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0. Foundations

Summary

In this chapter we review several mathematical topics that form the foundation of probability and mathematical statistics. These include the algebra of sets and functions, general relations with special emphasis on equivalence relations and partial orders, counting measure, and some basic combinatorial structures such as permuations and combinations. We also discuss some advanced topics from topology and measure theory. You may wish to review the topics in this chapter as the need arises.

Sets, Functions, and Relations

  1. Sets
  2. Functions
  3. Relations
  4. Partial Orders
  5. Equivalence Relations

Cardinality and Combinatorics

  1. Cardinality
  2. Counting Measure
  3. Combinatorial Structures

Topology

  1. Topological Spaces
  2. Metric Spaces

Measure Theory

  1. Measurable Spaces
  2. Special Set Structures

Apps

Sources and Resources

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