When given a question to answer, many students think only for a few seconds to figure whether they can see a method to answer the question, and give up otherwise. They are habituated to being given “exercises”, questions that test whether you can apply a known method for calculating the answer. But what is one to do when it’s not at all clear what method to use? A “problem” is a question that one does not know (at the outset) how to solve, and which hence appears to be difficult. In contrast to exercises, solving problems requires a very different mindset. You need to take time to patiently explore an unknown terrain, get your hands dirty, investigate what happens if you turn left or turn right, come up with strategies to get to the desired ‘destination’ (the solution), and see where they lead you. You have to learn to cope with failure, to encounter dead ends, to get lost, and keep exploring. All this makes solving problems more difficult than solving exercises, but also more fun. Isn’t hiking in an unknown terrain more fun than doing repetitive exercises in a gym? You can expect surprises, thrilling moments of discovery along with frustrating moments of feeling lost and confused.
In this course aimed at middle school students, we will learn the art of solving problems in mathematics. It will not only prepare you for contests like the Math Olympiad and deepen your understanding of the school curriculum, but also provide you plenty of moments of thrill and discovery where you will learn to use effective strategies to find your own creative solutions to problems. The problems will be drawn from the history of mathematics, from games and puzzles, from math contests and from real world situations.
Topics we will cover will include:
1. Problem Solving Strategies, along with plenty of examples of problems to hone each strategy. Some of the strategies we will cover are — drawing pictures/diagrams, systematic enumeration of possibilities (in the form of lists, tables, trees and graphs), solving simpler instances of the problem, uncovering patterns, making reasonable guesses, experimenting with models, working backwards, writing equations, changing your point of view, looking at extreme values, exploiting parity and symmetry, pigeonhole principle, invariants, geometric transformations, mathematical induction, etc.
2. The World of Mathematical Proofs and Logic: A proof is an argument that establishes the truth of a theorem using logic. We will look at different proof techniques to build creative mathematical arguments. Once you learn the art of proving claims, you will never be satisfied with just memorizing formulas. You will want to know WHY they’re true.
3. Special focus on some of the celebrity numbers (fibonacci numbers, prime numbers, i, pi, e), celebrity theorems (Pythagorean Theorem, etc), and celebrity people (Pythagoras, Euclid, Archimedes, Descartes, Newton, Fermat, Gauss, Euler, Riemann, etc) in mathematics.
Timings and Venue:
Our 8-week summer camp will be held from June 16, 2014 to August 15, 2014.
Classes will be held Mon-Fri from 9 am to noon. If there is enough demand, then we may have classes in the afternoon as well.
The classes will be held in Cupertino, on DeAnza Blvd (near McClellan/DeAnza).
Maximum class size will be 18 students.
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M.S & Ph.D, Electrical and Computer Engineering, Georgia Tech
B.Tech, Aerospace Engineering, IIT Bombay
A half-day summer camp (9 am to noon) will cost 275$ a week. You need not enroll for the full 8 weeks, in which case you will only be charged for the number of weeks you are enrolled in.
Contact Information and Registration Information:
If you have any questions about the program, please send us an email at firstname.lastname@example.org. To register, please fill out this form, or alternatively, please send us the following information by email:
1. Full name of your child
2. Name of school he/she will attend in Fall 2014, and Grade Level
3. Parent’s Email and Address (which will be used only for contacting you with information about our classes, and will not be shared with anyone outside)
4. Number of weeks you expect to enroll your child for (this can be tentative if your summer plans are not fully clear, but please mention the word “tentative” in that case)
5. Names of other math and science programs/classes your child is attending (or has attended) outside of school, in the last one year.