## 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