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# IDEASINMATHEMATICS MATH170

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This 20 page Class Notes was uploaded by Claudine Friesen on Monday September 28, 2015. The Class Notes belongs to MATH170 at University of Pennsylvania taught by E.So in Fall. Since its upload, it has received 50 views. For similar materials see /class/215393/math170-university-of-pennsylvania in Mathematics (M) at University of Pennsylvania.

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Date Created: 09/28/15

The Israeli Palestinian Conflict Post Oslo Accords Meira Levinson Math 170 3 19 O3 Historical Background After many years of conflict and war between Israelis and Arabs hope for peace finally seemed possible with the signing of the Oslo Accords in 1993 The Oslo Accords or IsraelPLO Declaration of Principles as it was otherwise known called for a five year trial period of peace between the two sides at the end of which 5 key issues would be decided upon 1 the extent of the territories that Israel would return 2 the possibility of a Palestinian state 3 the future of the settlements 4 water rights 5 the question of the Palestinian refugees and Jerusalem There are different opinions as to whether or not Oslo called for Israel to halt the building of settlements It did call for Israeli withdrawal of military presence from Palestinian territories and for Israel and the US to supply the PA with money and weapons so that the PA could establish a police force within their territories It also called for the PA to stop current incitement of the populace against Israel and for it to arrest certain known terrorists For the purposes of this presentation we will be focusing only on the question of the settlements and the cessation of Palestinian incitement against Israel Israel s Options in Order of Preference continue building settlements Even if the government does not prefer building additional settlements the opinion of the government can change radically very quickly due to the nature of the Israeli government system it still prefers to expand in the following ways given that there are Israelis living on settlements 1 building things that are necessary for the Israeli settlers safety such as roads from the settlements to major cities so that Israelis don t have to drive through Palestinian territories and 2 building things that are necessary for everyday life in the settlements such as schools or additional housing maintaining existing settlements but halting expansion dismantling current settlements This would mean the relocation of thousands of Israelis which the government obviously does not prefer Israel least prefers any path that will lead to violence from the Palestinians so if the 1St preference leads to violence but the 2ncl doesn t then Israel will go with the second over the 152 etc PA s Options in Order of Preference Stop current incitement to violence against Israel Continue incitement while refraining from directly instigating violence Actually instigating violence through terrorist ac ons The above is assuming that Israel chooses to either stop building or to dismantle but if Israel chooses to continue building then the PA prefers violence to the others This order of preferences is assuming that the PA s ultimate goal was to get back the occupied territories and establish an independent state Ifthe Palestinians stop incitement Israel will respond with further negotiations and the two sides will move on to the final stages of Oslo If the Palestinians either continue incitement or choose violence lsrael can respond either by choosing to ignore it amp moving on to further negotiations anyway or by doing something such as rebuilding in essence declaring the negotiations of the Oslo accords as failed If the Palestinians choose violence Israel will choose to respond With force The tree ends when one side reaches further negotiations failed negotiations or use of force in some instances in the tree you will see certain branches that evolve into an infinitely repeating pattern which for simplicity s sake I have labeled as failed negotiations Decision Tree Key D dismantle settlements Sb stop building settlements Cb continue building Si stop incitement Ci continue incitement V violence by Palestinians N further negotiations Fn failed negotiations F use of force by Israelis Oslo Accords The rest of the branches after cbcid and cb cicb are the same as sbcid and sb cicb there wasn t room to draw them out Fully Trimmed Tree Sb Israel stops building settlements l l Si Palestinians stop incitement N further negotiations Historical Comparison Israel did not in fact stop building settlements Rather it continued to build settlements and there were terrorist actions committed by fundamentalist Islamic groups such as Hamas and Jihad with the evidence uncovered during Operation Defensive Shield this past spring we now know that Arafat was directly involved with many of these acts of terrorism It is possible that Israel chose to increase the building of settlements because it was unaware that the consequences would be violence on the part of the PA However there were many other factors involved other than the settlements such as was mentioned before and therefore this decision tree presents a simplified version of what might have happened had these two issues the settlements and the incitement of violence been the only issues Additionally one might disagree over the orders of the two sides preferences which would lead to a different decision tree In choosing the order of the preferences