No one should take a course from that book. The authors of the book don't know the subject.
That book won't be a prerequisite for anything important.
So, if want a first course in probability and statistics, then get a college textbook and/or just go to college.
More generally, in college in the US, in math, physical science, and engineering, quite good texts are easy to find, and the best texts are excellent. Moreover, the prerequisites for college are quite basic, essentially just the '3Rs' where for 'rithmetic' we do include algebra and plane geometry (trigonometry and solid geometry would also be good).
So, in K-12, just get the 3Rs and then start with college texts and/or just college.
In particular, for anything much past the 3Rs, just f'get about K-12. Bluntly, as illustrated by the book of this thread, the K-12 system is rarely able to teach anything worthwhile much beyond just the basic 3Rs.
This conclusion is not new: Once I looked at AP calculus. Don't. The people who wrote the AP calculus materials don't understand calculus. Instead, for calculus, just get a good college text and dig in. I learned from Johnson and Kiokemeister, taught from Protter and Morrey, and have seen several other good college calculus texts, e.g., from Thomas. When I was studying and, later, teaching calculus in college, there was no shortage of good texts. Just why K-12 has so much trouble getting good calculus texts is strange and tragic.
Once I looked at some materials on optimization, i.e., linear programming, developed by the K-12 system in North Carolina. Don't. Those materials fill several much needed gaps on the library shelves and would be illuminating if ignited. The authors didn't understand linear programming.
has some excellent quotes from Feynman looking at K-12 texts. Feynman was correct, and apparently the situation has not changed.
My qualifications: I hold a Ph.D. from one of the world's best research universities; there I did research on optimization and also on stochastic optimal control. For calculus, I've done well studying it, advanced calculus, and well beyond, taught calculus in college, applied calculus in business and to problems of US national security, and published peer-reviewed original research using calculus. For optimization, I've studied it at advanced levels, applied it in both in business to problems of US national security, taught it in college and graduate school, and published peer-reviewed original research in it. My startup has some original, crucial, core, powerful, valuable 'secret sauce' that is based on some advanced topics in applied math including 'analysis' (way past calculus), probability, and statistics.
Not everybody on HN is able to judge textbook's quality, so I'd like to clarify:
There's nothing wrong with relative quality of this textbook, compared to regular high school textbooks on this subject. The thing is, all high school textbooks are total crap.
I wouldn't go as far as to state that author don't know the subject (although, saying from experience, it's highly likely). The problem is that they don't teach anything substantial, and what they do teach, is vague and unclear. The chapter about distributions and density functions is total nonsense.
Serious probability course covers all contents of this book on one or two 2-hours lectures, in much, much more general setting (i.e., probability being the measure on measurable space). This book seems to be meant for 40 hours (one hour per section). It's not like undergraduates are 20 times smarter than high school kids. They just want to learn it, or at least to get a passing grade. The same is the case with high school kids, but the amount of actual work to get a passing grade there is negligible, and they're motivated accordingly. High school teachers cannot just give a failing grade to 80% of her class, because it would mean that there's a problem with her, not with her students. She also cannot depend on necessary prerequisites to serious probability theory to be already known, because it's not, just like university professors cannot depend on probability to be known, because if one learns from books like this, it's not. Without system reform, there's not much that can be done from bottom up.
I'm not versed in the entire complexity of the issue at hand here, but isn't putting the text book in the hands of teachers a kind of reform?
Wouldn't having a teacher, or teachers, write their own text books give them better control over what to teach?
Couldn't a collection of teacher add something to the curriculum through the text book and watch it get adopted higher up structurally based mostly on the fact that if the teachers teaching those students specifically added material they found was necessary then it must be important enough to require it officially.
The story is written as a money saving venture first, and then a better alignment of course material to state standards, but I'd also like to think it might democratize what those state standards should be amongst a population of professionals who interact on a daily basis with the people who have to test against those standards.
You're qualifications also include using the name HilbertSpace [1] on Hacker News.
Seriously though, I've recently graduated from an undergraduate institution where the mathematics courses were rigorous and proof based. While I thought I was learning a lot of math in High School (I was working hard, which should mean I was learning, right?), it did very little to prepare me for any sort of real mathematics. I think this was a function of both the textbooks and the teachers.
However, when I entered college, for most of my mathematics courses, the professors taught out of their own books. Some of these were published texts, but most were collections of notes they had refined over years of teaching. In every case, I much preferred these to doing math from a random textbook. The professors just taught better when they were using their own book.
Part of this may be that better professors are more likely to write their own book. However, I think there actually would be value from K-12 teachers writing or at least collaborating on the main body of their course material. It might help to remove the scenario where a student asks a teacher a question, and they give an answer that directly contradicts what is said in the book.
Commonly in K-12, the best 'math' taught is plane geometry because there, at least when it's a theorem proving course instead of paper cutouts, which sometimes happens, can see in clear terms the roles of the big three -- definitions, theorems, and proofs. You can also see the role of one more -- intuition, especially its best form, geometric intuition. Right: Intuition doesn't prove anything, but it can be one of the best ways to guess what is true and how to prove it. For more, eventually you can get a useful intuitive feeling for a topic.
which at face value is supposed to be about women in math but describes Harvard's Math 55. At least at one time for that course the three main texts were:
Paul R. Halmos, 'Finite-Dimensional Vector Spaces, Second Edition', D. Van Nostrand Company, Inc., Princeton, New Jersey.
