Book announcements. Sukumar Das Adhikari ASPECTS OF COMBINATORICS AND COMBINATORIAL NUMBER THEORY CRC Press, Florida, 2002, 156pp.
|
|
|
- Elizabeth Gilmore
- 6 years ago
- Views:
Transcription
1 Discrete Mathematics 263 (2003) Book announcements Sukumar Das Adhikari ASPECTS OF COMBINATORICS AND COMBINATORIAL NUMBER THEORY CRC Press, Florida, 2002, 156pp. Notations and Terminologies Chapter 1: Classical Ramsey-Type Theorems Chapter 2: Van Der Waerden Revisited Chapter 3: Generalizations of Schur s Theorem Chapter 4: Topological Methods Chapter 5: Euclidean Ramsey Theory Chapter 6: Additive Number Theory and Related Questions Chapter 7: Partitions of Integers Chapter 8: Ramsey-Type Results in Posets Solutions to Selected Exercises Charalambos A. Charalambides ENUMERATIVE COMBINATORICS Chapman & Hall/CRC, New York, 2002, 609pp. Chapter 1: Basic Counting Principles Chapter 2: Permutations and Combinations Chapter 3: Factorials, Binomial and Multinomial Coecients Chapter 4: The Principle of Inclusion and Exclusion Chapter 5: Permutations with Fixed Points and Successions Chapter 6: Generating Functions Chapter 7: Recurrence Relations Chapter 8: Stirling Numbers X/03/$ - see front matter doi: /s x(03)
2 348 Book announcements / Discrete Mathematics 263 (2003) Chapter 9: Distributions and Occupancy Chapter 10: Partitions of Integers Chapter 11: Partition Polynomials Chapter 12: Cycles of Permutations Chapter 13: Equivalence Classes Chapter 14: Runs of Permutations and Eulerian Numbers Hints and Answers to Excercises Svante Janson, Tomasz Luczak, Andrzej Rucinski RANDOM GRAPHS John Wiley & Sons, New York, 2000, 333pp. Chapter 1: Preliminaries Chapter 2: Exponentially Small Probabilities Chapter 3: Small Subgraphs Chapter 4: Matchings Chapter 5: The Phase Transition Chapter 6: Asymptotic Distributions Chapter 7: The Chromatic Number Chapter 8: Extremal and Ramsey Properties Chapter 9: Random Regular Graphs Chapter 10: Zero-One Laws of Notation Mohamed A. Khamsi, William A. Kirk AN INTRODUCTION TO METRIC SPACES AND FIXED POINT THEORY John Wiley & Sons Inc., New York, 2001, 302pp. I. Metric Spaces Chapter 1: Introduction Chapter 2: Metric Spaces Chapter 3: Metric Contraction Principles Chapter 4: Hyperconvex Spaces Chapter 5: Normal Structures in Metric Spaces
3 Book announcements / Discrete Mathematics 263 (2003) II. Banach Spaces Chapter 6: Banach Spaces: An Introduction Chapter 7: Continuous Mappings in Banach Spaces Chapter 8: Metric Fixed Point Theory Chapter 9: Banach Space Ultrapowers Appendix: Set Theory M. Lothaire ALGEBRAIC COMBINATORICS ON WORDS Cambridge University Press, 2002, 504pp. Chapter 1: Finite and Innite Words Chapter 2: Sturmian Words Chapter 3: Unavoidable Patterns Chapter 4: Sesquipowers Chapter 5: The Plastic Monoid Chapter 6: Codes Chapter 7: Numeration Systems Chapter 8: Periodicity Chapter 9: Centralizers of Noncommutative Series and Polynomials Chapter 10: Transformations on Words and q-calculus Chapter 11: Statistics on Permutations and Words Chapter 12: Makanin s Algorithm Chapter 13: Independent Sets of Equations of Notation General Douglas R. Stinson CRYPTOGRAPHY: THEORY AND PRACTICE Chapman & Hall=CRC, Florida, 2002, 360pp. Chapter 1: Cryptography Chapter 2: Shannon s Theory Chapter 3: Block Ciphers and the Advanced Encryption Standard Chapter 4: Cryptographic Hash Functions Chapter 5: The RSA Cryptosystem and Factoring Integers
