PROGRAMMING IN MATHEMATICA, A PROBLEM
... able to assign data to them. As long as you use common sense, any names you choose for variables are valid in Mathematica. Names like x, y, x3, myfunc, xQuaternion, ... are all fine. Do not use underscore to define a variable 2. The underscore is reserved and will be used in the definition of functi ...
... able to assign data to them. As long as you use common sense, any names you choose for variables are valid in Mathematica. Names like x, y, x3, myfunc, xQuaternion, ... are all fine. Do not use underscore to define a variable 2. The underscore is reserved and will be used in the definition of functi ...
Chapter 8
... The theorem follows rather simply from some of our following work: (p – 1)! ≡ -1 (mod p) for all primes p. This result can be verified for p = 2. Now, let’s consider all odd p. Since each value 1, 2, …, p – 1 is relatively prime to p, each has an inverse mod p. We know that the inverse of 1 is 1 and ...
... The theorem follows rather simply from some of our following work: (p – 1)! ≡ -1 (mod p) for all primes p. This result can be verified for p = 2. Now, let’s consider all odd p. Since each value 1, 2, …, p – 1 is relatively prime to p, each has an inverse mod p. We know that the inverse of 1 is 1 and ...
Introduction to Mathematical Reasoning, Saylor 111 Fractions
... 10. Simpsons (with thanks to http://www.cut-the-knot.com) Bart and Lisa shoot free throws in two practice sessions to see who gets to start in tonight’s game. Bart makes 5 out of 11 in the first session while Lisa makes 3 out of 7. Who has the better percentage? Is it possible that Bart shoots the b ...
... 10. Simpsons (with thanks to http://www.cut-the-knot.com) Bart and Lisa shoot free throws in two practice sessions to see who gets to start in tonight’s game. Bart makes 5 out of 11 in the first session while Lisa makes 3 out of 7. Who has the better percentage? Is it possible that Bart shoots the b ...
Unit 1 Number I core
... universal set U, empty set or { }, complement of A, A’, number of elements in A, n(A) Sets in descriptive form {x } or as a list. NEW Venn diagrams with at most three sets. ...
... universal set U, empty set or { }, complement of A, A’, number of elements in A, n(A) Sets in descriptive form {x } or as a list. NEW Venn diagrams with at most three sets. ...
SECTION C Properties of Prime Numbers
... C2 Distribution of Primes We have already proven that there are an infinite number of primes. How are these primes distributed? This is one of the most interesting questions in the whole of mathematics. While we see our number system as an ordered, predictable set, its primes are unpredictable. Ther ...
... C2 Distribution of Primes We have already proven that there are an infinite number of primes. How are these primes distributed? This is one of the most interesting questions in the whole of mathematics. While we see our number system as an ordered, predictable set, its primes are unpredictable. Ther ...
7 Catalan Numbers
... Since the first and last terms of P must be 1 and −1, respectively, the operation of deleting those terms is reversed by adding 1 before and −1 after P 0 . Thus the function that takes P to P 0 is invertible. Hence, if an is the number of positive paths and bn the number of nonnegative paths from th ...
... Since the first and last terms of P must be 1 and −1, respectively, the operation of deleting those terms is reversed by adding 1 before and −1 after P 0 . Thus the function that takes P to P 0 is invertible. Hence, if an is the number of positive paths and bn the number of nonnegative paths from th ...
