Posts Tagged ‘AOPS’

The Art of Problem Solving has just announced a new course starting this fall in Group Theory.   Like all of the AOPS courses this is sure to be an excellent offering.   Here is the AOPS course description:

Group theory is the study of symmetry. Objects in nature (math, physics, chemistry, etc.) have beautiful symmetries and group theory is the algebraic language we use to unlock that beauty. This example-driven course will focus specifically on building groups from other groups, ways that groups can act on various sets, and using the tools of group theory to construct fields.

Group theory is the gateway to abstract algebra, one of the two core branches of higher mathematics. (Just as calculus is the gateway to the other core branch, analysis.) Algebra and analysis together hold the tools for most areas of advanced mathematics, from geometry to topology to applied mathematics and beyond. Algebra is what tells us (among many other things) that you can’t trisect an angle, that there are finitely many regular polyhedra, and that there is no closed form for solving a quintic, for example. In this class we will get a glimpse of the mathematics underlying these famous questions.

Note: We will not assume prior knowledge of what a group is. Group theory is a topic that is generally reserved for a sophomore or junior level abstract algebra course, but this class attempts to present the most important concepts and examples on a level appropriate for very strong high school students. The goal of this class, as with all of our classes, is to provide a much richer curriculum that challenges students who are otherwise exhausting the subjects available to them.


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Almost two years ago many of us were fortunate enough to hear Richard Rusczyk, the founder of The Art of Problem Solving speak here at our Math Circle.  Now for those who may have missed that memorable talk or for those who would like to share it with others, there is a video of  a very similar talk given by Richard at the prestigious Math Prize for Girls.

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Richard Rusczyk’s long awaited Precalculus Book is now available!  Here is the description:

Precalculus is part of the acclaimed Art of Problem Solving curriculum designed to challenge high-performing middle and high school students. Precalculus covers trigonometry, complex numbers, vectors, and matrices. It includes nearly 1000 problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions such as the American Invitational Mathematics Exam and the USA Mathematical Olympiad. Almost half of the problems have full, detailed solutions in the text, and the rest have full solutions in the accompanying Solutions Manual.

As with all of the books in Art of Problem Solving’s Introduction and Intermediate series, Precalculus is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which new techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text.

About the authors: Richard Rusczyk is the founder of http://www.artofproblemsolving.com. He is co-author of the Art of Problem Solving, Volumes 1 and 2 and Intermediate Algebra, and author of Introduction to Algebra and Introduction to Geometry. He was a national MATHCOUNTS participant, a three-time participant in the Math Olympiad Summer Program, a perfect scorer on the AIME, and a USA Math Olympiad Winner. The solutions are co-authored by Naoki Sato. He is a curriculum developer and the director of WOOT at Art of Problem Solving. He won first place in the 1993 Canadian Mathematical Olympiad and is a 2-time medalist at the International Mathematical Olympiad. He has been Deputy Leader of the Canadian IMO team three times.

ISBN: 978-1-934124-16-1
Text: 528 pages. Solutions: 272 pages.
Paperback. 10 7/8 x 8 3/8 x 1 1/16 inches.

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The Art of Problem Solving is hosting a free for Math Jam those interested in linguistics:

 Date: Nov 20 (Fri)
Time: 7:30 PM Eastern
Instructor: Christina Skelton
Two linguists discuss the the Comparative Method, a linguistic theory which describes how languages change over time, and use it to demonstrate that English is related to some exotic languages you never would have imagined, like Sanskrit and Hittite.


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180px-latex_logosvg1The math skills learned in our math circles have been helpful to students hoping to improve their scores on the AMC tests or the AIME.  But to be successful in olympiads or to answer the questions from USAMTS or AOPS requires that students can also articulate their problem solving in the form of proofs.

A preferred tool for writing proofs and indeed for writing many scientific papers is the typesetting system called LaTeX.  Whether you are a student who has never tried LaTeX and proof writing or you just want to improve your skills, this Saturday’s workshop is for you.  Even younger students will enjoy how easy it is to create very advanced mathematical expressions by mastering LaTeX.

Here is what our friends at the Art of Problem Solving have to say about LaTeX:

The LaTeX typesetting system (pronounced “Lay-Tek” or “Lah-Tek”) is widely used to produce well-formatted mathematical and scientific writing. With LaTeX, it is very easy to produce expressions like

Nearly every serious student of math and science will use LaTeX frequently.

In the second hour of the Metroplex Math Circle we will have a special private screening and discussion of the documentary Hard Problems.  If you have not seen it, Hard Problems recounts the selection and success of the US team at the 2006 International Mathematics Olympiad.  In this excellent film you will see many friends of MMC including Dr. Zuming Feng.

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With the holidays approaching many of you may be looking for gift ideas for young problem solvers.  A good place to start is the excellent Bookstore run by The Art of Problem Solving.

hard-problemsAmong the many excellent resources are two that have been featured on this site that might make particularly good gifts.  The DVD Hard Problems tells the story of the 2006 IMO team.  The profiles of the six team members and the story of how they qualified for and competed in the IMO should encourage any aspiring problem solver.

