for P/1 with this book over the summer and absolutely destroyed the first part of probability that fall semester. Grasping probability comes from tons of practice. Practice a lot, because you’ll find that no two problems are ever the same. By practicing, things begin to click, and you get your own method of solving problems. Being a stats major, you’re probably good at recognizing patterns. You’ll start to recognize patterns on how to solve certain types of problems, even if they are very different looking. Trust me: you’ll want to get frustrated and learn from your mistakes from the Actex book: not at the expense of your GPA 
</p>
<p>The second part of probability will get very convoluted. You really need to pay a lot of attention. If you’ve ever wondered where all of those formulas come from in statistics, you’re about to find out. It’s a lot of work, and honestly I found that to be the most difficult stats class. You’ll deal with some terrible equations, and you will be proving statistical concepts. I highly recommend you take proofs before taking this course, even if it is not a pre-req. You need to be okay with manipulating really terrible equations. The problem is recognizing certain properties. You may get a really awful looking equation, but in the end it simplifies to something extremely simple because many components in the equation end up zeroing out, or actually mean something more simple. Honestly, without seeing the examples and going to the classes, you would never ever realize a lot of these properties. Even now I still don’t recognize a few of them, but that’s what graduate school is for It’s going to be your hardest course. Just get it over with, pass it, and be done with it. It’s definitely not a course you would want to take again. But then again, you may enjoy it a lot. I’m just giving my opinion 
Even though it is difficult, you will find it very interesting.</p>
<p>**3. In the beginning, just realize what your stats professors tell you is correct, and don’t think too hard about where it came from. **</p>
<p>It’s good to ask questions, and you’re definitely on the right track if you are wondering where something came from; however, when you take your basic statistical methods class, they are going to throw a lot of relatively simple concepts at you. They are not difficult to understand conceptually, and some of the equations might seem to make no sense.</p>
<p>For example, your professor may tell you that variance is divided by n-1 to be unbiased. If you ask “why,” he/she will probably tell you something along the lines of it being pretty complicated. And it is: you’ll find out why in the 2nd part of probability. There is a formal, mathematical definition of bias, and showing that something is unbiased gets a bit ugly sometimes.</p>
<p>Just take it as you go. Don’t worry too much about why it is n-1, or why some equations seem a bit odd, etc. Yes, definitely question it, but don’t let it get in your way. Just trust what they say is correct, and perform the procedure as they have described. You will get into more advanced applications later. </p>
<p>This is one of the main reasons why many people find statistics very difficult. It is hard to teach because all of the end-result products come from extremely complicated proofs, and sometimes the best explanation for something that a professor can give is “It comes from a pretty long proof, I’d be glad to show it to you during office hours.” In fact, there is a conference held every year called CAUSE - Consortium for the Advancement of Undergraduate Statistics Education. Its entire purpose is to find better ways to teach students about statistics, especially during their first years. I went to this to help my advisor with some things, and it was very interesting. Software, books, etc. - hundreds of statisticians were there, all to see the latest and greatest ideas in teaching statistics.</p>
<p>4. If you were never a computer programmer, well, you’re about to be one.</p>
<p>All that stuff you do by hand in AP stats and your super basic stat classes? Yeah. No one does that by hand ever. You’ve probably found it tedious and stupid. That’s because you’re right: it is. Software is out there to solve these problems for you. Two you will need to know in particular are SAS and R. Personally, before you get into your first SAS class, I recommend that you take Intro to Java. It will make your experience much better in SAS and R.</p>
