<p>Ooops. Apologies and kudos to POIH!</p>
<p>Wait, so are Calculus/Analysis and Statistics considered the two main branches of mathematics? If so, then I think that answers my question.</p>
<p>I don’t think statistics is considered a “branch” so much as a mathematical science. Real analysis is just one of many branches of mathematics. It’s too simplistic to try to label them the two main branches. Back to the drawing board on the question :).</p>
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I was thinking more in terms of diagnostics and treatments.</p>
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<p>The three main branches of Math are Analysis, Algebra and Topology (as explained recently by a TA). Probability is a branch of Analysis. Statistics is an application of Probability, in the same way different areas of Physics are applications of various mathematical areas.</p>
<p>This is somewhat simplified though, as there are areas like Geometry and Number Theory that don’t really fit neatly in anywhere. And I think he may have completely forgotten Discrete Math and Logic.</p>
<p>There are something like 3000 recognized subfields of mathematics. Attempting to enumerate or even categorize them can only lead to heartache :).</p>
<p>"I am completely puzzled why medical schools require applicants to have taken a year of calculus, "</p>
<p>-They do not. Requirement is to have one year of math and lots of pre-emds are taking semester of stats, which means that they take only one semester of calc. Stats are more useful for pre-meds. Stats are used a lot in Med. Research.</p>
<p>Did not see comments above, I do not think that Stats have anything to do with calcs and math is not science, it is math. It is more like language that science is using, but we would not call it language either.</p>
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By calcs do you mean calculus? I’ll assume so.</p>
<p>You can study or apply certain parts of statistics without calculus. But more advanced area require calculus. Have you ever heard of a continuous random variable? Have you ever head of a Poisson distribution? There is a link between probablility and statistics. A lot of statistics is meaningless iwthout knowing the probablity distribution you are using. This requires calculus. Without it the tables you look things up in are meaningless.</p>
<p>That doesn’t mean you need to know calculus to use basic hypothesis testing. But those formulas you use - z test, or t test, or chi square test or whatever. THey do come from somewhere. </p>
<p>I’m way too rusty to explain this stuff, but rest assured, in my engineering statistics class I needed to know calculus.</p>
<p>But let me give a basic example. Would you consider the mean, or average to be a statistical concept? I do. How exactly so you calculate the average value of a function without knowing calculus? How could somebody tell you the RMS value of a sine wave without knowing calculus?</p>
<p>Edit- I know I said I wasn’t going to post on this. But I had to say something about this.</p>
<p>One addition to my post above. When I hear people talk about statistics they always seem to assume some discrete population of data, like a political poll or a medical trial. There is also a whole other world of continuous value statistics out there, with things like correlation and convolution (yes, I know these also have meaning in the discrete world). </p>
<p>These ideas are very important in signal analysis. Maybe not many other places, but it does exist.</p>
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<p>The still-applicable requirement at Harvard – to pick one leading medical school – is “one year of calculus is the minimum”. Starting four years from now, they are going to what they call a “more flexible” requirement that, as currently written, is incomprehensible, but that seems to translate into one semester of calculus and one of statistics, although they really hope you take more of both.</p>
<p>Stanford “recommends” but does not require course work in calculus, and does not mention statistics.</p>
<p>Hopkins says one year of calculus or statistics, and starting next year at least one semester of statistics will be required.</p>
<p>. . . Actually, it’s interesting. As I looked at more schools, it’s clear that calculus is no longer even close to a universal requirement. UCSF, Yale, and Chicago don’t formally require any math. Penn has a long discussion of math requirements that comes down to pre-calculus and statistics.</p>
<p>Plenty of calculus in statistics here:</p>
<p>[Normal</a> Distribution – from Wolfram MathWorld](<a href=“http://mathworld.wolfram.com/NormalDistribution.html]Normal”>Normal Distribution -- from Wolfram MathWorld)</p>
<p><a href=“http://mathworld.wolfram.com/CentralLimitTheorem.html[/url]”>http://mathworld.wolfram.com/CentralLimitTheorem.html</a></p>
<p>AP statistics and college statistics for social science majors just ignore the calculus part to make it simple for students.</p>
<p>“How exactly so you calculate the average value of a function without knowing calculus”</p>
<p>-You do not need to use integrals and differentials (which all starts with concept of limits) to calculate average value. You just use formula for average value. Maybe there is some kind of higher level of stats that uses calculus in statistical formulas, I mean uses integrals and differentials. However, using calculus for statistics does not mean that calculus and statistics are the same thing. One definitely does not need to know calc to learn stats or to know stats to learn calc.</p>
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Where do you think that formula comes from?
Of course everything starts with limits. What does that mean?</p>
<p>What is the formula for the average value of x^3+x^2+x+12 from 1 to 6? How do you figure it out without an integral?</p>
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You said they didn’t have anything to do with each other. That’s absurd.</p>
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One definitely needs to know calc to know some types of statistics.</p>
<p>Really, you don’t know what you are talking about.</p>
<p>Measure theory abstracts from both calculus and statistics. The central object of study is that of a measure space (just some collection of points, discreet or not) which is endowed with a measure function (this could be a probability density function or a volume element). In this framework one can prove theorems that apply to calculus and statistics and a whole lot of other areas. In this sense calculus and statistics (or at least probability theory) can both be classified under the same branch of mathematics.</p>
<p>If calculus is necessary for certain statistics applications is another question entirely.</p>
<p>^^^Deleted my post because now I see what you are saying.</p>
<p>^^^ I was trying to agree with you that calculus and statistics are intimately related (even in the case of discreet statistics), while pointing out that one need not master calculus for many elementary statistics applications. The message might have gotten lost in translation.</p>
<p>^^^
Okay, I got that after re-read. I agree with you 100%, even though I know nothing about measure theory, I think that’s beyond me.</p>
<p>And DAP is right that in general people don’t need calculus for many if not most applications of what is commonly called statistics.</p>
<p>I guess I’m just being ornery.</p>
<p>^^^ We should keep doing this for a while. Meanwhile the statisticians can try to predict the number of ^ symbols on this page by the time we are done :)</p>
<p>What’s taught in the typical AP Stat curriculum is not calc-based stat. We saw a huge difference in the course as it was taught at S1’s school vs. S2’s.</p>
<p>S2: standard AP Stat, full year course, nothing fancy.<br>
S1: Calc-based stat, one semester, went into some of the more interesting approaches to problems, so that folks could use those shortcuts on the hardest problems. 90% get 5s.</p>
<p>I think a lot of the interesting interconnections between various fields within math aren’t really revealed til beyond the levels of math most college students will typically take.</p>
<p>JHS: Chicago still has a math requirement – it just doesn’t have to be Calc, IIRC.</p>