Below is an hourly breakdown of a typical day at the Prove it! Math Academy summer program.
| 8 AM: | Breakfast at the dining hall. |
| 9 AM – 12 PM: | Morning class. These sessions consist of a mix of problem-solving activities and lectures by our expert instructors on advanced mathematics topics. There will be a break halfway through each morning session. |
| 12 PM: | Lunch at the dining hall. |
| 1 PM – 4 PM: | Afternoon class. These sessions consist of a mix of problem-solving activities and lectures by our expert instructors on advanced mathematics topics. There will be a break halfway through each afternoon session. |
| 5:30 PM: | Dinner at the dining hall. |
| 7:30 – 9 PM: | The evening sessions consist of either group work sessions or downtown excursions. The group study time is an opportunity for the students to work in teams on the problems and proof write-ups for the Prove it! Math Conference, which will take place near the end of the program. The excursions will consist of a variety of trips to downtown Fort Collins and the surrounding area. |
| 10 PM: | Check-in at the dorms. |
| 11 PM: | Lights out. |
The tentative schedule for the classes and activities at the 2020 Prove it! Math Academy is shown below.
| Morning | Afternoon | Evening | |
|---|---|---|---|
| Day 1 | Students Arrive | Greetings and Games | |
| Day 2 | Welcome; Introduction to Proof |
Toy Proofs, Propositional Logic, Quantifiers |
Excursion; Group Work |
| Day 3 | Peano Axioms, Proof Shortcuts |
Set Theory, Functions |
Group Work |
| Day 4 | Induction | Numbers, Rings, and Groups |
Excursion; Group Work |
| Day 5 | Rocky Mountain National Park / Colorado field trip |
||
| Day 6 | Combinatorial Proofs | Symmetry and Burnside’s Lemma | Group Work |
| Day 7 | Invariants, Extreme Principle |
Transformational and Hyperbolic Geometry, Inversion |
Excursion; Group Work |
| Day 8 | Generating Functions | Proof Writing Style, LaTeX |
|
| Day 9 | Introduction to q-analogs | Surreal Numbers and Games | Group Work |
| Day 10 | Local field trip | Existence Proofs | |
| Day 11 | 3x+1 Problem, 2-adic numbers |
Conference preparation | Group Work |
| Day 12 | Prove it! Conference | Prove it! Conference | Fractals; Excursion |
| Day 13 | Career Information | Solutions, Team Awards |
Final Excursion |
| Day 14 | Breakfast | Students Depart |
The program is a full two-week experience, and so students must arrive and depart on the scheduled arrival and departure days.
Note that all classes and activities are subject to change; the above is meant to give a general idea of the content of the curriculum and the planned excursions.