This is the program guidebook for “21st century mathematics”. It is a work in progress. It’s goal is to give you some ideas about ways of moving through the program, to help you find a way that works great for you. There will be additional guidance and suggestions once the program starts, but some people enjoy imagining and planning ahead of time; if that’s you, dig in!
Sections:
Ways to participate
Activities
Ways to stay informed
Calendar of events
Planning your experience
Norms and feedback
Ways to participate
Here are the main activities of this learning experience. You can customize how you participate, depending on your interests, goals, learning preferences, and availability.
– Spend time reading sections from “Theorems of the 21st Century”
– Do some reflecting on your reading
– Read and watch some additional resources
– Try some of the problems on the problem sets
– Participate in some of our Zoom sessions
– Interact with other participants through our message board and Zoom sessions
– Make a presentation about your experience, your work, and your take-aways
Descriptions for each of these are given below. I will also discuss them some at our first Zoom sessions.
“21st century mathematics” is intended to be a flexible experience with many ways to engage and grow as you explore some recent mathematical breakthroughs. You will figure out a combination of activities that works well for you. Broadly speaking, here are three ways you could approach the program:
– As a self-study opportunity: spend some time reading the book and reflecting on your reading. Maybe try some of the problem sets.
– As a course experience: the above, plus plan to attend some of the Zoom meetings on a regular basis, meet some other participants on Zoom, and maybe interact some on the program message board.
– As a social experience: the above, plus be active on the message board and/or connect with other participants through additional discussion and problem solving sessions that you schedule among yourselves or create spontaneously.
A different way of talking about this is a community pool analogy: we are all gathering at the same swimming pool, but we can go about our experience in different ways.
– Dip you toes in, get your feet wet – Make a first try with a few of the activities. See how it goes, find something positive for you. No hurry, no rush—the pool will still be here next year!
– Wade around, put your face in the water, maybe play some Marco Polo – Try a few things and keep at them, gather some courage and stretch yourself, make an effort to connect with others.
– Take a swim class – Plug into a routine to keep yourself accountable and on track, take advantage of the guidance offered in the program, make a plan to stretch yourself and keep at it.
– Swim some laps – Find a direction or two and really push yourself.
– Dive into the deep end – Carve out time to explore lots of directions in the program, find places where you want to dig deep and go for it.
– Do a bit of poolside lounging – Easy-breezy, nothing that feels too much like work, just enjoy being around others mathing out and tune into a talk or two. Rejuvenate for the year ahead and maybe you’ll take a dip next time around.
There are more ideas, too, if you keep following the analogy: you can help to make the experience fun for yourself and others, keep an eye out to help folks who are newer to the pool, ask for some floaties when your arms get tired but you want to keep swimming, …
Activities
– Spend time reading sections of “Theorems of the 21st Century” and related resources
During the program, a copy of the book is available for viewing in the Drive folder. The book can be viewed in a browser but cannot be downloaded or printed. The book will be available to you during the duration of the program. These limits are there to keep us on the safe side of copyright restrictions. If you are interested in purchasing the book, it is available from Springer on this page. An internet search will also turn up other ways to get a copy of the book.
Each of the book’s 106 sections describes a research result published in the Annals of Mathematics during the first decade of the 21st century. Each one is 3 to 4 pages long and gives an accessible introduction to the math involved in the research result.
We will highlight two of the sections during the program. You are particularly encouraged to read these sections during the program, but you might like to check out other sections as well. Investigating an additional section is one route to giving a presentation at the end of the program.
If reading these sections looks like a steep climb to you, don’t worry: there are many other resources that can help you to dig into this math—other readings and videos, my Zoom talks, the problem sets, conversations with other participants and me, and your own internet searching.
– Do some reflecting on your reading
I’ve put together some questions to guide your reflection on your reading of the book. For each section that you read, try reflecting on these questions. This can be for our “spotlight” sections and for other sections. You are welcome to do this reflecting in any of the following three ways:
1) Share your reflections with other participants on the message board (and/or publicly on social media, like your own blog or Twitter).
2) Share your reflection with me through this Google form or by email.
3) Don’t share your reflection at all and just do it for yourself.
Here is the list of reflection questions:
– What’s your name?
– What section of the book did you read?
– In a few sentences, try describing the main ideas of the section.
– What is a new word or term that you learned in your reading? What does it mean?
– Describe a place where you got stuck in reading. What steps did you take to try to get unstuck?
– What in the reading “clicked” for you? How did the math you read about connect with math you already knew? What did the reading make you wonder about?
– Try some of the problems on the problem sets
To help you to dig into the math of our spotlight sections from the book, I’ll share a problem set related to the sections. You can work on these problems on your own or with other participants or both. Maybe you’ll find some folks to chat about problems with on the message board or at Zoom problem solving sessions of in-person meetups.
