Mathematics

Graph Theory ()

Graph Theory ()

Math is something I can do with pen and paper. I have tried, in vain, over the last couple of years to enter into a research institution to carry out my other,mostlyphysical scientific studies, therefore, without a costly lab and a good team at hands, what I can only do is my math talents.

I arrived at mathematics mainly because without a research position in an university or institution, I am unable to conduct my researches on physical sciences such as thermodynamics, solar physics, fluiddynamics. And also because math is the basic science without a solid foundation one has no chance to carry out real world researches in any other sciences. And I am so busy that I cannot afford to maintain competences both in math and phyusical sciences. There are possibly other reasons why I finally chose math as my research area, either as hobby or as my academic career.

I have tried several areas of math, incl. functional, computation, diffrential equations, number theory, etc - see the list below - and still I am reading some books or papers on these subjects, for graph theory has something to do with all of them. Ｉ finally come to graph theory becasue VLSI is very much related to and dependent on graph theory for its development. Of course graph theory as well as VLSI has much more math to relate to.

I have tried

• Discrete Mathematics
• Complexity theory
• ALGEBRA / Linear Algebra Boolean Algebra / Logic Algebra
• Category Theory
• Computer Algorithm / Programming
• Information Theory
• Probability Theory
• (Computational) Geometry
• COMPUTATION
• NUMBER THEORY
• Cryptography
• Fractal Geometry
• FUNTIONAL ANALYSIS
• COMPLEX
• Calculus
• Differential Equations
• ERGODIC THEORY
• FOURIER ANALYSIS
• INVARIANT THEORY
• Laplace Equation
• Math4GoogleMaps
• Math4Music
• Math4Programming
• Math4SearchEngines
• Math General

but without any publications yet, and now I am working mainly on graphy theory, combinatorics and all other math related to chip technology. See my other pages of this site.

Refer to the following files for more info:

>>> combinatorics

• combinatorics.htm
• memetic_channel_routing.htm
• Search algorithms.htm
• simulated_annealing.htm

>>> math_branches

• Algebra.htm
• Algorithm.htm
• Boolean.htm
• Calculus.htm
• Category.htm
• Complex.htm
• Complexity.htm
• Computational.htm
• Cryptography.htm
• discrete_ref.htm
• Equations.htm
• Ergodic.htm
• Fourier.htm
• FractalGeometry.htm
• Functional.htm
• Geometry.htm
• Information.htm
• LaplaceEquation.htm
• Math4Music.htm
• Math4SearchEngines.htm
• MathGeneral.htm
• Number.htm
• Probability.htm

>>> others

• My Math Research Plan.htm
• whynotnumbertheorychina.htm

Number theory and cryptography (2010-Nov 2013)

Number theory was considered the crown of the mathematics, but I would consider algebra as its crown as number theory of today depends much on how modern algebra develops and provides tools for. Number theory today is very different from number theory of a century ago. I uses the theories and tools of many other maths and in return it also provides mechanism for many other branches of math and other sciences.

Since 2006, after the death of my father, people have persuaded me to do something to contribute to the society and not to waste my talents. Over this time period, I have studied very hard and tried many areas of researches and studies before finally a fixing my research area of computational number theory, particularly primality testing between November 2011 and December 2013.

My research area was number theory, and particularly prime number prove and later integer factorization related to cryptography. I was not born mathematician. It took me a long long way to finally decide to do math. My major was in thermal science and I have been in the energy and power industry since long. Over the past several years since 2007, I have tried various branches of sciences with some sorts of researches and authoring in process.

Although there is no way to enter the academic world except with my own research at hand, yet I am determined to carry out my researches on my own at any cost under any circumstances, how hard my condition may be. Therefore considering all the constraints to research capacity as a solo researcher without the necessary supports and working atmosphere of a well established academic entity, I am determined to reorient myself as a number theorist, in connection with cryptography and Internet security. With my superb math foundation and learning capacity, I can step in the number theory and other math and science areas fairly quickly.

I chose number theory as my future research area because first all my previous attempts in other branches of science were failed and no universities and organizations were willing to support my researches, and second, without good experimental facilities and a good team I am unable to continue most of my research projects. Number theory on other hand depends mainly on my personal talent and intelligence. On other hand, any serious researches on whatever topics you may choose involves lots of math, and sometimes math is a determining tools in researches of other sciences. But I don’t have so much time to cope with both of them. I came to number theory also as a result of my combat to Internet blockade. In 2009 I was determined to work on Internet security in order to ensure my free access to and my security of my identity while using the Internet with various encryption services. I was attracted by the cryptographic technologies, and later it was found the its mathematical foundation is modern algebra (DES) and number theory (RSA). So it was a natural conclusion that these sciences will become parts of my studies objects.

During the first years, I was focusing on prime number testing and integer factorization. But later my researches also extended to other branches of number theory. And finally I wished to join the world mathematician communities again with my researches on number theory, particularly those related to cryptography.

