Syllabus

HMC Math 131: Mathematical Analysis

Course and Contact Information

Instructors:	Dr. Lisette de Pillis (“Prof. de Pillis”)
Office Location:	Shan 3418
Email:	depillis@g.hmc.edu
Office Hours:	Prof. de Pillis: by appointment. Location: Shanahan 3418. Elliot, Grace, Maddie, Tito and Tommy, Grutoring: TBD
Class Days/Time:	Tuesdays and Thursdays — Section 1: 1:15-2:30 PM in Shan 2460, Section 2: 2:45-4:00 PM in Shan 2460

Course Overview and Goals

This course is a rigorous analysis of the real numbers, as well as an introduction to writing and communicating mathematics well.

We will:

Learn the content and techniques of analysis, so that you can creatively solve problems you have never seen before.
Learn to read and write rigorous proofs, so that you can convincingly defend your reasoning in the language of mathematics.
Learn good mathematical writing practices, so that you can communicate your results with precision and clarity.

Course Materials

Required Textbook: Principles of Mathematical Analysis (3rd Ed), by Walter Rudin. Available at Huntley Bookstore or online.

Supplemental Textbook (free): Understanding Analysis (2nd Ed), by Stephen Abbott. Available as a free download from the Claremont Colleges Library.

Wellness and Support

The humane option is the best option

We are going to focus on supporting each other as humans.
We are going to seek simple solutions when challenges arise.
We are going to share resources and communicate clearly.

We will remain flexible

Everybody needs support and empathy.
Some expectations may need to change.
Schedules may need to be adjusted.
If you need any help or accommodation, just ask. We’ll work with you.

HMC is committed to providing an inclusive learning environment and support for all students. Students with a disability (including mental health, chronic or temporary medical conditions) who may need accommodations in order to fully participate in this class are encouraged to contact the Office of Accessible Education at access@g.hmc.edu to request accommodations. Students may also speak with the Dean of Students Office.

Honor Code

All students are expected to abide by the HMC Honor Code. We encourage collaboration and group work. However, there is a clear difference between collaboration and violations of the Honor Code.

Examples of allowed activities:

Working with a peer group to discuss course concepts and problem approaches.
Using your notes, the textbook, and other class resources.
Asking a tutor or grutor for help understanding a concept.

Examples of not allowed activities:

Copying (or paraphrasing) someone else’s work. This includes looking at another student’s work or a solution found online, then writing up the solution in your own words. You should understand your solutions well enough to write them up yourself.
Using solutions from ChatGPT or other generative language models as your own work. This is equivalent to copying as in the previous two bullet points. For further detail, please see “AI Use Level 0” paragraph below.
Uploading your solutions to sites such as Chegg or providing your solutions for others to copy.

These will be regarded as a violation of the HMC Honor Code and will be handled accordingly.

AI Use Level 0: No AI Use Allowed as it Inhibits Learning in this Class

The goal of this policy is to encourage students to develop their own understanding of and fluency with course material. The learning objectives and assignments for this course are such that the use of generative AI tools will hinder your learning in this course. For this reason, the use of any generative AI tools is not allowed in this course and will be considered a violation of the HMC Honor Code.

Grading

The coursework that you do in Math 131 contributes to your overall course grade, which we will use to ultimately assign you a letter grade. Your overall course grade will be calculated as follows:

Assignments/Activities	% of Final Grade
Attendance	5%
Homework Assignments	20%
Project	5%
Quizzes	60%
Highest quiz score	10%

Grades will be assigned on a straight scale based on your overall percentage as calculated above. We commit to honor the following minimum cutoffs:

94% or higher guarantees an A,
84% or higher guarantees (at least) a B,
74% or higher guarantees (at least) a C,
64% or higher guarantees (at least) a D.

Remember that your grade in this course (and any other course, for that matter) is only a measurement of your learning at one moment in time. It is never a measure of your potential ability or your worth!

