|Course ID:||MATH 3200. 3 hours. |
|Course Title:||Introduction to Higher Mathematics|
|Preparation in mathematical reasoning and proof-writing necessary for upper division course work in mathematics. Topics include logic, integers and induction, sets and relations, equivalence relations and partitions, and functions (including injectivity and surjectivity).|
|Oasis Title:||INTRO HIGHER MATH|
|Prerequisite:||MATH 2210 or MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H|
|Offered fall, spring and summer semester every year. |
|Grading System:||A-F (Traditional)|
This is an introductory course aimed at teaching students the art of reading and
writing mathematical proofs. Topics are chosen from logic, the integers and
induction, sets and relations, equivalence relations and partitions, and functions.
Students will be expected to write detailed simple mathematical proofs. This course
students for advanced work in mathematics.
1. Basic mathematical language and logic: statements, converses,
contrapositives. Negation and quantifiers. Proofs by
contradiction. Basic properties of sets.
2. The positive integers and proof by mathematical induction.
3. Functions, inverse functions, image and preimage. Injective,
surjective, bijective functions.
4. Relations, equivalence relations. Fundamental example of