We will help a mouse and two ants to travel through and around a cube. The journeys reveal a wealth of ideas and serve as an intro to studying nets of cubes.
We will help a mouse and two ants to travel through and around a cube. The journeys reveal a wealth of ideas and serve as an intro to studying nets of cubes.
We'll start off this summer with a lecture on basic test-taking techniques. Students will take the 2018 AMC 8 as a diagnostic test. You can access the problems and solutions from that exam on the AoPS website.
After week one's diagnostic test, we start the official AMC 8 prep portion of the course with an introductory lesson on combinatorics. See the attached documents below for resources used in class that can be helpful for future study.
This week, we'll be using the combinatorial skills from week two to solve more advanced problems in statistics and probability. All handouts and resources should be posted below.
This week, we'll once again be building on our previous knowledge by learning about number theory, the mathematical study of integers. All associated resources used in class should be posted below.
This week, we'll be tackling one of the harder topics on the AMC 8, geometry. Typically, geometry problems appear in the last 5 questions of the exam, but hopefully, after this Sunday's lecture and problem set, students should have a firm grasp on what is expected of them on this portion of the AMC 8. As usual, all associated resources such as lectures notes and problem sheets should be posted below.
During our before-last class, we'll be going over miscellaneous AMC 8 topics such as Venn diagrams, speeds/rates, triangle congruency, and triangle similarity. Students will complete a problem set in-class, helping them review topics taught during the lecture as well as topics covered earlier in the summer. As usual, all associated resources will be posted here after class.
Students will use the mathematical knowledge they have accumulated over the last six weeks to complete a final AMC 8 assessment. As teachers, we will compare the results of this final assessment with those of the diagnostic test to judge our overall performance and identify potential improvements in our curriculum for next summer.
This year we will be starting off with a great worksheet filled with a variety of problems, and we will go through it in teams in competition. cant wait!
Many nontrivial Olympiad problems can be solved by angle chasing. This class we covered inscribed angles, cyclic quadrilaterals, and properties of the orthocenter.
We will return to the fair share problems that we introduced in week 1, by considering what happens when we have to divide among three people. We will also think about the geometry of plane figures and how many places lines will intersect with different figures.
We will be developing logic skills by looking at problems with different colored hats. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.
We will be developing logic skills by looking at problems with different colored hats. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.
We will finish up our review on modular math, learning how to subtract and divide in modular math as well as learning how to prove divisibility rules with modular math.
We will finish up our review on modular math, learning how to subtract and divide in modular math as well as learning how to prove divisibility rules with modular math.
This week, we'll finish up Venn Diagrams by going over any of the challenge problems the students may have had difficulty with. Afterward, we'll begin our exploration of a new topic: Egyptian Multiplication. We'll also explore its relationship with binary numbers.
This week, we'll finish up Venn Diagrams by going over any of the challenge problems the students may have had difficulty with. Afterward, we'll begin our exploration of a new topic: Egyptian Multiplication. We'll also explore its relationship with binary numbers.
To conclude our exploration of Egyptian Fraction Representation, we will complete the Egyptian Fractions part 1 handout and begin Egyptian Fractions part 2. Pages 6-8 EFR part 2 are assigned as homework.
To conclude our exploration of Egyptian Fraction Representation, we will complete the Egyptian Fractions part 1 handout and begin Egyptian Fractions part 2. Pages 6-8 EFR part 2 are assigned as homework.
The Fundamental Theorem of Algebra... Everyone's heard of it. If it's so fundamental then why haven't we seen a proof?! Look no further, we consider complex polynomials and graphing techniques to prove that every complex polynomial has a root.
This week, we'll continue with our exploration of Egyptian Multiplication and Binary Numbers. If we have additional time, we'll go through the Math Kangaroo problems.
This week, we'll continue with our exploration of Egyptian Multiplication and Binary Numbers. If we have additional time, we'll go through the Math Kangaroo problems.
This week we will be continuing what we stared last week and talk more about combinatorics. We will be starting with a brief review of what we spoke about last week, before moving onto completely new problems.
Today we will be starting on one of the most interesting and important topics in mathematics, at least in my opinion. I hope everyone learns something!
To start off the new year we are going to split the class into two competing groups. There will be a variety of problems to work on and it will be up to the teams to organize how they feel is best.
We will go over the winter break geometry homework and review last quarter's material, and do some Olympiad problems from other subjects if time allows.
This week, we'll take a deeper look into what happens when we multiply negative numbers and use what we learn to further our exploration of exponential functions.
This week, we'll take a deeper look into what happens when we multiply negative numbers and use what we learn to further our exploration of exponential functions.
This week we will continue the worksheet from last week and then move onto a worksheet going into the details of the number systems we went over last week.
We continue our unit on graph theory with a handout on graph colorings. We will define what it means to color a graph, connect this to coloring maps (geographically speaking), and prove some bounds on how many colors are needed.
This week we will learn how to convert between fractions and decimals, while also exploring the properties of terminating and non-terminating decimals.
This week we will learn how to convert between fractions and decimals, while also exploring the properties of terminating and non-terminating decimals.
This week, we'll continue with our exploration of exponential functions by using its properties to solve a myriad of problems. If we have extra time, we'll work through some Math Kangaroo problems.
This week, we'll continue with our exploration of exponential functions by using its properties to solve a myriad of problems. If we have extra time, we'll work through some Math Kangaroo problems.
We will continue to explore terminating and non-terminating decimals. WHY do decimals have these properties? How can we write non-terminating decimals as fractions?
We will continue to explore terminating and non-terminating decimals. WHY do decimals have these properties? How can we write non-terminating decimals as fractions?
Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions.
