- More "Circle Limit III" Patterns Douglas Dunham
- University of Minnesota Duluth June 2006 CS 4511: Computability and Complexity (4)
- Theory of computation: initial remarks (Chapter 11) For many purposes, computation is elegantly modeled with simple
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- 2.1 Functions A function is a special kind of relation. More precisely. . .
- Intuitively, a "set" is a collection of things, called its elements, or members. To say that x is an element of S, we write
- Recommended problems 12 --CS 3512 --Spring 2010 1 Use the Distinguishability Theorem to prove that any DFA that recognizes the
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- Columbia College, Chicago IL Enumerations of Hyperbolic Truchet Tiles
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- 2.4 (Part A) Comparing sizes of sets Sets A and B are the same size if there is a bijection from A to B.
- The Interplay Between Hyperbolic Symmetry and History
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- 11.2 Part B, 11.3 Recall A deterministic finite automaton is a five-tuple
- Mathematical induction (Weak) mathematical induction (which you are probably already familiar with)
- Recommended problems 4 --CS3512 --Spring 2010 You should be able to do the rest of the textbook exercises for Section 1.3. As
- A function is a special kind of relation. More precisely. . . A function f from A to B is a relation on A B such that
- UNIVERSITY OF MINNESOTA This is to certify that I have examined this copy of a master's thesis by
- A "Circle Limit III" Calculation Douglas Dunham
- Recommended problems 4 --CS 3512 You should be able to do the rest of the textbook exercises for Section 1.3. As
- Recommended problems 11 --CS 3512 --Spring 2010 1 Find a string of minimal length among those that belong to (the language
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- Recommended problems 10 --CS 3512 Our topic this time is asymptotic notation, discussed in Section 5.6 of the
- Comparing sizes of sets Sets A and B are the same size if there is a bijection from A to B.
- AMS Sectional Meeting, Richmond VA Special Session on Mathematics and the Arts
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- The symmetry of M.C. Escher's Circle Limit IV pattern and related patterns.
- H. S. M. Coxeter and Tony Bomford's Colored Hyperbolic Rugs
- Recommended problems 8 --CS 3512 Our topic this time is structural induction, which the textbook does not teach.
- Repeating Hyperbolic Pattern Algorithms --Special Cases
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- Inductively defined sets A = {3, 5, 7, . . . } .
- Recommended problems 2 --CS3512 --Spring 2010 If you're feeling a little shaky about what we've done so far, there are plenty of
- Recommended problems 12 --CS 3512 1 Use the Distinguishability Theorem to prove that any DFA that recognizes the
- University of Minnesota Duluth March 2009 CS 3512: Computer Science Theory(4)
- 3.2 Inductively defined sets, and recursively defined functions
- Recommended problems 1 --CS 3512 You should be able to do all the textbook exercises for Section 1.1. Look the
- Recommended problems 7 --CS 3512 From the textbook exercises for Section 3.1, you should be able to do problems
- Structural induction We now introduce a powerful method for proving claims about
- Intuitively, a "set" is a collection of things, called its elements, or members. To say that x is an element of S, we write
- Recommended problems 1 --CS3512 --Spring 2010 You should be able to do all the textbook exercises for Section 1.1. Look the
- Recommended problems 10 --CS 3512 --Spring 2010 Our topic this time is asymptotic notation, discussed in Section 5.6 of the
- Sets are useful for unordered, possibly infinite collections of elements. A tuple is a finite, ordered collection of elements (aka members, components).
- Inductively defined sets, and recursively defined functions
- Recall A deterministic finite automaton is a five-tuple M = (S, , T, s0, F)
- Growth of functions: asymptotic notation To characterize the time cost of algorithms, we focus on functions that map
- Recommended problems 6 --CS 3512 From the textbook exercises for Section 2.4, you should be able to do 13.
- Recommended problems 11 --CS 3512 1 Find a string of minimal length among those that belong to (the language
- More on comparing sizes of sets Recall: Sets A and B are the same size if there is a bijection from A to B.
- Creating Repeating Patterns with Color Symmetry Douglas Dunham
- Creating Repeating Patterns with Color Symmetry Douglas Dunham
- Bridges 2010 Hyperbolic Vasarely Patterns
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- An Algorithm to Generate Repeating Hyperbolic Patterns Douglas Dunham
- A "Circle Limit III" Calculation Douglas Dunham
- The Family of "Circle Limit III" Escher Patterns Douglas Dunham
- Hyperbolic Key Patterns Douglas Dunham
- Tony Bomford's Hyperbolic Hooked Rugs Douglas Dunham
- 168 Butterflies on a Polyhedron of Genus 3 Douglas Dunham
- Hyperbolic Celtic Knot Patterns Douglas Dunham
- University of Minnesota Duluth June 2007 CS 4521: Algorithms and Data Structures (4)
- University of Minnesota Duluth June 2008 CS 5551: User Interface Design (4)
- CS 3512, Spring 2011 Instructor: Doug Dunham
- 1.3 (Part A) Tuples Sets are useful for unordered, possibly infinite collections of elements.
- 1.3 (Part B) Alphabets and strings Strings are a simpler version of lists, in which all list elements come from a
- 2.4 (Part B) More on comparing sizes of sets Recall: Sets A and B are the same size if there is a bijection from A to B.
- 4.4 (Part A) Mathematical induction (Weak) mathematical induction (which you are probably already familiar with)
- 4.4 (Part B) Structural induction We now introduce a powerful method, structural induction ( called well-founded
- Distinguishability Recall A deterministic finite automaton is a five-tuple M = (S, , T, s0, F)
- Recommended problems 2 --CS 3512 If you're feeling a little shaky about what we've done so far, there are plenty of
- Recommended problems 9 --CS 3512 Our topic this time is mathematical induction.
- CS 3512, Spring 2010 Instructor: Doug Dunham
- Recommended problems 5 --CS3512 --Spring 2010 From the textbook exercises for Section 2.1, you should be able to do
- Recommended problems 7 --CS3512 --Spring 2010 From the textbook exercises for Section 3.1, you should be able to do problems
- Recommended problems 8 --CS 3512 --Spring 2010 Our topic this time is structural induction, which the textbook does not teach.
- A Circle Limit III Backbone Arc Formula Douglas Dunham1
- Recommended problems 6 --CS 3512 --Spring 2010 From the textbook exercises for Section 2.4, you should be able to do 13.
- Hyperbolic Vasarely Patterns Douglas Dunham
- Theory of computation: initial remarks For many purposes, computation is elegantly modeled with simple
- Alphabets and strings Strings are a simpler version of lists, in which all list elements come from a
- Recommended problems 5 --CS 3512 From the textbook exercises for Section 2.1, you should be able to do
- Seeing geometry through hyperbolic art Douglas Dunham
- 5.6 Growth of functions: asymptotic notation To characterize the time cost of algorithms, we focus on functions that map
- Recommended problems 9 --CS 3512 --Spring 2010 Our topic this time is mathematical induction.
- M.C. Escher's Use of the Poincare Models of Hyperbolic Geometry Douglas Dunham
- Hyperbolic Islamic Patterns --A Beginning Douglas Dunham
- Recall A deterministic finite automaton is a five-tuple M = (S, , T, s0, F)
- A Formula for the Intersection Angle of Backbone Arcs with the Bounding Circle for
- Bridges 2011 University of Coimbra, Portugal
- Enumerations of Hyperbolic Truchet Tiles Douglas Dunham
- Joint Mathematics Meetings 2012 A Family of Butterfly Patterns
- Hyperbolic Truchet Tilings Douglas Dunham
