MATHEMATICAL LOGIC

Prerequisites & course information

Requisites: ( MATH 234 or 375 ), ( MATH 320 , 340 , 341 , 345 , or 375 ), and ( MATH 341 , 375 , 421 , 467 , or 521 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) 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 2026 Learning Outcomes: 1. Recall and state the formal definitions of the first-order logic and their properties used in formal logic (e.g., truth assignments, syntax, semantics, theories, models, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue certain objects do or do not have the condition or property (e.g., decidability, compactness, undecidability, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of logic. (e.g., Soundness and Completeness Theorems, the Compactness Theorem, Godel's Incompleteness Theorem, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use concepts from logic in the context of larger arguments (e.g., nonstandard models of arithmetic, etc.). 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 first-order logic and their properties used in formal logic (e.g., truth assignments, syntax, semantics, theories, models, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue certain objects do or do not have the condition or property (e.g., decidability, compactness, undecidability, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of logic. (e.g., Soundness and Completeness Theorems, the Compactness Theorem, Godel's Incompleteness Theorem, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use concepts from logic in the context of larger arguments (e.g., nonstandard models of arithmetic, etc.). 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