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1: Foundations

Last updated

May 5, 2020
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- Sources and Resources
- 1.1: Sets

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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.

1.1: Sets
1.2: Functions
1.3: Relations
1.4: Partial Orders
Partial orders are a special class of relations that play an important role in probability theory.
1.5: Equivalence Relations
1.6: Cardinality
1.7: Counting Measure
1.8: Combinatorial Structures
1.9: Topological Spaces
1.10: Metric Spaces
Most of the important topological spaces that occur in applications (like probability) have an additional structure that gives a distance between points in the space.
1.11: Measurable Spaces
1.12: Special Set Structures

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