# PZMC Number Theory Camp

Learn to explore the theory of numbers by asking thoughtful questions, working out examples, looking for patterns, making conjectures, and finally, proving your results.

Application Deadline on April 28, 2023

JOIN US FOR OUR 11th YEAR!

## Number Theory Camp

### Camp Overview

Welcome to PZMC!

*PZ Math Camp: Number Theory & The Art of Mathematical Thinking.*

Formerly run as the Williams College Math Camp (WCMC), PZMC is the same camp with a new name. Same structure, same instructors, same location, same content!

PZMC is a residential math camp for about 25 mathematically gifted high school students who have completed or are currently enrolled in Algebra 2 or its equivalent. Students will be exposed to several different areas of mathematics through colloquia and other activities, but the primary focus of the camp will be Number Theory & The Art of Mathematical Thinking. Students will learn to explore the theory of numbers by asking thoughtful questions, working out examples, looking for patterns, making conjectures, and finally, proving their results. Students will learn through interactive lectures, group problem solving sessions, and final projects/presentations.

Note that although the mathematical pre-requisite is only Algebra 2, we often have students with more mathematics experience, from precalculus to calculus to multivariable and even linear algebra. One of the great things about number theory is that we don’t need those other math classes beyond Algebra 2. So we can have students with varying degrees of math experience working together successfully.

***We are planning to host camp in person this year. Specific covid precautions to follow.***

### Fees & Dates:

Location: **Williams College**

Camp Fee: **$2,450**

2023 Camp Dates: **July 3-14**

2023 Application Due Date: **April 28**

## Applying

**This year, all applications must be submitted through the mathprograms.org using this link.**

**This year, all applications must be submitted through the mathprograms.org using this link.**

To apply to the PZ Math Camp, you should be a current high school student, and be enrolled in or have completed Algebra 2 or its equivalent. Application deadline is on **April 28, 2023**

- 2023 Application Form
- PZMC Challenge Questions 2023
- Cover Letter (Personal Statement)
- High School Transcript (unofficial is fine) and any available standardized test scores
- 2 Recommendations (to be submitted directly by recommenders): 1 Personal & 1 Academic

**More information.**

*Recommendations :* Two recommendations (one academic and one personal) are required. Be sure to give each recommender a Recommender Form to read before writing their letter. One letter should address your mathematical abilities and accomplishments, while the other letter (from a teacher, mentor, or counselor) should address your personal character.

*Cover Letter (Statement of interest, 2 pages):* Why do you want to attend PZMC? Please include information about your mathematical background and interests, and why you think the camp will be a good fit for you.

*Math Challenge Questions*** : **Submit clear and detailed solutions for as many questions as you can. We do not necessarily expect full solutions for every question. We’re interested in your approach to the question as well as your ability to communicate your ideas clearly and effectively. Correct answers without explanations will not be considered.

### What’s Included?

**Tuition for in-person camp includes the following:**

**Tuition for in-person camp includes the following:**

- 3 meals per day, typically at a Williams College dining hall with vegetarian and vegan options
- Lodging in private rooms (shared bathrooms) on single-sex floors in a Williams College dorm
- PZMC t-shirt
- Field trip to MASS MoCA, including tour of the Sol Le Witt exhibit
- Private planetarium showing at Williams College
- Guest lectures by award-winning faculty
- 2-3 teaching assistants/residential advisors
- Social activities including scavenger hunt, hiking, math movie nights, and July 4
^{th}festivities - Access to the Williams College Libraries
- Access to Williams College facilities including gym and pool

## Testimonials

## Camp Experience

PZ Math Camp (PZMC) is a ten-day residential math camp for mathematically gifted high school students hosted at Williams College. Campers will be exposed to several different areas of mathematics through colloquia and other activities, but the primary focus of the camp will be Number Theory & The Art of Mathematical Thinking. Campers will learn to explore the theory of numbers by asking thoughtful questions, working out examples, looking for patterns, making conjectures, and finally, proving their results. One of our goals is to inspire students by showing them a fascinating world of mathematics not seen in standard high school courses and surrounding them by like-minded mathematically curious peers.

A typical day at math camp includes the following: group problem solving sessions, interactive lectures with ample time for student-driven mathematical discovery, a math talk by an award-winning mathematician or a panel discussion on what it’s like to major in mathematics at college, and plenty of time for fun including hiking, museum trips, and a math movie night!

## Meet the Instructor

Allison Pacelli, Professor of Mathematics at Williams College, is the Founder and Director of PZMC (formerly known as Williams College Math Camp WCMC). Pacelli received her Ph.D. in 2003 at Brown University, in the field of algebraic number theory. Pacelli is an award-winning teacher and the author of numerous research papers as well as the textbook (with Alan Taylor) *Mathematics and Politics: Strategy, Voting, Power, and Proof (2nd edition)*.

## FAQ’S

##### How much does it cost to attend PZMC?

2023: $2,450 (For those whose combined family income is at least $60,000 per year). Includes lodging and all meals while camp is in session. Financial aid is available to those domestic students whose combined family income is less than $60,000. Early Arrival or Late Departure: **$100** (each extra day)

##### Who is elegible to attend PZMC?

Current High School Students who are currently enrolled in or have completed Algebra 2 or its equivalent (many of our participants have considerably more math than this). Successful applicants will demonstrate strong interest and promise in the field of mathematics. Occasionally, we consider current 8th graders with very strong math backgrounds.

Note that although the mathematical pre-requisite is only Algebra 2, we often have students with more mathematics experience, from precalculus to calculus to multivariable and even linear algebra. One of the great things about number theory is that we don’t need those other math classes beyond Algebra 2. So we can have students with varying degrees of math experience working together successfully.

##### When is math camp?

July 3-14, 2023. Camp will begin at 8:30am on July 3rd, and end at 4pm on July 14th. It is possible to stay at Williams for the nights of July 2nd and or July 14th if necessary for transportation, but there will be an additional fee.

##### What will it be like to attend PZMC?

Campers will attend class and problem-solving sessions during the days. Evenings will offer opportunities for various recreational activities. Participants will also attend colloquium talks by leading mathematicians and panel discussions on what it’s like to major in math or opportunities for careers that involve mathematics. Participants will have some free time over the weekend and there will be organized recreational activities such as hiking or a museum trip.

##### Do you have more questions?

Contact Professor Allison Pacelli by clicking here.