# 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 MarylandPhysics DepartmentPhysics 374 Home