4 350 Book announcements / Discrete Mathematics 263 (2003) Chapter 6: Public-Key Cryptography Based on the Discrete Logarithm Problem Chapter 7: Signature Schemes Cryptosystem Algorithms Problem W.D. Wallis MAGIC GRAPHS Birkhauser, Boston, MA, 2001, 146pp. Table of contents List of Figures 1. Preliminaries 1.1. Magic 1.2. Graphs 1.3. Labelings 1.4. Magic labeling 1.5. Some applications of magic labelings 2. Edge-Magic Total Labelings 2.1. Basic ideas 2.2. Graphs with no edge-magic total labeling 2.3. Cliques and complete graphs 2.4. Cycles 2.5. Complete bipartite graphs 2.6. Wheels 2.7. Trees 2.8. Disconnected graphs 2.9. Strong edge-magic total labelings Edge-magic injections 3. Vertex-Magic Total Labelings 3.1. Basic ideas 3.2. Regular graphs 3.3. Cycles and paths 3.4. Vertex-magic total labelings of wheels 3.5. Vertex-magic total labelings of complete bipartite graphs 3.6. Graphs with vertices of degree one 3.7. The complete graphs 3.8. Disconnected graphs 3.9. Vertex-magic injections
5 Book announcements / Discrete Mathematics 263 (2003) Totally Magic Labelings 4.1. Basic ideas 4.2. Isolates and stars 4.3. Forbidden congurations 4.4. Unions of triangles 4.5. Small graphs 4.6. Totally magic injections Notes on the Research Problems Answers to Selected Exercises David S. Watkins FUNDAMENTALS OF MATRIX COMPUTATIONS, 2ND EDITION Wiley Interscience, John Wiley & Sons, Inc., New York, 2002, 618pp. Acknowledgements Chapter 1: Gaussian Elimination and Its Variants Chapter 2: Sensitivity of Linear Systems Chapter 3: The Least Squares Problem Chapter 4: The Singular Value Decomposition Chapter 5: Eigenvalues and Eigenvectors I Chapter 6: Eigenvalues and Eigenvectors II Chapter 7: Iterative Methods for Linear Systems Appendix: Some Sources of Software for Matrix Computations of MATLAB Terms Douglas B. West INTRODUCTION TO GRAPH THEORY Prentice Hall, Inc., Upper Saddle River, NJ, 2001, 588pp. Chapter 1: Fundamental Concepts 1.1. What is a Graph? 1.2. Paths, Cycles, and Trails 1.3. Vertex Degrees and Counting 1.4. Directed Graphs
6 352 Book announcements / Discrete Mathematics 263 (2003) Chapter 2: Chapter 3: Chapter 4: Chapter 5: Chapter 6: Chapter 7: Chapter 8: Trees and Distance 2.1. Basic Properties 2.2. Spanning Trees and Enumeration 2.3. Optimization of Trees Matchings and Factors 3.1. Matchings and Covers 3.2. Algorithms and Applications 3.3. Matchings in General Graphs Connectivity and Paths 4.1. Cuts and Connectivity 4.2. k-connected Graphs 4.3. Network Flow Problems Coloring of Graphs 5.1. Vertex Colorings and Upper Bounds 5.2. Structure of k-chromatic Graphs 5.3. Enumerative Aspects Planar Graphs 6.1. Embeddings and Euler s Formula 6.2. Characterization of Planar Graphs 6.3. Parameters of Planarity Edges and Cycles 7.1. Line Graphs and Edge-coloring 7.2. Hamiltonian Cycles 7.3. Planarity, Coloring, and Cycles Additional Topics (optional) 8.1. Perfect Graphs 8.2. Matroids 8.3. Ramsey Theory 8.4. More Extremal Problems 8.5. Random Graphs 8.6. Eigenvalues of Graphs Appendix A: Mathematical Background Appendix B: Optimization and Complexity Appendix C: Hints for Selected Exercises Appendix D: Glossary of Terms Appendix E: Supplemental Readings Appendix F: Author Subject
A Course in Combinatorics
A Course in Combinatorics J. H. van Lint Technical Universüy of Eindhoven and R. M. Wilson California Institute of Technology H CAMBRIDGE UNIVERSITY PRESS CONTENTS Preface xi 1. Graphs 1 Terminology of
MATH 363: Discrete Mathematics
MATH 363: Discrete Mathematics Learning Objectives by topic The levels of learning for this class are classified as follows. 1. Basic Knowledge: To recall and memorize - Assess by direct questions. The
Applications of Chromatic Polynomials Involving Stirling Numbers
Applications of Chromatic Polynomials Involving Stirling Numbers A. Mohr and T.D. Porter Department of Mathematics Southern Illinois University Carbondale, IL 6290 tporter@math.siu.edu June 23, 2008 The
Mathematics (MATH) MATH 098. Intermediate Algebra. 3 Credits. MATH 103. College Algebra. 3 Credits. MATH 104. Finite Mathematics. 3 Credits.
Mathematics (MATH) 1 Mathematics (MATH) MATH 098. Intermediate Algebra. 3 Credits. Properties of the real number system, factoring, linear and quadratic equations, functions, polynomial and rational expressions,
are the q-versions of n, n! and . The falling factorial is (x) k = x(x 1)(x 2)... (x k + 1).
