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Give a recursive algorithm to find the number of

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 36E Chapter 5.4

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 36E

Problem 36E

Give a recursive algorithm to find the number of partitions of a positive integer based on the recursive definition given in Exercise 47 in Section 5.3.

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Tuesday, March 22, 2016 Chapter 10 Decision Making by Individuals and Groups Figure 10.1: The Decision-Making Process 1.groups identify the symptoms of the problem, but underlying issue of the problem is still there 2.manager determines what is do be accomplished by the decision 3.conduct investigation as group members to find out as much as we can about the problem 4.come up with as many alternative solutions; a thorough “what-if” analysis should be conducted 5.if the problem has been diagnosed correctly and sufficient alternatives have been identified, selecting the best course of action becomes easier 6.once the solution is implemented, it must be monitored to see whether the decision has met its objective of fixing the issue 7.consistent monitoring and periodic feedback is encouraged “Make effective decisions in a timely manner to fulfill the desires, objectives, and goals of a company.” 1 Tuesday, March 22, 2016 - Rationality • logical, step-by-step approach to decision making, with a thorough analysis of alternatives and their consequences - decision makers strive to optimize the best possible alternatives • “the best” is considered having perfect complete knowledge - Criticism of Rational Model • there are time constraints and limits to human knowledge and information- processing capabilities • manager’s preferences and needs change often - Bounded Rationality • assumes that managers don't optimize, they satisfice - select the first alternative that is “good enough” - costs of optimizing in terms of time and effort are too great • assumes that managers develop heuristics - short cuts - to make decisions in order to make decisions to save mental activity - based on what has worked in the past - “Z Model” • capitalizes strengths on the four separate preferences of Sensing, Intuiting, Thinking, and Feeling - examine the facts and details. use sensing to gather information about the problem. - generate alternatives. use intuiting to develop possibilities. - analyze the alternatives objectively. use thinking to logically determine the effects of each alternative. - weight the impact. use feeling to determine how the people involved will be affected. 2 Tuesday, March 22, 2016 Figure 10.2: The Z Problem-Solving Model - Escalation of Commitment • the tendency to continue to support a failing course of action - those who make decisions that turn out to be poor choices tend to hold fast to those choices • people that dislike inconsistency strive to reduce dissonance • some people are overly optimistic and overestimate the likelihood that positive things will happen to them • people believe they have a special skills that give them the control to make changes that other people don’t have • some “throw good money after bad”; assuming they’ve already spent enough money, what’s a few more dollars - “Hindsight is 20/20.” 3 Tuesday, March 22, 2016 - De-Escalation • individuals with higher self-esteem and those given an opportunity to affirm an important value - Risk Aversion • the tendency to choose options that entail fewer risks and less uncertainty • inverse concept - shows that women tend to be more risk adverse than men • when women think of risk factors, they’re thinking more in groups whereas men are thinking of only themselves - older, more experienced employees tend to be more risk adverse than younger, less experiences employees • they have already made the mistake to know the risk of it • have a lot more to lose - Influences on Decision Making • intuition - fast, positive force in decision making that is utilized at a level below consciousness and involves learned patterns of information • creativity - a process influenced by individual and organizational factors that results in the production of novel and useful ideas, products, or both - Group Decision Making • synergy - a positive force that occurs in groups when a group members stimulate new solutions to problems through the process of mutual influence and encouragement within the group social decision schemes • - simple rules used to determine final group decisions 4 Tuesday, March 22, 2016 • majority-wins rule - group supports whatever position is taken by the majority of its members • truth-wins rule - the correct decision will emerge as an increasing number of members realize its appropriateness • two-thirds-majority rule - the decision is favored by two-thirds or more of its members is supported • first-shift rule - members support a decision represented by the first shift in opinion shown by a member - Advantages of Group Decision Making • more knowledge and information through the pooling of group member resources • increase acceptance of and commitment to the decision because the members had a voice in it • greater understanding the decision because members were involved in the various stages of the decision process - Disadvantages of Group Decision Making pressure within the group to conform and fit in • domination of the group by one forceful member or a dominant clique who may • ramrod the decision • the amount of time required because a group makes decisions more slowly than an individual - Limits of Group Decision Making • groupthink - a deterioration of mental efficiency, reality resting, and moral judgement from pressures within the group - high cohesive groups tend to favor solidarity because members identify strongly with the group - high-ranking teams that make decisions without outside help are likely to have shared models; more likely to think alike - homogenous groups - having to make highly consequential decisions 5 Tuesday, March 22, 2016 - time constraints why does one person in a groupthink group not speak their opinion until someone else does they don’t want everyone else to judge them of their opinion or disagree with them. group polarization - the tendency for group discussion to produce shifts toward • more extreme attitudes among members - 4 Important Group Decision Techniques • brainstorming - generating as many ideas as possible, suspending evaluation until all ideas have been suggested - participants are encouraged to build on the suggestions of others 6 Tuesday, March 22, 2016 • nominal group technique - generating alternatives and choosing one - overcomes bias and prejudice judgment - specific steps taken in this technique: • individuals silently list their ideas • all ideas are written on a chart one at a time until all ideas are listed • discussion is permitted, but no criticism written vote is taken • • devil’s advocacy - a group or individual is given the role or of critic - task is to come up with the potential problems of a proposed decision, helping to avoid costly mistakes in decision making dialectical inquiry - debate between two opposing set of recommendations • - bringing out benefits and limitations of both sets of ideas • focusing on reaching the most effective solution for all concerned and not a focus on lose-win attitude - Special Decision-Making Groups quality teams - team that is part of an organization’s structure and is empowered to • act on its decisions regarding product and service quality - formal groups ran by upper management • quality circles - small group of employees who work voluntarily on company time, typically one hour per week, to address work-related problems such as quality control, cost reduction, production planning and techniques, and even product design - informal groups based on volunteering not ran by upper management - Cultural Issues • some cultures teach that citizens should not question authority due to the high respects for the leaders of that country - Germany - taught to respect authority before WWII 7 Tuesday, March 22, 2016 - Malaysia - very much likes the status quo; dislike much change because it leads to conflict and they are a more calm culture 8

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Chapter 5.4, Problem 36E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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