By the end of this course, students will be able to
Research Skills
- Devise specific questions to answer important environmental questions
- Propose mathematical models appropriate to these questions
- Describe how data would be used in these models
- Describe how the result would be interpreted to make a better decision
Working Skills
- Develop time management habits that promote learning of difficult material
- Develop habits that support the consistent production of quality work
Estimations and Models
- Able to form plausible quantitative estimates with very little specific information given.
- Communicate clearly the assumptions and method of an estimation
- Recognize the use of models in estimation and calculations
- Identify type of model being used in an estimation
Place Value
- Recognize and manipulate the place value structure we use for numbers
- Convert between different base systems of numbers
- Convert between decimal numbers and scientific notation
- Understand and use scientific notation
- Use the appropriate number of significant figures in a calculation
Units and Dimensions and Quantities
- Able to use numbers to represent physical quantities
- Able to assign appropriate units to physical quantities
- Able to convert between units with the same dimensions
- Able to use dimensions as an analytical tool
- Use the factor-label method to convert units
- Recognize unit-conversion factors as having a value of one
- Use map scale to convert between length on paper and length on ground
Computation
- Describe correspondence between mathematical symbols and calculator and computer symbols
- Recognize multiple calculator and computer commands to execute a calculation
- Execute simple calculations on spreadsheets and scripting languages
Linear and proportional models
- Able to extrapolate from proportions
- Conceptual understanding of y-intercept
- Recognize physical systems with linear models
- Able to articulate the meaning of a slope for specific applications
- Able to estimate the slope from a topographical map
Areas and Volumes
- Able to estimate areas, volumes, and area densities of objects
- Able to convert between different units for areas, volumes, and area densities
- Able to apply area and volume models to other quantities and estimations
- Understand how areas and volume increases with changes in lengths (scaling)
- Able to equate volumes of different shapes and determine unknown dimensions
- Convert between map area on paper and area on ground
- Describe the implications of areas, volumes, and area densities
Exponential models
- Define exponential growth in terms of uniform relative increase and doubling time
- Recognize estimations that require exponential model
- Infer growth rates from graphs
- Predict future values from exponential graphs
- Recognize logarithms and exponents as inverses and use to solve simple equations
Histograms and distributions
- Describe situations where distributions are a good model
- Estimate the mean and median of a distribution or histogram
- Estimate percentiles using area under a curve
- Estimate the likelihood of an event given a distribution (interpret area under curve)
- Construct histograms from state-level data
- Connect state-level histograms to choropleth maps representing values
Populations and Samples
- Describe situations where different samples of a population can lead to different histograms
- Describe how to distinguish if the difference between two histograms is likely to be random or not
Linear Models with Gaussian Noise
- Describe situations that are well represented by a linear model with gaussian noise
- Estimate the slope of data presented in a table or a graph