<p>SAS is especially similar to many programming languages out there. Do loops, arrays, semicolons, etc. are all there. I was scared to death to program. I did not even know the first thing about writing one, let alone even understand the thought process in doing it. Unfortunately, I took my SAS programming class before Intro to Java, and I found it to be pretty difficult. My friend, who took Intro to Java before this class, breezed right through. When I took Intro to Java after my SAS class, I realized how similar Java was, and all I could tell myself was how much I wish I had taken Intro to Java beforehand. By the end of Java, I learned how to think programmatically. It’s a very cool feeling: at some point in the course, you’ll be writing your program and think, “Holy crap. I can make this computer do whatever I want.” That’s when you know you’ve got it down. I thought that day would never come, but it did, and boy am I glad to have taken Java.</p>
<p>Now, just because the computer can do it for you does not mean that you do not need to know stats. You need to know what it is doing. Any trained monkey can go out, type in a bunch of lines, and have it spit out some numbers. But are the numbers right? What do they mean? How do we interpret what we are seeing? Is your statistical model the right model, or is there a better one? Did you create your model properly? These are all questions that you need to answer, and are the questions that your stat classes will prepare you to answer for.</p>
<p>I find that for some more advanced regression analysis (I had to learn it as part of my undergraduate research job, do not worry too much about super advanced regression), I have to write down the equations and such on paper before I can input it into SAS. That is the only way I can know if I am telling SAS to do what I want. Remember, to get SAS to do what you want, you have to tell it how to do it properly. Otherwise, it’s going to give you odd results. </p>
<p>5. Don’t get too comfortable with equation sheets.</p>
<p>Every stat class I have taken has allowed equation sheets. But, most math classes do not. Do not get too comfortable with equation sheets, because your math classes may become more difficult for you since you are accustomed to studying a certain way. With your math classes, in order to memorize everything, you just practice a ton. It is possible It will also remind you why you are not a math major! It certainly did for me.</p>
<p>6. Choose interesting major electives. Don’t be lazy and choose something like Intro to Business Stats because it fulfills an elective and gets you an easy A.</p>
<p>Yes, you can do that, but do you really want to sit through a class you’ve essentially taken before? It is boring.</p>
<p>Spice things up a bit. Choose something odd or interesting. For example, my advisor suggested I take bioinformatics. It ended up being one of the most interesting courses I’ve taken! It combines statistics, biology, genetics, and computer science all into one. It was really, really cool. Think of your major electives as a way to help decide what kind of job you want, or as a way to scrape the surface of some more advanced concepts. I personally chose a few graduate-level courses. Don’t let them scare you: a lot of them are really not that bad, but you end up learning some very useful things. For example, one of my professors suggested I take a higher-level experimental design class because they teach about how to use SAS to do these things for you (oh, by the way, if I haven’t mentioned yet, you’ll experience the joy of hand-calculating ANOVA tables for various types of experimental designs :)). In fact, this class familiarized me with R and more SAS procedures that I did not know about. It ended up being extremely valuable overall.</p>
<p>7. Your classes are going to be small!</p>
<p>I go to NCSU. There are 30,000 people that go here, and the biggest complaint that everyone has is huge class sizes. But not me!</p>
<p>All of my classes have been relatively tiny, and I’ve gotten to know professors and people very easily. This has been the biggest plus of being a statistics major: because it is not a popular major, you will be running into the same people a lot! You may have the same professor twice (or even three times in my case). This may or may not be a good thing depending upon the situation, but it’s an awesome and easy way to get those valuable recommendations that you will need for your graduate school application. You will also make friends more easily, too. </p>
<p>Learning is much more personalized due to the smaller class sizes. It is also easier to persuade the professor to choose a better test date if the one he/she assigns is a bad date. I’ve had that happen a few times, in which we were able to tell the professor to move a test back a lecture due to another large stats test being the same day.</p>
<p>In the end, statistics is not a math major, but contains elements of math and computer science. It is very interesting, this major. There are a lot of conceptual pieces about it, but a lot of rigorously mathematical pieces about it. Just because you are not a pure-math person does not mean you will do poorly in statistics. All I can say is, if you tend to notice a lot of trends, enjoy looking at graphs, and like curvy lines, then statistics is right up your alley.</p>
