MAT 260, A Transition to
Theoretical Mathematics

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