COURSES
Math Circle participants take three courses every summer: two core classes, one from the Combinatorics sequence and one from the Number Theory sequence, and one elective class. All students in the 2018 Math Circle took Combinatorics I and Number Theory I, with the opportunity to move on to higher courses in later years. Emphasis in all courses is on developing critical thinking skills and problem-solving abilities, both individually and with other students. Students with sufficient background knowledge can place into higher-level courses.
Combinatorics
Sequence
Combinatorics I
Combinatorics II
Topics include advanced probability, random variables and distributions, and intermediate graph theory.
Prerequisites:
Combinatorics I
Combinatorics III
Topics include generating functions, recursion, advanced graph theory, and Ramsey Theory. (Will be offered in Summer 2020)
Prerequisites:
Combinatorics II
Topics include basic set theory, counting strategies such as permutations and combinations, introductory probability, and introductory graph theory.
Prerequisites:
Algebra I (HS)
Number Theory
Sequence
Number Theory I
Topics include the integers and divisibility, the Euclidean Algorithm, Diophantine Equations, modular arithmetic, and linear congruences.
Prerequisites:
Algebra I (HS)
Number Theory II
Topics include primitive roots, quadratic residues, reciprocity, continued fractions, and Gaussian integers.
Prerequisites:
Number Theory I
Number Theory III
Topics include nonlinear Diophantine equations and introduction to elliptic curves. (Will be offered in Summer 2020)
Prerequisites:
Number Theory II
Electives
Electives are chosen depending on interest from students and availability of instructors. To the right are electives from past years; topics will be finalized in late spring.
Coding
Electives in the coding theme may include Introductory and Advanced Python, Programming in Java, and Statistics with R.
Prerequisites:
Varies by course
Statistics
Electives in the statistics theme may include Intro to Statistics, Causal Inference, Spatial Statistics, and Experimental Design.
Prerequisites:
Varies by course
Mathematics
Electives in the mathematics theme may include Algebraic Geometry, Algebraic Topology, and Knot Theory.
Prerequisites:
Varies by course