Math 321: Introduction to Advanced Mathematics
Class Meets Tuesday/Thursday 10:30–11:45 virtually via Zoom

See here for the syllabus.

See here for information about how the Zoom class meetings are structured.

The meeting id and password for the Zoom meeting can be found on the Laulima site for the course. The Laulima site also has the reading assignments and short videos to accompany each class meeting.
Course Outline
The content of this course can be broken into four themes. For the most part, the themes will be covered in the order below. But at times we will take an early look at a theme or revisit an earlier theme with knowledge from a later theme.

I. Logic. The definitions and rules of firstorder logic.

II. Proofs. Strategies for proving mathematical statements, how to write proofs.

III. The language of mathematics. Sets, relations, functions.

IV. The limitations of the mathematical method. Alternative definitions, axioms, and rules of logic. How do we determine which are “correct”?
Tentative Weekly Schedule

(Aug 25&27) Introduction and overview

(Sept 1&3) Truth tables and logical connectives

(Sept 8&10) Set operations, variables, and logic

(Sept 15&17) Quantifiers

(Sept 22&24) Introduction to proofs

(Sept 29&Oct 1) Proof strategies: negations and conditionals

(Oct 6&8) Proof strategies: quantifiers

(Oct 13&15) Midterm; The universality of the logical connectives

(Oct 20&22) Proof strategies: conjunctions, disjunctions, and biconditionals

(Oct 27&29) Relations and orders

(Nov 5) Functions

(Nov 10&12) Equivalence relations

(Nov 17&19) Induction

(Nov 24) Cardinality

(Dec 1&3) Infinite sets and Cantor’s theorem

(Dec 8&10) Alternative axioms and logical rules; Proofs and Refutations
Announcements
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Homework
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