Past Student Classes

This is a new sub-program at Columbia University.

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.

GUEST SPEAKER: DR. PO-SHEN LOH. Date: November 5, 2023 @ Columbia University, 10am TITLE: Using Game Theory To Save the Next Generation From ChatGPT AUDIENCE: Parents of K-12 students in all years, educators of all years, students in grades 6-12. (Elementary students typically do not understand the discussions about life advice, but elementary parents find that part of the talk very useful, so elementary parents can come without their kids.)

Computer Algorithms workshop titles are: 1. How to compute with real numbers: interval arithmetic, 2. Numerical root finding for polynomial (real roots), 3. Extension (complex or complex roots, higher dimensions)

Elementary School Workshop: Introduction to Percentage: In this 3-session workshop, you will learn how to find the percent of a number, estimate percents, and find discounts and tax. Calculators will be used as well as websites.

Mass Point Geometry: The Method of Mass Points is an ingenious way to approach many geometry problems that involve intersecting segments inside triangles and other polygons. Mass Points can make solutions to otherwise difficult geometry problems simple and straightforward. In this 3-session 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, prove Ceva's Theorem and Menelaus' Theorem and use Mass Points to solve problems in three dimensions.

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.

HS Math Competitions: This is a 3 session workshop covering topics usually found in high school math competitions. The workshops will be held on 12/2, 12/16, 12/23. The difficulty of the workshop will change as each session progressively covers more difficult material, starting from AMC10 material for the first workshop. The main focus will be solving problems efficiently, contest-taking strategies, and the mental tricks used by contests.

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.

MSC Workshop: Although we are not currently running MSC classes, we are now offering an MSC workshop to cover a few topics we used to cover: 1. Vieta's Formulas 2. Pigeonhole Principle, and 3. Triangle Area Ratio Theorem. This workshop is ideal for MSA and MSB-level students who wish to study more advanced material but lack coverage of Algebra 1 topics to qualify for HSA.

Number Theory through Inquiry: In this three-session workshop, students will discover some basic and beautiful results in number theory. Students will be expected to prepare and present proofs for comment and discussion. Along the way, they will learn about the properties of prime numbers, Euler's theorem, the mathematics of RSA encryption, and quadratic reciprocity. Experience writing proofs is required.

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

The High School 2-year cycles start in the fall of even years (e.g., fall 2022). Students may enroll at any point of the cycle.

Parents are allowed to drop off students at 9:30 am. Classes are from 10:00 am to 3:00 pm. There will be a supervised lunch period from 12:00 pm to 1:00 pm in which students must bring lunch and drink. Students are NOT allowed to leave campus to purchase lunch. We will also have an optional after-school mathematical activities session from 3:00 pm to 5:00 pm.

Remote classes will be from 10-12pm, and 1-3pm. There will be an unsupervised lunch hour from 12pm-1pm.

Bring a notebook and pencil or pen to class. MS classes usually assign about half an hour of homework weekly, whereas HS classes assign about one hour. Year 1 for the HS curriculum starts in the fall of even years (e.g., fall 2022), and year two starts in the fall of odd years.

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

HSA is a two-year program appropriate for younger high school students and advanced middle 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.

Targeted audience: By invitation only. Alumni & High School Seniors only.

May 21, 2023 @ 10 am. Andrew Yang (Google) Software Careers: I’ll discuss my journey from studying math to entering software engineering. This will include a discussion of the differences between academia and industry, what has changed in the past 20 years, and how math broadly applies to some of the best jobs today.

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. Year 1 for the HS curriculum starts in the fall of even years (e.g., fall 2022), and year 2 starts in the fall of odd years.

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 a one-year intermediate 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 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

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

Presenting Polygons. In this three-day workshop, students will explore polygons. They will be able to identify them by the number of sides. They will distinguish between regular and irregular polygons. They will be able to find the sum of the measures of the angles of a polygon. They will be able to find the measure of each angle of any regular polygon. They will develop the formula for finding the area of a regular polygon. Students will need a scientific calculator and should have working knowledge of computers as there are several websites we will access.

MS Intro to Geometry: This three-day workshop is targeted at Middle School students who a have basic understanding of geometric shapes (triangle, quadrilateral, rectangle, square, parallelogram, rhombus, kite, trapezoid/isosceles trapezoid, circle) and angles (right angle, straight angle, parallel lines, acute angle, obtuse angle, degree measure). We will discuss problems involving circle geometry, the Pythagorean Theorem, and its applications, including coordinate geometry and finding areas of shaded regions (e.g., bounded by two sides of a right triangle and a circle inscribed into it.) The problems will be on the National MathCounts level.

HS Contest Topics in Geometry: This three-day workshop targets students with a solid foundation in basic geometry. For example, a score of 95+ on Geometry Regents would qualify a student for this class. This 3-class workshop will cover some common ideas in Plane Geometry, problems involving areas, and 3D geometry. The level of the problems will be AMC 10 #15-#25.

