The Meta Home Paige
Hi, I am Paige Bright. I am a rising junior at MIT. I am interested in math, specifically analysis and geometric measure theory. This is a simple webpage for hosting different URLs and whatnot of mine from projects to writing. Enjoy!
Blog: The Home Paige
Curriculum Vitae: CV (Last Updated: December 27, 2022)
Email: paigeb@mit.edu
Math Coursework Only: Listing
Current Projects
MITAdmissions: Working for MITAdmissions blogging! Blogs written are also put on The Home Paige.
Profile
UROP: Undergraduate Research Opportunity (Fall 2022-present). Extending my SPUR Project with Shengwen Gan and Larry Guth to the fall, continuing to explore exceptional set estimates and other such questions in metric geometry.
Spring 2023
UA: Undergraduate Assistant for 18.102: Introduction to Functional Analysis, taught by Richard Melrose.
PRIMES Circle: A high school mathematics enrichment program for underrepresented students. Will be meeting weekly with two high school students reading a purposefully chosen text and developoing a presentation and expository paper.
Math Coursework I am interested in:
- 18.156: Differential Analysis II, taught by Prof. David Jerison
- 18.158: Fourier Analysis to Analytic Number Theory, taught by Prof. Larry Guth
- 18.821: Project Lab in Mathematics, taught by Prof. Lisa Piccirillo
- 18.966: Geometry of Manifolds II, taught by Prof. Tobias Colding.
IAP 2023
Teaching 18.S190 (previously 18.S097): Introduction to Metric Spaces. Held TR9-10:30 in-person in 2-131. See IAP 2022 for more information on how the class was held last year and more general information.
This year, the module on applications to differential equations will be replaced with a module on completions of metric spaces (analogous to the completions of the rationals leading to the real numbers). This new module will discuss what the completion of a metric space is, and define L^p spaces, p-adic integers, and more.
Webpage
DRP: Directed Reading Program in Course 18 over IAP. Reading the lecture notes from Larry Guth's 2017 topics class on Decoupling (notes transcribed by various students in the course), as well as Steven Krantz' "A Panorama of Harmonic Analysis" with Postdoc Marjorie Drake. Will ultimately create a presentation on some topic in this reading.
MIT Monologues: In the process of writing a piece for this year's performance on my experiences as a trans-person.
UROP: Continuing my UROP with Shengwen Gan and Larry Guth.
OXes: Finishing the last few classes from Fall 2022.
MathComm: Editing the MathComm Website and working on projects for this website. More to come soon.
Past Projects
Fall 2022
UA: Undergraduate for 18.101: Analysis and Manifolds, taught by Richard Melrose. Providing feedback on lecture notes, grading problemsets, and typesetting problemset solutions weekly for this class. I have also been holding weekly office hours and occassionally review sessions.
Associate Advising: Traditional Associate Advisor for Bill Minicozzi.
Steering Committee: Providing Monthly feedback on Associate Advising for the Office of the First Year.
18.100*: Mentoring for undergraduate real analysis courses.
USWIM: Mentoring for the Undergraduate Society for Women in Mathematics.
Dead Maths Society: More to come soon!(?)
Math Coursework:
- 18.112: Complex Analysis, taught by Prof. Roman Bezrukavnikov
-
Using this time to explore deRham theory on real and complex manifolds so I can better understand the algebraic topology/homology theory behind certain theorems in complex analysis. Reading Bott and Tu's book on this matter.
- 18.965: Geometry of Manifolds I, taught by Prof. Bill Minicozzi
- 18.994: Seminar in Geometry, taught by Prof. Qin Deng
- On minimal surfaces, using the textbook developed by Bill Minicozzi and Tobias Colding.
- Presented on Section 3.3 of do Carmo's text with Victor Luo, discussing the minimizing properties of Geodesics.
- Presented on the first variation formula for minimal surfaces, defining minimal surfaces as being a critical point of the volume functional, and showing that this implies the mean curvature must be zero everywhere on the minimal surface (in fact this is an equivalent relationship).
- Presented on Section 4.3-4.5.1 with Carlos on 1) Solving the Plateau problem and 2) harmonic maps.
- Final project: Studying the relationship and the proofs of Sobolev inequalities and the Isoperimetric inequality on minimal surfaces. Related to my project paper developed in my 2021 Summer UROP (see below). In particular, studying the equivalence of these inequalities on Riemannian manifolds embedded into Euclidean space.
Paper
Summer 2022
SPUR: Summer Program for Undergraduate Research in Course 18, with Larry Guth and Shengwen Gan. Researching Marstrand's projection theorem and the high-low method.
Webpage
Paper
Associate Advising: One of two associate advising captains this summer, developing materials with OFY: The Office of the First Year to prepare associate advisors for the upcoming school year.
