ka March Highlights and 2025 AoPS Online Class Information
jlacosta0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.
Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!
Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.
Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Prealgebra 1
Sunday, Mar 2 - Jun 22
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Prealgebra 2
Tuesday, Mar 25 - Jul 8
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Introduction to Algebra A
Sunday, Mar 23 - Jul 20
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Introduction to Counting & Probability
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Introduction to Number Theory
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Intermediate: Grades 8-12
Intermediate Algebra
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AMC 10 Problem Series
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AMC 10 Final Fives
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Introduction to Programming with Python
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I have seen many posts talking about commonly asked questions, such as finding the value of ,,,, why or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[list]
[*]Firstly, the case of . It is usually regarded that , not because this works numerically but because it is convenient to define it this way. You will see the convenience of defining other undefined things later on in this post.
[*]What about ? The issue here is that isn't even rigorously defined in this expression. What exactly do we mean by ? Unless the example in question is put in context in a formal manner, then we say that is meaningless.
[*]What about ? Suppose that . Then we would have , absurd. A more rigorous treatment of the idea is that does not exist in the first place, although you will see why in a calculus course. So the point is that is undefined.
[*]What about if ? An article from brilliant has a good explanation. Alternatively, you can just use a geometric series. Notice that
[*]What about ? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[/list]
Hopefully all of these issues and their corollaries are finally put to rest. Cheers.
2nd EDIT (6/14/22): Since I originally posted this, it has since blown up so I will try to add additional information per the request of users in the thread below.
INDETERMINATE VS UNDEFINED
What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that is an indeterminate form.
But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of , or , obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function given by the mapping is undefined for . On the other hand, is undefined because dividing by is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.
WHEN THE WATERS GET MUDDIED
So with this notion of indeterminate and undefined, things get convoluted. First of all, just because something is indeterminate does not mean it is not undefined. For example is considered both indeterminate and undefined (but in the context of a limit then it is considered in indeterminate form). Additionally, this notion of something being undefined also means that we can define it in some way. To rephrase, this means that technically, we can make something that is undefined to something that is defined as long as we define it. I'll show you what I mean.
One example of making something undefined into something defined is the extended real number line, which we define as So instead of treating infinity as an idea, we define infinity (positively and negatively, mind you) as actual numbers in the reals. The advantage of doing this is for two reasons. The first is because we can turn this thing into a totally ordered set. Specifically, we can let for each which means that via this order topology each subset has an infimum and supremum and is therefore compact. While this is nice from an analytic standpoint, extending the reals in this way can allow for interesting arithmetic! In it is perfectly OK to say that, So addition, multiplication, and division are all defined nicely. However, notice that we have some indeterminate forms here which are also undefined, So while we define certain things, we also left others undefined/indeterminate in the process! However, in the context of measure theory it is common to define as greenturtle3141 noted below. I encourage to reread what he wrote, it's great stuff! As you may notice, though, dividing by is undefined still! Is there a place where it isn't? Kind of. To do this, we can extend the complex numbers! More formally, we can define this extension as which we call the Riemann Sphere (it actually forms a sphere, pretty cool right?). As a note, means complex infinity, since we are in the complex plane now. Here's the catch: division by is allowed here! In fact, we have where and are left undefined. We also have Furthermore, we actually have some nice properties with multiplication that we didn't have before. In it holds that but and are left as undefined (unless there is an explicit need to change that somehow). One could define the projectively extended reals as we did with , by defining them as They behave in a similar way to the Riemann Sphere, with division by also being allowed with the same indeterminate forms (in addition to some other ones).
Due to excessive spam and inappropriate posts, we have locked the Prealgebra and Beginning Algebra threads.
We will either unlock these threads once we've cleaned them up or start new ones, but for now, do not start new marathon threads for these subjects. Any new marathon threads started while this announcement is up will be immediately deleted.
ki Basic Forum Rules and Info (Read before posting)
jellymoop368
NMay 16, 2018
by harry1234
f(Reminder: Do not post Alcumus or class homework questions on this forum. Instructions below.)f
Welcome to the Middle School Math Forum! Please take a moment to familiarize yourself with the rules.
Overview:
[list]
[*] When you're posting a new topic with a math problem, give the topic a detailed title that includes the subject of the problem (not just "easy problem" or "nice problem")
[*] Stay on topic and be courteous.
[*] Hide solutions!
[*] If you see an inappropriate post in this forum, simply report the post and a moderator will deal with it. Don't make your own post telling people they're not following the rules - that usually just makes the issue worse.
[*] When you post a question that you need help solving, post what you've attempted so far and not just the question. We are here to learn from each other, not to do your homework. :P
[*] Avoid making posts just to thank someone - you can use the upvote function instead
[*] Don't make a new reply just to repeat yourself or comment on the quality of others' posts; instead, post when you have a new insight or question. You can also edit your post if it's the most recent and you want to add more information.
[*] Avoid bumping old posts.
[*] Use GameBot to post alcumus questions.
[*] If you need general MATHCOUNTS/math competition advice, check out the threads below.
[*] Don't post other users' real names.
[*] Advertisements are not allowed. You can advertise your forum on your profile with a link, on your blog, and on user-created forums that permit forum advertisements.
[/list]
As always, if you have any questions, you can PM me or any of the other Middle School Moderators. Once again, if you see spam, it would help a lot if you filed a report instead of responding :)
Marathons!
