This course is online and intended for students who have been active in math competitions for a couple of years (obtained mid to high AMC 8 scores up to low to mid AMC 10 scores) or students who have a strong background in algebra and have the drive to learn mathematics beyond the scope of what appears in a typical middle school or high school curriculum.
Is this course for you? Please take this self-assessment test before registering to understand the level of knowledge required for this online course.
|When||4:00pm - 5:30pm CST, Saturdays|
|Who||Most commonly suited for students from 7th grade to 10th grade students, either with some background in competition math or a strong background in algebra.|
|Course Size||Maximum 25 students, minimum of 6|
Spring 2019 Semester:
January: 12, 19, 26
February: 2, 9, 16, 23
March: 2, 9, 30
April: 6, 13
No classes: Mar 16, Mar 23
|Course Structure||The first 45-60 minutes of each class meeting will consist of an interactive lecture and example problems introducing the focal topic for the day. The remaining time will
be reserved for a problem session, giving students a hands-on opportunity to master the skills presented in the lesson. Students will be able to work together in a breakout room,
while the instructor helps moderate the room and give guidance or encouragement when necessary.
Students will be assigned 2-3 problems a week as homework with an expected minimum time requirement of 1-2 hours per week to be able to benefit from the class. However, students should not expect to achieve full mastery of the material by doing only the minimum, and to get the absolute most out of the class they should attempt more problems from the handout daily and seek advice via e-mail. The instructor will seek to respond with a helpful hint in the right direction within 24 hours of receiving an e-mail. In order for the guidance to be most effective, students should be specific on what ideas they have and what they have tried so far with a particular problem.
|Student Support||If students have questions or concerns, they can discuss them with their instructor after class (the instructor will stay online for 30 minutes after the class has ended) as well as by email. Emailed questions will be answered within 24 hours. Parents can help their students by guiding them towards constructing well thought out questions.|
|Curriculum||This course aims to add to a student's toolbox of mathematical skills by introducing them to proof techniques and more advanced notation. Students will be challenged
to generalize and rigorously justify their results, requiring more abstract thought and a more advanced, deeper understanding of the material. While most problems will focus on
numerical results, students are expected to be comfortable working with variables, and will be expected to solve problems and understand formulas involving variables.
Topics will include counting techniques such as permutations, combinations, stars and bars, complementary counting, and the principle of inclusion-exclusion. Basic probability and conditional probability will also be explored, as will recurrence relations. Students will also learn proof techniques such as combinatorial proof and the pigeonhole principle. Other topics may be covered as time permits.
|Additional Benefits||This class will help students hone their problem solving skills and equip them with strategies for approaching more abstract problems and concepts. It will also encourage students to rigorously justify their reasoning, improving their technical communication skills as well as their general critical thinking. These are skills that are essential not just to higher level mathematics, but to sciences, engineering, and humanities as well.|