Recursive Sequences: Two-day workshop. A sequence is a list of things (usually numbers) that are in order. Many sequences have patterns that a recursive formula can describe. In Algebra class, we learned that general methods exist to find the explicit formula for arithmetic and geometric sequences, but what about other recursive sequences? In this workshop, we will explore methods of writing explicit formulas for some sequences that are neither arithmetic nor geometric. We will also examine Fibonacci-style sequences in the form x_(n+1)=a*x_(n)+b*x_(n-1) and find the explicit formula of the Fibonacci Sequence with elementary algebraic methods. At the end of the workshop, we'll look at how the Golden Ratio is related to the Fibonacci Sequence. This workshop is recommended for students familiar with arithmetic and geometric sequences and solving systems of linear equations.

In this modular origami class, you'll learn how to create beautiful 3D shapes using the water base unit. With this versatile unit, you'll be able to make a variety of geometric shapes including a hexahedron, octahedron, 6-pointed star, flexastar, hollow star, hollow octahedron, and possibly even a butterfly bomb. Our instructor will guide you through each step, helping you to create stunning origami pieces that you can be proud of. There will be a raffle for a book with more advanced modular origami models. You can see the images of the models here. Link: https://share.icloud.com/photos/0f1kQoTsivVX_hDxUtR2XHk4g

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.

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.

This mini-course consists of 3 workshops that cover topics encountered in High School Math Contests such as AMC 10. FREE registration for AMC 10 is included - email us for a registration link.

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.

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

    July/August 2021
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The Online Summer Program is open to all high school students with an interest in learning and doing mathematics above and beyond the regular curriculum.

Interesting topics and intriguing problems will be explored in a casual setting, providing ample challenges for high school students of varying levels. This program emphasizes problem-solving and posing, through a variety of fascinating topics in number theory, algebra, geometry, and more.

This program is appropriate for students wishing to acquire a deeper insight into mathematics, to develop their reasoning and analytical skills, to practice for a math team, or simply to have fun learning and doing wonderful mathematics.

Students are expected to attend the entire 3-week program.

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.

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.

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 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.

This mini-course consists of 3 workshops that cover topics encountered in Middle School Math Contests such as Mathcounts. Students who are currently in MSB/B+ or MSC/C+ should take the advanced level whereas students in MSA/A+ should take the intermediate level. Students who are not currently in our program should contact admin at info@nymathcircle.org.

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 and AMC 8. MSA students should go into the intermediate level, and MSB/MSC students should register for the Advanced level. Students not in our program should take the appropriate placement test.

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 name and turn on their live video 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+: Circle, Numbers and Counting, and Math contest topics

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

    July/August 2020
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  2  3  4  5  6  7  8 

The Online Summer Program is open to all high school students with an interest in learning and doing mathematics above and beyond the regular curriculum.

Interesting topics and intriguing problems will be explored in a casual setting, providing ample challenges for high school students of varying levels. This program emphasizes problem-solving and posing, through a variety of fascinating topics in number theory, algebra, geometry, and more.

This program is appropriate for students wishing to acquire a deeper insight into mathematics, to develop their reasoning and analytical skills, to practice for a math team, or simply to have fun learning and doing wonderful mathematics.

Students are expected to attend the entire 3-week program.

This is a continuation of last semester's course consisting of 2 workshops covering more topics that will be encountered in intermediate level High School Math Contests (such as AMC 10). Students need to be in HSA or higher - new students will have to take the HSA placement test.

This is a REPEAT of the Fall 2019 Workshop and students who attended that workshop should not register for this one.

The theme of this workshop is an introduction to negative and positive whole numbers and zero. The 90-minute workshop will be interactive.  The students (grades 2-4) working alone and in groups will learn the meaning and relative value of integers, and will use number lines to add integers and discover patterns. They will also work on real-world examples involving the addition of integers.

In this interactive class, students will use a number line to add and subtract integers. Students may recognize patterns that allow them to add and subtract integers without the number line. Students will solve integer word problems and play a game involving addition of integers.

This is a new course consisting of 2 workshops that cover topics encountered in Middle School Math Contests such as MATHCOUNTS. MSA students should go into the intermediate level, and MSB/MSC students should register for the Advanced level. Students not in our program should take the appropriate placement test.

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.

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 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.

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.

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

This is a new course consisting of 2 workshops this semester that cover topics encountered in intermediate level High School Math Contests (such as AMC 10). Students need to be in HSA or higher - new students will have to take the HSA placement test.

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.

The theme of this workshop is an introduction to negative and positive whole numbers and zero. The 90-minute workshop will be interactive.  The students (grades 2-4) working alone and in groups will learn the meaning and relative value of integers, and will use number lines to add integers and discover patterns. They will also work on real-world examples involving the addition of integers.

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.

This is a new course consisting of 3 workshops that cover topics encountered in Middle School Math Contests. Students who have taken or are taking MSB or MSC are welcome to register; other students will have to take the MSB placement test.

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.

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 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.

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.

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, five hours a day. A typical day consists of a class in the morning, followed by lunch (provided by students’ parents), and a class on a different topic in the afternoon. Instructors are very friendly and helpful, and the atmosphere is open and collaborative.

