🧪 STEM Core: Mathematics, Physics, Chemistry

Mission: Build deep fluency in foundational sciences through problem-solving, not rote memorization. These are the languages in which physical reality is written.

📐 Mathematics Foundation

Algebra-Essentials

• Equations and inequalities
• Polynomial operations
• Factoring and simplification
• Word problems (translating real situations to math)

Problem Set: Algebra-Problems-01-to-25

Geometry-and-Trigonometry

• Triangle properties (angles, sides, similarity)
• Right triangles: Pythagorean theorem, trig ratios (sin/cos/tan)
• Circles (area, circumference, arc length)
• 3D geometry (volume, surface area)
• Application: Roof angles, pipe sizing, solar array orientation

Problem Set: Trig-Problems-Solar-Wind-Applications

Exponentials-and-Logarithms

• Exponential growth/decay (population, radioactive decay, compound interest)
• Logarithmic scales (decibels, pH, Richter scale)
• Half-life and doubling time

Application: Battery discharge curves, noise levels, soil pH

Problem Set: Exponential-Problems-Real-World-Contexts

Statistics-and-Probability

• Mean, median, standard deviation
• Normal distribution (bell curve)
• Hypothesis testing basics
• Interpreting data without lying (common misconceptions)

Application: Solar performance variation, crop yields, energy usage patterns

Problem Set: Statistics-Problems-Data-Interpretation

🌍 Physics Fundamentals

Mechanics-and-Motion

• Force, mass, acceleration (Newton's 2nd Law)
• Work, energy, power (useful and thermal)
• Simple machines (lever, pulley, incline, wheel)
• Momentum and collisions

Application: Calculating power requirements, mechanical advantage in tools

Problem Set: Mechanics-Problems-Real-Systems

Thermodynamics

• Heat vs. temperature
• Specific heat capacity (how much energy to raise temperature)
• Heat transfer: Conduction, convection, radiation
• Efficiency (useful output / total input)
• Entropy (disorder increases, can be slowed but not stopped)

Application: Building insulation, solar thermal design, engine efficiency

Problem Set: Thermodynamics-Problems-Energy-Systems

Electricity-and-Magnetism

• Charge, voltage, current (Ohm's Law: V = IR)
• Power dissipation (P = V × I = I²R = V²/R)
• Circuits: Series vs. parallel (voltage and current behavior)
• Magnetism (electromagnets, permanent magnets, motors)
• Induction (changing magnetic field induces voltage)

Application: Electrical system design, motor selection, power calculations

Problem Set: Electricity-Problems-DC-Systems

Waves-and-Optics

• Wave properties (frequency, wavelength, amplitude, speed)
• Light as wave and particle
• Reflection and refraction
• Color (visible spectrum, wavelength ranges)

Application: Solar cell response (wavelength), fiber optics for data

Problem Set: Waves-Problems-Light-and-Sound

🔬 Chemistry Fundamentals

Atomic-Structure-and-Bonding

• Electrons, protons, neutrons
• Atomic number and mass number
• Ionic vs. covalent bonding
• Oxidation states (electron transfer)

Application: Understanding battery chemistry, corrosion (electrochemistry)

Problem Set: Chemistry-Bonding-Problems

Acid-Base-Chemistry

• pH scale (logarithmic, 7 is neutral)
• Strong vs. weak acids and bases
• Buffers (resistance to pH change)
• Neutralization reactions

Application: Water treatment, soil pH management, battery electrolytes

Problem Set: Acid-Base-Problems-Water-Systems

Oxidation-Reduction-Reactions

• Electron transfer (oxidation and reduction)
• Electrochemistry (batteries, corrosion, electroplating)
• Combustion and rusting

Application: Battery operation, fuel cells, metal protection

Problem Set: Redox-Problems-Energy-Storage

Organic-Chemistry-Basics

• Carbon bonding (versatility, 4 bonds)
• Functional groups (alcohols, aldehydes, carboxylic acids)
• Polymers (long chains, plastics, biopolymers)
• Hydrocarbons and fuels

Application: Biofuel production, compost decomposition pathways, plastic alternatives

Problem Set: Organic-Problems-Bioregional-Applications

🧮 Applied Problem-Solving

Energy-Calculations

Power = Energy / Time
        → Watts = Joules / Seconds

Work = Force × Distance
     → Joules = Newtons × Meters

Efficiency = Useful Energy Out / Total Energy In
          → Losses are always non-zero

Practice: Energy-Problem-Set-01: Solar panel sizing, motor selection, heating requirements

Thermal-Calculations

Heat = Mass × Specific Heat × Temperature Change
Q = m × c × ΔT

Heat Loss = U-Value × Area × Temperature Difference
Q = U × A × ΔT

Practice: Thermal-Problem-Set-01: Building insulation, water heating, thermal storage

