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Calculus based statistics...


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#1 snowbeltmom

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Posted 10 February 2013 - 09:11 AM

can anyone recommend a textbook?

#2 mumto2

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Posted 10 February 2013 - 03:32 PM

I will bump you.
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#3 lewelma

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Posted 10 February 2013 - 04:55 PM

Having done 7 university classes and 5 years of statistical modelling, I will tell you that I have never used calculus in statistics. What exactly are you looking for?

Ruth in NZ

#4 Teachin'Mine

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Posted 10 February 2013 - 05:18 PM

I had no idea calculus was used in statistics either, but in doing a quick search this text came up.

http://www.amazon.co...n/dp/0155459651

No idea if it's good or not, but it does come with the typical math textbook sticker price. :glare:

Here's another one which looks interesting.

http://www.amazon.co...=pd_sim_sbs_b_3

#5 regentrude

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Posted 10 February 2013 - 05:28 PM

Having done 7 university classes and 5 years of statistical modelling, I will tell you that I have never used calculus in statistics.


That is strange. In our math courses for physics majors, we had a semester of statistics and probability theory where we most definitely had to integrate. How else would one deal with continuous probability distributions?
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#6 jennynd

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Posted 10 February 2013 - 05:31 PM

Nm

#7 snowbeltmom

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Posted 10 February 2013 - 05:37 PM

I really have no idea what I am looking for.

It was just suggested to me that a possible math course after BC calc would be calc-based statistics. He has already studied the material tested on the AP Stats exam, but that material is all algebra based.

I am basically clueless.

#8 regentrude

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Posted 10 February 2013 - 05:47 PM

I really have no idea what I am looking for.
It was just suggested to me that a possible math course after BC calc would be calc-based statistics. He has already studied the material tested on the AP Stats exam, but that material is all algebra based.
I am basically clueless.


You might want to look for a course that is not labeled "statistics", but "probability theory".
If you search online for "calculus based probability theory syllabus", you find several schools that offer such courses and can look what textbooks they use. Texts that came up when I did a quick search was
Introduction to probability and statistics for scientists and engineers by Sheldon Ross.
Mathematical statistics and data analysis by Rice
Probability and statistical inference by Hogg and Tanis

I have not seen any of these texts - but searching online syllabi should give you a good idea what frequently used texts are.
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#9 regentrude

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Posted 10 February 2013 - 05:59 PM

Just checked: our local university is using
Probability and statistical inference by Hogg
ISBN 9780321584755
for Intro to Probability and Statistics
Please note that multivariable calculus is a prerequisite.

#10 snowbeltmom

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Posted 10 February 2013 - 06:00 PM

Please not that multivariable calculus is a prerequisite.


Thanks! That helps me with his sequence!

#11 kiana

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Posted 10 February 2013 - 07:17 PM

For prob/stats after calc 3 (really, all you need is multiple integration) I like the book mathematical statistics with applications by wackerly, mendenhall, and schaefer (order of authors varies by edition). I found it easy to learn from as a student.

ETA: This is for a two-semester sequence.
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#12 lewelma

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Posted 10 February 2013 - 09:02 PM

That is strange. In our math courses for physics majors, we had a semester of statistics and probability theory where we most definitely had to integrate. How else would one deal with continuous probability distributions?


Oh, did this make me smile! My dh always says that I have a rolling 2 year memory, so perhaps I have simply forgotten! However, there is a difference between a course in statistics and a course in probability. They obviously inform one another, but if you are using statistics to answer real life questions in biology, business, or the social sciences, you certainty do not have to integrate probability distributions. But I will definitely not speak for engineering. However, statistics does not follow the same kind of progression as physics -- algebra-based and then calculus based. Instead, after a basic class, you take classes in Analysis of Variance, Regression, Non-parametric stats, Time Series, experimental design etc. I have not taken an isolated class on probability, so I wonder if this is the difference.

So why does your ds want to learn statistics? The most helpful thing I ever did was a survey course. How do you actually know what statistics to use unless you have been exposed to the different kinds of data and questions. Is your data continuous or discrete? Is your data independent? Does your question involve location, goodness of fit, association? (You don't want to know how many errors in statistics I have found in pee-reviewed published papers.) In general, the broader his knowledge the more useful it will be for interpreting research, reading the news, and analyzing his own questions. Statistics is a way of organizing your thinking about data. Once I understand the statistics being used, the work is crystal clear; without statistics to give it form, it is just a big morass. So personally if I were not going to take many statistics classes, I would rather spend my time on the big picture than get caught up in the details. It really depends on how many stats classes he will take and what will be his major.

Ruth in NZ

#13 regentrude

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Posted 10 February 2013 - 09:43 PM

Oh, did this make me smile! My dh always says that I have a rolling 2 year memory, so perhaps I have simply forgotten! However, there is a difference between a course in statistics and a course in probability. They obviously inform one another, but if you are using statistics to answer real life questions in biology, business, or the social sciences, you certainty do not have to integrate probability distributions. But I will definitely not speak for engineering. However, statistics does not follow the same kind of progression as physics -- algebra-based and then calculus based. Instead, after a basic class, you take classes in Analysis of Variance, Regression, Non-parametric stats, Time Series, experimental design etc. I have not taken an isolated class on probability, so I wonder if this is the difference.