<p>Now, onto the good part: jobs.</p>
<p>What can you get with an undergraduate stats major? Not a lot. BUT: what can you get with a Ph.D in statistics? A LOOOOOOOT. Every company out there needs someone to analyze data of some sort. The sheer amount of fields you can get into is nearly endless. Like biology? Go to biostatistics. Interested in genetics? Bioinformatics may be for you. Want to improve processes? Statistical quality control is going to be your thing. Want to analyze huge datasets, create models, and be directly involved in the direction of where major companies go and such? Analytics is the way to go, and is the route I am choosing (because within Analytics is an entirely different subset of possible jobs and job types that is also practically endless). Wanna teach? Absolutely doable. </p>
<p>These are just a few of the things you can do with statistics. Without a Ph.D in statistics, about the best you can do is be an actuary; however, you need to love, and I mean LOVE, probability and finance. Being an actuary is not easy, and the actuarial exams easily make up for not going to grad school. In the end, after all that hard work, you’ll have a job that is consistently ranked as one of the best jobs to have in America.</p>
<p>How much money can you make with your stats degree? Well, you’ll be certainly living comfortably after graduation, that’s for sure. You will be doing a lot better than the majority of college graduates, I guarantee you. Your major is too valuable for you to not get a good job.</p>
<p>So, is a stats major for you? If you read all of that and are excited to get into the field, then yes, it is for you, and you’ll love every single stat class. If you read all that and thought, “This all sounds really boring and dry,” then I do not recommend suffering through something that will make you miserable day in and day out. Difficulty compared to a math major, I honestly do not know. Statistics has its own difficulties associated with it, as does mathematics. I do not say I’d put them on-par with each other in difficulty, but they are both extremely, extremely close, with math being a little more difficult.</p>
<p>Just to give myself some credibility, I am part of the Mu Sigma Rho Statistical Honors Society and have really worked hard at maintaining a great GPA during my years here. I will be graduating next semester and only have one more stat class to go. Everything else is crap I’ve pushed off 'til the very end :p</p>
<p>If you plan to go to graduate school, you absolutely need to have Real Analysis. It is not that “difficult” (of course this depends on the instructor), and for my money is the most accessible of the possible proof based courses you can take. Thankfully you can get work with just a degree in Statistics, but - like most degrees - you will be limited long term. If you plan on doing only a masters, some analysis will be helpful but not expected. </p>
<p>If you go the pure math route - you will not in any way shape or form be able to get away from “proofs”. So if after you take your transitory math class (the class that gets you prepared to write proofs) you feel that this isn’t your bag, you need to have a long talk with an advisor.</p>
<p>Cool. Thanks wulfpack. That was incredibly helpful.</p>
<p>I think you should take a proof based class before completely writing it off. You may have the idea that you’ll be deriving equations or doing the type of things you see in geometry, and it’s really not the case. In most cases it’s probably not nearly as scary as it sounds.</p>
<p>Also, if you’re going to grad school in Statistics you should really know some linear algebra.</p>
<p>I would think that a semester or two of real analysis would be necessary to really understand mathematical statistics as well…</p>
<p>Most programs are not going to think you’re serious if you do not have a full years worth of Analysis. You can be assured that most people who are applying already have this requirement met (and probably some proof based Linear Algebra as well) so your application is going to look that much weaker compared to theirs.</p>
<p>I agree with all of the above postings about Statistics. I would add to not waste your time (or precious credits) taking something like a combined course “Probability & Statistics for Scientists & Engineers”. Take the separate Probability course and the separate Mathematical Statistics course.</p>
<p>Also there some applied stats-like courses that are sought after in the job market like Stochastic Processes, advanced Operations Research/Optimization and Data Mining.</p>
<p>There is no Applied Mathematics or Statistics major at Penn. The Statistics department is actually housed in Wharton, not the College.</p>
