Algebra: Algebra can essentially be considered as doing computations similar to that of arithmetic with non-numerical mathematical objects. Initially, these objects were variables that either represented numbers that were not yet known (unknowns) or represented an unspecified number (indeterminate or parameter), allowing one to state and prove properties that are true no matter which numbers are substituted for the indeterminates.
Arithmetic: It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operationsof addition, subtraction, multiplication and division with smaller values of numbers.
Calculus: The word "calculus" comes from Latin (calculus) and means a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and process calculus.
Geometry: It is concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.
Logic & Set Theory: In mathematics the study of logic deals with statements or propositions. A statement is a sentence that is either true or false, but not both. The statement is said to have a truth value.
(B) Probability Theory
Average: In mathematics, an average is a measure of the "middle" or "typical" value of a data set. It is thus a measure of central tendency. In the most common case, the data set is a list of numbers. The average of a list of numbers is a single number intended to typify the numbers in the list.
Statistical regularity: Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers, all central limit theorems and ergodic theorems.
Uncertainty: Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science. It applies to predictions of future events, to physical measurements already made, or to the unknown.
Statistical dispersion: A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured
Randomness: Randomness means different things in various fields. Commonly, it means lack of pattern or predictability in events.
1. Nonlinear Estimation: In the most general terms, Nonlinear Estimation will compute the relationship between a set of independent variables and a dependent variable. For example, we may want to compute the relationship between the dose of a drug and its effectiveness, the relationship between training and subsequent performance on a task, the relationship between the price of a house and the time it takes to sell it, ...