1 The How, When, and Why of Mathematics Spotlight: George Polya Tips on Doing Homework 2 Logically Speaking 3 Introducing the Contrapositive and Converse 4 Set Notation and Quantifiers Tips on Quantification 5 Proof Techniques Tips on Definitions …… 10 Relations Tips on Reading Mathematics 11 Partitions Tips on Putting It All Together 12 Order in the Reals 13 Consequences of the Completeness of R Tips: You Solved ItNow What? 14 Functions, Domain, and Range Spotlight: The Definition of Function 15 Functions, One-to-One, and Onto 16 Inverses 17 Images and Inverse Images Spotlight: Minimum or Infimum? 18 Mathematical Induction 19 Sequences 20 Convergence of Sequences of Real Numbers 21 Equivalent Sets 22 Finite Sets and an Infinite Set 23 Countable and Uncountable Sets 24 The Cantor–Schroder–Bernstein Theorem Spotlight: The Continuum Hypothesis ……

 What is image segmentation? Separation of image domain based on contents.  General image segmentation: ENERGY METHOD Mumford-Shah (MS) Model CURVE EVOLUTION Snake, Geodesic Active-Contour, Chan-Vese Model, Level Set Method BRAIN ANEURYSM SEGMENTATION ENERGY METHOD - REVISITED Approximations of Mumford-Shah Model

▪ Problem Definitions ▪ Previous Results ▪ An Implicit Moveable Dictionary ▪ An Implicit Dictionary with the Working-Set Property

Assignments · Remember: Problem set#1: Rules and Scheme due today September 15th, 2003 Reading Solving problems by searching: AIMA Ch 3 Homework for this lecture Problem set #2 due Monday, Sept. 22 Snas witha, Spring 03 Outline

Individuals are the objects described by a set of data. Individuals may be people, but they may also be animals Relationship or things Between Variables A variable is any characteristic of an individual. a variable can take different values for different ndividuals The 1997 survey data set, for example, includes data about a sample of women The individuals described are the women

ral questions that might arise concerning personal identity. When we ask\Who am I? we might be being we are, what our possiblities are, under what conditions\I\would continue to exist. We'll begin our discussionon n wonder what\makes us tick\, what we ultimately value, what matters to us. We might also be asking what sort personal identity with the latter set of questions Consider a parallel set of questions (Id) Under what conditions are baseball-events events in the same game? E. g, under what conditions are a

Dynamic order statistics OS-SELECT(i, S): returns the ith smallest element in the dynamic set S. OS-RANK(x, S): returns the rank of x ∈ S in the sorted order of S’s elements. IDEA: Use a red-black tree for the set S, but keep subtree sizes in the nodes

G( V, E ) where G ::= graph, V = V( G ) ::= finite nonempty set of vertices, and E = E( G ) ::= finite set of edges

1 Equivalence Relations 【Definition】A relation R is defined on a set S if for every pair of elements (a, b), a, b S, a R b is either true or false. If a R b is true, then we say that a is related to b

16 选择 FLOTRAN 各自由度相应的求解器 命令：FLDATA18, METH, Lable, Value 功能：选择每个自由度的解算方法 菜单：Main Menu>Preprocessor>FLOTRAN Set Up>CFD Solver Controls>VX Solver CFD Main Menu>Preprocessor>FLOTRAN Set Up>CFD Solver Controls>VY Solver CFD