Lecture A jacques@ucsd.edu Notation: N, R, Z, F, C naturals, reals, integers, a field, complex numbers. p(n), S n,, b(n), s n, partition numbers, Stirling of the second ind, Bell numbers, Stirling of the
GRAPHS & DIGRAPHS 5th Edition. Preface to the fifth edition
GRAPHS & DIGRAPHS 5th Edition Gary Chartrand Western Michigan University Linda Lesniak Drew University Ping Zhang Western Michigan University Preface to the fifth edition Since graph theory was considered
ALGEBRAIC COMBINATORICS. c1993 C. D. Godsil
ALGEBRAIC COMBINATORICS c1993 C. D. Godsil To Gillian Preface There are people who feel that a combinatorial result should be given a \purely combinatorial" proof, but I am not one of them. For me the
Oral Qualifying Exam Syllabus
Oral Qualifying Exam Syllabus Philip Matchett Wood Committee: Profs. Van Vu (chair), József Beck, Endre Szemerédi, and Doron Zeilberger. 1 Combinatorics I. Combinatorics, Graph Theory, and the Probabilistic
Cryptography. Number Theory with AN INTRODUCTION TO. James S. Kraft. Lawrence C. Washington. CRC Press
AN INTRODUCTION TO Number Theory with Cryptography James S Kraft Gilman School Baltimore, Maryland, USA Lawrence C Washington University of Maryland College Park, Maryland, USA CRC Press Taylor & Francis
AS 1 Math Structure for BSc (Ed) (Primary 2 CS Track) AS 1 Math Structure for BSc (Ed) (Secondary)
ACADEMIC SUBJECT: MATHEMATICS Table 1: AS 1 Math Structure for BSc (Ed) (Primary 2 CS Track) AS 1 Math Structure for BSc (Ed) (Secondary) Year 1 2 3 4 Course Code Title Course Category No. of AUs Prerequisites
Discrete Mathematics & Mathematical Reasoning Course Overview
Discrete Mathematics & Mathematical Reasoning Course Overview Colin Stirling Informatics Colin Stirling (Informatics) Discrete Mathematics Today 1 / 19 Teaching staff Lecturers: Colin Stirling, first half
REVIEW QUESTIONS. Chapter 1: Foundations: Sets, Logic, and Algorithms
REVIEW QUESTIONS Chapter 1: Foundations: Sets, Logic, and Algorithms 1. Why can t a Venn diagram be used to prove a statement about sets? 2. Suppose S is a set with n elements. Explain why the power set
Bounds on the Traveling Salesman Problem
Bounds on the Traveling Salesman Problem Sean Zachary Roberson Texas A&M University MATH 613, Graph Theory A common routing problem is as follows: given a collection of stops (for example, towns, stations,
Vector fields and phase flows in the plane. Geometric and algebraic properties of linear systems. Existence, uniqueness, and continuity
Math Courses Approved for MSME (2015/16) Mth 511 - Introduction to Real Analysis I (3) elements of functional analysis. This is the first course in a sequence of three: Mth 511, Mth 512 and Mth 513 which
Graph Theory(I): استاذ الماده: أ.م.د. أكرم برزان عطار
استاذ الماده: أ.م.د. أكرم برزان عطار Graph Theory(I): 1. An introduction to Graphs: The Definition of Graphs - Graphs as Models - Matrix Degree - Subgraphs- Paths and Cycles - the Matrix Representation
Series Editor KENNETH H. ROSEN INDUCTION THEORY AND APPLICATIONS. of Manitoba. University. Winnipeg, Canada. CRC Press. Taylor StFrancis Group
DISCIIETE MATHEMATICS AND ITS APPLICATIONS Series Editor KENNETH H. ROSEN HANDBOOK OF MATHEMATICAL INDUCTION THEORY AND APPLICATIONS David S. Gunderson University of Manitoba Winnipeg, Canada CRC Press
BASIC GRAPH THEORY. SUB CODE: 09MAT01 Total hours 52
SYLLABUS For the course work syllabus recommended by the Guide for doing Ph.D in the Department of Mathematics, Sri Siddhartha Institute of Technology under SSU, Tumkur. BASIC GRAPH THEORY SUB CODE: 09MAT01
On a Conjecture of Thomassen
On a Conjecture of Thomassen Michelle Delcourt Department of Mathematics University of Illinois Urbana, Illinois 61801, U.S.A. delcour2@illinois.edu Asaf Ferber Department of Mathematics Yale University,
(a) How many pairs (A, B) are there with A, B [n] and A B? (The inclusion is required to be strict.)
![(a) How many pairs (A, B) are there with A, B [n] and A B? (The inclusion is required to be strict.)](/thumbs/89/99851024.jpg "(a) How many pairs (A, B) are there with A, B [n] and A B? (The inclusion is required to be strict.)")
