Student Classes

This is a new sub-program at Columbia University. Columbia health protocols currently require students to be vaccinated, boosted, and wear masks in class. We will therefore need proof of vaccination as part of the registration process.

MSA Topics and sample questions.

HSA Topics and sample questions.

Note: At the main entrance (116th St and Broadway), ask the guard for directions to the mathematics department.

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.

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

Intro to Pascal's Triangle will allow students to work collaboratively and individually to become familiar with the characteristics and patterns found in the triangle. It will also allow exploration of the applications of the triangle as it relates to counting so that students can count the number of ways to have x heads given y flips of a coin. They will also be able to count word paths efficiently and paths on a grid. Targeted to MSA/MSA+ and MSB students.

Introduction to Proof and Paradox: Mathematical tools for studying what must be true and what seems to be impossible. In the workshop I'd like to introduce basic proof techniques, a few famous paradoxes, and play with a family of logic puzzles called liar paradoxes.Targeted to MSB+, MSC, and HSA students.

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.

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.