"The World of Probability and Quantum Mysteries" is part of our new Math Circles for Epsilons series. Meanwhile, "Understanding Air and Smog with Mathematics" continues our previous explorations in the LUMS Math Circle.
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Combinatorics, Probability and Quantum Mysteries
Combinatorics, Probability and Quantum Mysteries
The LUMS Math Circle recently conducted an engaging session titled “The World of Probability and Quantum Mysteries”, which was a sequel of our new series Math Circles for Epsilons, led by Mr. Ausaf Ahmad and Mr. Syed Asad Asif. The session introduced students to fundamental concepts in combinatorics, probability, and quantum mechanics through interactive discussions and hands-on activities.
Key Highlights:
Combinatorics:
The session began with an introduction to the basic counting principles. Students learned how to count arrangements using the multiplication rule and tree diagrams. The facilitators then introduced permutations and combinations, illustrating the concepts with simple yet thought-provoking examples. A brief explanation of Pascal’s Triangle highlighted its significance in combinatorics.
Probability:
Students explored the concept of probability and its connection to randomness in nature. The fundamental probability formula was introduced through real-life examples, and participants engaged in interactive experiments to estimate probabilities using coin tosses and number-guessing games.
Quantum Mysteries:
The session also delved into the basics of quantum mechanics, focusing on the probabilistic nature of quantum particles. Concepts such as the atomic structure were explained, followed by an introduction to Schrödinger’s cat experiment, which helped students understand the strange nature of quantum uncertainty.
Interactive Activities:
To reinforce the concepts, the session included several activities:
Calculating the number of outfit combinations using the Basic Counting Principle.
Using permutations to determine the number of possible arrangements of given digits for number plates.
Hands-on probability experiments with coin tosses and number-guessing games.
Overall, the session provided an insightful and engaging learning experience, showing students how probability and combinatorics play a key role in both everyday life and the world of quantum physics. The session concluded with the distribution of certificates among the participants.
Here are some highlights from the event:
Understanding Air And Smog With Mathematics
Understanding Air And Smog With Mathematics
The LUMS Math Circle organized an interactive session titled “Understanding Air and Smog with Mathematics”, led by Dr. Shahana Khurshid and Dr. Haniya Azam. This session explored how mathematical concepts can be used to analyze air pollution, particle sizes, and smog formation, particularly in the context of Pakistan’s environmental challenges.
Session Highlights:
Air Pollution and Particle Size:
Dr. Shahana initiated the discussion by asking students whether Pakistan faces environmental problems and whether pollution is a seasonal issue. The discussion revealed that pollution is most severe in winter but is a persistent problem throughout the year. The session covered:
The main causes of air pollution, including smoking, vehicular emissions, industrial pollution, and bioaerosols.
The size of airborne particles, comparing them to common objects such as human hair and cement dust particles.
The significance of surface-to-volume ratio and why smaller particles with higher ratios can penetrate deeper into the lungs.
Mathematical Explorations:
Students actively engaged in mathematical calculations to explore the properties of airborne particles:
Surface-to-volume ratio calculations for particles of different diameters.
Understanding how equivalent diameters are used for irregularly shaped particles.
The use of logarithms to simplify particle size calculations, given their small sizes (often expressed in powers of ten).
Tools for observing microscopic particles, including magnifying glasses, microscopes, and scanning electron microscopes (SEM).
Bernoulli’s Principle Activity:
The session also introduced Bernoulli’s Principle, demonstrating how an increase in air speed leads to a decrease in pressure. A hands-on experiment was conducted:
Students used a tube to blow between two hanging balloons.
They observed that as the airspeed increased, the balloons moved closer together, illustrating Bernoulli’s principle.
A real-world example was discussed; why it is dangerous to stand too close to a moving train, as the lower pressure near the train can pull a person towards it. Furthermore, it was discussed that how the flight of a plane depends on this principle.
The session successfully integrated mathematical concepts with real-world environmental challenges, providing students with valuable insights into air quality analysis. The session concluded with the distribution of certificates among the participants.
Here are some highlights from the event:
Both sessions successfully combined mathematical concepts with real-world applications, engaging students in interactive discussions and activities that deepened their understanding of probability, combinatorics, quantum mechanics, and environmental mathematics. Through hands-on learning, students developed a greater appreciation for how mathematics plays a role in everyday phenomena.
The LUMS Math Circle team extends its sincere gratitude to Dr. Shahana Khurshid, Dr. Haniya Azam, Mr. Ausaf Ahmad, and Mr. Syed Asad Asif for their engaging and insightful presentations. We also appreciate the continuous support of Ms. Noreen Sohail and Mr. Muhammad Qamar Hussain for their dedication in organizing these sessions.
We look forward to future sessions that continue to explore the beauty and relevance of mathematics in diverse fields!
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