1 Enumeration 11 Basic counting principles 1 June 2008, Question 1: (a) How many pairs (A, B) are there with A, B [n] and A B? (The inclusion is required to be strict) n/2 ( ) n (b) Find a closed form
Course Info. Instructor: Office hour: 804, Tuesday, 2pm-4pm course homepage:
Combinatorics Course Info Instructor: yinyt@nju.edu.cn, yitong.yin@gmail.com Office hour: 804, Tuesday, 2pm-4pm course homepage: http://tcs.nju.edu.cn/wiki/ Textbook van Lint and Wilson, A course in Combinatorics,
The expansion of random regular graphs
The expansion of random regular graphs David Ellis Introduction Our aim is now to show that for any d 3, almost all d-regular graphs on {1, 2,..., n} have edge-expansion ratio at least c d d (if nd is
UNIVERSITY OF SOUTH ALABAMA MATHEMATICS
UNIVERSITY OF SOUTH ALABAMA MATHEMATICS 1 Mathematics MA 105 Algebra for Math Placement 4 cr Introduction to equations of straight lines in various forms and transition between these forms; Manipulation
Bounded Treewidth Graphs A Survey German Russian Winter School St. Petersburg, Russia
Bounded Treewidth Graphs A Survey German Russian Winter School St. Petersburg, Russia Andreas Krause krausea@cs.tum.edu Technical University of Munich February 12, 2003 This survey gives an introduction
CS/MATH 111 Winter 2013 Final Test
CS/MATH 111 Winter 2013 Final Test The test is 2 hours and 30 minutes long, starting at 7PM and ending at 9:30PM There are 8 problems on the test. Each problem is worth 10 points. Write legibly. What can
Notation Index. gcd(a, b) (greatest common divisor) NT-16
Notation Index (for all) B A (all functions) B A = B A (all functions) SF-18 (n) k (falling factorial) SF-9 a R b (binary relation) C(n,k) = n! k! (n k)! (binomial coefficient) SF-9 n! (n factorial) SF-9
What you learned in Math 28. Rosa C. Orellana
What you learned in Math 28 Rosa C. Orellana Chapter 1 - Basic Counting Techniques Sum Principle If we have a partition of a finite set S, then the size of S is the sum of the sizes of the blocks of the
STUDY GUIDE FOR THE WRECKONING. 1. Combinatorics. (1) How many (positive integer) divisors does 2940 have? What about 3150?
STUDY GUIDE FOR THE WRECKONING. Combinatorics Go over combinatorics examples in the text. Review all the combinatorics problems from homework. Do at least a couple of extra problems given below. () How
CHAPMAN & HALL/CRC CRYPTOGRAPHY AND NETWORK SECURITY ALGORITHMIC CR YPTAN ALY51S. Ant nine J aux
CHAPMAN & HALL/CRC CRYPTOGRAPHY AND NETWORK SECURITY ALGORITHMIC CR YPTAN ALY51S Ant nine J aux (g) CRC Press Taylor 8* Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor &
Preface. Figures Figures appearing in the text were prepared using MATLAB R. For product information, please contact:
Linear algebra forms the basis for much of modern mathematics theoretical, applied, and computational. The purpose of this book is to provide a broad and solid foundation for the study of advanced mathematics.
Coloring k-trees with forbidden monochrome or rainbow triangles
Coloring k-trees with forbidden monochrome or rainbow triangles Julian Allagan & Vitaly Voloshin Department of Mathematics, University of North Georgia, Watkinsville, Georgia email: julian.allagan@ung.edu
A linear algebraic view of partition regular matrices
A linear algebraic view of partition regular matrices Leslie Hogben Jillian McLeod June 7, 3 4 5 6 7 8 9 Abstract Rado showed that a rational matrix is partition regular over N if and only if it satisfies
FINITE-DIMENSIONAL LINEAR ALGEBRA
DISCRETE MATHEMATICS AND ITS APPLICATIONS Series Editor KENNETH H ROSEN FINITE-DIMENSIONAL LINEAR ALGEBRA Mark S Gockenbach Michigan Technological University Houghton, USA CRC Press Taylor & Francis Croup
Mathematics Masters Examination
Mathematics Masters Examination OPTION 4 Fall 2015 MATHEMATICAL COMPUTER SCIENCE NOTE: Any student whose answers require clarification may be required to submit to an oral examination. Each of the twelve
M.Phil. (Mathematics) PROGRAMME CURRICULUM & SYLLABUS 2017 UGC MODEL
KALASALINGAM UNIVERSITY (KALASALINGAM ACADEMY OF RESEARCH AND EDUCATION) (Under Section 3 of the UGC Act 1956) Anand Nagar, Krishnankoil 626 126 Srivilliputtur(via), Virudhunagar(Dt.), Tamil Nadu, INDIA
Hamiltonicity in Connected Regular Graphs
Hamiltonicity in Connected Regular Graphs Daniel W. Cranston Suil O April 29, 2012 Abstract In 1980, Jackson proved that every 2-connected k-regular graph with at most 3k vertices is Hamiltonian. This
The candidates are advised that they must always show their working, otherwise they will not be awarded full marks for their answers.
