2. Teaching
3. MAT431
4. Homework

Instructions

On each homework assignment, please write (i) your name, (ii) name of course, and (iii) homework number. In general, late homework will not be accepted. However, you are allowed to turn in up to three late homework assignments. Unless you have made arrangements in advance with me, homework turned in after class will be considered late. When doing your homework, I encourage you to consult the I encourage you to consult the “Elements of Style for Proofs” appendix in the textbook.

Reviewing material from previous courses and looking up definitions and theorems you may have forgotten is fair game. Since mathematical reasoning, problem solving, and critical thinking skills are part of the learning outcomes of this course, all assignments should be prepared by the student. Developing strong competencies in this area will prepare you to be a lifelong learner and give you an edge in a competitive workplace. When it comes to completing assignments for this course, unless explicitly told otherwise, you should not look to resources outside the context of this course for help. That is, you should not be consulting the web (e.g., Chegg and Course Hero), generative artificial intelligence tools (e.g., ChatGPT), mathematics assistive technologies (e.g., Wolfram Alpha and Photomath), other texts, other faculty, or students outside of our course in an attempt to find solutions to the problems you are assigned. On the other hand, you may use each other, the textbook, me, and your own intuition. You are allowed and encouraged to work together on homework. Yet, each student is expected to turn in their own work. If you feel you need additional resources or support, please come talk to me and we will come up with an appropriate plan of action.

Assignments

The following assignments are due at the beginning of the indicated class meeting. However, most assignments will be collected at the end of the class meeting. I reserve the right to modify an assignment if the need arises. These exercises will form the basis of the student-led presentations. During class, you are encouraged to annotate your homework, but you are required to use a different color than what you used to complete your homework.

• Homework 1: Read the syllabus and write down 5 important items. Note: All of the exam dates only count as a single item. Turn in on your own paper at the beginning of class or email me a copy of your write up prior to class. (Due Wednesday, August 30)
• Homework 2: Read the Preface and Chapter 1: Introduction of our textbook. The purpose of Chapter 2: Preliminaries is to summarize most of the content from MAT 320 that we need to be familiar prior to starting something new. Read through this chapter and complete any 5 problems in Section 2.1, 1 problem in Section 2.2, and 5 problems in Section 2.3. I encourage you to try ones you aren’t quite certain how to do in order to maximize your review. In addition, make a list of a few problems you are not sure how to complete. (Due Wednesday, August 30)
• Homework 3: Complete Problems 3.2-3.5 from Chapter 3: The Real Numbers. (Due Friday, September 1)
• Homework 4: Complete Problems 3.8 (any 4 parts), 3.9, 3.13, 3.14 in Chapter 3: The Real Numbers. (Due Wednesday, September 6)
• Homework 5: Complete Problems 3.15 and 3.16 in Chapter 3: The Real Numbers. (Due Friday, September 8)
• Homework 6: Complete Problems 3.17 (do one of (a) or (b)), 3.18-3.20 in Chapter 3: The Real Numbers. (Due Monday, September 11)
• Homework 7: Complete Problems 3.21-3.23, 3.25, 3.28, 3.30 in Chapter 3: The Real Numbers. In addition, read and digest Problems 3.26, 3.27, and 3.29, which you can take for granted moving forward. (Due Wednesday, September 13)
• Homework 8: Complete Problems 3.31-3.35 in Chapter 3: The Real Numbers. (Due Friday, September 15)
• Homework 9: Complete Problems 3.37, 3.38, 3.41-3.45 in Chapter 3: The Real Numbers. (Due Monday, September 18)
• Homework 10: Complete Problems 3.47 and 3.48 in Chapter 3: The Real Numbers. (Due Wednesday, September 20)
• Homework 11: Complete any three problems among 3.49(a), 3.49(b), 3.50(a), 3.50(b), 3.51(a), 3.51(b) in Chapter 3: The Real Numbers. (Due Friday, September 22)
• Homework 12: Complete 3.52-3.57 in Chapter 3: The Real Numbers. (Due Monday, September 25)
• Homework 13: If you are up for a challenge, complete 3.58 in Chapter 3: The Real Numbers. Complete 4.2 and 4.3 Chapter 4: Standard Topology of the Real Line. (Due Wednesday, September 27)
• Homework 14: Complete 4.4-4.9 in Chapter 4: Standard Topology of the Real Line. If you are able to prove 4.6 without first doing 4.5(a), that’s fine. (Due Friday, September 29)
• Homework 15: Complete 4.11 in Chapter 4: Standard Topology of the Real Line. (Due Monday, October 2)
• Homework 16: Complete 4.12-4.15 in Chapter 4: Standard Topology of the Real Line. (Due Wednesday, October 4)
• Homework 17: Complete 4.18, 4.19, 4.21, 4.22 in Chapter 4: Standard Topology of the Real Line. (Due Friday, October 6)
• Homework 18: Complete 4.23-4.25 in Chapter 4: Standard Topology of the Real Line. (Due Monday, October 9)
• Homework 19: Complete 4.26-4.30 in Chapter 4: Standard Topology of the Real Line. (Due Wednesday, October 11)
• Homework 20: Complete 5.15 or 5.16 (or both), and 5.17-5.20 in Chapter 5: Sequences. (Due Monday, October 23)
• Homework 21: Complete 5.22, 5.23, 5.25 in Chapter 5: Sequences. (Due Wednesday, October 25)
• Homework 22: Complete 5.27-5.31 in Chapter 5: Sequences. (Due Friday, October 27)
• Homework 23: Complete 5.32-5.34 in Chapter 5: Sequences. (Due Monday, October 30)
• Homework 24: Complete 6.3-6.5, 6.7, 6.8 in Chapter 6: Continuity. (Due Wednesday, November 1)
• Homework 25: Complete 6.9, 6.11-6.14 in Chapter 6: Continuity. (Due Friday, November 3)
• Homework 26: Read 6.15 and complete 6.16, 6.23, and one of 6.19(a), 6.19(b), 6.19(c), 6.19(d), 6.20, 6.21 in Chapter 6: Continuity. (Due Monday, November 6)
• Homework 27: Complete 6.24-6.27 in Chapter 6: Continuity. (Due Wednesday, November 8)
• Homework 28: Complete 6.29-6.32, 6.34 in Chapter 6: Continuity. (Due Monday, November 13)
• Homework 29: Complete 6.38 and any three of 6.39-6.42 in Chapter 6: Continuity. (Due Wednesday, November 15)
• Homework 30: Complete 9.2, 9.7-9.9 in Chapter 9: Integration. (Due Wednesday, November 29)
• Homework 31: Complete 9.10-9.12, 9.14, 9.15, 9.17, 9.18 in Chapter 9: Integration. (Due Friday, December 1)
• Homework 32: Complete 9.21-9.24, 9.27 in Chapter 9: Integration. Problems 9.19 and 9.25 are optional. (Due Monday, December 4)
• Homework 33: Complete 9.29-9.32 in Chapter 9: Integration. (Due Wednesday, December 6)
• Homework 34: Complete 9.34-9.37 in Chapter 9: Integration. (Due Friday, December 8)