Online texts Professor Jim Herod and I have written Multivariable Calculus ,a book which we and a few others have used here at Georgia Tech for two years. We have also proposed that this be the first calculus course in the curriculum here, but that is another story.... Although it is still in print, Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative. Here is one that has also been used here at Georgia Tech. Linear Methods of Applied Mathematics, by Evans Harrell and James Herod. Yet another one produced at Georgia Tech is Linear Algebra, Infinite Dimensions, and Maple, by James Herod.
The Normal Distribution Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/AMS/Regular/Main.js \newcommand{\R}{\mathbb{R}}\newcommand{\N}{\mathbb{N}}\newcommand{\P}{\mathbb{P}}\newcommand{\E}{\mathbb{E}}\newcommand{\var}{\text{var}}\newcommand{\sd}{\text{sd}}\newcommand{\skew}{\text{skew}}\newcommand{\kurt}{\text{kurt}} The normal distribution holds an honored role in probability and statistics, mostly because of the central limit theorem, one of the fundamental theorems that forms a bridge between the two subjects. In addition, as we will see, the normal distribution has many nice mathematical properties. The normal distribution is also called the Gaussian distribution The Standard Normal Distribution A random variable Z has the standard normal distribution if it has the probability density function \phi given by \phi(z) = \frac{1}{\sqrt{2 \, \pi}} e^{-\frac{1}{2} z^2}, \quad z \in \R \phi is a probability density function. The standard normal density function \phi satisfies the following properties: Moments The The general
OSWINS - Mathematics Content: calculators , graphs , computational tools , math games , algebra , courses , tutorials and problem solving Quotes "The understanding of mathematics is necessary for a sound grasp of ethics." - Socrates "Mathematicians do not study objects, but relations between objects. "I will not define time, space, place and motion, as being well known to all." - Sir Isaac Newton "So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality." - Albert Einstein "The creator of the universe works in mysterious ways. (GPL) (Free) (Free, Geogebra License) (GPL) (Artistic License) (Free) (Free) (Free) (GPL) (GPL)
JOS Home Page Julius Orion Smith III Home Page Online Books Publications JOS Global Index Courses Curriculum Vitae Education | Work Experience | Honors | Publications | Music CCRMA World Update 2021 Blogs Videos Address Julius O. The Narrow Road » If We Taught English the Way We Teach Math Imagine that your only contact with “English” as a subject was through classes in school. Suppose that those classes, from elementary school right through to high school, amounted to nothing more than reading dictionaries, getting drilled in spelling and formal grammatical construction, and memorizing vast vocabulary lists — you never read a novel, nor a poem; never had contact with anything beyond the pedantic complexity of English spelling and formal grammar, and precise definitions for an endless array of words. You would probably hate the subject.You might come to wonder what the point of learning English was. In response perhaps the teachers and education system might decide that, to help make English relevant to students, they need to introduce more “Applied English”. This means teaching English students with examples from “real life” (for varying degrees of “real”) where English skills are important, like how to read a contract and locate the superfluous comma.
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Quotes « Let ε < 0. The four branches of arithmetic — ambition, distraction, uglification and derision. (Lewis Caroll, Alice in Wonderland) As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. (Albert Einstein) If you can’t explain what you are doing to a nine-year-old, then either you still don’t understand it very well, or it’s not all that worthwile in the first place. Only two things are infinite: the universe and human stupidity, and I’m not sure about the former. The two most common things in the Universe are hydrogen and stupidty. I’ve heard that the government wants to put a tax on the mathematically ignorant. Old mathematicians never die; they just lose some of their functions. I turn away with fear and horror from this lamentable plague of functions which do not have derivatives. Mathematics is a game played according to certain simple rules with meaningless marks on paper. Physics is much too hard for physicists.
What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree? « Ask a Mathematician / Ask a Physicist Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! You’re not allowed to divide by zero, which you did in the last step. which is true since anything times 0 is 0. Cleverest student : That doesn’t work either, because if then is so your third step also involves dividing by zero which isn’t allowed! and see what happens as x>0 gets small. So, since = 1, that means that High School Teacher: Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that . is undefined. does not have a value. Calculus Teacher: For all , we have Hence, That is, as x gets arbitrarily close to (but remains positive), stays at On the other hand, for real numbers y such that , we have that That is, as y gets arbitrarily close to Therefore, we see that the function has a discontinuity at the point . but when we approach (0,0) along the line segment with y=0 and x>0 we get Therefore, the value of that will make the function ! . as