MID SWEDEN UNIVERSITY TFM Examinations 2006 MAAB16 Discrete Mathematics B Duration: 5 hours Date: 7 June 2006 There are EIGHT questions on this paper and you should answer as many as you can in the time
B.C.S.Part I Mathematics (Sem.- I & II) Syllabus to be implemented from June 2013 onwards.
B.C.S.Part I Mathematics (Sem.- I & II) Syllabus to be implemented from June 2013 onwards. 1. TITLE: Subject Mathematics 2. YEAR OF IMPLEMENTATION : Revised Syllabus will be implemented from June 2013
Memorial University Department of Mathematics and Statistics. PhD COMPREHENSIVE EXAMINATION QUALIFYING REVIEW MATHEMATICS SYLLABUS
Memorial University Department of Mathematics and Statistics PhD COMPREHENSIVE EXAMINATION QUALIFYING REVIEW MATHEMATICS SYLLABUS 1 ALGEBRA The examination will be based on the following topics: 1. Linear
Random Lifts of Graphs
27th Brazilian Math Colloquium, July 09 Plan of this talk A brief introduction to the probabilistic method. A quick review of expander graphs and their spectrum. Lifts, random lifts and their properties.
Semester 3 MULTIVARIATE CALCULUS AND INTEGRAL TRANSFORMS
PC 11 Semester 3 MT03C11 MULTIVARIATE CALCULUS AND INTEGRAL TRANSFORMS Text 1: Tom APOSTOL, Mathematical Analysis, Second edition, Narosa Publishing House. Text 2: WALTER RUDIN, Principles of Mathematical
Discrete mathematics , Fall Instructor: prof. János Pach
Discrete mathematics 016-017, Fall Instructor: prof. János Pach - covered material - Lecture 1. Counting problems To read: [Lov]: 1.. Sets, 1.3. Number of subsets, 1.5. Sequences, 1.6. Permutations, 1.7.
Preliminaries. Graphs. E : set of edges (arcs) (Undirected) Graph : (i, j) = (j, i) (edges) V = {1, 2, 3, 4, 5}, E = {(1, 3), (3, 2), (2, 4)}
Preliminaries Graphs G = (V, E), V : set of vertices E : set of edges (arcs) (Undirected) Graph : (i, j) = (j, i) (edges) 1 2 3 5 4 V = {1, 2, 3, 4, 5}, E = {(1, 3), (3, 2), (2, 4)} 1 Directed Graph (Digraph)
On Chordal Graphs and Their Chromatic Polynomials
On Chordal Graphs and Their Chromatic Polynomials Geir Agnarsson Abstract We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques As a corollary
IVA S STUDY GUIDE FOR THE DISCRETE FINAL EXAM - SELECTED SOLUTIONS. 1. Combinatorics
IVA S STUDY GUIDE FOR THE DISCRETE FINAL EXAM - SELECTED SOLUTIONS Combinatorics Go over combinatorics examples in the text Review all the combinatorics problems from homewor Do at least a couple of extra
Random Graphs III. Y. Kohayakawa (São Paulo) Chorin, 4 August 2006
Y. Kohayakawa (São Paulo) Chorin, 4 August 2006 Outline 1 Outline of Lecture III 1. Subgraph containment with adversary: Existence of monoχ subgraphs in coloured random graphs; properties of the form G(n,
Variations on the Erdős-Gallai Theorem
Variations on the Erdős-Gallai Theorem Grant Cairns La Trobe Monash Talk 18.5.2011 Grant Cairns (La Trobe) Variations on the Erdős-Gallai Theorem Monash Talk 18.5.2011 1 / 22 The original Erdős-Gallai
Determining The Pattern for 1- fault Tolerant Hamiltonian Cycle From Generalized Petersen Graph P(n,k)
26 Determining The Pattern for 1- fault Tolerant Hamiltonian Cycle From Generalized Petersen Graph P(n,k) Wamiliana, F. A. M. Elfaki, Ahmad Faisol, Mustofa Usman, Isna Evi Lestari Department of Mathematics,
High School Mathematics Honors PreCalculus
High School Mathematics Honors PreCalculus This is an accelerated course designed for the motivated math students with an above average interest in mathematics. It will cover all topics presented in Precalculus.
