Math 287, Fall 2020
Meeting times: M,W from 1:30–2:40pm
Textbook: Edward Scheinerman, Mathematics: a discrete introduction, 3rd edition (recommended)
Homework: Weekly assignments
Office hours: TBA
The course title is ‘Mathematical proofs and methods’ and the catalog statement reads:
An introduction to formal mathematical language, mathematical experimentation, mathematical proofs, mathematical communication, and technologies supporting the above. Core content includes sets and functions, elementary number theory and induction, and distances and topology on the real line. Additional content drawn from logic, combinatorics and probability, graph theory, and modular arithmetic.
Math 287 is a successor to Math 187/189 and we will build on what you have learned there. The course is intended to support you in your transition to upper division, proof-based mathematics courses. I hope to help you hone your investigative powers, refine your ability to prove statements, and improve your mathematical writing style.
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: Review of induction, sets, and functions
- Weeks 4-7: Number theory and algebra
- Week 8: Midterm assessment
- Weeks 9-11: Combinatorics and graph theory
- Weeks 12-14: Real numbers, sequences, and topology
- Weeks 15-16: Review and final assessment
Materials for each week will be posted at the end of the previous week and the beginning of the week. The materials will typically include reading assignments and video lectures (posted Thursday–Saturday of the previous week), an activity assignment (posted before Monday), and a graded homework assignment (posted by Monday night).
Remote class sessions will be held every Monday and Wednesday. During these sessions we will work together to explore and learn from the week’s activity, and then interactively discuss the material and homework. The two class sessions will therefore be similar, and I strongly encourage you attend at least one of these sessions.
Your grade will be based on three areas.
To earn points for activities, you must either participate actively in the remote session, or turn in your activity via Gradescope. Participating actively may include asking math questions, answering math questions, doing the same in the chat, and even just raising your hand several times. If you do not receive credit for participation, submit your activity showing substantial effort via Gradescope (Friday night of the same week). I may also collect some activities to gauge the class or provide feedback. Please keep your completed activities for study purposes.
I will collect homework assignments weekly via Gradescope (Thursday night of the following week). Most homework 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.
Assessments 20% x2
Assessments will occur during the 8th week and finals week of the class. The majority of each assessment will consist of a take-home exam. I may supplement the assessments with a real-time remote component.
This syllabus is subject to change. I may make refinements and updates in the first week of classes. While I don’t expect any substantial changes, due to the unpredictable conditions of this semester, please allow for some flexibility. I will give notice before making any changes to the syllabus.