Electrical-Calculations

Ohm's Law: V = I × R
Power: P = V × I = I² × R = V² / R
Energy: E = P × t (Watt-hours)

Practice: Electrical-Problem-Set-01: Wire sizing, solar array wiring, inverter selection

Fluid-Dynamics

Flow Rate = Volume / Time  (gallons/min, liters/sec)
Pressure = Force / Area
Head = Pressure / (ρ × g)  (meters of water equivalent)

Hydro Power = Flow × Head × Efficiency × Gravity Constant

Practice: Hydro-Problem-Set-01: Water system sizing, pump selection, irrigation design

📊 Data Analysis & Interpretation

Reading-Scientific-Papers

• Abstract (TLDR)
• Methods (reproducible or not?)
• Results (data, not interpretation)
• Discussion (authors' interpretation, bias check)
• Conclusion (does it follow from data?)

Meta: Papers are conversations, not scripture. Author disagreement is how science advances.

Spotting-Bad-Data

• Correlation vs. causation (X went up, Y went up ≠ X caused Y)
• Cherry-picked timeframes (compare to longer history)
• Undefined variables (what exactly is being measured?)
• Missing error bars (uncertainty matters)
• Extraordinary claims (require extraordinary evidence)

Practice: Bad-Data-Critique-01: Real marketing claims, analyze the tricks

📚 Reference Materials

Conversion Factors (Obsidian native)

• Temperature: °F = (°C × 9/5) + 32
• Energy: 1 kWh = 3.6 million Joules
• Power: 1 horsepower = 746 watts
• Pressure: 1 atm = 101.325 kPa
• Speed: 1 m/s = 2.237 mph

Complete Table: Conversion-Factors-Complete

Physical Constants

• Gravitational constant: g = 9.8 m/s²
• Speed of light: c = 3 × 10⁸ m/s
• Planck constant: h = 6.626 × 10⁻³⁴ J·s
• Avogadro's number: 6.022 × 10²³ mol⁻¹

Periodic Table (By Function, Not Just Order)

• Metals-and-Uses: Iron, copper, aluminum, etc.
• Semi-Conductors: Silicon, germanium (electronics)
• Halogens: Chlorine, bromine, iodine (disinfection, reactions)
• Noble-Gases: Inert, used in specialty applications

🎓 Learning Paths

Path 1: Energy Systems (6 weeks)

• Week 1: Mechanics + Energy
• Week 2: Thermodynamics
• Week 3-4: Electricity
• Week 5: Applied calculations (solar, thermal, electrical)
• Week 6: Real system design (problem sets with actual parameters)

Path 2: Water Systems (4 weeks)

• Week 1: Fluid dynamics, pressure, head
• Week 2: Acid-base chemistry, pH
• Week 3: Electrochemistry (corrosion, disinfection)
• Week 4: System integration (real pump sizing, water quality)

Path 3: Growing & Soil (5 weeks)

• Week 1: Organic chemistry (decomposition, nutrients)
• Week 2: Biology (microbes, nutrient cycling)
• Week 3: Acid-base (pH management, nutrient availability)
• Week 4-5: Real soil management, interpretation of tests

✅ Mastery Checkpoints

Algebra Level: Can solve multi-step word problems without help

Geometry Level: Can work in 3D, understand spatial relationships

Physics Level: Can predict outcome of real-world system change (heating, loading, etc.)

Chemistry Level: Can explain why things react (electron transfer, bonding)

Applied Level: Can estimate costs and design for actual constraints

📖 Recommended Textbooks

Primary (Free/Cheap)

• OpenStax Physics (free, comprehensive)
• Khan Academy (video, foundational through advanced)
• MIT OpenCourseWare (actual course materials)

Secondary (Classic)

• Halliday & Resnick "Physics" (expensive but thorough)
• "Essential Organic Chemistry" (for plant, biofuel topics)
• "Chemistry the Central Science" (comprehensive reference)

Problem-Solving

• "Physics Problems and Solutions" (Irodov)
• "Chemistry Problems and Solutions" (McMurry)
• Real example: Problem-Set-Energy-System-Design

🔗 Quick Links

Math: Algebra-Problems | Trig-Problems | Statistics-Problems
Physics: Mechanics-Problems | Thermodynamics-Problems | Electricity-Problems
Chemistry: Bonding-Problems | Acid-Base-Problems | Redox-Problems
Applied: Energy-Calculations | Thermal-Calculations | Electrical-Calculations
Reference: Conversion-Factors | Physical-Constants | Periodic-Table-By-Use

Status: Growing, problem sets added regularly
Last Updated: [DATE]
Contributor: See Vault-Contributors