More on NP and Reductions
Indian Institute of Information Technology Design and Manufacturing, Kancheepuram Chennai 600 127, India An Autonomous Institute under MHRD, Govt of India http://www.iiitdm.ac.in COM 501 Advanced Data
Gaussian processes and Feynman diagrams
Gaussian processes and Feynman diagrams William G. Faris April 25, 203 Introduction These talks are about expectations of non-linear functions of Gaussian random variables. The first talk presents the
PALINDROMIC AND SŪDOKU QUASIGROUPS
PALINDROMIC AND SŪDOKU QUASIGROUPS JONATHAN D. H. SMITH Abstract. Two quasigroup identities of importance in combinatorics, Schroeder s Second Law and Stein s Third Law, share many common features that
18.312: Algebraic Combinatorics Lionel Levine. Lecture 19
832: Algebraic Combinatorics Lionel Levine Lecture date: April 2, 20 Lecture 9 Notes by: David Witmer Matrix-Tree Theorem Undirected Graphs Let G = (V, E) be a connected, undirected graph with n vertices,
Essentials of College Algebra
Essentials of College Algebra For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students
Lecture 5: January 30
CS71 Randomness & Computation Spring 018 Instructor: Alistair Sinclair Lecture 5: January 30 Disclaimer: These notes have not been subjected to the usual scrutiny accorded to formal publications. They
On minors of the compound matrix of a Laplacian
On minors of the compound matrix of a Laplacian R. B. Bapat 1 Indian Statistical Institute New Delhi, 110016, India e-mail: rbb@isid.ac.in August 28, 2013 Abstract: Let L be an n n matrix with zero row
MTH 152 MATHEMATICS FOR THE LIBERAL ARTS II. Course Prerequisites: MTE 1,2,3,4, and 5 or a placement recommendation for MTH 152
Revised: Fall 2015 MTH 152 COURSE OUTLINE Course Prerequisites: MTE 1,2,3,4, and 5 or a placement recommendation for MTH 152 Course Description: Presents topics in functions, combinatorics, probability,
On the adjacency matrix of a block graph
On the adjacency matrix of a block graph R. B. Bapat Stat-Math Unit Indian Statistical Institute, Delhi 7-SJSS Marg, New Delhi 110 016, India. email: rbb@isid.ac.in Souvik Roy Economics and Planning Unit
A multiplicative deformation of the Möbius function for the poset of partitions of a multiset
Contemporary Mathematics A multiplicative deformation of the Möbius function for the poset of partitions of a multiset Patricia Hersh and Robert Kleinberg Abstract. The Möbius function of a partially ordered
BOOK REVIEWS 297 WILLIAM D. SUDDERTH American Mathematical Society /85 $ $.25 per page
BOOK REVIEWS 297 4. S. Geisser, A predictivistic primer, Bayesian Analysis in Econometrics and Statistics, North-Holland, Amsterdam, 1980. 5. D. Heath and W. Sudderth, On finitely additive priors, coherence,
Eigenvectors Via Graph Theory
Eigenvectors Via Graph Theory Jennifer Harris Advisor: Dr. David Garth October 3, 2009 Introduction There is no problem in all mathematics that cannot be solved by direct counting. -Ernst Mach The goal
SIZE-RAMSEY NUMBERS OF CYCLES VERSUS A PATH
SIZE-RAMSEY NUMBERS OF CYCLES VERSUS A PATH ANDRZEJ DUDEK, FARIDEH KHOEINI, AND PAWE L PRA LAT Abstract. The size-ramsey number ˆRF, H of a family of graphs F and a graph H is the smallest integer m such
College Algebra and Trigonometry
GLOBAL EDITION College Algebra and Trigonometry THIRD EDITION J. S. Ratti Marcus McWaters College Algebra and Trigonometry, Global Edition Table of Contents Cover Title Page Contents Preface Resources
Mathematics (MA) Mathematics (MA) 1. MA INTRO TO REAL ANALYSIS Semester Hours: 3
Mathematics (MA) 1 Mathematics (MA) MA 502 - INTRO TO REAL ANALYSIS Individualized special projects in mathematics and its applications for inquisitive and wellprepared senior level undergraduate students.
CS/COE
CS/COE 1501 www.cs.pitt.edu/~nlf4/cs1501/ P vs NP But first, something completely different... Some computational problems are unsolvable No algorithm can be written that will always produce the correct
Discrete Mathematics
Discrete Mathematics 310 (2010) 3398 303 Contents lists available at ScienceDirect Discrete Mathematics journal homepage: www.elsevier.com/locate/disc Maximal cliques in {P 2 P 3, C }-free graphs S.A.
