Overview
What students can expect
Students should expect to walk into a stress-free environment where they are free to ask questions and explore at their own pace. Confusion and hurdles are not only expected, but what we believe is the hallmark of mathematical research and exploration.
Who it is for
Students grades 6 through 10 with any level of experience in mathematics are welcome! They may adore math or absolutely abhor it; what matters is the attitude they develop after they leave.
Meet the founder
The founder and the primary instructor for lessons is a junior in high school with a deep passion for mathematics. After trudging through grueling proof and logic textbooks, they have personally begun to optimize lessons suitable for a younger audience that turns something intimidating into a fun challenge.
What they learn
Students will learn the absolute rudimentary logical structures that any mathematics major learns in their first few years of schooling. Not only that, they will learn the most common proof-writing structures, such as proof by induction, proof by contradiction, and direct proofs.
What the workshops will look like
The workshops will span approximately 9 weeks with hour-long lessons on a date most suitable for every student in the cohort. Each lesson will build upon the next, and will feature various forms of problem-solving and exploration while embedding within the student the necessary knowledge and a sense of understanding. Students will be encouraged to seek out solutions to exercises and explain them to the instructor and to others to test their hypotheses. At the end of each lesson, students will be given a problem set to work on for that week, featuring exercises that they will be able to work on and a set of exploratory problems — unsolved theorems, elusive sequences, or unseeming structures that have interesting patterns. Where as students should be able to solve the exercises, the exploratory problems are offered solely to give the student an opportunity to engage in some of their own mathematical research and practice their skills.
In every lesson, students should run into at least one uncovered structure or solved proof. But if they feel particularly hesitant about a certain topic, they will also be able to use Logic of Mathematics' complementary website, featuring a written version of each lesson, short quizzes to ensure comprehension, and proof-writing exercises where students will construct their own proofs to be graded.
The Discord server will be the primary method of communication for online lessons. All lessons and announcements will be communicated there, alongside fun activities, communication channels, and other forms of recreation to encourage community bonding. Lessons will be held in the Discord server or over Google Meet. Students are encouraged to have a microphone to speak and a face cam if they wish, but they are not required to and are free to communicate entirely via text channels. Staff are there to cultivate a safe, healthy environment, and to aid each student if they have questions or concerns. If a student is hesitant about anything, they are always free to reach out as soon as possible!
What students leave with
The goal is not to leave with a memorized, step-by-step process for writing out a proof. They should leave with a new way of approaching a problem, be it related to mathematics or not: to observe things and notice patterns, propose their own conjectures, and test every and any idea. A proof is an explanation; the ability of a mathematician to summarize their findings. We want every student to leave with the ability to write at least a single proof and a goal accomplished.
Sure, one of the primary purposes of this workshop is to teach students about logic and proof-writing. But here's the thing: every change in perception comes with a different mindset. We want students who leave Logic of Mathematics to emerge with a different outlook on mathematics, and maybe in other aspects of life, too. Sometimes, there is not always a right answer to everything — and if there is, students should be determined to find it.