FUNDAMENTALS OF SET THEORY

Prerequisites & course information

Requisites: ( MATH 234 and 467 ) or ( MATH 341 , 375 , 421 or 521 ) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2025 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in set theory (e.g., sets, power sets, cardinality, ordinals, Zermelo-Fraenkel Axiom System etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that sets do or do not have the condition of a particular property (e.g., that a set is countable, enumerable, well ordered, etc.). Audience: Both Grad & Undergrad 3. Describe the role of the axiom system of Zermelo-Fraenkel set theory. Audience: Both Grad & Undergrad 4. Recall and state the standard theorems of set theory (e.g., the Axiom of Choice, Zorn’s Lemma, the Well-ordering Theorem, construction of the real numbers from the natural numbers, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 5. Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.). Audience: Both Grad & Undergrad 6. Convey arguments using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 7. Identify applications of course content in areas of modern research. Audience: Graduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in set theory (e.g., sets, power sets, cardinality, ordinals, Zermelo-Fraenkel Axiom System etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that sets do or do not have the condition of a particular property (e.g., that a set is countable, enumerable, well ordered, etc.). Audience: Both Grad & Undergrad 3. Describe the role of the axiom system of Zermelo-Fraenkel set theory. Audience: Both Grad & Undergrad 4. Recall and state the standard theorems of set theory (e.g., the Axiom of Choice, Zorn’s Lemma, the Well-ordering Theorem, construction of the real numbers from the natural numbers, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 5. Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.). Audience: Both Grad & Undergrad 6. Convey arguments using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 7. Identify applications of course content in areas of modern research. Audience: Graduate