tag:blogger.com,1999:blog-5664727215839401210.post3587976533881338275..comments2023-03-17T11:41:29.749+02:00Comments on Puzzling Queen: Arthur Benjamin about Math EducationLeena Helttulahttp://www.blogger.com/profile/07125296730932636809noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5664727215839401210.post-81929007956545309692009-12-07T10:16:39.546+02:002009-12-07T10:16:39.546+02:00Actually your comment shows I was not very clear i...Actually your comment shows I was not very clear in my post. <br /><br />I think what you need to teach the students in school is the basic tools and leave the applications to the higher education when the students understand the limitations.<br /><br />Mathematics has actually two different schools of scientists, the pure math and the applied math. I feel like a mathematician lost on track to become a teacher but my field is the pure math, combinatorics, number theory, coding theory etc. I prefer the applications which have exact answers which also has applications like RSA coding. <br /><br />If the other scientists don't have enough knowledge about the basics and limitations, the results can be disastrous. In Finland in the University of Turku Statistics is part of the social studies and the math they are using is not expressed the way I would need it to be. That is the reason I never studied it, expect as a part of the probability theory which covers as much as I need it, enough to show how much people using statistics really ignore the initial conditions and draw wrong conclusions.<br /><br />As for Sudokus, I am not interested in the fastest way to solve them. I am much more interested in questions like how many valid sudokus you can create, what is the minimum amount of clues needed and so on. These problems are hard. Since the amount of 9x9 sudokus is finite, these problems are a bit easier but the theory of nonograms and their solvability is in NP.Leena Helttulahttps://www.blogger.com/profile/07125296730932636809noreply@blogger.comtag:blogger.com,1999:blog-5664727215839401210.post-15002109466875328552009-12-04T10:39:14.181+02:002009-12-04T10:39:14.181+02:00"I have a master's degree and my major is..."I have a master's degree and my major is mathematics, I have even had some predoctoral studies, but I never had a single course in real statistics."<br /><br />I'm afraid that I think that your view of Statistics is probably based on not having studied it in any depth. Results like the Central Limit Theorem are very broadly applicable, entirely rigorous, and statistical. Similarly for properties of maximum likelihood estimation, etc.,<br /><br />(Whether the assumptions hold exactly in a given application may be open to debate, but the same may be said of much Newtonian mechanics. I never encountered a frictionless slope or "point mass" in my life - presumably because the existence of the latter would lead to a black hole!)<br /><br />Statistics and probability underlie things that we use every day, e.g. google search, efficient micro-processors, insurance. <br /><br />As science becomes more and more data-intensive almost every field now relies heavily on statistics. Examples are: DNA sequencing, mass spectroscopy, phylogenetic reconstruction (i.e. working out what are different species and how they are related), proteomics, climate prediction, evaluating new medical treatments, etc., etc.,<br /><br />Differential calculus alone is quite insufficient for any of the above modern scientific fields.<br /><br />The real problem is that the theory of mathematical statistics is actually somewhat harder than the calculus - understanding the calculus is really a pre-requisite to understanding mathematical Statistics. Consequently at a high-school level the temptation is to teach statistics in "cookbook - recipe" form without giving any explanation of the underlying theory.<br /><br />"something as vague as predicting the future"<br /><br />This statement really betrays a simple lack of knowledge.<br /><br />To take an example, it may be very hard to predict when a specific individual is going to die, but we may be able to make very accurate predictions about what proportion of people in a certain population are going to die. <br />This is the entire basis for insurance, pension funds, etc., etc.,<br /><br />Similarly, it is hard if not impossible predict whether a couple will conceive a boy or a girl, but <br />for several hundred years we have been able to predict with great accuracy what proportion of births lead to males vs. females.<br /><br />(I suggest you read up on the weak law of large numbers, central limit theorem, etc.,)<br /><br />A look back through history also reveals that many of the minds we associate with classical mathematics have been involved in the development of Probability and Statistics: Newton, Bernoulli Gauss, Laplace, Pascal, Kolmogorov, etc., etc.,<br /> <br />I think your post actually serves rather well to illustrate what Arthur Benjamin is saying.<br /><br />----<br /><br />Incidentally, you maybe interested to know that Sudoku puzzles may be solved easily via probabilistic Markov chain Monte Carlo algorithms, and further these puzzles are closely related to the theory of experimental design in statistics.Anonymousnoreply@blogger.com