Basic Mathematics:

1
Basic Mathematics

• The Language of Natural Science

2
Scientific Method

• Cyclic in nature
• Hypothesis/Theories
• Experiment
• Compare experiment with theory
• Theory may not be proven, only disproven
• Reproducibility

3
Fact versus Theory

• Facts are observations
• Laws are well tested and accepted theories
• Gravity, Thermodynamics, Newtonian Mechanics
• Theory vary in acceptance and completeness
• Nearly complete (Evolution, Nuclear Magnetism)
• Under development (Superconductivity, String
  theory)

4
Branches of Science

• Physics and Astronomy
• Chemistry
• Biology
• Geology and Earth Sciences
• Engineering
• Mathematics

5
Basic Algebra

• Solving linear equation
• 8 9 x 3
• Systems of linear equations
• 8 x 4 y 162 x 9 y 32
• Solving polynomial problems
• 3 x2 4x 18
• Trigonometry, powers and roots

6
Graphical Representations

• Linear Data
• Logarithmic Data
• Doing Ln or Log of data on one axis
• Exponential Data
• Doing exp or 10x of data on one axis
• Other functions
• Best Fit concept - least squares

7
Statistical Models

• Averages
• X 7, 4, 6, 4, 3, 7, 8, 6 (sum 45)
• ltXgt 5.62, s 1.65
• X 6.2, 6.3, 5.8, 4.2, 5.3, 6.2, 5.6, 5.1 (sum
  44.7)
• ltXgt 5.59, s 0.66
• Comparison of two sets of data
• Standard Deviation/Confidence Level
• Risk Assessment

8
Trigger Effect (Burke Video)

• Power outage and technological traps
• Technology (the plow) led to change in
  civilization
• What are other triggers in history?

9
Technology Trap Elements

• Circuit breaker
• Elevator
• Plow and other farming tools
• Flooding, Seasons and Time