Schedule

Overview

GirlsxMRO's program will run from 06/27/21-07/25/21. The first week is dedicated to overview and crash course, which introduces basic proof techniques and skills useful in mathematical reading. Weeks 2,3, and 4 will be dedicated to one advanced topic each week, which also contains the reading group. Students are not required to attend all Zoom sessions, instead, you can choose the ones that you are interested/have time for. All Zoom live sessions will be held on Sunday at 10:00-11:30 AM PDT/1:00-2:30 PM EDT, with the exception that the first week also contains two live sessions happening during the week. All reading groups will be meeting twice a week on Tuesday and Friday. In addition, Office hours will be held every Thursday. You can view more about the details of times and general structure for reading groups and zoom live sessions by clicking the tabs below. You can also view more details of motivation/goals of zoom live sessions and reading groups.

Weekly Schedule

Week 1: Overview & Crash Course

Welcome to GirlsxMRO: Overview and Q&A Sunday 6/27/21 10:00-11:30 AM PDT/1:00-2:30 PM EDT

In our first meeting on Sunday, we will be introducing GirlxMRO and providing a detailed overview of the 2021 program, including structure and motivation as well as eligibility and difficulty. This is a good chance to see if you are fit for the program in terms of difficulty and commitment. We will also have time for Q&A. All students are encouraged to attend.

Crash Course Day 1: Proof Techniques Tuesday 6/29/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Crash Course Day 2: Mathematical Reading Friday 7/2/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

There will not be reading groups during the first week of our program. Instead, we have live Zoom "Crash Course" sessions that are open to all students. During these sessions on Tuesday and Friday, we will cover core skills in math that will be useful for the lectures and reading groups in the rest of the program. We strongly recommend that all students to attend these sessions.

Week 2: Group Theory

Intro to Group Theory Sunday 7/4/21 10:00-11:30 AM PDT/1:00-2:30 PM EDT

Reading Group Meeting 1 Tuesday 7/6/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Office Hours Thursday 7/8/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Reading Group Meeting 2 Friday 7/9/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Group theory is central to many fields in advanced math. However, this abstract algebra concept can be found in our daily lives everywhere, from symmetries of a square to solving a Rubik's cube. Further, even though group theory is rarely taught in the classroom, it turns out that we have already worked with many of the abstract concepts as early as in Algebra I.

Students are encouraged to have participated in the crash courses from Week 1 before attending the live session. Reading group students are expected to attend the live session and both reading group meetings. All students are welcome to come to office hours.

Potential topics in Live Zoom Sessions include:

  • Basic definitions of groups (including formal axioms and introductory proofs)

  • Fun/important examples of groups (Dihedral group, Symmetric group, Symmetry group, integers, rationals, etc.)

  • Introducing cool applications of groups theory

Potential topics in Reading Groups include:

  • Extending basic definitions in live zoom sessions to modular arithmetic, complex numbers, etc. with formal mathematical notation

  • More introductory proofs (with formal mathematical notation)

  • Cyclic groups

    • Subgroups/Normal subgroups

    • Cosets

    • Generators

    • Lagrange Theorem

Week 3: Algebraic Combinatorics

Intro to Algebraic Combinatorics Sunday 7/11/21 10:00-11:30 AM PDT/1:00-2:30 PM EDT

Reading Group Meeting 1 Tuesday 7/13/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Office Hours Thursday 7/15/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Reading Group Meeting 2 Friday 7/16/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Those of you who have participated in math competitions have likely already had some experience with counting & probability problems. However, there is so much more to combinatorics than this! If you haven't participated in competitions, that's totally fine! The combinatorics concepts in this session are different than those commonly found in contest problems.

Students are encouraged to have participated in the crash courses from Week 1 before attending this session. However, participation in the group theory live session and/or reading group from Week 2 is independent from this week's material. Reading group students are expected to attend this week's live session and both reading group meetings. All students are welcome to come to office hours.

Potential topics in Live Zoom Sessions include:

  • Catalan numbers with multiple examples & proof of the closed form of Catalan numbers

  • counting parenthesis/count paths on a grid with combination/crossing paths

  • Bijective/combinatorial proof

Potential topics in Reading Groups include:

  • Standard Young Tableaux (partition, young diagram, SYT)

  • Hook Length Formula

  • Frobenius young identity statement

  • RSK correspondence

Week 4: Topology

Intro to Topology Sunday 7/18/21 10:00-11:30 AM PDT/1:00-2:30 PM EDT

Reading Group Meeting 1 Tuesday 7/20/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Office Hours Thursday 7/22/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Reading Group Meeting 2 Friday 7/23/21 3:00-4:00 PM PDT/6:00-7:00 PM EDT

Topology the field of mathematics associated with the deformations with a geometric object! To a topologist, a coffee mug is the same shape as a donut but different from a baseball. This might seem quite abstract at first, but

Students are encouraged to have participated in the crash courses from Week 1 before attending this session. However, participation in the group theory live session and/or reading group from Week 2 as well as the algebraic combinatorics live session and/or reading group from Week 2 are both independent from this week's material. Further, reading group students are expected to attend the live session and both reading group meetings. All students are welcome to come to office hours.

Potential topics in Live Zoom Sessions include:

  • Euler characteristic

  • Continuous maps (introductory without formal math language)

  • Homeomorphism (introductory without formal math language)

Potential topics in Reading Groups include:

  • Extending basic definitions in live zoom sessions to formal math language (continuous maps & homeomorphism)

  • Metric spaces

  • Formal definition of a topological space

  • Brief introduction to other interesting topics in topology


Week 5: Research Presentations

Research Presentations Sunday 7/25/21 10:00-11:30 AM PDT/1:00-2:30 PM EDT

In GirlsxMRO's Summer 2021 Program's final meeting, our mentors will briefly present research they have been working on this year/worked on in previous years at MIT PRIMES. This presentation is not organized by MIT or the PRIMES program. This is a great opportunity to see what math research is about. All students are highly encouraged to attend this live session.