I planed first to propose my own improvements to existing deterministic, unconditional and polynomial time prime number tests – particularly the AKS test and go a step further to figure out my own. My second phase of research would be to benchmark the probabilistic and the deterministic primality tests based on complexity considerations in order to find out the threshold between these two and to put forward criteria of the real world optimal algorithms for various applications. I hoped these studies will contribute to the development of practical cryptographic systems used for Internet security over the next years.

I was doing my researches on my own – that is, I did not work in any university or any math institute in China. I also paid all the expenses in doing the researches, therefore I have to earn money to support my researches. But it was very difficult, if not impossible, to achieve what I have in mind when I continued to do this way, because during the day I have to earn money and only in the evening can I find 1 or 2 hours for number theory, if I still have to study number theory alone.

Therefore I hoped that someone could provide me with some help. I would appreciate it very much if he or she would provide me with a place where I can quietly conduct my researches on number theory and other related topics. It would also greatly help me if he or she could provide me with the recent development of the AKS algorithm.

Upto now, I am not only reading number theory and its sub branches, but also related branches of math - such as complex functions, functional analysis, computational math - and have been compiling some preliminary paper as a result of studies. Although my current studies of math concentrates on mathematics related to information exchange security and cryptography, incl. also number theory, algebra, combinatorics and others.

Primality testing

AKS primality testing

Algebra.pdf - recording of my abstract algebra studies, in particular some key concepts and theorems

Also see these documents for more details:

MathDraft.doc

MathDraft1.doc

MathDraft2.doc

Complexity theory

NP Conpleteness

Arora ComputationalComplexityModernApproachp489

Blakey, Ed: A Model-Independent Theory of Computational Complexity: From Patience to Precision and Beyond , 2010         37

Cai Lectures in Computational Complexity p169

Gacs Complexity of Algorithms p242

Parberry Parallel Complexity Theory p212

Talbot Complexity and Cryptography An Introduction p305

Trevisan, Luca: Lecture Notes on Computational Complexity, May 2004, p171 ...................... 46

===================================

ALGEBRA / Linear Algebra

Ash, Robert B.: Abstract Algebra: The Basic Graduate Year, October 2000

BARR, MICHAEL AND WELLS, CHARLES: CATEGORY THEORY FOR COMPUTING SCIENC, 2012.

Brin, Matthew G.: MODERN ALGEBRA, NOTES FOR MATH 401-402 at Binghamton University, 2011

Knighten, Robert L.: Notes on Category Theory, November 9, 2007

Stewart, Ian: Galois Theory, Chapman & Hall, 2003

Adamek ALGEBRAIC THEORIES A CATEGORICAL INTRODUCTION TO GENERAL ALGEBRA p228

Albuquerque FromLieAlgebrasToQuantumGroups p214

Ash, Robert B.: Abstract Algebra: The Basic Graduate Year, October 2000, p407.................73

Ash Algebra Abstract The Basic Graduate Year p298

Barr CATEGORY THEORY FOR COMPUTING SCIENCE p558            39

Baumslag Shaums_Group_theory p285

Borel Linear Algebraic Groups 2ed p300

Bowen IntroductionToVectorsAndTensorsVol1 Linear and Multilinear Algebra p304

Brin MODERN ALGEBRA p314                92

BurrisSanka A Course in Universal Algebra p331

Cartan homological algebra p421

Cvitanovic GroupTheory p297

Davis Lecture Notes in Algebraic Topology p392

DHoker quantum_field_theory p255

DOLGACHEV Classical Algebraic Geometry a modern view p721

Dolotin Introduction to Non-Linear Algebra p141

Durbin Modern Algebra an Introduction p350

Dutta Introduction to Commutative Algebra p162

Elman Lectures in Abstract Algebra Preliminary Version p409

Evens Algebraic Topology p250

Fuller Analysis of affine equivalent boolea functions to encryption p167

GarrettPaul Abstract Algebra p412

Gasarch Van der Waerdens Theorem Variants and Applications p210

Hermann Abstract Algebra p383

higheralgebra p950

Hill Abstract Algebra for Secondary Mathematics Teachers p383

Hobby The structure of finite algebra p212

Hungerford Algebra p528

Jezek UNIVERSAL ALGEBRA p233

Johannson Variations on a theorem by van der Waerden p209

Joyner Adventures in Group Theory p322

Judson Abstract Algebra Theory and Applications 2012 p442

Kersten Symmetries in Algebra and Number Theory p213

Kleshchev Lectures on Algebraic Groups p166

Kleshchev Lectures on Abstract Algebra for Graduate Students p267

Knighten Notes on Category Theory p416                  44

Kreck Differential Algebraic Topology From Stratifolds to Exotic Spheres p232

Kreck Differential Algebraic Topology p168

LAWVERE Conceptual Mathematics A first introduction to categories p376

Lemmermeyer Class Field Theory p212

maclane categories for the workig mathematicians p315

Madapusi Commutative Algebra p177

Martini Elements of Basic Category Theory p160

May A Concise Course in Algebraic Topology p251

May More Concise Algebraic Topology p406

McCrimmon_A_Taste_of_Jordan_Algebras_(2003)(en)(545s)

