Student Classes

HIGH SCHOOL

The Sum-Product Problem

DESCRIPTION: The sum-product problem is a major open problem in mathematics. Several of the world's leading mathematicians have been struggling with this problem over the past decades, making slow progress. At the same time, hardly any mathematical background is required for understanding this problem, since it only deals with sums and products of numbers. We will discuss the sum-product problem and see one of the major breakthroughs that was made for it. We will also have a brief chat about math research projects for high-school students.

Adam Sheffer is a professor of mathematics at the CUNY Graduate Center and the Director of Computer Science at CUNY's Baruch College. He is also the director of two programs where promising college students from across the country pursue math research, sponsored by the National Science Foundation. This year, his book "Polynomial Methods and Incidence Theory" was published by Cambridge University Press.

This is targeted to HS students. Due to limited space available, parents and guests are not invited. Light snacks will be served from 12:00pm to 12:30pm.

Students attending the Clinton School classes should wear a mask unless the instructor indicates otherwise.

Bring a notebook and pencil or pen to class. MS classes usually assign about half an hour of homework per week, whereas HS classes assign about one hour.

MSA is a one-year program appropriate for Elementary or Middle School students who are new to problem-solving. They should have strong arithmetic skills and an interest in learning mathematics beyond the school curriculum. Topics and sample questions.

MSB is an intermediate one-year program appropriate for students who have completed the equivalent of MSA. Topics and sample questions.

MSC is an advanced one-year program appropriate for students who have completed the equivalent of MSB and have had exposure to Algebra 1. Topics and sample questions.

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

Elementary School Workshops consist of three one hour sessions, and classes are capped at 12 students. Class A (1-2 pm) is for students below fourth grade. Class B (2-3 pm) is for fourth- and fifth-grade students and will go faster than Class A. Students will work in groups to solve problems. We will discuss efficient methods of problem-solving.

ES PROBLEM-SOLVING 1: Logic and patterns.

ES PROBLEM-SOLVING 2: Guess and check; draw a picture.

ES PROBLEM-SOLVING 3: Make a chart/table; simplify.

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Middle School Workshops consist of three two hour sessions.

MS CONTEST 1 TOPICS: Algebra - Digits Problems, Base-n numbers, Discussion of cases.

MS CONTEST 2 TOPICS: Geometry - Triangles & Quadrilaterals, Circles & Volume, Funky Figures.

MS CONTEST 3 TOPICS: Probability - Probability, Geometric Probability, Combinations, and Permutations.

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Mathematics of Origami: During this two-session workshop, we will explore modular origami - ways of combining origami units to make more complicated shapes. This workshop is hands-on - we will make some of the models in this video.

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.