This week, we'll finish up our exploration of exponential functions by finish the remaining challenge problems. Afterward, we'll solve some Math Kangaroo problems.
This week, we'll finish up our exploration of exponential functions by finish the remaining challenge problems. Afterward, we'll solve some Math Kangaroo problems.
We will write and define sequences and numbers through explicit and recursive definitions. We will also explore arithmetic sequences and how we can generalize the sum of n-terms in the sequence.
We will write and define sequences and numbers through explicit and recursive definitions. We will also explore arithmetic sequences and how we can generalize the sum of n-terms in the sequence.
Today we will be investigating some ideas in probability in combination with some familiar ideas in geometry. We think today's handout will be great for those that found our previous topics less than exciting compared to usual. We hope that these probability problems will be a good change of pace!
We introduce the concept of metrics using a motivating example: the taxicab metric. This worksheet is especially useful for all those of you who are part time students and part time taxi drivers in New York City.
We introduce the taxicab metric, a new way of measuring distance in Euclidean space. We will study its properties and figure out how it relates to the Euclidean metric.
This week, we will begin by working through the remaining math kangaroo problems in the packet. Afterward, we'll begin our exploration of the world of polyhedra.
This week, we will begin by working through the remaining math kangaroo problems in the packet. Afterward, we'll begin our exploration of the world of polyhedra.
Hello everyone! This week we will be working on some problems that have to do with number theory! Number theory is a very important subject in math and is considered one of the most difficult!
We use the first part as motivation to define metrics in general. We talk about a few different examples and introduce the notion of convergence of a series.
We generalize different notions of distances, as motivated by the taxicab distance, into something called a metric space. We then discuss convergence of sequences in metric spaces.
This week we are continuing our problems on the Chinese Remainder Theorem (CRT) along with a small introduction to ‘if and only if' proofs within the context of remainders and divisibility.
This week we are continuing our problems on the Chinese Remainder Theorem (CRT) along with a small introduction to ‘if and only if' proofs within the context of remainders and divisibility
In economics, the Gini index is a measure intended to represent income inequality. We will take a mathematical approach to the study of the Gini index.
This week we are continuing some more on divisibility with problems around the greatest common divisor as well as Euclid's division algorithm. The handout is attached below.
Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.
Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.
We finished up the first part of our exploration of Polyhedra and went through the Math Kangaroo problems. This week, we'll explore a new topic: Sets and Venn Diagrams.
We finished up the first part of our exploration of Polyhedra and went through the Math Kangaroo problems. This week, we'll explore a new topic: Sets and Venn Diagrams.
Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.
This week will start off by learning about the difference between a set and a list as well as some new notation to learn about some special sets such as the empty set and the set of natural numbers.
This week will start off by learning about the difference between a set and a list as well as some new notation to learn about some special sets such as the empty set and the set of natural numbers.
We'll define the most common lattice and get some results relating regions to lattice points. We'll also see an application to Polya's Orchard problem.
We explore the field of Incidence Combinatorics, learning about the Szemeredi-Trotter Theorem, sum-product estimates, and Erdos's unit and distinct distances problems.
This Sunday, we will continue with our exploration of sets by practicing with the concepts we have learned so far, learning about cardinality, and potentially attempting some challenging problems.
This Sunday, we will continue with our exploration of sets by practicing with the concepts we have learned so far, learning about cardinality, and potentially attempting some challenging problems.
This week we introduce some general ideas about functions and proofs.
As a friendly reminder, please change your zoom profile name to your actual ORMC registered name (this will help us identify you at the beginning of class)!
We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.
We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.
We explore the field of Incidence Combinatorics, learning about the Szemeredi-Trotter Theorem, sum-product estimates, and Erdos's unit and distinct distances problems.
We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.
This week, we'll finish up the final challenge problem in the first part of our exploration of sets and afterward, begin exploring the connection between sets and Venn DIagrams.
This week, we'll finish up the final challenge problem in the first part of our exploration of sets and afterward, begin exploring the connection between sets and Venn DIagrams.
This week we introduce some ideas about area approximation, which is very useful in calculus. After this week we will have at least two handouts on one my favorite topics in math: graph theory!
This Sunday we are working on some graph theory and geometry problems, with a bit of area approximation remaining from last week.
As a friendly reminder please change your zoom profile name to your actual ORMC registered name (this will help us identify you at the beginning of class)!
Sequences are a fundamental part of advanced mathematics. We continue our study of metric spaces from last quarter by using them to define and study sequences.
We will define what it means for a sequence to converge in different metric spaces. We will explore many different examples like convergence with the taxicab metric or the discrete metric.
This week we'll go through the challenge problems in the second sets handout and then take a short quiz on everything we've learned so far. If we have extra time, we'll work on some Math Kangaroo problems and Futoshiki puzzles.
This week we'll go through the challenge problems in the second sets handout and then take a short quiz on everything we've learned so far. If we have extra time, we'll work on some Math Kangaroo problems and Futoshiki puzzles.
How can probability be applied to more than dartboards, dice, and coins? Genetics! Today we will explore how we can use probability in biological applications to figure out blood types, hair colors, nose shapes, and more!
How can probability be applied to more than dartboards, dice, and coins? Genetics! Today we will explore how we can use probability in biological applications to figure out blood types, hair colors, nose shapes, and more!
We define the notion of a continuous function using limits in arbitrary metric spaces. We apply the Intermediate Value Theorem to a range of functions on the real line.
We will finish our genetics worksheet from last week and then start with a new topic: herd immunity! What needs to happen in a population to reach herd immunity? How can we approach it mathematically?
We will finish our genetics worksheet from last week and then start with a new topic: herd immunity! What needs to happen in a population to reach herd immunity? How can we approach it mathematically?