Meinke universal algebra p212

Milne Fields and Galois Theory p230

MilneAG Algebraic Geometry p260

MilneAGS Affine Group Schemes p275

MilneALA Algebraic Groups, Lie Groups p422

MilneAV Abelian Varieties p172

MilneCFT Class Field Theory p287

MilneGTe6 Group Theory p270

MilneL Etale Cohomology p202

Milne Algebraic Groups and Arithmetic Group p219

Mishra AlgorithmicAlgebra p425

Monks Modern Algebra I Lecture Notes p132

Morett Notes on Multi-Linear Algebra and Tensor Calculus p61

Morse homologic alalgeba p421

Payne Topics in Algebra and Number Theory p140

Pivato Visual Abstract Algebra p243

Quantum Algebra,Algebraic Topology,Category Theory,Higher Dimensional Algebra p434

Ramanathan Lectures on the Algebraic Theory of Fields p228

Rotman Advanced_modern_algebra_2003 p1056

Rotman-An Introduction to Homological Algebra 2nd Ed p721

Rydeheard Computational Category Theory p263

Simmons An introduction to Category Theory p436

Spivak Category Theory for Scientists p267

Stein A Brief Introduction to Classical and Adelic Algebraic Number Theory2004 p190

stein Modular Forms A Computational Approach p282

Steinberger algebra p558

Stewart Galois Theory p325                      86

Tornero An introduction to global class field theory p206

van der Waerden Modern Algebra Vol2 p227

Vercruysse Galois Theory for Corings and Comodules p274

weibel AN INTRODUCTION TO HOMOLOGICAL ALGEBRA p462

Zeidler Abstract Algebra p488

Also see these documents for more details:

Algebra.docx

===============================

Boolean Algebra / Logic Algebra

Switching Algebra

ANDREKA et al: ALGEBRAIC LOGIC, Aug 2003, p129.....................ok

Blumensath, Achim: Logic, Algebra & Geometry, DARMSTADT Jan 11, 2014,..p596................11 / .35

============================

Couturat, LOUIS: The Algebra of Logic. 2004, p102.

Kang, Sungho: Boolean Algebra, July 2003, p107.................31

==========================================================

Computer Algorithm / Progamming

Design and Analysis of Algorithms

algorithmic computer science

algorithms for linear and convex optimization

Network flow algorithms

Parallel Computing

Agarwal A Survey of Techniques Used in Algebraic and Number Theoretic Algorithms Kunming Tutorial, May 2005 p307

Cormen, Thomas H.: Introduction.to.Algorithms, Second Edition, The MIT Press, 2002    p1203..................................998

Knuth The Art Of Computer Programming Vol 4 p200

Knuth The Art of Computer Programming Vol 2 p704

Knuth The Art of Computer Programming Vol 3 p792

Knuth The Art of Computer Programming Vol 4 prefascle oc p65

Knuth The art of computer progamming mmix p140

Knuth The art of computer programming GAC p65

==========================================================

Probability Theory

Durrett, Rick: Probability - Theory and Examples, Fourth Edition, Cambridge University Press, 2010, p440           41

Feller, William: An Introduction to probability Theory-and its applications, John Wiley & Sons, 1967, p525..........................130

Grinstead Introduction to Probability p520

Steinsaltz, David: Introduction to Probability Theory and Statistics for Psychology and Quantitative Methods for Human Sciences . Lectures notes, 2011-2012, p302     

Wu, Yaokun: Elementary Probability Theory 2006 p231

==========================================================

COMPUTATION

Wei, Liang: Direct Numerical Simulation of Compressible and Incompressible Wall Bounded Turbulent Flows with Pressure Gradients, December 2009, p215................................60         

NUMBER THEORY

Adleman Algorithmic Number Theory 1994 p168

AGRAWAL PRIMALITY TESTING IN POLYNOMIAL TIME p218

Allahabad Factoring integers, Producing primes and the RSA cryptosystem p170

Apostol Introduction_To_Analytic_Number_Theory_p350            48

Apostol, Tom M.: Introduction to Analytic Number Theory, Springer-Verlag, 1976

Arnoux Factoring and primality testing I p189

Arnoux Factoring and primality testing III p160

Arun-Kumar Algorithmic number theory (web draft p200

Bach Algorithmic number theory vol 1 Efficient algorithms p516

Baker Algebraic Number Theory2006 p152            18

Baker, Matthew: Algebraic Number Theory Course Notes (Fall 2006)

Boeyens_Levendis-Number_Theory_and_the_Periodicity_of_Matter p387

BOREVITCH Z. I. and CHAFAREVITCH, I. R. Number theory, Academic Press, 1966, p439...............95

Borevich: Number theory, Academic Press, 1966

Borwein Computational excursions in Analysis and Number Theory p225

BOSMA PRIMALITY PROVING WITH CYCLOTOMY p337

Brent Factoring Integers – an Introduction p99

Bressoud Factorization_and_Primality_Testing p250

BU Primes in Context Using Technology_ Toward a Didactical Model p331

Buhler Algorithmic Number Theory p660

Cassels Algebraic Number Theory p388

Cassels-Frohlich-Algebraic_Number_Theory p192

Clark Number Theory A Contemporary Introduction p259

Cohen A course in computational algebraic number theory p563

Cohn Advanced Number Theory P283

Conrad Algebraic Number Theory p255

Conway The Book of Numbers p330

CrandallPomerance Prime Numbers A Computational Perspective p604

dajani A Short Introduction to Ergodic Theory of Numbers p58

Duke Analytic Number Theory A Tribute to Gauss and Dirichlet p266

Einsiedler Ergodic Theory with a view towards Number Theory p171

Game_Thesis_Binary integer wavelet transform p331

Goldstein The_Shaping_of_Arithmetic_after_C.F.Gausss_Disquisitiones_Arithmeticae p596