Relays might be a better way to describe it, but these threads definitely go the distance! One person starts off by posting a problem, and the next person comes up with a solution and a new problem for another user to solve. Here's some of the frequently active marathons running in this forum:
[list][*]Algebra
[*]Prealgebra
[*]Proofs
[*]Factoring
[*]Geometry
[*]Counting & Probability
[*]Number Theory[/list]
Some of these haven't received attention in a while, but these are the main ones for their respective subjects. Rather than starting a new marathon, please give the existing ones a shot first.
In a complete graph with vertices, each edge has one of the colors ,, or . For each , if the vertices can be divided into groups such that any two vertices connected by an edge of color are in different groups, find the minimum possible value of .
Hey, I was just wondering if anybody here takes the MathCon Competition or not. And if so, what's the best way to get the highest score possible?
Thank you! and pls respond
update: it did NOT go well i got 220:sob:
i was not locked in and was going hella slow
Hey guys
im in new jersey a third grader who got 12 on amc 8. I want to make mop in high school and mathcounts nationals in 6th grade is that realistic how should I get better
Multiple states have announced their top students who will advance to the 2025 MATHCOUNTS National Competition in May:
• From Alabama: Henry Gladden of Mobile, Austin Lu of Birmingham, Jessie Shi of Vestavia, and Minlu Wang-He of Auburn.
• From Arkansas: Ryan Fan of Fayetteville, Vivek Kalyankar of Fayetteville, Evan Ning of Fayetteville and Charles Yao of Conway.
• From Connecticut: Hayden Hughes of Newtown, Ethan Shi of Riverside, Alex Svoronos of Greenwich and Elaine Zhou of Hamden.
• From the Department of Defense: Narmin Guliyeva of Ankara, Turkey; Taeyul Kim of Manana, Bahrain; Nathan Liang of Wiesbaden, Germany; and Lucas Sze of Okinawa, Japan.
• From Hawaii: Taehwan Jeon, Hilohak Kwak, Isaac Qian and Thien Tran, all from Honolulu.
• From Kansas: Haidan Anderson & Jayden Xue of Overland Park, Christopher Spencer of Manhattan, and Ruby Jiang of Lawrence.
• From Maine: Ana Kanitkar & Connor Kirkham of Falmouth, Anna McClary of Hermon and Poppy Sandin of Bar Harbor.
• From Massachusetts: Eric Huang of Acton, Shlok Mukund & Brandon Ni of Lexington, and Soham Samanta of Medford.
• From Missouri: Lucas Lai of Columbia, Kevin Shi of St. Louis, Charles Yong & Jay Zhou of Chesterfield.
• From Montana: Titus Gilder of Missoula, Otis Heggem of Billings, Kaleb Houtz of Great Falls and Evan Newcomer of Missoula.
• From Nevada: Solomon Dumont of Las Vegas, Aaron Lei of Reno, Leeoz Nebat of Henderson and Maxwell Tsai of Las Vegas.
• From New Mexico: Mark Goldman, Daniel He, Iris Huang and Patrick McArdle, all from Albuquerque.
• From New York: Derrick Chen of Great Neck, Victor Yang of Great Neck, Hanru Zhang of Jericho and Ryan Zhang of Jericho.
• From Rhode Island: Kahlan Anderson of the Wheeler School, Julian Bernhoft & Colin Hegstrom of Providence, and Theodora Watson of Barrington.
• From South Carolina: Yukai Hu of Elgin, Justin Peng of Clemson, Geonhoo Shim of Columbia, and Aaron Wang of Mount Pleasant.
• From South Dakota: Seth Chaplin & Maxwell Wang of Sioux Falls, Laukia Gundewar of Aberdeen, and Cohwen Heimann of Aberdeen.
• From Texas: Shaheem Samsudeen & Ayush Narayan of Plano, Nathan Liu of Richardson, and James Stewart of Southlake.
• From Vermont: Mohid Ali of South Burlington, Vivek Chadive of South Burlington, Joshua Kratze of St. Johnsbury and Albert Zhang of South Burlington.
• From Wisconsin: August Reeder & Lucy Chen of Fitchburg, Junhao Feng of Milwaukee, and Jiyan Singh of River Hills.
===
Updated on 3/15/2025:
• From Colorado: Noah Liu, Christopher Zhu, Neo Luo, and Andrew Zhao.
• From Florida: Arnav Bhatia, Gnaneswar Peddesugari, Edwin Gao, and Rananjay Parmar.
• From Indiana: Roland Li, Hrishabh Bhowmik, Sophia Chen, and Arjun Raman.
• From Kentucky: Sri Shubhaan Vulava, Joyce Liu, Victor Gong, and Brandon Tedja.
• From Maryland: Eric Xie, Angie Zhu, Roger Huang, and Leo Su.
• From Michigan: Arnav Vunnam, Eric Jin, Akshaj Malraj, and Chaithanya Budida.
• From Minnesota: Ahmed Ilyasov, Will Masanz, Anshdeep Singh, and Branden Qiao.
• From New Jersey: Ethan Imanuel, Advait Joshi, Jay Wang, and Easton Wei.
• From North Carolina: Shivank Chintalpati, Steven Wang, Lucas Li, and Leo Hong.
• From Ohio: Henry Lu, Andy Mo, Archishmen Dey, and Caleb Tan.
• From Oregon: Sophia Han, Kevin Cheng, Garud Shah, and Ryan Zhang.
Consider a regular pentagon. Choose 3 points along the perimeter of the pentagon, and form a triangle with those 3 points. What is the probability that this triangle contains the center of the pentagon.
Whenever possible, I will be posting problems twice a week! They will be roughly of AMC 8 difficulty. Have fun solving! Also, these problems are all written by myself!