Enumerative and Algebraic Combinatorics
MATH 511
Overall Course Reflection
Combinatorics is a branch of mathematics that mainly deals with counting, arrangements, and combinations of objects. Some of the main things that we focused on this course were combinations and permutations, the fundamental counting principle, partitions, and combinatorial proofs. This branch of math is really prevalent in computer science, which is probably why this was one of my favorite math classes that I have taken.
What I love about combinatorics is how it very tangible and accessible for students. For example, a question as simple as asking them how many ways to create a group is something that feels easy to do but can quickly prove to be quite complicated. This makes it an excellent way to build problem-solving skills and logical reasoning in mathematics. I have used some of the techniques that I learned in this course to help structure the way that I teach combination and permutations for my Algebra 1 students.
Course Artifacts
Homework Assignments
These are the homework assignments from this course. These showcase my ability to engage with combinatorics at a graduate level, particularly through my construction of proofs and analyzing various theorems. They demonstrate not only my understanding of combinatorial techniques but also my ability to communicate mathematical reasoning clearly and rigorously.
(Creation time: 7-10 hours per assignment)