Spring 2022
18.100A: Real Analysis (on Rn) prior to this spring was not available on MIT OpenCourseWare (OCW), which I advocated for. Working with Dr. Casey Rodriguez and OCW, I typed lecture notes for the Fall 2020 course taught by Casey, recorded asynchronously. The material is now found on OCW, including notes, lecture videos, problemsets, and notes from some of the recitations. Both a link to the OCW site and a folder of my typed notes is included below.
Webpage
Typed Notes (.zip)
Primes Circle: A high school mathematics enrichment program for underrepresented students. Met weekly with two high school students reading Thomas Sibley's "Thinking Geometrically: A Survey of Geometries". Guided the writing of a 15 page expository paper on triangles in spherical, hyperbolic, and single elliptic geometries.
Paper
Math Coursework:
- 18.157: Microlocal Analysis, taught by Prof. Richard Melrose
- 18.099: Independent Study with Prof. Richard Melrose
- To ask clarifying questions about Microlocal Analysis over the course of the semester.
- 18.118: Introduction to Chaotic Dynamics, taught by Prof. Semyon Dyatlov
- 18.952: Introduction to Differential Forms, taught by Prof. Victor Guillemin
IAP 2022
18.S097: Introduction to Metric Space, developed and taught by me. Advocated for and created a bridge class between real analysis on Rn and real analysis on a general metric space to make the mathematics department more accessible.
Webpage
OCW Class
Blog Post by Peter Chipman
DRP: Directed Reading Program in Course 18 over this IAP. Read the first chapter of John Conway's "A Course in Operator Theory", and created a presentation in Beamer with my partner Esha Bhatia and mentor Elena Kim. Learned quite a bit about the functional calculus as presented in Conway's "A Course in Functional Analysis".
Presentation
Fall 2021
18.100B Mentoring: Mentoring students weekly in 18.100A and 18.100B through the UMA mentoring program.
18.A09: Associate advising for 18.A09: Symmetry with Haynes Miller, advising eight first years.
Math Coursework:
- 18.155: Differential Analysis, taught by Prof. Semyon Dyatlov
- 18.101: Analysis and Manifolds, taught by Prof. Richard Melrose
- 18.705: Commutative Algebra, taught by Prof. Wei Zhang
Summer 2021
UROP: Undergraduate Research Opportunities Program, with Larry Guth and Yuqiu Fu. Closely analyzed "A View from the Top" by Alex Iosevich, solved exercises and presented proofs. Wrote a clear and digestible expository paper proving a Sobolev inequality in 2-dimensions.
Paper
Notes (Rough)
Spring 2021
Started work with OCW for the first time, helping develop a online modulized version of 18.03: Differential Equations with Jennifer French.
Math Coursework:
- 18.702: Algebra II, taught by Prof. Michael Artin
- 18.102: Introduction to Functional Analysis, taught by Prof. Casey Rodriguez
- 18.901: Introduction to Topology, taught by Prof. George Lusztig
IAP 2021
Tetrahedra UROP: Looked into finding the algebraic relations relating the six side lengths and the cosines of the
dihedral angles of a tetrahedron under Prof. Bjorn Poonen, as a volunteer.
18.S097: Grader for the 18.S097 Proof Writing Workshop developed by the UMA.
Math Coursework:
- 18.03: Differential Equations (ASE)
Fall 2020
Math Coursework:
- 18.701: Algebra I, taught by Prof. Bjorn Poonen
- 18.100B: Real Analysis, taught by Prof. Tobias Colding
- 18.A06: What is a Number, taught by Prof. Haynes Miller
- A first year seminar on the construction of numbers, with numerous philosophical conversations on what objects should or shouldn't be considered numbers.
- Discussing Peano Axioms, Dedekind cuts, constructions of the real numbers, construction of the complex numbers, quarternions, surreal numbers, p-adic numbers, etc.
Before MIT
Before MIT, I attended Design Science Middle College High School (DSMCHS) in Fresno, California.
Here, I had the opportunity to study math problemsolving skills with Fresno Math Circle, which I heavily recommend to anyone in the area. If you have the ability to do so, I also recommend donating to their program as it gives the opportunity for many underpriviledged kids to learn mathematics skills.
While here, I also got to work with Fresno City College as an embedded tutor and drop-in tutor, tutoring from college algebra (precalculus) to linear algebra. In fact, at Fresno City College I graduated with my Associate's Degree in Mathematics for Transfer. This allowed me the opportunity to transfer over coursework listed below.
Math Coursework:
- Math 5A: Mathematical Analysis I (Differential Calculus)
- Math 5B: Mathematical Analysis II (Integral Calculus), taught by Travis McDonald
- Math 6: Mathematical Analysis III (Multivariable Calculus), taught by Matt Woods
- Math 7: Differential Equations, taught by Travis McDonald
- Math 26: Linear Algebra, taught by Matt Woods
Last updated: December 27, 2022