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).
Athena Title
Intro to Higher Mathematics
Equivalent Courses
Not open to students with credit in MATH 3200W
Prerequisite
MATH 2260 or MATH 2260E or MATH 2260H or MATH 2310H
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Student Learning Outcomes
Students will be able to 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
Students will be able to generate examples and non-examples of mathematical objects associated with the topics above.
Students will use correct mathematical notation associated with the topics above.
Students will formulate logically sound arguments using style conventions common in mathematical practice.
Students will identify appropriate proof techniques for assigned proofs.
Students will 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
Students will 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
Basic mathematical language and logical rules
Sets and their properties
Proof techniques, including case arguments, proof by contrapositive, proof by contradiction, and induction
Functions, including injectivity, surjectivity, images, and preimages
