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.

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.

MS CONTEST WORKSHOP 1 TOPICS: arithmetic, algebra, geometry (numeric/algebraic expressions/equations, percents/fractions, ratios/proportions, sequences/series/patterns, coordinate geometry, plane geometry, solid geometry)

MS CONTEST WORKSHOP 2 TOPICS: number theory, counting & probability, statistics (divisors/multiples, remainders/mods, counting, combinations/permutations, binomial probability, geometric probability, mean/median/mode/residues)

Please note that Workshop 2 assumes competence in algebra and geometry from Workshop 1, for topics like binomial probability and geometric probability.

ELEMENTARY SCHOOL STUDENTS WORKSHOP Grades 5 and under. Topics covered will include those that feature in Kangaroo Math and MOEMS.

Three workshops taught by Amy Lee will be held from 10:00am to 11:00am on 5/15, 5/22, 5/29. Special presentation on 6/5, from 1pm to 3pm, by Jonathan Rolf @ National Security Agency (NSA) on Cryptanalysis 101. Attendance is mandatory.

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.

Intro to Graph Theory: In 1736, famous mathematician Leonhard Euler "solved" the Seven Bridges of Konigsberg puzzle and thereby gave birth to a new topic in math: Graph Theory. In this workshop, we'll introduce Graph Theory and discuss topics such as Euler Path, Isomorphism, Planar Graph, Kuratowski's Theorem, and Euler's Formula. We will explore various games and puzzles that are related to Graph Theory.

Mass Point Geometry: This 3-session workshop is targeted at students who are fluent in the topics covered in Regents Geometry. In this workshop, we will see how Mass Points are related to medians, angle bisectors, and altitudes. We will use Mass Points to solve both AMC and AIME problems and to prove Ceva's Theorem and Menelaus' Theorem. If there is time, we may also solve some problems in 3D.

Guest Speakers from National Security Agency (NSA): The National Security Agency/Central Security Service (NSA/CSS) leads the U.S. Government in cryptology that encompasses both signals intelligence (SIGINT) insights and cybersecurity products and services and enables computer network operations to gain a decisive advantage for the nation and our allies.

Cryptanalysis 101: Speaker: Jonathan Rolf. Target audience: Grades 4-6. Description: Students learn basic cryptology terminology and four classic encryption techniques plus the mathematics behind the cryptanalysis (frequency counts and cipher patterns). Students decrypt several messages using substitution and transposition techniques.

Winning Games: Luck or Logic: Speaker: Andrew Shue Target audience: Grades 6-8 Description: Students are introduced to the basic concepts of game theory. They play familiar games such as tic-tac-toe and rock-paper- scissors and examine the strategies required to win or avoid losing. Students are also introduced to variations on these games and must extend their analysis to determine how to adapt winning strategies.

Fermat’s Last Theorem: Speaker: Mervin Bierman Target audience: Grades 8-12 Description: Fermat’s Last Theorem is a demonstration of the differences among a conjecture, a proof, and a theorem. In Number Theory, Fermat’s Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. Students are offered two potential ‘answers’ and are asked to prove or disprove these solutions, demonstrating the rigor a proof must meet. SCIENTIFIC CALCULATOR IS REQUIRED.

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 Middle School Math Contests such as Mathcounts. Students who are not currently in our program should contact admin at info@nymathcircle.org. FREE registration for AMC 8 is included - email us for a registration link.