Attendance

You will be expected to attend class regularly. Contact the DSA staff if you require extended absence, and the instructor will work in consultation with DSA to make a plan for your situation.

Homework

Homework assignments serve several important purposes, including to further familiarize you with the course material, practice mathematical techniques, provide challenges in creative problem solving, and improve your mathematical writing skills and style.

Homework will be assigned most weeks. Assignments will be submitted directly to Gradescope.

Using Gradescope: If you are registered for this course, you should have already been added to the Gradescope class page. Contact your instructor if you are having problems with access.

LaTeX is an important part of written mathematical communication, and one aim of this course is for students to gain comfort and confidence in LaTeX. To this end, homework assignments must be typed in LaTeX.

Late Homework Policy: You have a total of 72 grace hours to use throughout the semester for late homework submissions. Once you exceed your grace hours, late homework may receive a score of zero. If you require extensions for extenuating circumstances (e.g., prolonged illness or family emergency), you should contact the DSA staff and the instructor will work in consultation with DSA to make a plan for your situation.

The grading team works to make sure that homework sets that are submitted by the deadline will be graded and returned in a timely manner. In order to maintain this workflow, be aware that late homework submissions might not be graded.

Quizzes

Quizzes are an opportunity for you to review and synthesize your learning, demonstrate your proficiency with the material, and assess your progress.

Quiz 1: Topics covered on this quiz may include induction; countability; fields, order, and bounds; metric spaces, neighborhoods and limit points; open and closed sets; compact sets.
Quiz 2: Topics covered on this quiz may include sequences: convergence and divergence; sequence properties; subsequences; Cauchy sequences. Topics from previous sections may also be included.
Quiz 3: Topics covered on this quiz may include completeness of the rationals and the reals; topics from previous sections may also be included.
Quiz 4: Topics covered on this quiz may include series; convergence tests for series; sums, products, and rearrangements of series. Topics from previous sections may also be included.
Quiz 5: Topics covered on this quiz may include limits of functions; continuity of functions; continuity continued. Topics from previous sections may also be included.
Quiz 6: Topics covered on this quiz may include the derivative; mean value theorem; Taylor’s theorem; differentiation and continuity; sequences of functions; uniform convergence. Topics from previous sections may also be included.
Optional Comprehensive Quiz: If your score on this comprehensive quiz is higher than your lowest quiz score, then this score will replace your lowest quiz score.

Quiz details: in-class, 30 minutes, closed note

You will have 30 minutes to complete a quiz. You will only need a pen/pencil. No notes, calculators, or electronic devices are allowed.

Preferred Name and Pronouns

You deserve to be addressed in the manner you prefer. To guarantee that we address you properly, you are welcome to tell us your preferred name and/or pronouns at any time, either in conversation or via email.

Title IX

You deserve a learning community that is free from discrimination, sexual harassment, a hostile environment, sexual assault, domestic violence, and stalking. If you experience or witness a Title IX violation, you have many options for support and/or reporting. See the Title IX Resources Chart.

As faculty members, we are obligated to report any disclosures related to the HMC community that involve Title IX violations.

Accessibility

Our goal is to make our course accessible to all of you! If you anticipate or experience academic barriers based on your disability (including mental health, chronic or temporary medical conditions), or you have any questions about current or possible accommodations, please work directly with the Office of Accessible Education to establish reasonable accommodations. To request academic accommodations, visit the Office of Accessible Education website.

Please send us any questions; we are happy to help.

Student Rights and Responsibilities

Harvey Mudd College’s policy on Student Rights and Responsibilities can be accessed on the HMC website.

Additional Resources

The Claremont Colleges Library — Databases, journals, and more
HMC Writing Center — It provides a welcoming space for writers to get feedback on their composition projects, whether written, spoken or visual pieces. Writing Center Consultants are prepared to assist students in any discipline with any stage of the writing process, from developing an idea to polishing a final draft.
CIS Help Desk — 607.7777 / helpdesk@hmc.edu