Math 287, Fall 2022
Meeting times: M,W from 12:00–1:15pm
Textbook: Materials from several sources will be provided
Lecture notes: Lecture notes will be made available via OneNote
Homework: Homework is published here and collected via Gradescope
Office hours: TBA, and by appointment
Math 287 ‘Mathematical proofs and methods’ builds on what you learned in Math 189 (and its equivalents). The course is intended to support you in your transition to upper division courses by strengthening your investigative powers, refining your ability to prove statements, and improving your mathematical writing style.
The content of the course will include sets and functions, elementary number theory and induction, combinatorics, and limits and topology in the real number line.
Anticipated learning outcomes
- Explore mathematical definitions and evaluate mathematical statements
- Read and write mathematical proofs at an intermediate level
- Possess knowledge in content areas so as to be prepared for upper-division mathematics classes
- Use technologies to support mathematical exploration and communication
- Weeks 1-3: Induction, sets, and functions
- Weeks 4-7: Number theory and algebra
- Week 8: Review and midterm assessment
- Weeks 9-11: Combinatorics and/or graph theory
- Weeks 12-14: Real numbers, sequences, and topology
- Weeks 15-16: Review and final assessment
The course will be delivered through synchronous remote class sessions. Each session will include a mixture of questions on previous material, discussion of new material, and an in-class activity.
Attendance, participation, and group activities 20%
You are expected to attend remote class sessions, and to be prepared to ask questions and discuss the material. Following the discussion, we will start a group activity, which will be submitted as a group. A portion of your grade will be based on your attendance, preparedness, attention, collaboration, and completion of these activities.
Homework assignments 40%
Homework will be assigned each week and collected the following week. Most exercises will be graded for both correcteness and mathematical style. Some will be graded for completeness only. You are encouraged to collaborate with your peers, and you are welcome to use online resources when you are stuck (please reference). But please keep in mind that you must always fully understand your solutions and most importantly write them in your own words.
Take-home exams 20% x2
Take-home exams will be given during the 8th week and the finals week of the class.
This syllabus is subject to change. While I don’t expect any substantial changes, please allow for some flexibility. I will give notice before making any changes to the syllabus.