Meetings

2021-2022 School Year

Handouts and lecture slides are distributed only during meetings.

1. 9/29/2021: Kickoff Meeting - Overview of AMC, competitive vs. real math, introductions, advanced math snapshot.

2. 10/6/2021: Single-variable Calculus - Limits, continuity, derivatives, integration.

3. 10/13/2021: No Meeting (PSAT).

4. 10/20/2021: Infinite Series - Definitions, convergence tests, summation techniques.

5. 10/27/2021: Infinite Series - Summation techniques, Taylor series, Euler's method.

6. 11/3/2021: Group Theory - Set theory, abstract operators, group axioms, Cayley tables.

7. 11/10/2021: Group Theory - Homomorphisms, isomorphisms, dihedral groups, generators, subgroups.

8. 11/17/2021: Group Theory - Review and concrete examples.

9. 11/24/2021: No Meeting (Thanksgiving break).

10. 12/1/2021: Group Theory Review & LaTeX Tutorial - Lagrange theorem, group actions, LaTeX basics.

11. 12/8/2021: LaTeX Tutorial - Hands-on LaTeX practice.

12. 1/19/2022: Complex Analysis - Complex numbers, complex plane, operations.

13. 1/26/2022: Complex Analysis - Complex differentiation, contour integrals, Cauchy-Goursat theorem, Cauchy's integral formula.

14. 2/2/2022: Functional Analysis - Functionals, metric spaces, linearity, distance measures, Euclidean metric.

15. 2/9/2022: Graph Theory - Graph characteristics, types, history, Eulerian and Hamiltonian paths.

16. 2/16/2022: Differential Equations - Types, exponentials, complex replacement, applications, variation of parameters.

17. 3/2/2022: Differential Equations - Review, separation of variables.

18. 3/9/2022: Differential Equations - Second-order diff. eqs., physics application: dampening.

19. 3/30/2022: Differential Equations - Matrices, vector transformations, eigenvectors.

20. 4/20/2022: Differential Equations - Physics and biology applications, eigenvectors, eigenvalues, partial differential equations.