MATH 1113 Review Sheet for the Final Exam
... Defining Inverse of a function Inverse Function of a function; connection between domains and ranges of these functions Defining the terms one to one and one to one function o Intuitively, one to one means no partner sharing o Determining when a graph that represents a function is one to one; ...
... Defining Inverse of a function Inverse Function of a function; connection between domains and ranges of these functions Defining the terms one to one and one to one function o Intuitively, one to one means no partner sharing o Determining when a graph that represents a function is one to one; ...
Slides
... Rule 1. Name must be comprised of digits, upper case letters, lower case letters, and the underscore character “_” Rule 2. Must begin with a letter or underscore A good name for a variable is short but suggestive of its role: Circle_Area ...
... Rule 1. Name must be comprised of digits, upper case letters, lower case letters, and the underscore character “_” Rule 2. Must begin with a letter or underscore A good name for a variable is short but suggestive of its role: Circle_Area ...
exponential and logarithmic series
... Four of the following five groups of letters are alike in some way while one is different. Find out which one is different. (a) ISLOJ (b) LUOQM (c) AKDGB (d) FPILG 6. In a class Smita is 6th from the top and Harsha is 18th from the bottom. Mangesh is 14 ranks below Smita and 15 ranks above Harsha. H ...
... Four of the following five groups of letters are alike in some way while one is different. Find out which one is different. (a) ISLOJ (b) LUOQM (c) AKDGB (d) FPILG 6. In a class Smita is 6th from the top and Harsha is 18th from the bottom. Mangesh is 14 ranks below Smita and 15 ranks above Harsha. H ...
Secondary Mathematics_7
... 2. Every integer and fraction is a rational number but the converse may not be true. 3. A rational number is said to be positive if both numerator and denominator are of same sign. If numerator and denominator are of opposite signs, then rational number is said to be negative. ...
... 2. Every integer and fraction is a rational number but the converse may not be true. 3. A rational number is said to be positive if both numerator and denominator are of same sign. If numerator and denominator are of opposite signs, then rational number is said to be negative. ...
Jacobi`s Two-Square Theorem and Related Identities
... Indeed, I gave such a proof in [4]. The proof there consists of two parts. First, it is shown that ...
... Indeed, I gave such a proof in [4]. The proof there consists of two parts. First, it is shown that ...
math placement test
... Placement Test. The guide includes a sample test question for each topic. The answers are given at the end. 1. Arithmetic. Calculators may not be used for this test because part of the test involves knowledge of basic arithmetic. a) Adding whole numbers. You must know the sum of any two one-digit nu ...
... Placement Test. The guide includes a sample test question for each topic. The answers are given at the end. 1. Arithmetic. Calculators may not be used for this test because part of the test involves knowledge of basic arithmetic. a) Adding whole numbers. You must know the sum of any two one-digit nu ...
mixed number
... A fraction is proper when its numerator is smaller than its denominator (3/4, 5/8, 6/10). A fraction is improper when its numerator is larger than its denominator (4/3, 8/5, 10/6). Which are improper fractions? ...
... A fraction is proper when its numerator is smaller than its denominator (3/4, 5/8, 6/10). A fraction is improper when its numerator is larger than its denominator (4/3, 8/5, 10/6). Which are improper fractions? ...
Pseudoprimes and Carmichael Numbers, by Emily Riemer
... Let n be an odd integer and write n − 1 = 2k · q with q odd. If both of the following conditions are true for some a not divisible by n, then n is a composite number: (a) aq 6≡ 1(mod n) (b) a2i ·q 6≡ −1(mod n) for all i = 0, 1, 2, ..., k − 1 The Rabin-Miller test is stronger than Fermat’s Little The ...
... Let n be an odd integer and write n − 1 = 2k · q with q odd. If both of the following conditions are true for some a not divisible by n, then n is a composite number: (a) aq 6≡ 1(mod n) (b) a2i ·q 6≡ −1(mod n) for all i = 0, 1, 2, ..., k − 1 The Rabin-Miller test is stronger than Fermat’s Little The ...
CS21Lecture3
... 3. Getting used to navigating the system 4. rmdir can only remove empty directories 5. A lot of environment variables are automatically set, but not every one will be ...
... 3. Getting used to navigating the system 4. rmdir can only remove empty directories 5. A lot of environment variables are automatically set, but not every one will be ...
Document
... Successors and Predecessors | TOC A postulate is a statement that a bunch of people agree is true. Algebra books are loaded with postulates that mathematicians agree are true. Postulates provide the foundation on which we can build algebraic structures. Here are our first postulates for natural numb ...
... Successors and Predecessors | TOC A postulate is a statement that a bunch of people agree is true. Algebra books are loaded with postulates that mathematicians agree are true. Postulates provide the foundation on which we can build algebraic structures. Here are our first postulates for natural numb ...
Chapter5 Sections 1 to 3
... To raise a product to a power, raise each factor of the product to that power. To raise a quotient to a power, raise the numerator and the denominator to that power. For any numbers x and y, and any natural number n: (xy)n = xnyn and (x/y)n = xn/yn, where y ≠ 0. ...
... To raise a product to a power, raise each factor of the product to that power. To raise a quotient to a power, raise the numerator and the denominator to that power. For any numbers x and y, and any natural number n: (xy)n = xnyn and (x/y)n = xn/yn, where y ≠ 0. ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.