At the end of the semester, a successful student will be able to:

1. Define and correctly use basic vocabulary associated with the following topics:
a. Logic 	
b. The real numbers, especially the integers
c. Induction
d. Set theory
e. Relations, especially equivalence relations
f. Functions

2. Generate examples and non-examples of mathematical objects associated with the topics above.

3. Use correct mathematical notation associated with the topics above.

4. Formulate logically sound arguments using style conventions common in mathematical practice.

5. Identify an appropriate proof technique for an assigned proof.

6. Write mathematically valid proofs using the following techniques:
a. Direct proof
b. Biconditional proof
c. Proof by cases
d. Proof by contrapositive
e. Proof by contradiction
f. Induction

7. Write mathematically valid proofs in the following subject areas:
a. The real numbers, especially the integers
b. Sets
c. Relations, especially equivalence relations
d. Functions

1. Basic mathematical language and logical rules.
2. Sets and their properties.
3. Proof techniques, including case arguments, proof by contrapositive, proof by contradiction, and induction.
4. Functions, including injectivity, surjectivity, images, and preimages.
5. Relations, especially equivalence relations.
6. The integers and other number systems.