MATH 5615H-002: Honors Analysis I — Fall 2025
Course Details
- Class Meetings:
- Time: 02:30 PM – 04:25 PM, Monday, Wednesday
- Location: Amundson Hall 158
- Instructor:
- Name: Erkao Bao
- Office: vincent hall 356
- Email: my last name at umn dot edu
- Course Management:
- Platform: Canvas
- All class announcements and assignments will be posted on Canvas.
- Instructor Office Hours:
- To be announced
- By appointment
- Textbook:
- Title: Elementary Analysis–The Theory of Calculus Second Edition by Kenneth A. Ross
Course Description
This course provides a rigorous introduction to real analysis, emphasizing proof-based understanding of fundamental concepts. We begin with the construction and properties of the natural, rational, and real number systems, including the completeness axiom and extended real numbers. We then study sequences and series of real numbers, convergence criteria, and related topological concepts in metric spaces. Topics include monotone and Cauchy sequences, subsequences, limsup/liminf, and convergence tests for series.
We next develop the theory of continuous functions, uniform continuity, and limits of functions in metric spaces, including connectedness. The course then covers power series, uniform convergence of sequences and series of functions, and applications such as term-by-term differentiation and integration. We conclude with a rigorous treatment of differentiation and Taylor’s theorem, the Riemann integral and its generalizations, improper integrals, and selected advanced topics such as nowhere-differentiable functions.
Weekly course outline
Prerequisites: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574.
Enrollment Requirements: Math honors students; 5000-level courses.
Important Dates — Fall 2025
- Classes start: September 2, 2025
- Midterm Exam 1: October 1, 2025 (in class)
- Midterm Exam 2: November 5, 2025 (in class)
- Last Day of Instruction: December 10, 2025
- Finals Week: Friday, December 12 – Thursday, December 18
- Common Math Finals: Friday, December 12; 12:00 PM – 3:00 PM
Academic Support
- Participate in study groups.
- Utilize the SMART Learning Commons for free tutoring across Twin Cities Campuses.
- Attend instructor’s office hours (refer to ‘Course Details’ for timing).
Assessments
Homework
- Frequency: Weekly on Canvas
- Submission: Via Canvas
- Evaluation: A few problems from each problem set will be selected for grading. Your lowest problem set score will be dropped from your final grade.
In-Class Midterm Exam 1
- Duration: 50 mins
- Date & Time: October 1, 2025, during regular class time
- Location: in class
In-Class Midterm Exam 2
- Duration: 50 mins
- Date & Time: November 5, 2025, during regular class time
- Location: in class
Final Exam
- Duration: 3 hours
- Time: Friday, December 12, 2025 — 12:00 PM – 3:00 PM
- Location: TBA (Common Math Final)
Make-up Exams
- We usually do not allow make-up exams.
- Missing a midterm is permitted only for the most compelling reasons.
- In extraordinary situations, obtain permission from the lecturer (not your TA!) to miss an exam in advance; otherwise, a score of 0 will be awarded.
- If excused from a midterm, the course grade will be determined by giving extra weight to the final exam.
- In extremely exceptional situations, students missing the final exam will fail the course.
Grading Policy
- Homework: 40%
- Each Midterm: 15%
- Final Exam: 30%
Calculator Policy
- Calculators are not required and will not be permitted during exams.