Gouvea Advances in Number Theory p553

Granville Multiplicative number theory p190

Gries Applied number theory in computing and cryptography p112

Hackman Elementary Number Theory p415

Hardy An Introduction to the Theory of Numbers p642

HardyRight An introduction to the theory of numbers p438

Hildebrand Introduction to Analytic Number Theorymain p197

Holden Algebraic Number Theory p341

Holden Number Theory p561

Jia Analytic Number Theory p213

Koshy Elementary-Number-Theory-with-Applications p801

Lauridsen integerfactorization p174

Lenstra Computational Methods in Number Theory p213

Malisrev Linik ergodic method to nuumber theory p23

Mihailescu Cyclotomy of Rings and Primality testing p186

Milne Algebraic Number Theory2011 p327

MINKOWSKI diophantischeapp00minkuoft p260

Montgomery Multiplicative Number Theory I Classical Theory p571

Motohashi Lectures on Sieve Methods and Prime Number Theory p180

Murty Problems In Algebraic Number Theory 2Ed p371

Nathanson Elementary methods in number theory 2000 p518

Neukirch Algebraic Number Theory-1 p294

Niven An introduction to the theory of numbers p541

Pollack Not Always Buried Deep p323

Pollard The Theory of algebraic numbers p173

RademacherZZZ Lectures on Analytic Number Theory p283

Ribenboim My Numbers My Friends p384                73

Ribenboim, Paulo: My Numbers, My Friends: Popular Lectures on Number Theory, Springer-Verlag, 2000

Ribenboim The Little Book of Bigger Primes p381

Ribenboim The New Book Of Prime Number Records 3ed p285

Sandor Handbook of number theory, vol.2 p635

Sharifi ALGEBRAIC NUMBER THEORY p182

Shoup A Computational Introduction to Number Theory and Algebra ver2 p598

Siegel On Advanced Analytic Number Theory p241

stein an explicit appraoch to elementary number theory54 p168

Stein Algebraic Number Theory a Computational Approach November 14 2012 p215

Stein A Brief Introduction to Classical and Adelic Algebraic Number Theory p190

Stein Algebraic Number Theory a Computational Approach2012 p213

Stewart Algebraic number theory and Fermats last theorem 3ed p334

STROMBERGSSON ANALYTIC NUMBER THEORY LECTURE NOTES p295

Tattersall, JAMES J.: Elementary number theory in nine chapters, Cambridge University Press 1999, p417 .......................... 40

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

VINOGRADOV NUMBER_THEORY Russian p178

Venturi Lecture Notes on Algorithmic Number Theory p217

Wedeniwski Primality Tests on Commutator Curves p167

Wells PRIME NUMBERS The Most Mysterious Figures in Math p291               40

Wells, David: PRIME NUMBERS, The Most Mysterious, John Wiley & Sons, Inc., 2005

Weston Algebraic Number Theory notes p173

Yan Song Y Primality Testing and Integer Factorization p386

Also see these documents for more details:

aks.docx

AKSOutline.docx

Factorization.doc

NumberTheory.doc

Primality.doc

RandomNumber.doc

Nunmber Theory for Cryptography

Bernstein Post Quantum Cryptography p248

Bernstein, Daniel J. ·Buchmann, Johannes and Dahmen, Erik: Post-Quantum Cryptography, Springer-Verlag Berlin Heidelberg, 2009 ................ 13

Adida Advances in Cryptographic Voting Systems p254

Attrapadung A Survey on Recent Advances in Broadcast Encryption p138

Attrapadung Broadcast Encryption p155

Attribute-Based Cryptography p114

Batuwantudawe New Techniques for Security Proofs of Quantum Cryptography p122

BellareRogaway Introduction to Modern Cryptography p283

Bernstein Post Quantum Cryptography p248                 31

Beuchat An Introduction to Pairing-Based Cryptography p440

Blake Advances in Elliptic Curve Cryptography p299

Bregman Public Keys and Private Keys in Quantum Cryptography p112

Broadcast Encryption and Some Other Primitives p113

Brown Elliptic Curve Cryptography p144

Brydon On the Security of Leakage Resilient Public Key Cryptography p100

Carlet Boolean Functions for Cryptography and Error Correcting Codes p148

Chen New Techniques for Cryptanalysis of Cryptographic Hash Functions p213

Cohen, Henri and Frey, Gerhard: Handbook of Elliptic and Hyperelliptic Curve Cryptography, 2006, Chapman & Hall/CRC, p843            81

craig A FULLY HOMOMORPHIC ENCRYPTION SCHEME p209

DAVID Lightweight Cryptography for Passive RFID Tags p148

Debdeep Desig of cellular automata encryption p259

Denning-CryptographyDataSecurity p419

Doumen Some Applications of Coding Theory in Cryptography p88

Fisher Coding and Cryptography p61

Funder Cryptography_with_Quantum_Mechanics p103.pdf           17

goldwasser_bellareZZZ_Lecture Notes on Cryptography p283

GoldwasserBellare Lecture Notes on Cryptography p289

Goluch The development of homomorphic cryptography p112

Greveler Applications of Broadcast Encryption for Digital Rights Management of Multimedia Broadcasts p251

