Math 1536 Chapter 3: Proportion and the Golden Ratio The Game Of Fim The Game Start with any number of coins on the table. Two players take turns removing coins. Whoever removes the last coin wins. Rules

ByNondeterministic Finite State Machines. Chapter 5. Nondeterminism. Imagine adding to a programming language the function choice in either of the following forms: 1. choose (action 1;; action 2;; … action n ) 2. choose ( x from S : P ( x )). Implementing Nondeterminism.

ByCounting Permutations When Indistinguishable Objects May Exist. How many rows , each one consisting of 3 A’s 1 B, and 4 C’s are there? (Here are some such rows: BACCCAAC ABCACACC CCCCAAAB Etc.) Answer: (3+1+4)! / (3!1!4!). In general:

ByChapter 2 Limits and the Derivative. Section 3 Continuity. Objectives for Section 2.3 Continuity. The student will understand the concept of continuity The student will be able to apply the continuity properties The student will be able to solve inequalities using continuity properties.

ByCalculating Limits Using the Limit Laws. Limit Laws Suppose that c is a constant and the limits lim f(x) and lim g(x) exist. Then. x -> a. x -> a. lim [ f(x) + g(x) ] = lim f(x) + lim g(x). 2. lim [ f(x) - g(x) ] = lim f(x) - lim g(x) .

ByLesson 48 -- Polynomials -- Degree -- Addition of Polynomials. Polynomials. The following are some expressions that we have seen so far:. Polynomials. Each algebraic expression is in the form ax n . The numerical coefficient of each algebraic expression, a, is a real number.

ByContinued Fractions in Combinatorial Game Theory. Mary A. Cox. Overview of talk. Define general and simple continued fraction Representations of rational and irrational numbers as continued fractions Example of use in number theory: Pell’s Equation

ByCSE115/ENGR160 Discrete Mathematics 05/03/11. Ming-Hsuan Yang UC Merced. 8.4 Equivalence relation. In traditional C, only the first 8 characters of a variable are checked by the complier

ByInduction Practice. CS1050. Prove that whenever n is a positive integer. Proof: Basis Case: Let n = 1, then . Prove that whenever n is a positive integer. Inductive Case: Assume that the expression is true for n, i.e., that Then we must show that:.

By10.3: Continuity. Definition of Continuity . A function f is continuous at a point x = c if 1. 2. f ( c ) exists 3. A function f is continuous on the open interval ( a , b ) if it is continuous at each point on the interval.

ByTest 4 Review. For test 4, you need to know: Definitions the recursive definition of ‘formula of PL ’ atomic formula of PL sentence of PL bound variable free variable. Test 4 Review. You need to know: The kinds of formulas of PL How to identify formulas of each kind

ByPrecalculus Section2.3 Graph polynomial functions. A polynomial function takes the form: f(x) = ax n + bx n-1 + cx n-2 + … dx + e where n is a positive integer. Linear function f(x) = mx + b. Quadratic function f(x) = ax 2 + bx + c. Cubic function

ByCounting Loops. for Syntax. for (expression1; expression2; expression3) statement . for Syntax. for (expression1; expression2; expression3) statement . for Syntax. for (expression1; expression2; expression3) statement . for Syntax.

ByWarm-Up: May 7, 2012. What are the next three terms in each sequence? 17, 20, 23, 26, _____, _____, _____ 9, 4, -1, -6, _____, _____, _____ 500, 600, 700, 800, _____, _____, _____. Section 11-1. Arithmetic Sequences. Arithmetic Sequences.

ByDiscrete Methods in Mathematical Informatics Lecture 5 : Elliptic Curve Cryptography Implementation(I) 8 th January 2012. Vorapong Suppakitpaisarn vorapong@mist.i.u-tokyo.ac.jp , Eng. 6 Room 363 Download Slide: http://misojiro.t.u-tokyo.ac.jp/~vorapong/. Course Information . Grading.

ByON THE EXPRESSIVE POWER OF SHUFFLE PRODUCT. Antonio Restivo Università di Palermo. A very general problem :. Given a basis B of languages , and a set O of operations , characterize the family O(B ) of languages expressible from the basis B by using the operations in O .

ByMath/CSE 1019C: Discrete Mathematics for Computer Science Fall 2012. Jessie Zhao jessie@cse.yorku.ca Course page: http://www.cse.yorku.ca/course/1019. Test 3 Nov 26 th , 7pm-8:20pm Ch 2.6, 3.1-3.3, 5.1, 5.2, 5.5 6 questions Locations SLH F (Last name A-L) SLH A (Last name from M-Z).

By7.3 Divide-and-Conquer Algorithms and Recurrence Relations. If f(n) represents the number of operations required to solve the problem of size n, it follow that f satisfies the recurrence relation f(n) = af (n/b) + g(n)

ByAdding Integers. Cornell Notes for September 2- September 3 . Do you remember what an Integer is ?. Integers are the set of whole numbers and their opposite: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 …. So now that you remember…. We are going to do some magic and add and subtract them today.

ByThis work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License . CS 312: Algorithm Analysis. Lecture #4: Primality Testing, GCD. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick. Announcements. HW #2 Due Now

ByView Positive integer PowerPoint (PPT) presentations online in SlideServe. SlideServe has a very huge collection of Positive integer PowerPoint presentations. You can view or download Positive integer presentations for your school assignment or business presentation. Browse for the presentations on every topic that you want.