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Sample pages 2 PDF
Sample pages 2 PDF

Notes on generating Sobol sequences
Notes on generating Sobol sequences

... where ⊕ is the bit-by-bit exclusive-or operator. The initial values m1,j , m2,j , . . . , msj ,j can be chosen freely provided that each mk,j , 1 ≤ k ≤ sj , is odd and less than 2k . The so-called direction numbers {v1,j , v2,j , . . .} are defined by mk,j vk,j := k . ...
Scientific Notation Powerpoint
Scientific Notation Powerpoint

... How would you reverse Scientific Notation (write in standard form)? Do the OPPOSITE. 1. Move the decimal point the number of places as the exponent in the Power of 10 to the RIGHT. ...
scientific-notation-pdf
scientific-notation-pdf

extraProblems - weeks 1 and 2
extraProblems - weeks 1 and 2

Working with three, four and five digit numbers - 3
Working with three, four and five digit numbers - 3

Mac: new
Mac: new

Intermediate Math Circles October 22, 2008 Number Theory III
Intermediate Math Circles October 22, 2008 Number Theory III

Rational numbers and their decimal representation
Rational numbers and their decimal representation

Remainder Theorem
Remainder Theorem

... If the remainder f(r) = R = 0, then (x-r) is a factor of f(x). The Factor Theorem is powerful because it can be used to find the roots of polynomial equations. Example 3: Is x  4 a factor of 3x 3  x 2  20 x  5 ? For this question we need to find out if dividing 3x 3  x 2  20 x  5 by x  4 lea ...
Squares & Square Roots
Squares & Square Roots

... Estimating Square Roots Not all numbers are perfect squares. Not every number has an Integer for a square root. We have to estimate square roots for numbers between perfect squares. ...
2.3
2.3

... number of significant digits in our answers matches the number of significant digits in the least significant number given in the original problem. Also, we round our answers only and not any of the numbers in the intermediate steps. ...
Polygonal Numbers
Polygonal Numbers

Recursive Worksheet
Recursive Worksheet

1.5 Adding and Subtracting Real Numbers Template
1.5 Adding and Subtracting Real Numbers Template

Lesson 1
Lesson 1

... • Inductive Reasoning- the process of arriving at a general conclusion based on observations of specific examples. • We can never be certain that these conclusions are true. • For this reason conclusions are called conjectures, hypotheses, or educated guess. ...
1-1 Expressions and Formulas
1-1 Expressions and Formulas

... It is a mathematical statement with variables. 3x + 4  So what is an Equation? It an expression that equals a given value, thus you can solve an equation. ...
PRACTICE: Mixed practice with roots √4 = √144 = √9 = √64
PRACTICE: Mixed practice with roots √4 = √144 = √9 = √64

Adding, Subtracting, Multiplying, and Dividing Integers
Adding, Subtracting, Multiplying, and Dividing Integers

Adding, Subtracting, Multiplying, and Dividing Integers
Adding, Subtracting, Multiplying, and Dividing Integers

HW-06 due 02/22
HW-06 due 02/22

Number Theory - Colts Neck Schools
Number Theory - Colts Neck Schools

Solution Week 90 (5/31/04) The game of NIM As with many
Solution Week 90 (5/31/04) The game of NIM As with many

... other triplets, this appears to be true in general for an LP. We will prove this with the following theorem. Theorem: Call a triplet an E-triplet (the “E” stands for “even”) if it has the following property: When the three numbers are written in base 2, there is an even number (that is, either zero ...
Introduction to Prime Time: Factors and Multiples
Introduction to Prime Time: Factors and Multiples

Solutions to USC’s 21st High School Math Contest
Solutions to USC’s 21st High School Math Contest

< 1 ... 370 371 372 373 374 375 376 377 378 ... 456 >

Location arithmetic

Location arithmetic (Latin arithmeticæ localis) is the additive (non-positional) binary numeral systems, which John Napier explored as a computation technique in his treatise Rabdology (1617), both symbolically and on a chessboard-like grid.Napier's terminology, derived from using the positions of counters on the board to represent numbers, is potentially misleading in current vocabulary because the numbering system is non-positional.During Napier's time, most of the computations were made on boards with tally-marks or jetons. So, unlike it may be seen by modern reader, his goal was not to use moves of counters on a board to multiply, divide and find square roots, but rather to find a way to compute symbolically.However, when reproduced on the board, this new technique did not require mental trial-and-error computations nor complex carry memorization (unlike base 10 computations). He was so pleased by his discovery that he said in his preface ... it might be well described as more of a lark than a labor, for it carries out addition, subtraction, multiplication, division and the extraction of square roots purely by moving counters from place to place.
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