Things of Math
Review of Mathematical Structures and Principles
In our application of math to physics, it is essential to understand the mathematical structures we use to represent physical quantities. In assigning particular mathematical structures to physical objects, we have to match the mathematical character to the characteristics displayed by the physical system. (Can our physical object be represented by one number? A sequence of numbers? A function? Does it change when we change our measurement scales? Our coordinate system? Is it intricately and inextricably related to some other objects? etc., etc., etc.)
In our content web pages here, we give brief descriptions of the basic structures and fundamental principles that are relevant for this class. These also contain references to readings in various mathematical physics texts.
Mathematical structures
 Numbers: Integers, The Number Line, Rational, and Real
 Complex Numbers
 Linear Spaces
 Rules of Combination: Groups
 Scaling numbers
 Functions
 Fields
Mathematical systems and principles
 Algebra
 Calculus
 Power Series
 Expansions: The Taylor Series
 Fourier Series
 Taylor Series
Calculational tools
 Taking a derivative numerically
 Doing an integral numerically
 Solving ODEs numerically
 Solving a transcendental equation numerically
 Solving a partial differential equation numerically
RETURNS
University of Maryland  Physics Department  Physics 374 Home 


