1. Stimulus 1: WHO (Kamini)
1.1. Health Statistics and Bio Statistics
1.1.1. Life expectancy and Alculations
1.1.2. Standard deviation and confidence intervals
1.1.3. Probability in clinical trials
1.2. Epidemiology and disease modelling
1.2.1. Statistical models (SIR Model)
1.2.2. Growth curves and exponential growth (influenza)
1.2.3. Data visualisation (Heart Map)
1.3. Medical Research and Data Analysis
1.3.1. Data Science in global health trends
1.3.2. Correlation and regression in medical data
1.3.3. Statistics and Hypothesis testing
1.4. Pubic Health Surveillance
1.4.1. Data Collection and survey design
1.4.2. Sampling Techniques for population studies
1.4.3. Health Metrics and performance indicators
2. Home Vegetable Garden Mark
2.1. Seed starting Bok Choy
2.1.1. 'legginess' of seedlings
2.1.1.1. grow light intensity and height
2.1.1.2. Effect of airflow
2.1.1.3. Effect of temperature
2.1.2. number of days for true leaves to appear
2.2. Soil moisture decay
2.2.1. exponential decay model
2.2.2. logistic decay model
2.2.3. water retention function
2.3. Effect of temperature on photosynthesis rate
2.3.1. Oxygen production rate as a proxy
2.3.2. Possible quadratic model
2.3.3. Possible logistic model
2.3.4. Finding the optimal temperature for photosynthesis (based on a plant of choice)
3. Optimizing basketball free throw trajectories Xinni
3.1. What launch angle/velocity maximizes scoring probability? (Combines sports, physics, and Calculus)
3.2. Data Collection
3.2.1. Video analysis of real shots
3.2.2. NBA/Player statistics (Success rates vs. Angle/Velocity)
3.2.3. Physics Parameters (Gravity, Rim height, Ball diameter)
3.3. Modelling
3.3.1. Quadratic funtions (Parabolic motion)
3.3.2. Derivatives (Maxima/minima for optimization)
3.3.3. Parametric Equations (Horizontal/Vertical Velocity)
3.3.4. Probability (Accounting for human error)
3.4. Potential Challenges
3.4.1. Air resistance, spin
3.4.2. Data accuracy (Human variability)
3.5. Real world application (What's next)
3.5.1. Training recommendations for players
3.5.2. Physics of Ball Sports Design
4. Applications of Mathematics in Geography Tingru
4.1. Population Density and Urban Planning
4.1.1. Statistical Analysis
4.1.2. Voronoi Diagrams
4.1.3. Traffic Flow Analysis
4.2. Geospatial Data and Mapping
4.2.1. Map Scale Calculations
4.2.2. Topographical Analysis
4.2.3. GIS (Geographic Information Systems) Modelling
4.3. Ebvironmental Mathematical Modelling
4.3.1. Climate Change Analysis
4.3.2. River Flow Rate Calculations
4.3.3. Ecosystem Modelling
5. Traffic Flow with Calculus Ben
5.1. Understanding traffic flow concepts
5.1.1. Traffic flow
5.1.2. Density
5.1.3. Speed
5.2. Basic relationships
5.2.1. Traffic flow = Density x Speed
5.3. Calculus in traffic flow
5.3.1. Differential equations
5.3.2. Rate of change
5.4. Modelling scenarios
5.4.1. Congestion Models
5.5. Simulation and graphing
5.5.1. Graphing functions
5.5.2. Numerical simulation