I bore in mind arguments from both ProPalestinian and ProIsraeli sources Lecture Notes for Math 170 Ideas in Mathematics Spring 2007 by Nathanael Leedom Ackerman January 8 2007 1 TALK SLOWLY AND WRITE NEATLY AND BIG 2 1 TALK SLOWLY AND WRITE NEATLY AND BIG 2 Introduction Before Class 1 Write my name7 o ice and o ice hours on the board 2 Write name of teaching assistants Dan Pomerleano dpomerlemathupennedu Chintan Mehta Chintanmmathupennedu 3 Write the course web address wwwmathupennedunateteaching2007springmath170ind Also write my homepage address wwwmathupennedu nateindexhtml 1 Introduce myself and tell about my o ice hours Wednes days 2215 pm 315 pm 2 Introduce the TA7s 2 INTRODUCTION 3 3 Say that for each class l took when l was in college outside my major7 if you were to ask me one year afterwards what l learned7 l would be lucky to tell you a single fact However l am greedy My goal in this class is for each of you7 one year from not7 not to remember just one fact but 3 My goal in ths class is for you to learn and remember 1 Math is a way of thinking 2 Math is beautiful 3 Math is all around us 4 Explain structure of the grading and how there are two types of grades The main grade is made up of Homework Weekly homeworks worth 30 These will be 2 INTRODUCTION 4 due each week at the beginning of class There is no better way to learn niath than doing problems and so these are Vital for learning the material gtllt Math is also meant to be a social activity So you are all strongly encouraged to nd a cou ple friends in this class and to discuss the the problems and your solutions However when it comes time to do the homework you must do it write up the solutions yourself gtllt lf not turned in to class7 turned in to math o ice by 5 pm No late honieworks will be accepted Presentation gtllt Each student will also be responsible for a 10 15 minute presentation in section on material 2 INTRODUCTION 5 96 96 96 related to what we are covering This will be worth 20 of your grade You will all have to sign up for a week to present in your rst section You must also meet with me and your TA before your presentation so we can go over what we want you to discuss This will most likely take place the Friday before but l will let you know next time for sure You will also be responsible for typing your notes up to your presentation and e niailing them to me so they can be posted on the web site Midterm Paper 20 of your grade gtllt gtllt 3 4 pages on a work of mathematical ction You must sign up with your TA by Monday N INTRODUCTION 6 January 29 no two people With the same TA can do the same book so rst come rst serve gtllt Due Friday March 2 Final To be announced 4 Bonus points Pure extra credit Quizzes in class 5 Reading related to the class can be found on the website And When l have them l Will post my lec ture notes there as well lt is very important to stay caught up With the reading so you dont fall behind 6 Say that we are going to be covering a lot of niaterial7 so it is important to stay on top of it And if at any point during the lecture something is unclear7 please ask about it Because if something doesnt make sense to you7 then it probably doesnt make sense to others as well 3 BIRTHDAY PROBLEM 7 3 Birthday Problem As it is the rst day7 lets play a game We all know that there are 365 days in a given year Now our intuition tells us that if we were to have half that many people7 say 18257 in a rooni7 there is a descent Chance that two of them would have the same birthday What if we only have 110 that niany7 say 36 people Do we think that it will be 0 Very likely 0 Somewhat likely c As likely as unlikely o Unlikely 0 Very unlikely that they would have the same birthday 4 DEFINITIONS 8 Take a vote and write on the board what people think Ask them to bet their grades do the experiment 2 3 times depending on the number of people Have anyone who wants to write on a piece of paper how many time they think it would happen Collect the papers and go through the class and gure out how many 4 De nitions l Repeated Experiment Say we want to assign a value between 0 and 1 to express how likely some thing is Go through simpler example Ask about ipping coins Observe that all the possible outcomes add to 1 Explain that if we do the same experiment over and over 4 DEFINITIONS 9 again7 the more likely an event is the more times we would expect it to happen Write on m calculator a r0 139 y p g Take them through several hundred coin ips start with 17 then 107 then 1007 ect Observe that as we do more and more coin ips we get closer and closer to 12 De nition 401 We say the probability of an outcome OUTCOME for an event EVENT is equal to the limit of NUMBER OF TIMES OUTCOME OOOURSNUMBER OF TlMES EVENT OOOURS as number of events goes to in nity This has two problems 1 ln general it often isnlt practical to perform an event 5 IF EXTRA TIME 10 more than a few times 2 While in the limit we get the right answer7 along the way we might not 5 If Extra Time Work out the probability after ipping three coins they all come up the same List options Observe that any one coin ip has two equally likely out comes so each of the above is equally likely Explain how to use that to get the probability Work out how many possibilities they are for the birth day case 5 IF EXTRA TIME 11 Theorem 502 If the probability of event X happens is Y and the probability of event A is B and they are independent the probability ofX and A is Y B Proof Proof with marbles D Explain how to get the birthday solution we gure it out

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