the review sheet for the final exam
... Section 2.1: What is a Function? 1. Definitions: A function f is a rule that assigns to each element x in a set A exactly one element f(x), in a set B. The set A is the domain of the function. f(x) is the image of x under f. The range is the set of all possible values of f(x) as x varies through the ...
... Section 2.1: What is a Function? 1. Definitions: A function f is a rule that assigns to each element x in a set A exactly one element f(x), in a set B. The set A is the domain of the function. f(x) is the image of x under f. The range is the set of all possible values of f(x) as x varies through the ...
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... We shall make use of the famous Euler polyhedron formula. Theorem 1.2. If a closed polyhedron has V vertices, E edges and F faces, then V − E + F = 2. Given a lattice polygon with a partition into primitive lattice triangles, we take two identical copies and glue them along their common boundary. Im ...
... We shall make use of the famous Euler polyhedron formula. Theorem 1.2. If a closed polyhedron has V vertices, E edges and F faces, then V − E + F = 2. Given a lattice polygon with a partition into primitive lattice triangles, we take two identical copies and glue them along their common boundary. Im ...
Introduction to Discrete Mathematics
... vertices containing a distinguished vertex called the root, and edges connecting these vertices, can be defined recursively by these steps: BASIS STEP: A single vertex r is a rooted tree. RECURSIVE STEP: Suppose that T1, T2, …, Tn are disjoint rooted trees with roots r1, r2, …, rn, respectively. The ...
... vertices containing a distinguished vertex called the root, and edges connecting these vertices, can be defined recursively by these steps: BASIS STEP: A single vertex r is a rooted tree. RECURSIVE STEP: Suppose that T1, T2, …, Tn are disjoint rooted trees with roots r1, r2, …, rn, respectively. The ...
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... begin by sketching the graph of y = a b x. Then translate the graph horizontally by h units and vertically by k units. ...
... begin by sketching the graph of y = a b x. Then translate the graph horizontally by h units and vertically by k units. ...
Teacher Booklet Shining Term 3 - Hamilton Secondary Numeracy
... programme operate. Some sets of pupils will be using the same level of materials for more than one year. This is because their skills, once acquired, are simply being kept ‘on-the-boil’, so to speak. To accommodate this, we shall be providing a second and even third set of these materials so that pu ...
... programme operate. Some sets of pupils will be using the same level of materials for more than one year. This is because their skills, once acquired, are simply being kept ‘on-the-boil’, so to speak. To accommodate this, we shall be providing a second and even third set of these materials so that pu ...
Midpoints and Exact Points of Some Algebraic
... a floating-point system that follows the IEEE 754-1985 standard for radix-2 floating-point arithmetic [1], the user can choose an active rounding mode, also called roundingdirection attribute in the newly revised IEEE 754-2008 standard [5]: rounding toward $1, rounding toward þ1, rounding toward 0, ...
... a floating-point system that follows the IEEE 754-1985 standard for radix-2 floating-point arithmetic [1], the user can choose an active rounding mode, also called roundingdirection attribute in the newly revised IEEE 754-2008 standard [5]: rounding toward $1, rounding toward þ1, rounding toward 0, ...
Fast Sorting and Selection A Lower Bound for Worst Case
... One common computation in data visualization and analysis is computing a histogram. For example, n students might be assigned integer scores in some range, such as 0 to 100, and are then placed into ranges or “buckets” based on these scores. ...
... One common computation in data visualization and analysis is computing a histogram. For example, n students might be assigned integer scores in some range, such as 0 to 100, and are then placed into ranges or “buckets” based on these scores. ...
Pre-Calculus 12: Permutations and Combinations – Extra Review
... 32. A committee of five is to be selected from nine persons. In how many ways can this selection be made if: a) Jack must be on the committee b) Jack must not be on the committee 33. How many “words” of five different letters can be made from the English alphabet if each word: (NOTE: Treat Y as a co ...
... 32. A committee of five is to be selected from nine persons. In how many ways can this selection be made if: a) Jack must be on the committee b) Jack must not be on the committee 33. How many “words” of five different letters can be made from the English alphabet if each word: (NOTE: Treat Y as a co ...
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.