Mgf1107 Survey Of Mathematics Project Descriptionproject Select A ✓ Solved

MGF1107 – Survey of Mathematics Project Description PROJECT Select a popular culture reference that involves legitimate mathematics (play, movie, tv show, book). Create a PowerPoint presentation outlining the reference, the mathematics used and any useful facts. GRADING CRITERIA 1) PowerPoint presentation should be a minimum of 20 slides which may include title, outline, conclusions. 2) The Title/first slide MUST contain your name and the class name (MGF1107 – Survey of Mathematics). 3) It is recommended, but NOT required, that an outline like the following be used a.

Title b. Outline c. Cultural Reference d. History of the mathematics/mathematician involved e. Discussion of the importance or relevance of the mathematics involved f.

Unusual features of the mathematics g. Conclusions DUE DATE: 24-APRIL-2021 The project MUST be submitted via D2L on or before 23:59 (11:59PM) on Saturday, April 24, 2021. Project Grading Criteria Due Date: 24-April-2021

Paper for above instructions

Slide 1: Title

- Name: [Your Name]
- Course: MGF1107 – Survey of Mathematics
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Slide 2: Outline

1. Introduction to "A Beautiful Mind"
2. Overview of Mathematics in the Film
3. Historical Context of John Nash
4. Game Theory Explained
5. Nash Equilibrium
6. Applications of Game Theory
7. Importance of Game Theory in Economics
8. Mathematical Models in Decision Making
9. Unusual Features of Game Theory
10. Conclusion
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Slide 3: Cultural Reference

The film “A Beautiful Mind” released in 2001 highlights the life of John Nash, a brilliant mathematician who made significant contributions to game theory. The film showcases the challenges he faced due to mental illness and how he eventually overcame them to achieve recognition for his work.
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Slide 4: Overview of Mathematics in the Film

"A Beautiful Mind" intertwines the fields of mathematics and psychology, particularly focusing on:
- Game Theory: a branch of mathematics dealing with strategy and decision-making.
- Cryptography: Nash's work on Encrypted Communications.
The narrative illustrates how these concepts shaped American economics and political strategy.
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Slide 5: Historical Context of John Nash

- Born on June 13, 1928, in Bluefield, West Virginia.
- Contributed groundbreaking theories in mathematics and economics.
- Awarded the Nobel Prize in Economic Sciences in 1994 for his work in Game Theory (Nobel Prize, 1994).
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Slide 6: Game Theory Explained

Game theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.
Key components include:
- Players
- Strategies
- Payoffs
- Information conditions
It provides a methodological framework for analyzing competitive scenarios (Osbourne & Rubinstein, 1994).
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Slide 7: Nash Equilibrium

The Nash Equilibrium occurs when players in a game reach a state where no player can benefit by unilaterally changing their strategy.
- Example: In the Prisoner’s Dilemma, both players choosing to betray the other is a Nash Equilibrium, as any unilateral change leads to a worse payoff (Nash, 1950; Myerson, 1991).
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Slide 8: Applications of Game Theory

Game theory has applications in various fields such as:
1. Economics: Predicting market behavior.
2. Political Science: Analyzing competitive strategies.
3. Biology: Evolutionary strategies among species.
4. Computer Science: Algorithm design and auction structures (Camerer, 2003).
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Slide 9: Importance of Game Theory in Economics

Game theory revolutionized the field of economics by:
- Providing analytical tools to assess competitive behaviors.
- Supporting the development of new market strategies.
Examples include:
- Pricing strategies among competing brands.
- Negotiation strategies in international trade (Mas-Colell et al., 1995).
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Slide 10: Mathematical Models in Decision Making

Mathematical modeling allows for effective decision-making in uncertain environments. It encompasses predictive analytics and optimization strategies used in:
- Supply chain management.
- Investment strategies.
- Risk assessment (Winston, 2004).
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Slide 11: Unusual Features of Game Theory

- Non-cooperative versus cooperative games: While non-cooperative games consider individual strategies, cooperative games emphasize alliances.
- Zero-sum games: Player losses are exactly balanced by player gains; useful in competitive sports and strategic games (Tullock, 1981).
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Slide 12: Conclusion

"A Beautiful Mind" not only portrays the personal struggles of John Nash but also educates audiences about the profound impact of mathematics on real life. Understanding game theory provides insight into strategic interactions in our daily lives.
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References

1. Camerer, C. (2003). Behavioral Game Theory: Experiments in Strategic Interaction. Princeton University Press.
2. Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic Theory. Oxford University Press.
3. Myerson, R. B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.
4. Nash, J. (1950). Equilibrium Points in N-person Games. Proceedings of the National Academy of Sciences, 36(1), 48-49.
5. Nobel Prize. (1994). The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1994. NobelPrize.org.
6. Osborne, M. J., & Rubinstein, A. (1994). A Course in Game Theory. MIT Press.
7. Tullock, G. (1981). Economics of Income Redistribution. Kluwer Academic Publishers.
8. Winston, W. L. (2004). Operations Research: Applications and Algorithms. Cengage Learning.
9. Gibbons, R. (1992). A Primer in Game Theory. Pearson.
10. Kreps, D. M. (1990). A Course in Microeconomic Theory. Princeton University Press.
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This presentation should thoroughly cover the mathematical concepts illustrated in "A Beautiful Mind," showcasing the integration of mathematics into popular culture while maintaining clarity and engagement within the audience.