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| | Wednesdays from 9 pm-10:30 pm (Eastern Standard Time) | | Wednesdays from 9 pm-10:30 pm (Eastern Standard Time) |
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| − | ==Course Description==
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| − | From the CTY Online Catalog:
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| − | This course is a very challenging problem-solving course for students who have participated in the AMC and are eager to take their skills to the next level.
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| − | In one part of the course, general problem-solving techniques are introduced, such as:
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| − | * the pigeon hole principle
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| − | * invariance principle
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| − | * extremal principle
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| − | * induction principle
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| − | * systematic checking
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| − | Some of these general problem-solving paradigms enjoy applicability outside of mathematics. In the other part of the course, these metholds are discussed in specific mathematical contexts such as:
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| − | number theory
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| − | combinatorics, sequences
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| − | polynomials
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| − | In tackling non-routine problems whose solutions are not immediate, students are encouraged to approach problems from different angles. A further goal of this course is to improve a student's ability to write proofs. Students attend weekly virtual classroom sessions to discuss challenging problems.
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| − | Each topic covered in the course is independent of the other topics. One topic is taught a week on a continuous repeating basis. Students will not necessarily start with "Topic 1" in their first week of enrollment, but all topics will be covered in a 3-month enrollment. When all topics are covered, a student then takes the final exam.
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