A Framework for Research and Curriculum Development in Undergraduate Mathematics Education Mark Asiala Purdue University W. Lafayette, Indiana Anne Brown Indiana University South Bend South Bend, Indiana David J. DeVries Georgia College Milledgeville, Georgia Ed Dubinsky Purdue University W. Lafayette, Indiana David Mathews Central Michigan University Mt. Pleasant, Michigan Karen Thomas University of Wisconsin-Platteville Platteville, Wisconsin c November 4, 1997 Abstract Over the past several years
Words: 14530 - Pages: 59
APPEARED IN BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 30, Number 2, April 1994, Pages 161-177 ON PROOF AND PROGRESS IN MATHEMATICS WILLIAM P. THURSTON This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, “Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics”. Their article raises interesting issues that mathematicians should pay more attention to, but it also perpetuates some widely
Words: 8970 - Pages: 36
truth of a theorem. Nature & Importance of Proofs • In mathematics, a proof is: – a correct (well-reasoned, logically valid) and complete (clear, detailed) argument that rigorously & undeniably establishes the truth of a mathematical statement. • Why must the argument be correct & complete? – Correctness prevents us from fooling ourselves. – Completeness allows anyone to verify the result. • In this course (& throughout mathematics), a very high standard for correctness and completeness
Words: 2416 - Pages: 10
Sections 1.1 Classify the variable as qualitative or quantitative. 22. Student ID number Answer: Quantitative Determine whether the quantitative variable is discrete or continuous. 24. Volume of water lost each day through a leaky faucet Answer: Continuous variable Determine the level of measurement of each variable. 32. Movie ratings of one star through five stars Answer: Ordinal 34. Year of birth of college students Answer: Interval Application of concept 52. Retirement Planning The Principal
Words: 1491 - Pages: 6
CARIBBEAN EXAMINATIONS COUNCIL Caribbean Secondary Education Certificate CSEC MATHEMATICS SYLLABUS Effective for examinations from May/June 2010 CXC 05/G/SYLL 08 Published in Jamaica © 2010, Caribbean Examinations Council All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means electronic, photocopying, recording or otherwise without prior permission of the author or publisher. Correspondence
Words: 9978 - Pages: 40
PRE LAB #2 % This script creates a signal, and then quantizes it to a specified number % of bits. It then calculates the quantization error. clc clear all close all Change the #of bits means change in resolution Change the #of bits means change in resolution fprintf(' Sampling and Quantization\n'); b=5; % Number of bits. N=100; % Number of samples in final signal. n=0:(N-1); %Index Change the value
Words: 371 - Pages: 2
Preface During the past century, the impact of mathematics on humanity has been more tremendous than ever since Galileo's agonizing fight against the old establishment and the revolution which physics experienced after Newton's subsequent synthesis. At the beginning of the last century, mathematical ideas and techniques were spread to theoretical and applied physics by the influence of two of the greatest mathematicians of all times, D. Hilbert and H. Poincar6, being then at the zenith of
Words: 40272 - Pages: 162
Advanced Problems in Core Mathematics Stephen Siklos Fourth edition, October 2008 ABOUT THIS BOOKLET This booklet is intended to help you to prepare for STEP examinations. It should also be useful as preparation for any undergraduate mathematics course, even if you do not plan to take STEP. The questions are all based on recent STEP questions. I chose the questions either because they are ‘nice’ – in the sense that you should get a lot of pleasure from tackling them – or because I
Words: 47679 - Pages: 191
Chapter 1 Discrete Probability Distributions 1.1 Simulation of Discrete Probabilities Probability In this chapter, we shall first consider chance experiments with a finite number of possible outcomes ω1 , ω2 , . . . , ωn . For example, we roll a die and the possible outcomes are 1, 2, 3, 4, 5, 6 corresponding to the side that turns up. We toss a coin with possible outcomes H (heads) and T (tails). It is frequently useful to be able to refer to an outcome of an experiment. For example, we might
Words: 16766 - Pages: 68
to public key via Discrete Logarithm. Examples are Diffie-Hellman Key Exchange, Digital Signature Algorithm (DSA), Elgamal which are based on DLP in finite multiplicative group. 1 2. Discrete logarithm problem The Discrete Logarithm Problem (DLP)is the problem of finding an exponent x such that g x ≡ h (mod p) where, g is a primitive root for Fp and h is a non-zero element of Fp . Let, n be the order of g. Then solution x is unique up to multiples of n and x is called discrete logarithm of h to
Words: 1261 - Pages: 6
