DIRECTED STUDY

Prerequisites & course information

Requisites: Consent of instructor Course Designation: Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: Yes, unlimited number of completions Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in an area of mathematics. Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property. Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of an area of mathematics and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use such theorems in the context of longer arguments by examining their premises. 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 an area of mathematics. Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property. Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of an area of mathematics and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use such theorems in the context of longer arguments by examining their premises. 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