I only took one semester that was combined statistics and probability theory, and the course our majors take here is entitled "Introduction to statistics and probability".
Here is the TOC
http://search.barnes...e/9780321584755
I am not an expert in statistics, but it looks to me as if this text addresses the basic concepts of discrete statistics as well, sufficiently for an introductory class.
For the physics student, dealing with continuous distributions is an essential prerequisite to statistical and thermal physics - it is impossible to understand thermodynamics at undergraduate level without some knowledge about dealing with a continuous (in this particular case, Maxwell's) distribution. Statistical physics essentially deals with integrating over distributions to find expectation values for quantities. So, for applications of statistics in physics, calculus is vitally important. (My DH does stuff like this pretty much all day long.)
Of course, doing analysis of, for example, experimental results, does involve discrete data as well.

#14 In The Great White North

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Posted 10 February 2013 - 09:55 PM

I only took one semester that was combined statistics and probability theory, and the course our majors take here is entitled "Introduction to statistics and probability".



My probability and statistics course was combined also, and was designed to come after multi-integral calculus and differential equations. I was surprised when I heard that AP Statistics was algebra based.

#15 lewelma

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Posted 10 February 2013 - 11:52 PM

I'm happy to be over-ruled!

I only started taking statistics classes in grad school, so perhaps I missed a standard basic undergrad course. If so, it never hurt me. go figure.

Ruth in NZ

#16 JennyD

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Posted 11 February 2013 - 12:42 AM

I showed this thread to my DH, who has a Ph.D. in statistics and teaches stats to non-majors. His recommendation for a general introductory text is this:

http://www.amazon.co...n/dp/0393929728

He says that this book is unusually thoughtful and does a good job of clearly presenting the underlying concepts, which students often lose track of once they get deep into the math. However, if your son has already covered this material thoorughly in AP Stats, then he agrees with regentrude's recommendation of the Ross probability book. And possibly even this, which is DH's all-time favorite stats text:

http://www.amazon.co...ference casella

The Casella is approximately a junior-level text, according to DH.
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#17 jwatkins

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Posted 12 May 2013 - 10:30 AM

I have some notes

http://math.arizona....ns/statbook.pdf

that attempt to show how you can use calculus and computation using R to give a sense of how statistics is done.

#18 Candid

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Posted 12 May 2013 - 03:18 PM

I also had a bunch of statistics in college and calculus really doesn't get used. They do this weird stuff where you calculate subsets of totals instead of doing real calculus.

I can also remember my brilliant professor telling use that most of the tests we were running in the early 80s were just then being able to be actually calculate because before that it would have taken years to run the calculations without a computer (MANOVA for instance). He had been able to get us special access to SAS and we could easily run up a bill of $300,000 to run one test. (I presume that no one was actually paying that bill.) Told us that they couldn't run it on the university's mainframe. The part that freaks me out is knowing I could probably run it on my current computer.
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#19 arborite

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Posted 12 May 2013 - 03:19 PM

In my doctoral economics sequence at MIT, we used multivariable calculus (integrals and derivatives) in our stats and probability class. In our follow-on regression class we used matrix algebra.

Best high school training for any eventuality (major, field) is the general math sequence, through multivariable calculus. Number and counting theory (e.g. Art of Problem Solving's books) will be useful for college stats and probability classes. If you finish those consider matrix algebra.

I would not send a high school student into a calculus-based stats class. Too specialized for this stage. And, um, boring!

#20 kiana

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Posted 12 May 2013 - 05:41 PM

In my doctoral economics sequence at MIT, we used multivariable calculus (integrals and derivatives) in our stats and probability class. In our follow-on regression class we used matrix algebra.

Best high school training for any eventuality (major, field) is the general math sequence, through multivariable calculus. Number and counting theory (e.g. Art of Problem Solving's books) will be useful for college stats and probability classes. If you finish those consider matrix algebra.

I would not send a high school student into a calculus-based stats class. Too specialized for this stage. And, um, boring!


Gosh, I thought matrix algebra was a lot more boring than calc-based prob/stats. The prob/stats class was one of my favorite ever.

#21 arborite

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Posted 12 May 2013 - 06:38 PM

I agree matrix algebra is not a hoot. But it is a more general academic skill than is calculus-based statistics.

#22 snowbeltmom

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Posted 13 May 2013 - 05:34 AM

Update to my original post:

I found an online provider with positive reviews that fits what I was looking for. NetMath from the University of Illinois offers math beyond single variable calculus. I am going to combine the class below with AoPS Intermediate C & P book.


Math 461: Introduction to Probability Theory

Overview


Introduction to mathematical probability; includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and central limit theorem.

#23 arborite

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Posted 13 May 2013 - 09:03 AM

Please report back! Would love to hear how it goes.
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