Honors Introduction to Analysis
Honors Introduction to Analysis
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Professor: T. ParkerOffice: D-216 Wells Hall parker@msu.edu
Office hours on Zoom:
Monday: 4--5 pm Tuesday 7-8 pm Thursday 3-4 pm or by appointment
Office hours on Zoom:
Monday: 4--5 pm Tuesday 7-8 pm Thursday 3-4 pm or by appointment
Zoom Link Course Syllabus
Goals: Mathematical Analysis is a subject that subsumes and generalizes calculus. It does this my shifting the focus from calculational techniques to a broad study of approximations – approximations of numbers, to functions, and to points in abstract spaces. The natural setting to discuss approximations is a metric space, which is simply a set in which one can measure the distance between points. Accordingly, the emphasis for first semester is on the application of metric space ideas to the real numbers, to n-dimensional euclidean space, and to spaces of functions. This leads to the other topics of the course: convergence of sequences, series, and sequences of functions; continuity, and differentiation and integration in n dimensions.
Prerequisites: : Math 317H (Honors Linear Algebra) or equivalent, and a willingness to work hard on challenging mathematics.
Textbook: Principles of Analysis by W. Rudin. Supplemental reading from Undergraduate Analysis by S. Lang. For additional material, see the Textbooks page.
Exams and grades: There will be weekly homework assignments, a Midterm Exam (format will be determined later), and a take-home Final Exam. Course grades will be determined by the weighted sum of Homework (67%), Midterm (11%) and Final (22%).
Class format: This is a small lecture class, with lots of student interaction. Most classes will be live lectures via Zoom. The split between online and in-person classes is not yet determined.
Goals: Mathematical Analysis is a subject that subsumes and generalizes calculus. It does this my shifting the focus from calculational techniques to a broad study of approximations – approximations of numbers, to functions, and to points in abstract spaces. The natural setting to discuss approximations is a metric space, which is simply a set in which one can measure the distance between points. Accordingly, the emphasis for first semester is on the application of metric space ideas to the real numbers, to n-dimensional euclidean space, and to spaces of functions. This leads to the other topics of the course: convergence of sequences, series, and sequences of functions; continuity, and differentiation and integration in n dimensions.
Prerequisites: : Math 317H (Honors Linear Algebra) or equivalent, and a willingness to work hard on challenging mathematics.
Textbook: Principles of Analysis by W. Rudin. Supplemental reading from Undergraduate Analysis by S. Lang. For additional material, see the Textbooks page.
Exams and grades: There will be weekly homework assignments, a Midterm Exam (format will be determined later), and a take-home Final Exam. Course grades will be determined by the weighted sum of Homework (67%), Midterm (11%) and Final (22%).
Class format: This is a small lecture class, with lots of student interaction. Most classes will be live lectures via Zoom. The split between online and in-person classes is not yet determined.
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