We have also mentioned an excellent new book by Dr. Titu Andreescu called Problems from the Book.  This book has received excellent reviews and is one of the most searched items on the Metroplex Math Circle site.

If you have any other recommendations for appropriate gift ideas please feel free to post them to the comments.

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Our very good friends at the Art of Problem Solving have worked very hard to develop a new online learning system called “Alcumus.”  Alcumus is a game that students can play to compete against themselves, compare their progress on the leader’s board and identify gaps or weaknesses in their math preparation.

Alcumus features over 1100 different problem representing a wide variety of subjects.  In addition, the Art of Problem Solving instructors have developed over 60 video tutorials to help students better understand the subjects they are likely to see on contests like AMC 8, AMC 10 and AMC 12.

Alcumus is currently free to members of the Art of Problem Solving community so login or create an account today.


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Our friends at Art of Problem solving hosted a Math Jam interview with Matt McGann, Associate Director of Admissions and Kiran Kedlaya, Associate Professor of Mathematics at MIT.  Here are a couple of highlights and a link to the full transcript:

Q:  What is MIT’s admission rate?

A: Last year, if memory serves, we received 13,396 applications and admitted 1589 students, for an admission rate of about 11.9%. But remember, just the admission rate tells you very little about the admissions process or the quality of the school.

Q:  Where are the math major students go and what do they do once they graduated from MIT?

A: Our math majors choose a variety of career paths. Some pursue PhDs in math and continue in academic careers; some do likewise in related subjects (physics, computer science). Finance is a popular option, as are various IT-oriented careers.

Q:  What are some of the research opportunities available during the vacations?

A:MIT has an extensive Undergraduate Research Opportunities Program (UROP), through which undergrads can get funding to do research projects with faculty either during vacations or academic terms. The burden is on the student to find a faculty mentor, but many faculty participate in the program. (I’ve advised maybe 10 students in this way.)

Q:  What kinds of things make an undergraduate application “jump off the page” during the MIT admissions process? In other words, what makes someone’s application stand out from the rest of the applicants who are most likely very studious as well?

A:  I know you’re very anxious to have this question answered! It’s a tough question, and one that doesn’t have an easy answer. Lots of things can make an application stand out. A 42 at the IMO would be great, but it can be many, many things. Some students stand out for their personality, or their extra-curricular accomplishments, or for overcoming a challenging situation. But all of these students must have strong academics and an alignment with MIT’s mission and culture. For more detailed thoughts on this, I’d read the blogs at our website, http://mitadmissions.org

Q:  Not everyone gets to IMO. Are USAMO qualifiers also considered for admission?

A:  Of course! And even non-USAMO qualifiers!

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Our good friends at the Art of Problem Solving are hosting a Math Jam this Thursday with representatives from MIT to discuss their math programs and what they are looking for in applicants. MIT has done a particularly good job in recent years of recruiting top math talent including friends of MMC like Ivan Borsenco.

Math Jams are a free online chat format sponsored by AOPS. You will want to go to the site a bit before the start to make sure your computer is set up properly. If you cannot make this time a full transcript of the event is generally available the next day.

Date: Oct 23 (Thu)
Time: 7:30 PM Eastern
Instructor: Matt McGann

Matt McGann, Associate Director of Admissions at MIT, and Kiran Kedlaya, Associate Professor of Mathematics, will discuss MIT and the admissions process.

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The first Math Circle of the 2008-2009 season succeeded on multiple levels. In its third year, Metroplex Math Circle finally exceeded the capacity of its current (large) lecture hall with over 100 students, teachers and parents in attendance. We were pleased to see many friends return, but even more new faces who were discovering Math Circles for the first time.

Comparative Advantage

Richard Rusczyk’s talks also exceeded all expectations. His first lecture was on the concept of comparative advantage and the benefits of free trade which many adults fail to grasp. Like many lessons in Math Circle, Mr. Rusczyk allowed the students to discover the meaning of the concept by playing out a game between two imagined countries. “Games” and the importance of “play” would be stressed throughout the day.

Option Pricing

The second segment introduced the audience to the principles of market prices and call options. With the current turmoil on Wall Street, parents were just as interested in this topic as the students. Mr. Rusczyk presented the students with a problem that he would use when he was recruiting for D.E. Shaw. Only the best students from elite schools ever made it to this stage in the interview process and apparently all but a handful (accomplished problem solvers) ever answered the problem correctly.


In his final lecture, Richard Rusczyk sent students, parents and teachers home with a great deal to consider. He spoke very frankly and persuasively about the short comings of the standard school curriculum. But rather than just criticize, he also laid out concrete ways that students, parents and teachers can all improve the situation.

We won’t attempt to summarize this excellent talk particularly since an early version of the slides can be accessed below. However, a couple of themes should be highlight. First was his emphasis on play and the importance of giving students the time and freedom to work on challenging problems. A second theme was the importance of building a math community for young problem solvers, and the central role that a Math Circle can play. Finally, Mr. Rusczyk endorsed what many of us have already discovered, that Dr. Titu Andreescu’s books and leadership have been critical to the Renaissance in global problem solving.

Richard Rusczyk has committed himself to fulfilling the principles in his presentation by founding the Art of Problem Solving. Please take the time to see his presentation and the other excellent resources he has collected and developed.

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