A List of Mathematical Topics

These are the topics covered in a variety of geology courses and are organized by the math courses where students first experience them. This list may be surprising to some geoscientists as we often assume that they have experienced topics before they ever reach our classes.

High School

• Convert Units (physics)
• Scientific Notation
• Coordinate Systems (Algebra I)
• Slopes of lines (Geometry)
• Pythagorean Theorem (Geometry)
• Area of Circles and Polygons (Geometry)
• Volumes of Spheres and Polyhedra (Geometry)
• Triangle Trigonometry (Algebra II)
• Trigonometric functions (Algebra II)
• Manipulating Exponents (Algebra II)
• Logarithms (Algebra II)
• Systems of Equations (Algebra II)

Calculus I

• Area of general regions
• Volumes of general solids
• Limit
• Derivative: slope
• Derivative: error analysis
• Derivative: rate
• Integral: area, volume
• Integral: accumulationof small changes
• Force, Work, Energy, Power

Calculus II

• Area of general regions
• Trigonometric functions
• Manipulating Exponents
• Volumes of general solids
• Coordinate Systems
• Waves: wavelength, period, amplitude
• Exponential Growth/Decay
• Approximations of functions
• Force, Work, Energy, Power

Calculus III

• Area of general regions
• Volumes of general solids
• Vectors Physics
• Vectorfields, Flux, Divergence
• Coordinate Systems
• Dimension
• Systems of Equations
• Force, Work, Energy, Power

Linear Algebra

• Systems of Equations
• Transformations
• Vectors
• Matrices
• Dimension
• Eigenvalues and eigenvectors

Statistics

• Data Analysis
• Experimental Design
• Sampling
• Hypothesis testing
• Probability
• Distributions
• Random Variables
• Curve Fitting
• Regression
• Analysis of Variance
• Spatial Statistics
• Approximations of functions

Physics

• Force, Work, Energy, Power
• Newton's Laws
• Coordinate Systems
• Waves: wavelength, period, amplitude
• Mechanical Systems, Oscillators

Differential Equations

• Waves: wavelength, period, amplitude (ODE)
• Mechanical Systems, Oscillators (ODE)
• Exact and Approximate Solutions (ODE)
• Linear vs Non-linear Equations (ODE)
• Systems of ODEs (ODE)
• Exponential Growth/Decay (ODE)
• Eigenvalues and eigenvectors (ODE, PDE)
• Wave equation (PDE)
• Diffusion (PDE)
• Fourier Series/Transforms (PDE)
• Approximations of functions (PDE)
• Curve Fitting (PDE)
• Spectral Analysis (PDE)

Computer Science

• Elementary Programming

Not covered in most math classes

• Log-Linear and Log-Log Plots
• Mathematical software
• Spreadsheets