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- MAT 260 A Transition to Theoretical Mathematics

**Exit Skills**

- Read, understand and state propositions, conjunctions, disjunctions and negations.
- Read, understand and state conditional and bi-conditional sentences, antecedents and consequents.
- Use quantifiers correctly in mathematical statements.
- Use direct and indirect methods to write mathematical proofs.
- Use mathematical induction, when appropriate, to write mathematical proofs.
- Define null sets, power sets, subsets and disjoint sets then use these definitions to write mathematical proofs.
- Define union, intersection, difference and complements then use these definitions to write mathematical proofs.
- Define and understand the Well Ordering Principle and utilize it, when appropriate, in writing mathematical proofs.
- Define Cartesian Products and use this definition in writing mathematical proofs.
- Define domain and range use these definitions in writing mathematical proofs.
- Define the reflexive, symmetric and transitive properties and use these definitions in writing mathematical proofs.
- Define equivalence relations and use this definition in writing mathematical proofs.
- Define a partition and use this definition in writing mathematical proofs.
- Define functions and composition of functions and use these definitions in writing mathematical proofs.
- Define injective and surjective functions and use these definitions in writing mathematical proofs.
- Define finite and infinite sets and use these definitions in writing mathematical proofs.
- Define the countability of sets and use this definition in writing mathematical proofs.
- Define the Pigeonhole Principle and use this definition in writing mathematical proofs.
- Define a general algebraic structure and use this definition in writing mathematical proofs.
- Define groups and use this definition in writing mathematical proofs.
- Define sequences and use this definition in writing mathematical proofs.
- Define the “Limit of a Sequence,” using the delta-epsilon definition, and use this definition in writing mathematical proofs.
- State and prove the Heine-Borel Theorem and use the results of this theorem to write mathematical proofs.
- State and prove the Bolzano-Weierstrauss Theorem and use the results of this theorem to write mathematical proofs.

8 a.m.-4:30 p.m. Monday-Friday

Administration Building, Room 1242

636-922-8496

Phyllis Marchand

636-922-8496

phyllis_marchand@stchas.edu

Joseph (Joe) W. Howe

636-922-8318

jhowe@stchas.edu