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## New AOPS Course: Group Theory

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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## Richard Rusczyk – Problem Solving: A 21st Century Education

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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## New AOPS Precalculus Book!

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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## November 20 – AOPS Linguistics Math Jam

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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## April 4th – LaTeX and Proof Writing Workshop

The 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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## Shopping for Problem Solvers

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.

Among 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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## Alcumus

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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