MATH 5615H-002: Honors Analysis I — Fall 2025
Links
Course Details
- Class Meetings:
- Time: 02:30 PM – 04:25 PM, Monday, Friday
- 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: (tentative)
- Monday, Wednesday 10am - 11am in person. Vincent Hall, Office 356.
- Monday 9:30pm - 10:30pm via zoom.
- Textbook:
- Title: Elementary Analysis–The Theory of Calculus Second Edition by Kenneth A. Ross
Course Description
This course offers a rigorous introduction to real analysis with a strong emphasis on proof-based understanding of foundational concepts. We begin with the construction and properties of the natural, rational, and real number systems, including the completeness axiom and the 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.
Next, we develop the theory of continuous functions, uniform continuity, and limits of functions in metric spaces, including connectedness. The course proceeds to 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 Final Exam: 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 office hours (see ‘Course Details’ for times).
Assessments
Homework
- Frequency: Weekly on Canvas
- Submission: Via Canvas
- Evaluation: A few problems from each problem set will be graded. Your lowest problem set score will be dropped.
- Late Homework: Accepted only for the most compelling reasons.
In-Class Midterm Exams
- Duration: 1 hour 55 minutes
- Midterm 1: October 1, 2025 (during regular class time, in class)
- Midterm 2: November 5, 2025 (during regular class time, in class)
Final Exam
- Duration: 3 hours
- Date & Time: Friday, December 12, 2025 — 12:00 PM – 3:00 PM
- Location: TBA (Common Math Final)
Make-up Exams
- Make-up exams are generally not allowed.
- Missing a midterm is permitted only for the most compelling reasons.
- In extraordinary situations, obtain permission from the lecturer (not your TA) in advance; otherwise, a score of 0 will be recorded.
- In extremely exceptional cases, missing the final exam will result in failure of the course.
Grading Policy
- Homework: 30%
- Each Midterm: 20%
- Final Exam: 30%
After the final exam, two scores are computed:
- Score 1: Homework (30%) + Midterm 1 (20%) + Midterm 2 (20%) + Final Exam (30%)
- Score 2: Homework (30%) + max(Midterm 1, Midterm 2) (30%) + Final Exam (40%)
Your final score is max(Score 1, Score 2).
Your letter grade is assigned as the higher of:
- Grade 1 (fixed scale out of 100):
- 90: A
- 80: B
- 65: C
- 50: D
- Grade 2 (approximate curve):
- Top 25%: A
- Next 30%: B
- Next 35%: C
- Remaining 10%: D and F
Letter grades may also include A-, B+, B-, C+, C-, D+, D-.
Calculator Policy
- Calculators are not required and will not be permitted during exams.