Angle contraction between geodesics
Angle contraction between geodesics arxiv:0902.0315v1 [math.ds] 2 Feb 2009 Nikolai A. Krylov and Edwin L. Rogers Abstract We consider here a generalization of a well known discrete dynamical system produced
arxiv: v1 [math.co] 20 Sep 2012
![arxiv: v1 [math.co] 20 Sep 2012](/thumbs/73/69429055.jpg "arxiv: v1 [math.co] 20 Sep 2012")
arxiv:1209.4628v1 [math.co] 20 Sep 2012 A graph minors characterization of signed graphs whose signed Colin de Verdière parameter ν is two Marina Arav, Frank J. Hall, Zhongshan Li, Hein van der Holst Department
and Other Combinatorial Reciprocity Instances
and Other Combinatorial Reciprocity Instances Matthias Beck San Francisco State University math.sfsu.edu/beck [Courtney Gibbons] Act 1: Binomial Coefficients Not everything that can be counted counts,
HOMEWORK #2 - MATH 3260
HOMEWORK # - MATH 36 ASSIGNED: JANUARAY 3, 3 DUE: FEBRUARY 1, AT :3PM 1) a) Give by listing the sequence of vertices 4 Hamiltonian cycles in K 9 no two of which have an edge in common. Solution: Here is
My favorite application using eigenvalues: Eigenvalues and the Graham-Pollak Theorem
My favorite application using eigenvalues: Eigenvalues and the Graham-Pollak Theorem Michael Tait Winter 2013 Abstract The famous Graham-Pollak Theorem states that one needs at least n 1 complete bipartite
An enumeration of equilateral triangle dissections
arxiv:090.599v [math.co] Apr 00 An enumeration of equilateral triangle dissections Aleš Drápal Department of Mathematics Charles University Sokolovská 83 86 75 Praha 8 Czech Republic Carlo Hämäläinen Department
Cluster algebras, snake graphs and continued fractions. Ralf Schiffler
Cluster algebras, snake graphs and continued fractions Ralf Schiffler Intro Cluster algebras Continued fractions Snake graphs Intro Cluster algebras Continued fractions expansion formula via perfect matchings
ON THE EDGE COLORING OF GRAPH PRODUCTS
ON THE EDGE COLORING OF GRAPH PRODUCTS M. M. M. JARADAT Received 11 October 2004 The edge chromatic number of G is the minimum number of colors required to color the edges of G in such a way that no two
UCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis
![UCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis](/thumbs/77/75937586.jpg "UCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis")
UCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis Final Exam Review Session Class URL: http://vlsicad.ucsd.edu/courses/cse21-s14/ Notes 140608 Review Things to Know has
MATH 102 Calculus II (4-0-4)
MATH 101 Calculus I (4-0-4) (Old 101) Limits and continuity of functions of a single variable. Differentiability. Techniques of differentiation. Implicit differentiation. Local extrema, first and second
Hanoi Graphs and Some Classical Numbers
Hanoi Graphs and Some Classical Numbers Sandi Klavžar Uroš Milutinović Ciril Petr Abstract The Hanoi graphs Hp n model the p-pegs n-discs Tower of Hanoi problem(s). It was previously known that Stirling
UNIVERSITY OF PUNE, PUNE BOARD OF STUDIES IN MATHEMATICS SYLLABUS. F.Y.BSc (Computer Science) Paper-I Discrete Mathematics First Term
UNIVERSITY OF PUNE, PUNE 411007. BOARD OF STUDIES IN MATHEMATICS SYLLABUS F.Y.BSc (Computer Science) Paper-I Discrete Mathematics First Term 1) Finite Induction (4 lectures) 1.1) First principle of induction.
