Homework #3
... and is used to detect errors in individual digits and transposition of digits. If the ISBN of a book is 0-201-57Q89-1, where Q is a digit, find Q. 1*0 + 2*2 + 3*0 + 4*1 + 5*5 + 6*7 + 7*Q + 8*8 + 9*9 + 10*1 = 0 (mod 11) That is, 230 + 7Q = 0 (mod 11) Subtracting 230 from both sides 7Q = 1 (mod 11) be ...
... and is used to detect errors in individual digits and transposition of digits. If the ISBN of a book is 0-201-57Q89-1, where Q is a digit, find Q. 1*0 + 2*2 + 3*0 + 4*1 + 5*5 + 6*7 + 7*Q + 8*8 + 9*9 + 10*1 = 0 (mod 11) That is, 230 + 7Q = 0 (mod 11) Subtracting 230 from both sides 7Q = 1 (mod 11) be ...
Algorithms
... “a finite sequence of unambiguous, executable steps or instructions, which, if followed would ultimately terminate and give the solution of the problem”. ...
... “a finite sequence of unambiguous, executable steps or instructions, which, if followed would ultimately terminate and give the solution of the problem”. ...
To: - Bridge of Don Academy – Faculty of Mathematics and Numeracy
... a) Use a number line to add/subtract whole numbers to/from integers (e.g. 5 – 8 = –3). b) Able to add/subtract integers to/from integers (e.g. 7 + (–2) = 7 – 2 = 5). Make sure they use brackets so that no two operators are touching (e.g. 5 3 5 (3) ). c) Know how to multiply an integer by a w ...
... a) Use a number line to add/subtract whole numbers to/from integers (e.g. 5 – 8 = –3). b) Able to add/subtract integers to/from integers (e.g. 7 + (–2) = 7 – 2 = 5). Make sure they use brackets so that no two operators are touching (e.g. 5 3 5 (3) ). c) Know how to multiply an integer by a w ...
Fibonacci
... • This implies that we want a loop! • Remember: A Loop lets the computer do things over and over again so we don’t have to! ...
... • This implies that we want a loop! • Remember: A Loop lets the computer do things over and over again so we don’t have to! ...
Fraction IX Least Common Multiple Least Common Denominator
... least common denominator or least common multiple. ...
... least common denominator or least common multiple. ...
3.2
... How to tell if one fraction is bigger than another A. See if the fractions have the same denominator B. If not, scale them up to the LCM of the denominators (find the common denominator) C. Compare the numerators to see which is bigger Ex1: 5/12 and 7/18 A. Denominators not the same B. LCM of 12 & 1 ...
... How to tell if one fraction is bigger than another A. See if the fractions have the same denominator B. If not, scale them up to the LCM of the denominators (find the common denominator) C. Compare the numerators to see which is bigger Ex1: 5/12 and 7/18 A. Denominators not the same B. LCM of 12 & 1 ...
PKE Fundamentals
... Keeping in mind that the arithmetic operations addition and multiplication (and by extension subtraction, division, exponentiation) are just shortcuts for more efficient counting, we realize that we can perform all modulus operations just as regular addition and multiplication as long as we remember ...
... Keeping in mind that the arithmetic operations addition and multiplication (and by extension subtraction, division, exponentiation) are just shortcuts for more efficient counting, we realize that we can perform all modulus operations just as regular addition and multiplication as long as we remember ...
Number Theory for Mathematical Contests
... This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions s ...
... This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions s ...
Chapter 6 - James Bac Dang
... If A, B, mid C are the measures of the angles of a triangle, and a, b, and c are the lengths of the sides opposite these angles, then a2 b2 + c2 - 2bc cos A ...
... If A, B, mid C are the measures of the angles of a triangle, and a, b, and c are the lengths of the sides opposite these angles, then a2 b2 + c2 - 2bc cos A ...
ROOT NUMBERS OF HYPERELLIPTIC CURVES 1. Introduction
... where k is the residue field of K, Σk is the set of the singular k-points of the reduction X of X over k, nk = |Σk |, sk is the number of irreducible k-components of X and τ[z] = ±1 is defined in Proposition 4.2 below. We also give examples of hyperelliptic curves of genus 2 over Q, for which the ob ...
... where k is the residue field of K, Σk is the set of the singular k-points of the reduction X of X over k, nk = |Σk |, sk is the number of irreducible k-components of X and τ[z] = ±1 is defined in Proposition 4.2 below. We also give examples of hyperelliptic curves of genus 2 over Q, for which the ob ...
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.