Class Information

Course Title Math 217M1: Introduction to Mathematical Proof

Instructor Julia Kameryn Williams

Website http://kamerynjw.net/teaching/2024/math217m/

Email kwilliams [at] simons-rock (dot) edu

Primary out of class contact course website or email me

Class Hours and Room

  • MWF 1:35–2:30

  • CL1-01

Office Hours M 3:45–4:45, WF 2:35–3:35

Office 2T Hall College Center

Textbook Joel David Hamkins, Proof and the Art of Mathematics, MIT Press (2020)

Course Description Mathematics is a structure going from basic facts and assumptions to complicated truths expressed as theorems. The different levels of this structure are connected by layers of mathematical argument and proof, and the whole edifice is only as solid as its weakest link. Mathematicians have developed a number of methods of valid argumentation, and specialized vocabulary to be able to communicate these arguments and ideas. This course will explore various common techniques of mathematical proof, such as direct proofs, proof by contradiction, mathematical, induction, and epsilon-delta arguments. All methods will be illustrated by proving statements in elementary number theory, set theory, and calculus (and other topics, depending on student interest). There will also be a focus on reading, understanding, and writing mathematical proofs using the proper style and vocabulary. While this course is not a prerequisite, it is recommended for students interested in further studies in mathematics.

Prerequisite Math 210 or instructor permission.

Learning Outcomes

Proofs are the currency of mathematics. This class is an introduction to the methods of truth discovery within mathematics. After taking this class you should be able to analyze the logical structure of a mathematical statement, read and write proofs for elementary assertions, and communicate mathematical arguments to your peers. This class prepares you for 300-level mathematics courses.

Grading Policy

Grading for this class is done a specifications model. What this means is, rather than averaging together numerical scores to determine your overall grade, your grade is determined based on meeting specifications in multiple categories. There are three categories: Problems, Final, and Participation. Problems and Final are graded on a high pass/pass/fail scale, while Participation is graded on a pass/fail scale.

Here’s the specifications to earn each grade:

  • A: High pass in Problems and Final, pass in Participation.

  • B: Not meet the requirements for an A, and one high pass and two passes.

  • C: Not meet the requirements for a B, and passes in all categories.

  • D: Not meet the requirements for a C, and pass in participation plus one other pass.

  • F: Not meet the requirements for a D.

I reserve the right to use +’s or -‘s for borderline cases.

Here’s the overview of how each category is graded. Details about the categories are later in the syllabus.

  • Problems. Weekly problem sets are assigned for all but the final week of the class. Each problem set is graded on a high pass/pass/fail scale, with your overall problems grade determined as follows.

    • High Pass. Do all problem sets. Up to two may be at a pass level, the others must be at a high pass level.

    • Pass. Don’t meet the requirements for a high pass, do at least all but one problem set at a pass level or higher.

    • Fail. Don’t meet the requirements for a pass.

  • Final. The final week you will be assigned a take-home final. This amounts to a problem set but given special weight in grading.

  • Participation

    • Pass. Give a good faith effort at engaging in the course material and miss at most one Friday.

    • Fail. Don’t meet the requirements for a pass. If you are in danger of failing your Participation grade I will reach out to you.

I reserve the right to modify the grading requirements for an individual student based on special circumstance. For example, if you have an emergency and have to miss class for a week that shouldn’t be a mark against your Participation grade. But you have to communicate with me. If anything comes up that seriously impairs your ability to engage in the class please let me know as soon as possible.

Problems

Problem sets are assigned weekly, due in-class the Monday of the following week. Most problems will ask you to write a mathematical proof of some assertion. Others will ask you to explain the flaw in an argument.

Your solutions should adhere to the standards of mathematical writing. Clearly state what you are proving before giving your proof. You are encouraged to follow the theorem/proof format explained in the Note to the Reader at the beginning of the textbook. You should write in complete paragraphs and adhere to the grammatical standards of academic writing. Where you need to write a mathematical formula you should either include inline in the middle of a paragraph or, for important or large formulae, on a separate line. Handwritten solutions are preferred; I will only accept electronic/printed submissions which were typeset using LaTeX.

To earn credit, solutions must be high quality. Arguments must be complete with sufficient detail that I can follow along. The mathematical work must be correct. Work that is not high quality will be returned with the opportunity to redo it for credit. Redone problems should be submitted with the next homework assignment.

