Class Content I  >Modeling with mathematics

2.2

While all of you have had lots of math – from basic arithmetic through algebra, trig, calculus, and probability, the way math is typically done in a math course is very different from the way the math is actually used in science courses.  In math, they rarely tell you why they do something or what it’s good for.  This can make it hard to understand what math to reach for in thinking about a situation in science or to know what to do with it when you’ve finished a mathematical analysis.  Here are some short readings that review the basic math you will need to know for this class and that explain what good they will do us.

• Significant (and insignificant) figures
• Scientific notation 
• The idea of algebra: unknowns and relationships
• Functions and functional dependence 
• Powers and exponents
• Log-log plots 
• Values, change, and rates of change
• Derivatives
• What is a derivative, anyway?
• Differential equations 
• Integrals
• What do I actually have to know about integrals?
• Approximations ***
• Trigonometry
• The small angle approximation 
• Trig functions for any value of the argument
• The derivatives of trig functions 
• Probability
• Expected values 
• Why probability matters 

And here are two general discussions about the use of math in science.

• Modeling with Mathematics (2013)  
• How math in science is different from math in math

Joe Redish 6/15/11