Technology & Mathematics Michael Herzog Qiyam Tung.

Slides:



Advertisements
Similar presentations
Which table below represents a linear function? Explain how you determined this. What is the function rule for this table? A)C) B)D)
Advertisements

Transform & Conquer Replacing One Problem With Another Saadiq Moolla.
Proofs, Recursion, and Analysis of Algorithms Mathematical Structures for Computer Science Chapter 2 Copyright © 2006 W.H. Freeman & Co.MSCS SlidesProofs,
Degree and Finite Differences. How the degree translates to a function DegreeFunction 0Constant 1linear 2quadratic 3cubic.
Sorting and Searching. Searching List of numbers (5, 9, 2, 6, 3, 4, 8) Find 3 and tell me where it was.
Review for Test 2 i206 Fall 2010 John Chuang. 2 Topics  Operating System and Memory Hierarchy  Algorithm analysis and Big-O Notation  Data structures.
CPSC 411, Fall 2008: Set 2 1 CPSC 311 Analysis of Algorithms Sorting Lower Bound Prof. Jennifer Welch Fall 2009.
CS 206 Introduction to Computer Science II 09 / 05 / 2008 Instructor: Michael Eckmann.
Alyce Brady CS 510: Computer Algorithms Depth-First Graph Traversal Algorithm.
Projectile Motion. Once a difficult problem for cannoneers If the vertical and horizontal components are separated, the problem becomes simple.
Chapter 2: Fundamentals of the Analysis of Algorithm Efficiency
Searching Chapter Chapter Contents The Problem Searching an Unsorted Array Iterative Sequential Search Recursive Sequential Search Efficiency of.
1 Section 2.3 Complexity of Algorithms. 2 Computational Complexity Measure of algorithm efficiency in terms of: –Time: how long it takes computer to solve.
7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each.
1. 2 MATHEMATICAL REASONING INSTITUTE LESSON GOALS 3  A.2.c – Write one-variable and multi-variable linear equations to represent context.  A.3.a –
5.8 Rational Zero Theorem. T HE R ATIONAL Z ERO T HEOREM : If f(x) = a n x n + a n-1 x n-1 + a n-2 x n-2 + … + a 1 x 1 + a 0 has integer coefficients,
Brute Force Average of 88 checks Worst possible algorithm if there is a ship in the bottom right cell Best search: 25.
Searching Given a collection and an element (key) to find… Output –Print a message (“Found”, “Not Found) –Return a value (position of key ) Don’t modify.
Ch 18 – Big-O Notation: Sorting & Searching Efficiencies Our interest in the efficiency of an algorithm is based on solving problems of large size. If.
Finding Real Roots of Polynomial Equations
Projectile Motion. We are going to launch things, and then find out how they behave.
September 26, 2011 Sorting and Searching Lists. Agenda Review quiz #3 Team assignment #1 due tonight  One per team Arcade game Searching  Linear  Binary.
Chapter 2 Polynomial and Rational Functions. Warm Up
Sketching Graphs of Polynomials 9 November Basic Info about Polynomials They are continuous 1 smooth line No breaks, jumps, or discontinuities.
Warm Up The woodland jumping mouse can hop surprisingly long distances given its small size. A relatively long hop can be modeled by y = -2/9x(x-6) where.
Physics of WiiSports Tennis Equations of motion for an object moving in two dimensions.
© Copyright 2012 by Pearson Education, Inc. All Rights Reserved. 1 Chapter 19 Binary Search Trees.
 Day 1  Use long division to find (x 2 – 2x – 15) ÷ (x – 5).
X + 5 4x +20x R + 3 3x x Tues 11/24 Lesson 5 – 4 Learning Objective: To divide polynomials by synthetic division Hw: Pg.
Binary Search Trees (BST)
Lecture 9COMPSCI.220.FS.T Lower Bound for Sorting Complexity Each algorithm that sorts by comparing only pairs of elements must use at least 
Computer Vision Spring ,-685 Instructor: S. Narasimhan WH 5409 T-R 10:30am – 11:50am Lecture #23.
Search Algorithms Written by J.J. Shepherd. Sequential Search Examines each element one at a time until the item searched for is found or not found Simplest.
(c) University of Washington20c-1 CSC 143 Binary Search Trees.
Quadratic Inequalities First day: Review inequalities on number lines. Review inequalities of linear equations Review inequalities of systems of linear.
Factoring to Solve Quadratic Equations – Solving Quadratic Equations by Factoring A quadratic equation is written in the Standard Form, where a,
Essential Questions How do we use long division and synthetic division to divide polynomials?
Synthetic Division Examples
Balanced Search Trees 2-3 Trees AVL Trees Red-Black Trees
CSE 373 Binary search trees; tree height and balance
CMSC201 Computer Science I for Majors Lecture 23 – Sorting
Introduction to Machine Learning
Searching Given a collection and an element (key) to find… Output
Algorithmic Efficency
Intro to Computer Science CS1510 Dr. Sarah Diesburg
Introduction to complexity
CS 2511 Fall 2014 Binary Heaps.
Linear Motion, Free Fall, and Vectors Combined!
The 3-Way Light Switch and The If-And-Only-If Statement
Learn what binary and denary mean.
1.5 – Projectile Motion (pg )
And now for something completely different . . .
Intro to Computer Science CS1510 Dr. Sarah Diesburg
searching Concept: Linear search Binary search
Motion with constant acceleration
Further Mathematics Support Programme
Quadratic Models Objectives;
Warm-up: Can we use quadratics to represent projectile motion?
Synthetic Division Much easier shortcut to Polynomial division.
Lecture 12 CS203 1.
FINAL JEOPARDY Quadratics Polynomials Division
Analyzing an Algorithm Computing the Order of Magnitude Big O Notation
Warm Up Factor completely. 1. 2y3 + 4y2 – 30y 2y(y – 3)(y + 5)
Quadratic Models Objectives;
CSC 143 Binary Search Trees.
1.5 – Projectile Motion (pg )
Binary Search Counting
Polynomial and Rational Functions
Algebra: Variables and Expressions
Data Structures Using C++ 2E
Presentation transcript:

Technology & Mathematics Michael Herzog Qiyam Tung

Logicomix

Simple Classification Pictorial Explanation What creatures fall between the lines? Width Height

Modeling Videogames and Mathematics 3D Games and Hit Detection

Video Games and Mathematics Pictorial Explanation Banjo “switches gears” once he touches the surface of the water.

1. 6=2(0.5)+3 = 4 2. False! 3. 5=2(1)+3 = 5 4. True! 5. 1=2(2)+3 =7 6. False! Video Games and Mathematics (1,5) (0.5,6) (2,1) l y1=2x1+3, y1 = 6

Projectile Motion

Simulating Jumping with Quadratics Task: decide which model is better for simulating a jump and find their coefficients.

Simulating Jumping with Quadratics The actual code for the two models

Programming Synthetic Division

Algorithm Analysis l How long would it take to find any name in a phonebook in the worst case scenario?

Search Time height =log 2 (n) 2 (base) = number of children per node height = seconds it will take to search n = the number of names.

Comparing Linear and Binary Searches y = time x = number of names