Fall 2024
Course Information
Course | MATH 3150 · Real Analysis |
Instructor | Alex Suciu · a.suciu@northeastern.edu |
Teaching Assistant | Zhaoming Li · li.zhaom@northeastern.edu |
Course Web Site | https://suciu.sites.northeastern.edu/courses/math3150-fall2024 |
Place and Time | Wednesday & Friday 11:45 am–1:25 pm in Cahners Hall 5 |
Office | 435 LA – Lake Hall |
Office Hours | Wednesday 10:30 am–11:30 am & Friday 1:45 pm–2:45 pm, or by appointment |
Prerequisites | MATH 2321 (Calculus 3 for Science and Engineering) and MATH 2331 (Linear Algebra) |
Textbook | Elementary Analysis, Kenneth A. Ross, Springer Verlag, Undergraduate Texts in Mathematics, 2013. Solutions to exercises are available here. |
Syllabus | Schedule of topics, problem sets, and midterm test |
Course Description | This course will provide the theoretical underpinnings of calculus and the advanced study of functions. Emphasis will be on precise definitions and rigorous proof. Topics include the real numbers and completeness; limits and convergence; continuity, uniform continuity, and differentiability; power series and Taylor series; the Riemann integral and the Fundamental Theorem of Calculus. |
Course Learning Objectives | At the end of the course, students will be able to demonstrate an understanding of theorems in analysis, write proofs based on the theorems covered in the course, and clearly present their reasoning and steps in their solutions to problems. |
Grade | Based on problem sets (40%), midterm test (20%), and final exam (40%). |
Problem sets
There will be 5 problem sets posted on Canvas and here. You will have at least one week to work on each problem set and submit your work. It is expected that you will work on the problem sets together; however, they must be written up separately.
- Problem Set 1, due Friday, September 13. Solutions.
- Problem Set 2, due Friday, September 27. Solutions.
- Problem Set 3, due Friday, October 11. Solutions.
- Problem Set 4, due Friday, November 8. Solutions.
- Problem Set 5, due Monday, November 25.
Exams
- Midterm: Notes sheet
- Midterm Exam: Wednesday, October 23 (in class)
- Midterm: Solutions
Class Materials
Fall 2024
- Solved exercises: Problem 9.5, Problem 9.15.
- Notes on continuity and uniform continuity
Fall 2023
- Problem Set 1, with solutions. Problem Set 2, with solutions.
- Problem Set 3, with solutions. Problem Set 4, with solutions.
- Problem Set 5, with solutions.
- Notes for Midterm Exam. Midterm Exam, with solutions.
- Notes for Final Exam. Final Exam, with solutions.
Fall 2022
- Problem Set 1, with solutions. Problem Set 2, with solutions.
- Problem Set 3, with solutions. Problem Set 4, with solutions.
- Problem Set 5, with solutions.
- Handout: Pointwise and uniform convergence.
- Notes for Midterm Exam. Midterm Exam, with solutions.
- Practice problems for Final Exam, with solutions.
- Notes for Final Exam. Final Exam, with solutions.
Fall 2016
- Solutions to Homework 1, Homework 2, Homework 6.
- Handout: Limits of derivatives.
- Midterm exam, with solutions.
- Practice final: Fall 2015. Final Exam
Fall 2014
- Homework 1, with solutions. Homework 2, with solutions.
- Homework 3, with solutions. Homework 4, with solutions.
- Homework 5, with solutions. Homework 6, with solutions.
- Homework 7, with solutions. Midterm Exam, with solutions.
- Practice finals: Spring 2011 (with solutions), Fall 2013 (with solutions)
- Final Exam.