Each problem set has a range of problems. The ones at the start are to help you to better understand the math from that week’s spotlight section. The later problems can be very challenging, and sometimes they are even problems related to currently unsolved problems that are still being researched by mathematicians. I try to make the problem sets “low threshold, high ceiling”—or even “no ceiling”—so that everyone can make progress on them and everyone can find a challenge in them.
On the problem sets, feel free to skip around, try things out, and see what interests you. Remember that the goal isn’t to “finish” but to learn and grow.
– Participate in some of our Zoom sessions
There are several “live” Zoom sessions each week. I will send out reminders at the start of the week and also ahead of the sessions. The link for all Zoom sessions is the same, and you may want to bookmark it.
At some sessions I will give a presentation about the process of math research and there will be some discussion. At others I will discuss the spotlight chapter for the week and there will be time to work on the problem set in breakout rooms. We will also have sessions where guest mathematicians will visit to talk about their work and to do Q&A with us.
All the sessions are relatively stand-alone, in the sense that if you show up for any one of them you’ll be able to make sense of things. This is particularly true for the green “talk and Q&A” sessions with visiting mathematicians.
If you want to set yourself up to follow a “live” strand of the program, and don’t have time for everything, I would recommend prioritizing either the blue “research overview” sessions or the orange “section highlight” sessions. If you pick one of those two strands, you could aim to attend those Zoom sessions on a regular basis and catch the recordings of the ones you can’t attend live. Along with the difference in themes, another consideration in choosing between the threads is that there will be a breakout room component to each meeting. The “research overview” breakouts will be small group discussions and related activities, while the “section highlight” breakouts will be problem solving sessions for the problem sets. So if you’re looking more for problem solving with other participants, maybe the “section highlight” is more appealing. Or if you want to be more in chatting-about-ideas mode, or if your schedule is such that plugging into problem solving at other times or with other groups of people is a good fit for you, then that might make joining for the “research overview” sessions more appealing.
Each week I will also have “office hour” sessions over Zoom where I will just be available to chat about whatever aspect of the program is on your mind in an informal setting. This is also an additional opportunity to interact with other participants.
– Interact with other participants through our message board
Signing up for our Zulip message board takes just a few easy steps. First, click the link I’ve shared in the welcome email. If you already have an account, click that option. Otherwise, follow the steps on the screen to submit your name (which will be your user name) and other basic info about yourself. You’ll need to confirm your email address by clicking a confirmation link you’ll be emailed. You can either use Zulip in your browser or download the desktop app.
Once you have Zulip loaded up, you will see several “channels” listed. If you click on any of these, you can add a message to this channel by typing into the text box at the bottom of the screen. A great place to start is the introductions channel! And then you can start to explore the others. Each channel has a short description explaining its purpose.
I encourage you to use your real full name on the Zulip, if this is possible for you. This is helpful in people getting to know each other.
– Make a presentation about some of the math you’ve dug into
A week after the program wraps up, we’ll have a Zoom session where participants will share about the math they’ve been learning about and thinking about. For more details, check out this write-up about presentations.
Ways to stay informed
Here are the communication channels I’ll use to share program information with you:
1) Through regular emails to the whole group, reminding you about upcoming sessions and encouraging you toward engaging in the program.
2) At Zoom meetings, where I’ll share ideas about math research and about particular math results, and also remind you about upcoming opportunities.
3) Through our message board. I encourage you to join, but also know that all information about the program will also be shared through email and Zoom meetings.
Calendar of events
A calendar with all of the program events will be shared a few weeks before the program begins. It will stay updated throughout the program.
Planning your experience
There is a lot that I’ve planned, and you will find ways to participate that match your interests and your schedule. Let me offer a few ways you could plan to participate:
– “vertically”, where you pick a kind of event and then plan to attend that each week.
– “horizontally”, where maybe you aren’t available some weeks, but you could plan to really dig in during a certain week or two.
– “pick and choose”, where you select whatever interests you and fits with your schedule, maybe playing some of it by ear.
– and of course there’s always the option of “just as much as I can” 🙂
Know that it will be also be important for you to make time for yourself to think, read, and work on your own or with a small group. The events are there to help guide and enhance your experience, but there’s a lot to gain from the other modes of participating as well.
Norms and feedback
A couple of important norms to keep in mind throughout the program, which you agree to follow when you register:
1) We will be considerate and respectful towards other participants.
2) We will be patient and generous towards ourselves and others, recognizing we are all on our own math journeys.
3) We are always welcome to ask for help, and we are also always welcome to choose to wrestle further with math on our own.
If you find that you are having a negative experience in the program or have a negative interaction with another participant that needs to be addressed, please reach out to me. You can do this by email or through this anonymous feedback form.
Justin Lanier 