Walter Rudin, 'Principles of Mathematical Analysis, Third Edition', McGraw-Hill.
Michael Spivak, 'Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus', W. A. Benjamin, New York.
Working successfully through those three is quite sufficient to understand proof-based college math!
Those three are all old; in particular Halmos wrote the first edition of his book in 1942 when he was an assistant to von Neumann at the Institute for Advanced Study.
I had Rudin's book in college but later rushed to work carefully through both Halmos and Spivak ASAP after college.
Instead of Spivak, I preferred:
Wendell H. Fleming, 'Functions of Several Variables', Addison-Wesley, Reading, Massachusetts.
Might also consider:
Lynn H. Loomis and Shlomo Sternberg, 'Advanced Calculus', ISBN 0-201-04305-X, Addison-Wesley, Reading, Massachusetts.
For exterior algebra, now can get in English:
Henri Cartan, 'Differential Forms', ISBN 0-486-45010-4, Dover, Mineola, NY.
Since mentioned Halmos and since this thread is about probability and statistics, should mention that Halmos was one of the best in those topics in the US in the 20th century.
Halmos was a student of J. Doob at University of Illinois as in:
J. L. Doob, 'Stochastic Processes', John Wiley and Sons, New York, 1953.
and has a very nice start on probability in:
Paul R. Halmos, 'Measure Theory', D. Van Nostrand Company, Inc., Princeton, NJ, 1950.
Halmos also wrote:
Paul R. Halmos, "The Theory of Unbiased Estimation", 'Annals of Mathematical Statistics', Volume 17, Number 1, pages 34-43, 1946.
and also the crucial:
Paul R. Halmos and L. J. Savage, "Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics", Annals of Mathematical Statistics, Volume 20, Number 2, 225-241, 1949.
Yes 'Finite-Dimensional Vector Spaces' is really a finite dimensional introduction to Hilbert space which mostly have to attribute to von Neumann (who once reminded Hilbert what it was).
The set of all real valued random variables X such that E[X^2] is finite forms a Hilbert space. The amazing part is completeness, and there is a proof in:
Walter Rudin, 'Real and Complex Analysis', ISBN 07-054232-5, McGraw-Hill, New York.
which also has a nice chapter on Hilbert space.
Yes, having professors write their own books is now more common and can make a course more efficient for the students. It was long the case that a student had to copy the 'text' off the board or just take notes and turn them into a text. Now with TeX and LaTeX, PDF, and the Internet, finally the word whacking for the math can often be less work than the math!
Still, it will be difficult to improve on some of the best texts, e.g., Halmos. Rudin went through at least three editions of his 'Principles', and the level of polish started high and increased. A good book is actually NOT easy to write.
http://moodle.anoka.k12.mn.us/mod/resource/view.php?inpopup=...
and I started reading it.
Don't.
No one should take a course from that book. The authors of the book don't know the subject.
That book won't be a prerequisite for anything important.
So, if want a first course in probability and statistics, then get a college textbook and/or just go to college.
More generally, in college in the US, in math, physical science, and engineering, quite good texts are easy to find, and the best texts are excellent. Moreover, the prerequisites for college are quite basic, essentially just the '3Rs' where for 'rithmetic' we do include algebra and plane geometry (trigonometry and solid geometry would also be good).
So, in K-12, just get the 3Rs and then start with college texts and/or just college.
In particular, for anything much past the 3Rs, just f'get about K-12. Bluntly, as illustrated by the book of this thread, the K-12 system is rarely able to teach anything worthwhile much beyond just the basic 3Rs.
This conclusion is not new: Once I looked at AP calculus. Don't. The people who wrote the AP calculus materials don't understand calculus. Instead, for calculus, just get a good college text and dig in. I learned from Johnson and Kiokemeister, taught from Protter and Morrey, and have seen several other good college calculus texts, e.g., from Thomas. When I was studying and, later, teaching calculus in college, there was no shortage of good texts. Just why K-12 has so much trouble getting good calculus texts is strange and tragic.
Once I looked at some materials on optimization, i.e., linear programming, developed by the K-12 system in North Carolina. Don't. Those materials fill several much needed gaps on the library shelves and would be illuminating if ignited. The authors didn't understand linear programming.
The site
http://boston.conman.org/2004/01/21.1
has some excellent quotes from Feynman looking at K-12 texts. Feynman was correct, and apparently the situation has not changed.
My qualifications: I hold a Ph.D. from one of the world's best research universities; there I did research on optimization and also on stochastic optimal control. For calculus, I've done well studying it, advanced calculus, and well beyond, taught calculus in college, applied calculus in business and to problems of US national security, and published peer-reviewed original research using calculus. For optimization, I've studied it at advanced levels, applied it in both in business to problems of US national security, taught it in college and graduate school, and published peer-reviewed original research in it. My startup has some original, crucial, core, powerful, valuable 'secret sauce' that is based on some advanced topics in applied math including 'analysis' (way past calculus), probability, and statistics.