Students are expected to work hard in the program, but also to have fun. Early drop-off (9-10am) and late pick-up (3-6pm) are also available at no added cost. The late pick-up session will consist of mathematical games and videos.

MSA/MSA+: Geometry and Algebra to describe patterns

MSB/MSB+: Math contest topics, and Transformations and Symmetries

MSC/MSC+: Math contest topics, and Graph Theory

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 us at info@nymathcircle.org

      July 2019
Su Mo Tu We Th Fr Sa
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14 15 16 17 18 19 20
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28 29 30 31  1  2  3 
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The Summer Program is open to all high school students with an interest in learning and doing mathematics above and beyond the regular curriculum.

Interesting topics and intriguing problems will be explored in a casual setting, providing ample challenges for high school students of varying levels. This program emphasizes problem solving and posing, through a variety of fascinating topics in number theory, algebra, geometry, and more.

This program is appropriate for students wishing to acquire deeper insight into mathematics, to develop their reasoning and analytical skills, to practice for a math team, or simply to have fun learning and doing wonderful mathematics.

Students are expected to attend the entire 3-week program.

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.

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 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.

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. Gomprecht will cover advanced geometry topics that appear on mathematical olympiads such as USAMO and IMO. 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.

The second part of the course will be given by Dr. Ustinovskiy on Number Theory.

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

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. 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 C Students are expected to have taken pre-calculus and to have 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.

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.

Misha Sklyar will teach "Algebra topics found in USAMO," where we use USAMO questions as a resource for teaching advanced algebra topics. There is a short placement test to identify suitable students.

The second part of the course will be given by Professor Hartung on Probability.

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

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. The AM sessions will cover various elementary topics in Geometry; the PM session will cover the use of algebra to describe patterns.

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.

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.

Late pickup - Mathematical Activities

      July 2018
Su Mo Tu We Th Fr Sa
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The Summer Program is open to all high school students with an interest in learning and doing mathematics above and beyond the regular curriculum.

Interesting topics and intriguing problems will be explored in a casual setting, providing ample challenges for high school students of varying levels. This program emphasizes problem solving and posing, through a variety of fascinating topics in number theory, algebra, geometry, and more.

This program is appropriate for students wishing to acquire deeper insight into mathematics, to develop their reasoning and analytical skills, to practice for a math team, or simply to have fun learning and doing wonderful mathematics.

Students are expected to attend the entire 3-week program.

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. 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 C Students are expected to have taken pre-calculus and to have 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.

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

Jan Siwanowicz will teach "Bases in Mathematical Spaces", looking at how bases occur naturally in different mathematical contexts. Some knowledge of Linear Algebra would be beneficial.

Professor Pogudin from NYU will talk about approximating and representing real-world data with polynomials using, for example, interpolation at cleverly chosen nodes or splines. Students should have a working knowledge of Python.

Students will be required to take a placement test and to provide a reference from a teacher or NYMC instructor to complete registration. Students already taking other classes may take this class as well if they meet the admission standards.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve most of the following: problems.

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 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. Students are expected to be able to solve most of the following: problems.

College Bridge is a new course designed to challenge our most advanced students who plan to take advanced mathematics classes in college. It will provide preparation for the formal theorem/proof approach taken in college by examining underlying structures and developing proof-writing skills.

Misha will teach Complex Variables - we will begin by solving geometry problems using Complex Analysis and will proceed to some well-known theorems and their applications, culminating with the proof of the Fundamental Theorem of Algebra. Dr. Angelika Manhart, an NYU Post-doc, will teach Mathematical Modeling - we will discuss how mathematical models can be used to describe phenomena in the real world and what their limitations are.

Students will be required to take a placement test at home which they can submit by email; they will also be required to provide a reference either from their High School teacher or their NYMC instructor to complete registration. Students already taking other classes may take this class as well if they meet the admission standards.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

      July 2017
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The Summer Program is open to all high school students with an interest in learning and doing mathematics above and beyond the regular curriculum.

Interesting topics and intriguing problems will be explored in a casual setting, providing ample challenges for high school students of varying levels. This program emphasizes problem solving and posing, through a variety of fascinating topics in number theory, algebra, geometry, and more.

This program is appropriate for students wishing to acquire deeper insight into mathematics, to develop their reasoning and analytical skills, to practice for a math team, or simply to have fun learning and doing wonderful mathematics.

Students are expected to attend the entire 3-week program.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve the following: problems.

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. They should be able to solve most of the following: problems.

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 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. Students are expected to be able to solve most of the following: problems.

College Bridge is a new course designed to challenge our most advanced students who plan to take advanced mathematics classes in college. It will provide preparation for the formal theorem/proof approach taken in college by examining underlying structures and developing proof-writing skills. Three instructors will teach three topics (calculus, set theory and abstract algebra) after an introductory session by Larry Zimmerman. Students will be required to take a placement test at home which they can submit by email; they will also be required to provide a reference either from their High School teacher or their NYMC instructor to complete registration. Students already taking other classes may take this class as well if they meet the admission standards.