Gruska, Jozef: CODING, CRYPTOGRAPHY and CRYPTOGRAPHIC PROTOCOLS p1450 (slides), December 6, 2011     82

GUNEYSU CRYPTOGRAPHY AND CRYPTANALYSIS ON RECONFIGURABLE DEVICES p213

HankersonMenezesVanstoneZZZ Guide to elliptic curve cryptography p332

Hendrych, Martin: Experimental Quantum Cryptography, Doctoral Thesis, September 2002, p104               44

Henry The Theory and Applications of Homomorphic Cryptography p139

Hitchcock, Yvonne Roslyn: Elliptive curve for light weight crypto p247, Dec 2003           133

hudde-code-based-cryptography-library p122

Hughes Quantum Cryptography p84

Juma Leakage resilience and black-box impossibility results in cryptography p180

Katz Introduction_to_Modern_Cryptography p512

Khader Attribute Based Authentication Schemes p173

Korner Coding and Cryptography p104

Kranakis Primality and cryptography p225

kupcu Efficient Cryptography for the Next Generation Secure Cloud p275

Leander Lightweight_cryptography p166

LeeWang Advances_in_Cryptology_ASIACRYPT_2011 p775

lorenz Cryptography Based on Error Correcting Codes p94

Lynn thesis ON THE IMPLEMENTATION OF PAIRING-BASED CRYPTOSYSTEMS p126

Mao ModernCryptographyTheoryandPractice p755

Mathar Cryptography Advanced Methods of Cryptography p124

Menezes Handbook Of Applied Cryptography p794

Meskanen On the NTRU Cryptosystem p126

Mogollon Cryptography.and.Security.Services Mechanisms.and.Applications p489

Mollin An INTRODUCTION to CRYPTOGRAPHY p393

Mullan Some results in group-based cryptography p101

nemes Quantum Resistant Cryptography p42

Oppliger Contemporary Cryptography p469

Peikert Some Recent Progress in Lattice-Based Cryptography p74

Pelzl PRACTICAL ASPECTS OF CURVE-BASED CRYPTOGRAPHY AND CRYPTANALYSIS p222

Persichetti Improving the efficiency of Code-Based Cryptography p147

Persochetti Improving the efficiency of code based encryption p142

Porschman LIGHTWEIGHT CRYPTOGRAPHY, Cryptographic Engineering for a PervasiveWorld, DISSERTATION for the degree Doktor-Ingenieur, February 2009, p197.            127

Rose LATTICE-BASED CRYPTOGRAPHY A PRACTICAL IMPLEMENTATION p103

Ruohonen MATHEMATICAL CRYPTOLOGY p136

Rădulescu Public-key Cryptography - The RSA and the Rabin Cryptosystems p160

rupp COMPUTATIONAL ASPECTS OF CRYPTOGRAPHY AND CRYPTANALYSIS p251

Schneier Applied Cryptography p662

Silverman The Arithmetic of Elliptic Curves p522

Silverman An Introduction to the Theory of Lattices and Applications to Cryptography p76

smart-Cryptography An Introduction p432

Stallings Cryptography and Network Security Principles and Practice 5th Edition p900

Stinson CryptographyTheoryandpractice(3ed) p611

Tehan White-Box Cryptography p76

Trappe, Wade and Washington Lawrence C: Introduction to Cryptography with Coding Theory, Pearson, 2006, p591 ..............          414

Umana, Valerie Gauthier: Post-Quantum Cryptography p156.pdf,  PhD Thesis, October 2011         32

Vahlis Cryptography Leakage Resilience Black Box Separations and Credential-free Key Exchange p164

Verneuil, Vincent: Cryptographie à base de courbes elliptiques et sécurité de composants embarqués, Elliptic curve cryptography and security of embedded devices, Thèse présentée pour obtenir le grade de Docteur, p200     le 13 juin 2012        83

Washington, LAWRENCE C.: ELLIPTIC CURVES NUMBER THEORY AND CRYPTOGRAPHY, SECOND EDITION, Taylor & Francis Group, 2008 p 524      45

Wehner quantum_cryptography-an_introduction p82

Weir Visual cryptography and its applications p144

WongKenneth_Thesis Cryptology p201

Yang, Bo-Yin: Post -Quantum Cryptography p307, 4th InternationalWorkshop, PQCrypto 2011, Taipei, Taiwan, November 29 – December 2, 2011, Proceedings, Springer                      4

