

Course ID:  MATH 3200. 3 hours. 
Course Title:  Introduction to Higher Mathematics 
Course Description:  Mathematical reasoning and writing mathematical proofs, the two essential skills for success in upper division course work in mathematics. Topics include logic, integers and induction, sets and relations, equivalence relations, and functions (including injectivity and surjectivity). 
Oasis Title:  Intro to Higher Mathematics 
Duplicate Credit:  Not open to students with credit in MATH 3200W 
Prerequisite:  MATH 2260 or MATH 2260E or MATH 2260H or MATH 2310H or MATH 2410 or MATH 2410H or MATH 2270 or MATH 2270H or MATH 2500 or MATH 2500E 
Semester Course Offered:  Offered fall, spring and summer semester every year. 
Grading System:  AF (Traditional) 

Course Objectives:  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 nonexamples 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 
Topical Outline:  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. 