ANALYSIS I

Prerequisites & course information

Requisites: ( MATH 234 and 467 ), ( MATH 322 , 341 , 376 , or 421 ), 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 2026 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in classical real analysis (e.g., the of a set, continuity of a function, limit of a sequence, etc.). Audience: Both Grad & Undergrad 2. Use the above definitions to prove if a mathematical construct does or does not have the condition of being a particular mathematical object or having a particular property (e.g., that a given function is continuous, that a given set is compact, that a series converges absolutely, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of classical real analysis. (e.g., the Bolzano- Weierstrass theorem, monotone bounded sequences converge, the fundamental theorem of calculus, etc.). Moreover, the student will be able to recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use the above theorems in the context of longer arguments by examining their premises (e.g., proving that a function has a maximum by verifying that it is continuous on a compact set). 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 in oral and written forms 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 classical real analysis (e.g., the of a set, continuity of a function, limit of a sequence, etc.). Audience: Both Grad & Undergrad 2. Use the above definitions to prove if a mathematical construct does or does not have the condition of being a particular mathematical object or having a particular property (e.g., that a given function is continuous, that a given set is compact, that a series converges absolutely, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of classical real analysis. (e.g., the Bolzano- Weierstrass theorem, monotone bounded sequences converge, the fundamental theorem of calculus, etc.). Moreover, the student will be able to recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Use the above theorems in the context of longer arguments by examining their premises (e.g., proving that a function has a maximum by verifying that it is continuous on a compact set). 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 in oral and written forms 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