Zhang IMPROVEMENTS AND GENERALISATIONS OF SIGNCRYPTION SCHEMES p126

Also see these documents for more details:

Math4Security.doc

Math4SecurityOldtimes.doc

Postquantum.doc

Quantum.doc

FUNTIONAL

Avramidi, Ivan: Methods of Mathematical Physics, February 12, 2005, p173              44

Belton Functional Analysis_notes p127                     9

Sunder Functional Analysis Spectral Theory p317

Differential Equations

Salamon, Simon: Differential Equations and Discrete Mathematics October 1996 p115.......................... 10

Schweizer, Ben: Partielle Differentialgleichungen, 25. Oktober 2011. p222                44

ANALYSIS COMPLEX

Berg, Christian: Complex Analysis p192, 2010,.k

Schlag A concise course in complex analysis and Riemann surfaces p207

Stein, Elias M. and Shakarchi, Rami: Complex Analysis, PRINCETON UNIVERSITY PRESS, October 20, 2007, p398 ........................ 25

Sternberg Theory of functions of a real variable p393

Taylor, Michael: Introduction to Complex Analysis, May 2011, p243 ............... 7

Teschl Topics in Real and Functional Analysis p177

Wiegerinck Advanced Function Theory p154

DYNAMIC SYSTEMS

ERGODIC THEORY

Dajani, Karma and Dirksin, Sjoerd: A Simple Introduction to Ergodic Theory, December 18, 2008, p134 ................18

Kettler Ergodic Theory p33

Sarig Lecture Notes on Ergodic Theory p137

Sarig Lecture Notes on Ergodic Theory p115

Steif Notes on Ergodic Theory p52

=========================================

FOURIER ANALYSIS

Berg Fourier Analysis p116

Schoenstadt An Introduction to Fourier Analysis p270......................222

=========================================================

(Computational) Geometry

Audin, Michele: Geometry, May 2002           10

Belyaev, Oleg A.: Fundamentals of Geometry, February 28, 2007, p256 ................28

Chen, Jianer: Computational Geometry - Methods and Applications, Third Edition, 1996, p227          

de Berg, Mark et al: Computational Geometry - Algorithms and Applications, Second Edition, Springer, 2000

de Berg, Mark: Computational Geometry - Algorithms and Applications, Third Edition, 2008

Virginia Department of Education: Geometry For Elementary School Teachers, February 2003

O'Rourke, Joseph: Computational geometry in C, Cambridge University Press, 2004

=================================

Information Theory

Cover, Thomas M. and Thomas, Joy A. :Elements of Information Theory, John Wiley & Sons, Inc., 1991 , p563 .........................104

INVARIANT THEORY

Math4GoogleMaps

Math4Music

Math4Programming

Math4SearchEngines

================================

Math General

McLennan, Andrew: The Nature and Origins of Modern Mathematics: an Elementary Introduction, July 27, 2009

Graham Concrete_Mathematics_A_Foundation_of_Computer_Science_2nd_Edition p690

Hwang An Introduction to Abstract Mathematics p487

Marsden Lectures on Geometric Methods in Mathematical Physics p134

McLennan The Nature and Origins of Modern Mathematics an Elementary Introduction p462.........  48

