PPT-Fermat’s Principle of Infinite Descent

and Other Forms of Induction Proof Sanghoon Lee amp Theo Smith Honors 391A Mathematical Gems Prof Jenia Tevelev March 11 2015 How does induction work 1 Base Case Show the First Step Exists. How Yep Take derivative set equal to zero and try to solve for 1 2 2 3 df dx 1 22 2 2 4 2 df dx 0 2 4 2 2 12 32 Closed8722form solution 3 26 brPage 4br CS545 Gradient Descent Chuck Anderson Gradient Descent Parabola Examples in R Finding Mi This can be generalized to any dimension brPage 9br Example of 2D gradient pic of the MATLAB demo Illustration of the gradient in 2D Example of 2D gradient pic of the MATLAB demo Gradient descent works in 2D brPage 10br 10 Generalization to multiple Gradient descent is an iterative method that is given an initial point and follows the negative of the gradient in order to move the point toward a critical point which is hopefully the desired local minimum Again we are concerned with only local op PRINCIPLE 2UNEXPECTED PRINCIPLE 3COPRINCIPLE 4CREDIBLE PRINCIPLE 5EMTINAL PRINCIPLE 6 SORIES Raymond Flood. Gresham Professor of Geometry. Newton’s . Laws. Tuesday . 21 October 2014 . Euler’s Exponentials. Tuesday . 18 November 2014 . Fourier’s Series. Tuesday 20 January 2015 . Möbius. Dszquphsbqiz. . Day . 9. Announcements:. Homework 2 due now. Computer quiz Thursday on chapter 2. Questions?. Today: . Finish . congruences. Fermat’s little theorem. Euler’s theorem. Important . Geometrical optics. All of geometrical optics boils down to…. Law of reflection:. q. i. normal. n. 1. n. 2. q. r. q. t. Law of refraction. “Snell’s Law”:. Easy to prove by two concepts:. Huygens’ principle. Presenter: . Hanh. Than. FLT video. http://www.youtube.com/watch?v=SVXB5zuZRcM. Pierre de Fermat. Pierre de Fermat. . (17 August 1601– 12 January 1665): . . a French lawyer and an amateur mathematician.. Series. Find sums of infinite geometric series.. Use mathematical induction to prove statements.. Objectives. infinite geometric series. converge. limit. diverge. mathematical induction. Vocabulary. In Lesson 12-4, you found partial sums of geometric series. You can also find the sums of some infinite geometric series. An . Randomized Primality Testing. Carmichael Numbers. Miller-Rabin test. MA/CSSE 473 Day 08. Student questions. Fermat's Little Theorem. Implications of Fermat’s Little Theorem. What we can show and what we can’t. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. The purpose of this section is to discuss sums that contain infinitely many terms. Gresham Professor of Geometry. Newton’s . Laws. Tuesday . 21 October 2014 . Euler’s Exponentials. Tuesday . 18 November 2014 . Fourier’s Series. Tuesday 20 January 2015 . Möbius. . and his band . Gresham Professor of Geometry. Newton’s . Laws. Tuesday . 21 October 2014 . Euler’s Exponentials. Tuesday . 18 November 2014 . Fourier’s Series. Tuesday 20 January 2015 . Möbius. . and his band . David J. Stucki. Alerts. FYS announcement.... Pythagorean Triples & Euclid's Primes due today. Archimedes . calculations.... This worksheet will be due next Wednesday!. 12 of 40 . FYE . reports (7 days left).