Advanced Topics in Math
Advanced Topics in Mathematics (ATM)
Instructor: Dylan Frake
Contact info: dtfrake@gmail.com
About Me
I am an 11th grader at Cupertino High School who deeply enjoys competitive math. Having loved numbers all my life, I like competition math because it makes you think deeply about many problems. I have been a TA for Math Olympiads for five years and have assisted Mr. G in correcting, teaching, and writing numerous problems in that time. My biggest achievement in competitive math was achieving honorable mention in the Spring 2023 USAJMO. Besides math, I enjoy hiking, bike riding, running, and board/card games.
SCHEDULE
Classes will be every Thursday at Creekside Park from 8:00-9:00 PM. Classes will follow the Math Olympiads calendar. Advanced Topics in Math is currently only available to Cupertino students!
Note
If you took ATM last year (taught by Arthur Chen), then this class will be very similar to that, but all the problems and homework will be brand new.
Class Description
This class teaches a wide variety of difficult high-school level math concepts and problem solving. Each class, I will hand out one problem and give students 15-20 minutes to work on it. Then, I will go over the solution for the remainder of the class. Finally, one homework problem related to the one done in class will be assigned each week, and its solution will be sent out the following Wednesday.
Besides allowing students to grow in mathematical problem-solving ability, this class is aimed at preparing students for the following AMC contests:
● AMC 10: In this contest, you have 75 minutes to solve 25 multiple-choice questions, ranging in difficulty from straightforward to difficult. Only 10th graders and below can take this contest, and this contest only covers material up to 10th grade level.
● AMC 12: Just like the AMC 10, you have 75 minutes to solve 25 multiple-choice questions. However, the questions are slightly harder, and concepts like trigonometry and logarithms are introduced. All high-schoolers can take this contest.
● AIME: If you do well on the AMC 10 or AMC 12, you are invited to take this contest, where three hours are given to solve 15 short-answer questions (each answer is an integer from 0 to 999). The questions are much harder than the AMC 10 or the AMC 12; they range from fairly hard to extremely challenging. If you do well enough on the AMC 10/12 combined with the AIME, then you are invited to take the USA(J)MO, a proof-writing exam.It also helps in preparing you for almost all other math contests, like the Berkeley Math Tournament (BMT), American Regions Mathematics League (ARML), and the Harrison Chen Memorial Math Competition (HCMMC).
Problem Difficulty
Problems covered will range in difficulty between late AMC-10 level (#21-25) to mid AIME level (#6-9).
Topics Covered
Concepts covered will be broken down into four main categories: Algebra, Counting and Probability, Number Theory, and Geometry. There will be a roughly equal amount of problems from each category.
Expectations
As you all have other commitments besides this class, homework is optional. However, to get the most out of this course, it is strongly encouraged that you try the homework assignments.
Note: As mentioned earlier, the problems covered both in class and at home are HARD! Hence, it is fine if you get only 20%, 10%, or even none of them correct, and getting even half of them correct is very good! Most people who took this class last year were not able to solve most of the problems. What matters is that during class you keep trying ideas on each problem for the full 15-20 minutes until I show the solution, and that you do the same for the homework questions.
Finally, you are encouraged (but not required) to take the AMC 10/12 and AIME (if you qualify).
Who Should Take this Class?
ATM is targeted towards high schoolers or extremely motivated middle schoolers. I would only recommend a middle schooler to take this class if they felt comfortable taking ATM last year, or if they feel confident in qualifying for the AIME. Otherwise, I would recommend taking standard Math Olympiads taught by Mr. G or Brandon’s Mathematical Explorations.