Megill Metamath p211

Stone Mathematics for Physics II p455

math_branches
├<Algebra>
│ ├<Category>
│ │ ├AWODEY Category Theory p328.pdf
│ │ ├Barr Category Theory p133.pdf
│ │ ├Riehl Category theory in context p258.pdf
│ │ └Streicher Introduction to CATEGORY THEORY and CATEGORICAL LOGIC p117.pdf
│ ├<InvariantTheory>
│ │ ├Draisma Invariant Theory with Applications p72.pdf
│ │ └Kraft CLASSICAL INVARIANT THEORY A Primer p129.pdf
│ ├<Linear>
│ │ ├Beezer A First Course in Linear Algebra p980.pdf
│ │ ├Byrne Applied and Computational Linear Algebra A First Course p504.pdf
│ │ ├Cherney Linear Algebra p430.pdf
│ │ ├Dawkins Linear Algebra p331.pdf
│ │ ├Finan Fundamentals of Linear Algebra p196.pdf
│ │ └Hefferon Linear Algebra p449.pdf
│ ├<Manifold>
│ │ └Petersen Manifold Theory p103.pdf
│ ├<ModelTheory>
│ │ ├Dawar Infinite and Finite Model Theory Part II p67.pdf
│ │ ├Libkin Elements of Finite Model Theory p326.pdf
│ │ └Weiss Fundamentals of Model Theory p64.pdf
│ ├<SetTheory>
│ │ ├Andre Axioms and Set Theory p459.pdf
│ │ ├Nesin Foundations of Mathematics I Set Theory p170.pdf
│ │ ├Roitman Introduction to Modern Set Theory p129.pdf
│ │ └Weiss AN INTRODUCTION TO SET THEORY p119.pdf
│ ├<UniversalAlgebra>
│ │ └Burris A Course in Universal Algebra p331.pdf
│ └Wallace Beginning and Intermediate Algebra p489.pdf
├AlgebraTerminology.docx
├<AlgorithmsZZZ>
│ └Dasgupta Algorithms p318.pdf
├<CalculusZZZ>
│ ├Chung Understanding Basic Calculus p292.pdf
│ ├LOOMIS ADVANCED CALCULUS p592.pdf
│ ├Predoi DIFFERENTIAL CALCULUS p279.pdf
│ ├Thompson Calculus Made Easy p292.pdf
│ └Thompson Calculus Made Easy1 p315.pdf
├<ComplexAnalysisZZZ>
│ ├Agarwal An Introduction to Complex Analysis p346.pdf
│ ├Beck Complex Analysis p159.pdf
│ ├Bennewitz COMPLEX ANALYSIS p116.pdf
│ ├Berg Complex Analysis p192.pdf
│ ├Marsden Basic Complex Analysis p519.pdf
│ ├Mathews Complex Analysis for Mathematics and Engineering p528.pdf
│ ├Schlag A concise course in complex analysis and Riemann surfaces p181.pdf
│ └Stein COMPLEX ANALYSIS p398.pdf
├<ComplexityTheory>
│ ├Arora Computational Complexity A Modern Approach p489.pdf
│ ├Gacs Complexity of Algorithms p242.pdf
│ ├Raghavendra Approximating NP-hard Problems Efficient Algorithms and their Limits p314.pdf
│ └Thompson A Complexity Theory for VLSI p106.pdf
├CRYPTOGRAPHY.doc
├CRYPTOGRAPHYOldtimes.doc
├<DifferentialZZZ>
│ ├Chasnov Introduction to Differential Equations p128.pdf
│ ├Miersemann Partial Differential Equations Lecture Notes p205.pdf
│ ├Shen 积分方程 p248.pdf
│ ├Terrell Notes on Differential equations p100.pdf
│ ├Tesch 常微分方程与动力系统 p246.pdf
│ ├Teschl Ordinary Differential Equations and Dynamical Systems p364.pdf
│ └Tracy Lectures on Differential Equations p175.pdf
├<ErgodicTheoryZZZ>
│ ├Dajani A Simple Introduction to Ergodic Theory p145.pdf
│ └Sarig Lecture Notes on Ergodic Theory p137.pdf
├<FourierZZZ>
│ └Gripenberg Fourier Analysis p137.pdf
├<FractalGeometryZZZ>
│ ├Falconer Fractal Geometry p155.pdf
│ └PEARSE AN INTRODUCTION TO DIMENSION THEORY AND FRACTAL GEOMETRY FRACTAL DIMENSIONS AND MEASURES p22.pdf
├<FunctionalZZZ>
│ ├Bass Functional analysis p182.pdf
│ ├Buhler FUNCTIONAL ANALYSIS p375.pdf
│ ├Cannarsa Lecture Notes on Measure Theory and Functional Analysis p216.pdf
│ ├Sunder Functional Analysis Spectral Theory p317.pdf
│ └Teschl Topics in Real and Functional Analysis p177.pdf
├<GeneralZZZ>
│ └Michelsen Funky Mathematical Physics Concepts p193.pdf
├<GeometryZZZ>
│ ├Africk Elementary College Geometry p374.pdf
│ ├Demailly Complex Analytic and Differential Geometry p455.pdf
│ ├Khudaverdian Riemannian Geometry p107.pdf
│ ├Preparata 计算几何导论 p499.pdf
│ └Vince Geometry for Computer Graphics p359.pdf
├<Information_TheoryZZZ>
│ ├Board Foundations and Trends in Communications and Information Theory p116.pdf
│ └Carter An introduction to information theory and entropy p139.pdf
├<LaplaceEquationZZZ>
│ ├Analytic Solutions to Laplace’s Equation in 2-D.pdf
│ ├Laplace equation in a rectangle, Fourier series.pdf
│ ├Laplace's equation Complex variables.pdf
│ ├LAPLACE’S EQUATION IN SPHERICAL COORDINATES.pdf
│ ├Laplace’s Equation, Analytic and Numerical Solution.pdf
│ ├Laplace’s Equation.pdf
│ ├Laplace’s Equation2.pdf
│ ├Laplace’s Equation3.pdf
│ ├Laplace’s Equation4.pdf
│ ├Numerical Solution of Laplace Equation.pdf
│ └The Planar Laplace Equation.pdf
├<MathAnalysisZZZ>
│ ├JOLY Introduction a lanalyse mathematique de la propagation d'ondes en regime harmonique p104.pdf
│ ├Rudin Principles of mathematical analysis p351.pdf
│ ├Trench INTRODUCTION TO REAL ANALYSIS p586.PDF
│ └Zakon Mathematical Analysis p365.pdf
