A Brief Introduction to Olympiad Inequalities

Evan Chen (April 30, 2014) A Brief Introduction to Olympiad Inequalities Example 1.2 Prove that a2 + b2 + c2 ab+ bc+ caand a4 + b4 + c4 a2bc+ b2ca+ c2ab. Proof. By AM-GM, a2 + b2 2 aband 2a4 + b4 + c4 4 a2bc: Similarly, b2 + c2 2 bcand

Introduction to Functional Equations

Evan Chen (October 18, 2016) Introduction to Functional Equations Remark 2.4. There are of course other approaches. Here is an outline of another one. After showing f is an involution, one can simultaneously let x = f(t), y = f(u) and instead obtain f(t2 + u) = tf(t) + f(u) (check this!). This quickly becomes a \Cauchy equation", see below ...

  Equations

Math 55a Lecture Notes - Evan Chen

X0 g? f 2-f 1 Lemma 2.2 In the above commutative diagram, if gis surjective then f 1 = f 2. Proof. Just use gto get everything equal. Yay. §2.3Groups De nition 2.3. A semi-group is a set Gendowed with an associative1 binary operation: G2!G. Lots of groups work. Example 2.4 (Star sh) Let Gbe an arbitrary set and x a g 0 2G. Then let ab= g 0 for ...

  Lecture, Notes, Math, Math 55a lecture notes

Math Olympiad Hardness Scale (MOHS) - Evan Chen

2 Speci cation Here is what each of the possible ratings means.1 Rating 0M: Sub-IMO. Problems rated 0 are too easy to use at IMO. I can often imagine such a problem could be solved by a strong student in an honors math class, even without olympiad training. Rating 5M: Very easy. This is the easiest rating which could actually appear while

  Math, Easy

Barycentric Coordinates in Olympiad Geometry

problems with a formula sheet beside them. I’ve included Appendix B to facilitate these needs; I also have a version which includes just the formula sheet and the problems, which should be oating around. Happy bashing! 1For ABC counterclockwise, this is positive when P, Q and R are in counterclockwise order, and negative other-wise.

  Sheet, Coordinates, Formula, Formula sheet, Barycentric coordinates, Barycentric

The Incenter/Excenter Lemma - Evan Chen

midpoint of arc BC. Show that L is the center of a circle through I, I A, B, C. A BC I L I A Proof. This is just angle chasing. Let A = \BAC, B = \CBA, C = \ACB, and note that A, I, L are collinear (as L is on the angle bisector). We are going to show that LB = LI, the other cases being similar. First, notice that \LBI = \LBC + \CBI = \LAC ...

  Lemma, Incenter, The incenter excenter lemma, Excenter

Combinatorics and Graph Theory - Lagout.org

represent a broad range of the subfields of graph theory, and in turn they provide the reader with a sound introduction to the subject. Second, and just as important, these topics relate particularly well to topics in Chapters 2 and 3. Chapter 2 develops the central techniques of enumerative combinatorics: the

  Introduction, Graph, Combinatorics, Combinatorics and graph

Thirty-three Miniatures: Mathematical and Algorithmic ...

Introduction Some years ago I started gathering nice applications of linear algebra, and here is the resulting collection. The applications belong mostly to the main fields of my mathematical interests—combinatorics, ge-ometry, and computer science. Most of them are mathematical, in proving theorems, and some include clever ways of computing ...

  Introduction, Combinatorics

Bachelor of Science in Computer Science

MAD 3301-Graph Theory Prereq: COP2210 & (Prereq: COP2210 & (COT3100 or MAD2104)) MAD 3401-Numerical Analysis (Prereq: COP2210, MAC2312) MAD 3512-Theory of Algorithms Prereq: COP3530(Prereq: COP3530) MAD 4203-Combinatorics (Prereq: MAD2104, MAC2312) MHF 4302-Math Logic (Prereq: MAD3512Prereq: MAD3512) Systems CAP 4453-Robot Vision …

  Graph, Combinatorics

Guide to Competitive Programming - GitHub Pages

The purpose of this book is to give you a comprehensive introduction to modern competitive programming. It is assumed that you already know the basics of pro-gramming, but previous background in algorithm design or programming contests is not necessary. Since the book covers a wide range of topics of various difficulty,

  Guide, Introduction, Programming, Competitive, Guide to competitive programming

Syllabus for Scientist B 20201201 - National Institute of ...

Stream wise syllabus for Recruitment Exam for the Post of Scientist B (Electronics) 1. Engineering Mathematics Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and Eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and Minima, Multiple integrals, Fourier series, …

  Syllabus, Scientist, Syllabus for scientist b

Discrete Structures Lecture Notes - Stanford University

Discrete Structures Lecture Notes Vladlen Koltun1 Winter 2008 1Computer Science Department, 353 Serra Mall, Gates 374, Stanford University, Stanford, CA 94305, USA; vladlen@stanford.edu.

  Structure, Discrete, Discrete structures