The number of Euler tours of random directed graphs
The number of Euler tours of random directed graphs Páidí Creed School of Mathematical Sciences Queen Mary, University of London United Kingdom P.Creed@qmul.ac.uk Mary Cryan School of Informatics University
The Turán number of sparse spanning graphs
The Turán number of sparse spanning graphs Noga Alon Raphael Yuster Abstract For a graph H, the extremal number ex(n, H) is the maximum number of edges in a graph of order n not containing a subgraph isomorphic
Vertex colorings of graphs without short odd cycles
Vertex colorings of graphs without short odd cycles Andrzej Dudek and Reshma Ramadurai Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 1513, USA {adudek,rramadur}@andrew.cmu.edu
Exercise Set 7.2. Skills
Orthogonally diagonalizable matrix Spectral decomposition (or eigenvalue decomposition) Schur decomposition Subdiagonal Upper Hessenburg form Upper Hessenburg decomposition Skills Be able to recognize
Asymptotic Behavior of the Random 3-Regular Bipartite Graph
Asymptotic Behavior of the Random 3-Regular Bipartite Graph Tim Novikoff Courant Institute New York University, 10012 December 17,2002 Abstract In 2001, two numerical experiments were performed to observe
COURSE OUTLINE CHAFFEY COLLEGE
COURSE OUTLINE CHAFFEY COLLEGE Discipline: Mathematics 1. COURSE IDENTIFICATION: MATH 425 2. COURSE TITLE: Intermediate Algebra 3. UNITS: 4 Lecture Hours: Normal: 72 Range: 64-76 4. GRADING: Letter Grade
A Graph Polynomial Approach to Primitivity
A Graph Polynomial Approach to Primitivity F. Blanchet-Sadri 1, Michelle Bodnar 2, Nathan Fox 3, and Joe Hidakatsu 2 1 Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro,
The super line graph L 2
Discrete Mathematics 206 (1999) 51 61 www.elsevier.com/locate/disc The super line graph L 2 Jay S. Bagga a;, Lowell W. Beineke b, Badri N. Varma c a Department of Computer Science, College of Science and
ACO Comprehensive Exam October 18 and 19, Analysis of Algorithms
Consider the following two graph problems: 1. Analysis of Algorithms Graph coloring: Given a graph G = (V,E) and an integer c 0, a c-coloring is a function f : V {1,,...,c} such that f(u) f(v) for all
Contents. CHAPTER P Prerequisites 1. CHAPTER 1 Functions and Graphs 69. P.1 Real Numbers 1. P.2 Cartesian Coordinate System 14
CHAPTER P Prerequisites 1 P.1 Real Numbers 1 Representing Real Numbers ~ Order and Interval Notation ~ Basic Properties of Algebra ~ Integer Exponents ~ Scientific Notation P.2 Cartesian Coordinate System
Linear Algebra and Probability
Linear Algebra and Probability for Computer Science Applications Ernest Davis CRC Press Taylor!* Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor Sc Francis Croup, an informa
Dominator Colorings and Safe Clique Partitions
Dominator Colorings and Safe Clique Partitions Ralucca Gera, Craig Rasmussen Naval Postgraduate School Monterey, CA 994, USA {rgera,ras}@npsedu and Steve Horton United States Military Academy West Point,
DISCRETIZED CONFIGURATIONS AND PARTIAL PARTITIONS
DISCRETIZED CONFIGURATIONS AND PARTIAL PARTITIONS AARON ABRAMS, DAVID GAY, AND VALERIE HOWER Abstract. We show that the discretized configuration space of k points in the n-simplex is homotopy equivalent
Dominating a family of graphs with small connected subgraphs
Dominating a family of graphs with small connected subgraphs Yair Caro Raphael Yuster Abstract Let F = {G 1,..., G t } be a family of n-vertex graphs defined on the same vertex-set V, and let k be a positive
The cycle polynomial of a permutation group
The cycle polynomial of a permutation group Peter J. Cameron School of Mathematics and Statistics University of St Andrews North Haugh St Andrews, Fife, U.K. pjc0@st-andrews.ac.uk Jason Semeraro Department
How do we analyze, evaluate, solve, and graph quadratic functions?
Topic: 4. Quadratic Functions and Factoring Days: 18 Key Learning: Students will be able to analyze, evaluate, solve and graph quadratic functions. Unit Essential Question(s): How do we analyze, evaluate,
Chromatic bases for symmetric functions
Chromatic bases for symmetric functions Soojin Cho Department of Mathematics Ajou University Suwon 443-749, Korea chosj@ajou.ac.kr Stephanie van Willigenburg Department of Mathematics University of British
A note on Gallai-Ramsey number of even wheels
A note on Gallai-Ramsey number of even wheels Zi-Xia Song a, Bing Wei b, Fangfang Zhang c,a, and Qinghong Zhao b a Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA b Department
MATH 682 Notes Combinatorics and Graph Theory II
MATH 68 Notes Combinatorics and Graph Theory II 1 Ramsey Theory 1.1 Classical Ramsey numbers Furthermore, there is a beautiful recurrence to give bounds on Ramsey numbers, but we will start with a simple
Matching Polynomials of Graphs
Spectral Graph Theory Lecture 25 Matching Polynomials of Graphs Daniel A Spielman December 7, 2015 Disclaimer These notes are not necessarily an accurate representation of what happened in class The notes
On representable graphs
On representable graphs Sergey Kitaev and Artem Pyatkin 3rd November 2005 Abstract A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in
Counting independent sets of a fixed size in graphs with a given minimum degree
Counting independent sets of a fixed size in graphs with a given minimum degree John Engbers David Galvin April 4, 01 Abstract Galvin showed that for all fixed δ and sufficiently large n, the n-vertex
DISCRETE AND ALGEBRAIC STRUCTURES
DISCRETE AND ALGEBRAIC STRUCTURES Master Study Mathematics MAT40 Winter Semester 015/16 (Due to organisational reasons register for the course at TU and KFU) Edited by Mihyun Kang TU Graz Contents I Lectures