Advanced Topics in Probability Theory - Doctor of Philosophy (Ph.D.) in Mathematics by Slidesgo.pptx

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1. Here is where your presentation begins Advanced Topics in Probability Theory - Doctor of Philosophy (Ph.D.) in Mathematics

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3. T able of contents You can describe the topic of the section here You can describe the topic of the section here You can describe the topic of the section here You can describe the topic of the section here You can describe the topic of the section here You can describe the topic of the section here 01 04 02 05 03 06 Introduction Concepts Theorems Processes Applications Investigations

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5. Introduction 01 You can enter a subtitle here if you need it

6. Advanced probability theory Mercury takes a little more than 58 days to complete its rotation, so try to imagine how long days must be there! Since the temperatures are so extreme, albeit not as extreme as on Venus, Mercury has been deemed to be non-habitable for humans Mercury is the closest planet to the Sun and the smallest one in the entire Solar System. Contrary to popular belief, this planet's name has nothing to do with the liquid metal. Mercury was, instead, named after the famous Roman messenger god Mercurius

7. Fundamental concepts Do you know what helps you make your point crystal clear? Lists like this one: They’re simple You can organize your ideas clearly You’ll never forget to buy milk! And the most important thing: the audience won’t miss the point of your presentation

8. S ample space Venus has a beautiful name and is the second planet from the Sun. It’s hot and has a poisonous atmosphere Mercury is the closest planet to the Sun and the smallest one in the Solar System—it’s only a bit larger than the Moon Mercury Venus

9. C onditional probability Mercury is the closest planet to the Sun and the smallest of them all Venus has a beautiful name and is the second planet from the Sun Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Mercury Venus Mars

10. R andom variables Mars is actually a very cold place Venus is the second planet from the Sun Jupiter is the biggest planet of them all Saturn is a gas giant and has several rings Mars Jupiter Venus Saturn

11. Venus has extremely high temperatures Neptune is the farthest planet from the Sun M athematical notation Mars is actually a very cold place Mercury is the closest planet to the Sun Saturn is a gas giant and has several rings Jupiter is the biggest planet of them all Mars Venus Neptune Mercury Saturn Jupiter

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15. A picture always reinforces the concept Images reveal large amounts of data, so remember: use an image instead of a long text. Your audience will appreciate it

16. 98,300,000 Big numbers catch your audience’s attention

17. Jupiter’s rotation period 9 h 55m 23s 333,000 The Sun’s mass compared to Earth’s 386,000 km Distance between Earth and the Moon

18. Probability distributions Mercury is the closest planet to the Sun and the smallest of them all Mercury Venus has a beautiful name and is the second planet from the Sun Venus Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Mars 50% 75% 25 %

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21. Recent research centers Venus is the second planet from the Sun Neptune is the farthest planet from the Sun Saturn is a gas giant and has several rings Jupiter is the biggest planet of them all Venus Neptune Saturn Jupiter

22. Markov chains Venus has extremely high temperatures Neptune is the farthest planet from the Sun Mars is actually a very cold place Mercury is the closest planet to the Sun Saturn is a gas giant and has several rings Mars Venus Neptune Mercury Saturn A B C D E

23. Poisson distribution Step 1 Step 2 Step 3 Step 4 Mercury is a small planet Jupiter is a huge gas giant Earth is the planet with life Saturn is the ringed planet

24. Day tasks Tasks Notes 9:00 Mercury is very small Add your notes here 10:00 Venus has a toxic atmosphere Add your notes here 11:00 We all live on Earth Add your notes here 12:00 Mars is full of iron oxide dust Add your notes here 13:00 Jupiter is a gas giant Add your notes here 14:00 Saturn is the ringed planet Add your notes here

25. Law of large numbers Follow the link in the graph to modify its data and then paste the new one here. For more info, click here Earth is the only planet known to harbor life Despite being red, Mars is very cold Saturn is a gas giant and has several rings Jupiter is the biggest planet of them all Mars Earth Saturn Jupiter

26. Kaliyah Harris Sofia Hill O ur team You can speak a bit about this person here You can speak a bit about this person here You can speak a bit about this person here Paul Smith

27. Stochastic processes Mars is actually a very cold place Mars 01 Venus has extremely high temperatures Neptune is the farthest planet from the Sun Jupiter is the biggest planet of them all Venus Neptune Jupiter 02 03 04

28. Month planner Mon Tue Wed Thu Fri Sat Sun 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Activities Status Yes No Saturn has rings X Mercury is small X Venus is very hot X Earth has life X Mars is very cold X Jupiter is big X

29. Assignment brief Project title Saturn is the ringed planet Tutor Fran Smith Start date 00/00/00 Deadline 00/00/00 Description Specification References Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Venus has a beautiful name and is the second planet from the Sun Mercury is the closest planet to the Sun and the smallest of them all

30. Rubric Criteria Competent (3) Basic (2) Limited (1) Pts D emonstrated understanding of advanced probability concepts Saturn was named after a Roman god Earth is the third planet from the Sun Neptune is far away from us 5 O riginality and creativity in problem solving Mercury is the closest planet to the Sun Mars is full of iron oxide dust The Moon is Earth’s only natural satellite 15 C larity and rigor in mathematical reasoning Venus is the second planet from the Sun Jupiter doesn’t have a solid surface Ceres is located in the main asteroid belt 30 Total points 50

31. P ractical problems Solve and discuss the following probability theory problems 01 B ayesian inference challenge Given a complex real-world dataset, design a Bayesian model to infer the underlying probability distribution and provide a detailed analysis of your approach 02 S tochastic processes mastery Investigate the properties of a specific stochastic process (e.g., Markov process, Brownian motion) and discuss its applications in diverse fields, highlighting any recent advancements 03 E xtreme value theory exploration Explore the principles of extreme value theory and apply them to analyze rare events in a chosen domain, discussing the implications and potential applications 04 Q uantum probability Investigate the application of probability theory in quantum mechanics, discussing the challenges and advancements in this interdisciplinary field

32. Case studies Illustrates the practical use of probability theory through real-life case studies Case study title Application Comments Write the title here… Explain your application… Make your comments here… Write the title here… Explain your application… Make your comments here… Write the title here… Explain your application… Make your comments here… Write the title here… Explain your application… Make your comments here…

33. Trends research Research and present recent trends and developments in probability theory Trends Developments Write a new trend here… Write a new trend here… Write a new trend here... Write a new trend here... Write a new trend here... Write a new trend here... Write about a new development here… Write about a new development here… Write about a new development here… Write about a new development here… Write about a new development here… Write about a new development here...

34. Discussion on challenges Divide into two groups and discuss the current challenge s facing probability theory and how to address them Group A Current challenges How to approach C omplex systems modeling Write here... M achine learning integration Write here... Q uantum probability Write here... Group B Current challenges How to approach Foundations of probability Write here... Interdisciplinary applications Write here... Bayesian nonparametrics Write here...

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