Student Classes

The Summer MSHS Math Circle is a weekday program for students entering grades 6-12 in the fall that runs for two weeks, four hours a day. A typical day consists of a class in the morning, followed by an offline, unsupervised one-hour lunch, and a class on a different topic in the afternoon. Instructors are very friendly and helpful. We do expect students to use their registration names and turn on their live videos during online class sessions. Virtual backgrounds are allowed.

MSA/MSA+: Geometry and Algebra to describe patterns

MSB/MSB+: Algebra and Graphing, and Math contest topics

MSC/MSC+: Continued Fractions, from Pythagorean triples to Fermat's last theorem for n=3 and n=4

HS Problem Solving: Math contest topics, and Algebra

New students are required to take a placement test. You will receive a link to download the exam after registering your child. Please submit the exam within 48 hours of registration. We will need to see FULL SOLUTIONS HANDWRITTEN.

Current students wishing to move up a section will also need to take a placement exam. Please email a request to us at info@nymathcircle.org

Visit the High School Summer Program page for information.

Introduction to the Pythagorean Theorem: This 3-session workshop is for those who have not been exposed to the Pythagorean Theorem. It will include: an informal proof of the Pythagorean Theorem, a brief history of the Pythagorean Theorem, common Pythagorean triples and their multiples, determining whether or not a triangle is a right triangle, and application of the Pythagorean Theorem to find areas of composite figures. It will not include irrational numbers.

Intermediate Pythagorean: This 3-session workshop is for those who are familiar with Pythagorean triples It will include an informal proof of the Pythagorean theorem, special triangles, finding the third side of any right triangle, determining whether or not a triangle is a right triangle, and application of the Special triangles to find the area of composite figures. It will include irrational numbers.

Exploding Dots Workshop: Exploding Dots is a construct of organized play and exploration to develop a deep sense of numeracy. Join us as we explore how “Exploding Dots,” James Tanton’s web-based project, can be used to enhance students’ understanding of place value and how to apply ideas of place value to binary numbers. Students will explore some of the introductory activities together, then break into smaller groups to examine the more complex applications.

Probability Workshop: The most important questions of life are, for the most part, really only problems of probability" - French mathematician Pierre-Simon Laplace. This probability workshop will cover topics such as Axioms of probability, conditional probability, and Bayes' Theorem, random variables, and expected values. We will examine not only the mathematics of probability theory but also its applications in problem-solving through examples. All students with basic algebra skills are welcome. Understanding of basic counting principles is preferred, but not required.

Do We Understand Infinity?: We will begin with a trip down a memory lane by recounting multiple proofs of the infinitude of primes, including two proofs by Euclid and a proof by Erdos. Then we will switch gears and talk about paradoxes involving infinities, which will lead us to discussions about differences between finite and infinite sets. For example, if one finite set is a strict subset of another finite set, then the latter is larger than the former. However, this statement no longer holds for infinite sets and we will show why this is so. We will then move on to discussions about well-known infinite sets, like integers, even numbers, rational numbers, and real numbers, and will discuss the sizes of infinite sets. We will prove a theorem for comparing infinite sets and we will also prove that there are "more" real numbers than integers. We will prove some abstract theorems about infinite sets and, if time permits, will discuss multidimensional infinite sets and more general notions of infinity. This class has no prerequisites beyond Algebra II, but it will tackle abstract concepts, which may prove challenging to younger students.

MS A is appropriate for students who are new to problem-solving. In addition to having a strong interest in learning mathematics above and beyond the school curriculum, they should be well-versed in arithmetic, including order of operations, fractions, decimals, and percents. Topics and sample questions.

Note: Due to high interest, we are offering multiple sections of this course this semester. They constitute the same course but the “+” sections, when available, are taught at a deeper level and designed for students who have already taken this class 2 or more semesters in the past.

MS B is appropriate for students who have strong arithmetic skills and have some basic experience with algebra. They should have the equivalent of 2-4 semesters of MS A. Topics and sample questions.

Note: Due to high interest, we are offering multiple sections of this course this semester. They constitute the same course but the “+” sections, when available, are taught at a deeper level and designed for students who have already taken this class 2 or more semesters in the past.

MS C is appropriate for students who have strong arithmetic skills and considerable experience with algebra including some exposure to Algebra 1. They should have the equivalent of 2-4 semesters of MS B. Topics to be covered include continued fractions, graph theory, and Vieta’s formulas. Topics and sample questions.

Note: Due to high interest, we are offering multiple sections of this course this semester. They constitute the same course but the “+” sections, when available, are taught at a deeper level and designed for students who have already taken this class 2 or more semesters in the past.

HS A is appropriate for younger high school students who may be new to problem-solving. They should be comfortable with regular high school material, including at least Algebra 1. Topics and sample questions.

Note: Due to high interest, we are offering multiple sections of this course this semester. They constitute the same course but the “+” sections, when available, are taught at a deeper level and designed for students who have already taken this class 2 or more semesters in the past.

HS B Students are expected to have completed the equivalent of two years of high school, and have a solid understanding of algebra, geometry, and elementary number theory. Experience with problem solving, such as prior NYMC or math team participation, is desirable but not required. Proof-writing will be an important component of this course. Topics and sample questions. Here is a sample of Student Work

Note: Due to high interest, we are offering multiple sections of this course this semester. They constitute the same course but the “+” sections, when available, are taught at a deeper level and designed for students who have already taken this class 2 or more semesters in the past.

HS C Students are expected to have taken pre-calculus and to have a deeper knowledge of algebra, geometry, and trigonometry, as well as experience with mathematical problem-solving. Problems will require sustained effort, and writing proofs will play an important role. Topics and sample questions. Here is a sample of Student Work

College Bridge is a course designed to challenge our most advanced students who plan to take higher-level mathematics classes in college. Emphasis will be on proof-writing and examination of underlying structures in mathematics.

Dr. Ustinovskiy will cover some topics that typically appear on USAMO. These topics are not only useful for Olympiad participants but are also of intrinsic interest. There is a short placement test to identify suitable students. Topics.

Students already taking other classes may take this class as well if they meet the admission standards.

This mini-course consists of 3 workshops that cover topics encountered in High School Math Contests such as AMC 10 (Intermediate) and AMC 12 (Advanced). NYMC is offering limited online seats for these two exams on February 10, 2021 - priority will be given to students who attend these workshops. The deadline to ask for a seat is January 13.