<p>The closest majors for students in the College would be [Mathematics[/url</a>], which requires four semesters of rigorous, proof-based courses, but gives you leeway to count statistics and other “applied math” courses towards your major. You can also look into the [url=<a href=“http://logic.sas.upenn.edu/]Logic”>http://logic.sas.upenn.edu/]Logic</a>, Information and Computation](<a href=“http://www.math.upenn.edu/ugrad/major.html]Mathematics[/url”>Undergraduate | Department of Mathematics) major.</p>
<p>I suggest you investigate proofs, either through a class or on your own, to see how much you like it. That will help you determine what you want to major in.</p>
<p>I am thinking about possibly transferring to Wharton in order to major in Statistics</p>
<p>Keyan, I just looked at the math and stat program on Penn’s website. Obviously, with stat, you get the basic Wharton business classes. However, when you look at the stat versus math major, you would be able to take the basic classes (430 and 431, not 101-102 and 430, you are too good for the 100 level business stat classes and I say this from personal experience) regardless of major. Then when you look at the electives, there are 3 additional classes to take which includes at least one class that could be applied to a math major. So basically with the stat major, you would be taking 2 stat classes that might not be available as a math major and the business core course.</p>
<p>Also, I looked at the stat department minor and found this: A Math Major might take Math 114, Stat 430, Stat 431, Stat 432, 433, 471 and Math 412.</p>
<p>You really have to decide what you want from life.</p>
<p>As someone that just completed a BS in Statistics, I completely agree with almost everything Wulfpack had to say in his (or her) long description of what to expect when obtaining an undergraduate degree in Statistics.</p>
<p>Probability Theory and Mathematical Statistics are two classes that you just have to sludge through. I’ve never dedicated more time studying for any class than I did with those two. If you get a professor that is very proof happy, the class can get real difficult. Maximum Likelihood Estimators and Sufficient Statistics are just really a pain in the a$$.</p>
<p>Someone above mentioned Linear Algebra, which is probably required for most Statistics degrees. Having a good grasp behind the theory of Linear Algebra can really pay huge dividends when attempting to understand the theory of many different forms of Statistical Analysis (at a higher level). Orthogonality is a concept that comes up over and over again.</p>
<p>Something tells me those classes would have been less of a “struggle”, if there had been a tiny bit of upper division math involved (assuming there is no math requirement beyond Vector Calculus). </p>
<p>Most stat courses it seems views a lot of that stuff as optional (and only recommended for those going into graduate programs in Statistics).</p>
<p>This is a Penn-specific post:</p>
<p>As a student in the College, you can take as many classes outside the college as you want (in particular, statistics classes in Wharton), but they might not count towards your graduation requirements. <a href=“Source”>url=http://www.college.upenn.edu/courses/policies/noncollege.php</a></p>
<p>A Wharton degree is useful, but if you’re set on math/stat I don’t think you’d be too partial to the core curriculum. Besides the intro STAT101/102, you only need to take four classes to declare a statistics concentration. <a href=“Source”>url=http://spike.wharton.upenn.edu/ugrprogram/advising/concentrations/index.cfm</a></p>
<p>falafel, this is a high-functioning math student. STAT 101/102 would be child’s play. </p>
<ul>
<li>Students who take STAT 101 and 102 as Business Fundamentals should also take STAT 430 and then three more courses for the concentration. </li>
<li>Students who take STAT 430 and 431 for the Business Fundamentals should take four more courses for the concentration. </li>
</ul>
<p>If you were a high-functioning math student, which would you take. Personally, I go the 430/431 route. I speak from experience (though not at Penn) when I say that Math Stat is much more interesting than Introductory Business Statistics.</p>
<p>Thanks everybody for your advice!</p>
Pure Math = proofs
Applied Math = numbers
@wulfpack its been years since you wrote this but I’m a high school sophomore, like math and numbers and like business- I was thinking of majoring in a qunatititative field like econ or applied math or stats? Since you did stats, could you tell me if there is a course of something I could check out to see if I like stats? I’m in pre-calculus now, taking calc BC junior year, so I’ll probably only take stats senior year and I want to know whether I would like that early on.