You are encouraged to work together on homework, but the work you turn in is expected to be your own. If you do collaborate with classmates, please say so and give their names with your submitted work.

For this class you should expect to spend roughly two hours out of class for each hour of in-class time, for a total of six hours. Homework is due weekly to give you flexibility in when to fit in those six hours. That said, I strongly encourage you to start your homework as soon as possible.

If you will not be able to submit your completed homework on Monday, send me an email to let me know and you can turn it in on Wednesday. Late work is not penalized, but I need to be able to give you timely feedback for you to have the opportunity to redo missed problems.

If exceptional circumstances make it impossible to get work done, please talk to me so we can figure out the best solution for what to do.

Final

The last week there will be a take-home final instead of a problem set. The final amounts to another problem set but given special weight. Details to be announced.

Textbook Information

Joel David Hamkins, Proof and the Art of Mathematics, MIT Press (2020). ISBN: 978-0262539791.

Some homework will be exercises from the textbook, and I will ask you to read selections.

Attendance Policy and Class Participation Guidelines

You are expected to attend class sessions, as per the college attendance policy, and to satisfy the participation category for your grade.

You are expected to participate in all parts of class sessions. Mondays and Wednesdays will mostly be used for lecture. Fridays are reserved for group discussions and presentations. For lecture you should be actively listening, taking notes, and asking questions as appropriate. For group discussions you should engage in the work, sharing ideas with your classmates. Outside of class you should keeep up with the reading assignments.

Mathematics has a reputation for being removed from social concerns and identities. Whether or not this is true for the content of mathematics, it is certainly false for the process of learning mathematics. Our classroom is to be a welcoming one, where everyone feels able to participate and learn regardless of their background or identity. As learners it is your obligation to treat others with respect and generosity, and be willing to exchange ideas with others.

If you miss a class, it is your responsibility to ensure you make up the missed lesson. The schedule on the course website gives the textbook sections we will cover each week, and any worksheets or handouts will be posted on the course website. If you know in advance you will have to miss a class, please email me.

If exceptional circumstances make it so you must miss multiple classes, please talk to me so we can figure out the best solution for what to do.

Communication Policy and Office Hours

Announcements and homework will be posted to the course website.

The best way to contact me outside of class is by email. Please put “math 217” in the subject line of your email.

Office hours are held multiple times in the week, to give you an opportunity to ask questions and receive help in-person outside of class time. If you prefer to meet at a different time, please contact me to arrange that.

Accessibility

Students with disabilities are legally entitled to reasonable accommodations to ensure equal access to education. I am committed to providing you with equal access to this class, and am happy to work with you to ensure reasonable accommodations. Because the accommodations offered are usually forward-looking modifications, it is important to get them set up as soon as possible.

Anyone who feels they may need accommodation based on the impact of a disability should contact Jeannie Altshuler, Director of Accessibility and Academic Support, in the Win Commons (jaltshuler@simons-rock.edu; 413-528-7383).

The Americans with Disabilities Act defines a disability as a medical condition that substantially limits one or more major life activities—including things like walking, sleeping, taking care of yourself, learning, and regulating your emotions—or major bodily functions. If you have a medical condition—including mental health conditions—that significantly interferes with your schoolwork, you probably qualify. You do not need to disclose your condition to your instructors to receive accommodations.

Academic Honesty

You are expected to know and uphold the college’s policies on academic honesty as described in the Student Handbook. Mathematics classes form part of the core base of skills you need to succeed in many later classes, and you are harming yourself if you try to avoid learning the material for this class.

The use of ChatGPT or other AI tools is prohibited. Submitted work using these tools will receive a zero, with no chance for making up the lost points. I reserve the right to escalate the consequences for repeated violations.

You are encouraged to collaborate with classmates for homework, but the work you submit is expected to be your own. If you do work with others, please say so and give their names with your submitted homework.

Other Campus Resources

The Wellness Center Health and Counseling Services, as the name says, offers health and counseling services.

The Win Student Resources Commons offers academic support, tutoring, accessibility, and career advice.

Notice of Changes

This syllabus is subject to change. If this happens, you will be informed of any additions or changes.