Lecture 12-13
... By induction hypothesis, the positive integers a and b have prime factorizations, say, a = p1 p2 · · · pk and b = q1 q2 · · · ql . Then n + 1 = p1 p2 · · · pk q1 q2 · · · ql . This means that n + 1 is a product of prime numbers. ...
... By induction hypothesis, the positive integers a and b have prime factorizations, say, a = p1 p2 · · · pk and b = q1 q2 · · · ql . Then n + 1 = p1 p2 · · · pk q1 q2 · · · ql . This means that n + 1 is a product of prime numbers. ...
Section 9.2 – Arithmetic Sequences
... Name: ________________________ Date: ___________________ Period: ____________ Algebra 2: Section 9.2 Arithmetic Sequences Notes Definition of an Arithmetic Sequence An arithmetic sequence is a sequence in which each term after the first differs from the preceding term by a _____________ amount. The ...
... Name: ________________________ Date: ___________________ Period: ____________ Algebra 2: Section 9.2 Arithmetic Sequences Notes Definition of an Arithmetic Sequence An arithmetic sequence is a sequence in which each term after the first differs from the preceding term by a _____________ amount. The ...
Official_paper_(12-16)_submitted version - Rose
... University of Hartford In a differential equations class last year I saw an explicit function that generated a sequence of alternating 0’s and 1’s which was used to select specific terms in a series. This sequence prompted me to wonder what functions might produce other periodic sequences with longe ...
... University of Hartford In a differential equations class last year I saw an explicit function that generated a sequence of alternating 0’s and 1’s which was used to select specific terms in a series. This sequence prompted me to wonder what functions might produce other periodic sequences with longe ...
Lecture Note
... sin(0.3) for example? One might grab a pocket calculator and compute the value. But then the question arises how the calculator gets its value. Or, suppose we want sin(0.3) to a higher precision than the one provided by the pocket calculator, what should we do then? The difference between the functi ...
... sin(0.3) for example? One might grab a pocket calculator and compute the value. But then the question arises how the calculator gets its value. Or, suppose we want sin(0.3) to a higher precision than the one provided by the pocket calculator, what should we do then? The difference between the functi ...
Thomas Meade September 18, 2008 MAE301 Class Notes: 9/16/08
... integer with respect to being odd or even”. In order to determine if there is an equivalence relation based on the parity of integers reflexivity, symmetry and transitivity must be checked. Another good thing to take note of is the set being worked with, the integers in this case, and also the relat ...
... integer with respect to being odd or even”. In order to determine if there is an equivalence relation based on the parity of integers reflexivity, symmetry and transitivity must be checked. Another good thing to take note of is the set being worked with, the integers in this case, and also the relat ...
Parent Letter September-October Transitions
... Some quadratic functions, such as f(x) x2 4, have no x-intercepts. Likewise, the equation 0 x2 4 has no real roots because you get x 4 . The square root of a negative number is called an imaginary number, and the imaginary unit is i 1 . So, 0 x2 4 does have two imaginary roots, x ...
... Some quadratic functions, such as f(x) x2 4, have no x-intercepts. Likewise, the equation 0 x2 4 has no real roots because you get x 4 . The square root of a negative number is called an imaginary number, and the imaginary unit is i 1 . So, 0 x2 4 does have two imaginary roots, x ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.