Even though I have some prior background in mathematics and problem solving, this course was still challenging - and that is why it is so great. Full disclosure: I was an alternate (a few years ago .
Then see how parity leads naturally into graph theory, a playground for investigation that has nothing to do with conventional graphs....Having used symmetrical principles to tackle problems in earlier lectures, take a closer look at this powerful tactic. So - an excellent course for those with a particular interest in this area. Publisher: JOHN WILEY & SONS, INC. . Discover how this granddaddy of all problem-solving tactics-which involves quantities and qualities that stay unchanged-can be used almost anywhere and encompasses such ideas as symmetry and parity....What is the largest number that is the product of positive integers whose sum is 1,976? In the first lecture the professor presented a pill problem and its supposed solution. It is an excellent and detailed discussion of approaches to solving the sort of math problems tackled by high school math teams, and many fascinating (and some not-so-fascinating) problems are described and solved in detail. In my opinion, in the "hard"sciences at least, if you are not presented with problems that require deep thinking and problem-solving struggle then you are not really learning. Martin Gardner's airplane problem and a question about how many times a laser beam reflects between two intersecting mirrors help you warm up to a solution....Focusing on geometry, consider some baffling problems that become almost trivial once you know how to apply rotations, reflections, and other geometric transformations of your normal point of view. Try to decipher a puzzling reply to a census question, and determine whether three jumping frogs will ever land on a given point....Delve deeper into the psychological aspects of problem solving-especially concentration, creativity, and confidence-and ways to enhance them. Math texts, online classes, and more
Suitable for grades 6–12. Even though I have some prior background in mathematics and problem solving, this course was still challenging - and that is why it is so great. These typically occur in recursive situations, where a complicated structure emerges from a simpler one....Continuing your use of inductive proof, calculate the probability that a randomly chosen number in Pascal's triangle is even. Professor Zeitz is certainly expert and enthusiastic. So if you want a real learning opportunity try this course. In technical skills, he is undoubtedly very well prepared to coach the math Olympiad team and to teach mathematical puzzle seminars. Paul Zeitz is Professor of Mathematics at the University of San Francisco. Learn that, amazingly, the answer is yes....In a lecture that Professor Zeitz compares to walking along a mathematical cliff edge, use the pigeonhole principle to find patterns within apparently random and mind-bogglingly large structures. One is the "puppies and kittens" exercise, a series of moves and countermoves that can be taught to children but that is amazingly hard to play well; that is, until you uncover its secrets with symmetry and a few other ideas....Take your problem-solving skills to extremes on a variety of mathematical puzzles by learning how to contemplate the minimal or maximal values in a problem. My course is all about problems.Dr. This "extreme" principle is a simple idea, but it has the nearly magical ability to solve hard problems almost instantly....Detour into the hidden world of problem solvers-young people and their mentors who live and breathe nontraditional, nontextbook mathematics such as what you have been studying in this course. Tackle this question from the 1976 International Mathematical Olympiad with the method of algorithmic proof, in which you devise a sequence of steps-an algorithm-that is guaranteed to solve the problem....Draw on your skills developed so far to solve a tricky problem about marbles colliding on a circular track.
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