├<MathematicalPhysicsZZZ>
│ ├Agoshkov METHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS p335.pdf
│ ├Avramidi Methods of Mathematical Physics0 p173.pdf
│ ├Avramidi Methods of Mathematical Physics1 p78.pdf
│ ├Govaerts Contemporary Problems in Mathematical Physics p326.pdf
│ ├KRASIL0SHCHIK Homological methods in equations of mathematical physics p149.pdf
│ ├Li 数学物理方程 p267.pdf
│ ├Marsden Lectures on Geometric Methods in Mathematical Physics p134.pdf
│ ├Meusburger Concepts and Methods of Mathematical Physics p142.pdf
│ ├Plenio Mathematical Physics Theory 2003 p133.pdf
│ ├Rybkin Math Physics Lecture Notes p270.pdf
│ ├Stone Mathematics for Physics I p459.pdf
│ ├Stone Mathematics for Physics II p455.pdf
│ └Stone Methods of Mathematical Physics I p316.pdf
├NumberTheory.doc
├<NumberXXX>
│ ├Milne Algebraic Number Theory p164.pdf
│ ├Rademacher Lectures on Analytic Number Theory p283.pdf
│ ├Raji An Introductory Course in Elementary Number Theory p171.pdf
│ ├Shoup Computational Introduction to Number Theory v2 p598.pdf
│ └Stein Elementary Number Theory Primes, Congruences, and Secrets p172.pdf
├Number_aks.docx
├Number_AKSOutline.docx
├Number_Primality.doc
├Number_RandomNumber.doc
├<NumericalZZZ>
│ ├Bastian Numerical Computation of Multiphase Flows in Porous Media p236.pdf
│ ├Benzoni-Gavage Analyse mathematique et numerique de la dynamique des fluides compressibles p114.pdf
│ ├Deturck Lectures on Numerical Analysis p125.pdf
│ ├FEM_FEPG 基于FEPG的有限元方法 p142.pdf
│ ├Feng Boundary Element Methods p501.pdf
│ ├Hoffman Computational Thermodynamics1 p217.pdf
│ ├Huang 数值计算方法及其程序设计 p445.pdf
│ ├KANE ANALYSE MATHéMATIQUE ET SIMULATION NUMéRIQUE DE MODèLES D'éCOULEMENT DE FLUIDES INCOMPRESSIBLES EN SURFACE LIBRE ET MILIEU POREUX DéFORMABLE p119.pdf
│ ├Konstantinov FOUNDATIONS OF NUMERICAL ANALYSIS p278.pdf
│ ├Krafczyk Lattice Boltzmann methods for CFD p183.pdf
│ ├Luo LBM for Two Dimensional Hdrofynamics p183.pdf
│ ├Magnus Analyse numerique 2 p205.pdf
│ ├METIER Modelisation, analyse mathematique et applications numeriques de problemes d'interaction fluid -structure instationnaires p220.pdf
│ ├Quarteroni Numerical Mathematics p669.pdf
│ ├Rung Numerische Methoden der Thermo- und Fluiddynamik p166.pdf
│ ├Scheid 全美经典数值分析第二版 p398.pdf
│ ├Scott Numerical Analysis p341.pdf
│ ├XuDH 偏微分方程数值解法 p441.pdf
│ └Young Introduction to Numerical Methods and Matlab Programming for Engineers p180.pdf
├<Probability>
│ ├Dekking A Modern Introduction to Probability and Statistics Understanding p483.pdf
│ ├Grinstead Introduction to Probability p520.pdf
│ ├Kerns Introduction to Probability and Statistics Using R p412.pdf
│ ├Montgomery Applied Statistics and Probability for Engineers p976.pdf
│ └Soong FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS p408.pdf
├<ProofTheoryZZZ>
│ ├Buss Lectures on Proof Theory p123.pdf
│ ├Restall proof theory and philosophy p168.pdf
│ └Tait Lectures on Proof Theory p119.pdf
├<Topology>
│ ├Dundas Differential Topology p210.pdf
│ ├Edelsbrunner COMPUTATIONAL TOPOLOGY AN INTRODUCTION p294.pdf
│ ├Guillemin DIFFERENTIAL TOPOLOGY p236.pdf
│ └Renzo Introduction to Topology p118.pdf
└<VectorTensorAnalysisXXX>
├Bowen INTRODUCTION TO VECTORS AND TENSORS p314.pdf
├Brannon Functional and Structured Tensor Analysis for Engineers p323.pdf
├Flügge Tensor Analysis and Continuum Mechanics p214.pdf
├Heinbockel Introduction to Tensor Calculus and Continuum Mechanics p373.pdf
├Marsden Manifolds, Tensor analysis, and Applications p617.pdf
├MARSDEN MATHEMATICAL FOUNDATIONS OF ELASTICITY p576.pdf
├Nelson Tensor analysis p138.pdf
├VANICEK TENSORS p101.pdf
├Yang 张量 p426.pdf
└郭日修 弹性力学与张量分析 p287.pdf

My Math Research Plan

Since 2006, after the death of my father, people have persuaded me to do something to contribute to the society and not to waste my talents. Over this time period, I have studied very hard and tried many areas of researches and studies before finally and eventually fixing my research area of computational number theory, particularly primality testing in November 2011..

My current and future research area is and will always be number theory, and particularly prime number prove and later integer factorization related to cryptography. I was not born mathematician. It took me a long long way to finally decide to do math. My major was in thermal science and I have been in the energy and power industry since long. Over the past several years since 2007, I have tried various branches of sciences with some sorts of researches and authoring in process.

Although there is no way to enter the academic world except with my own research at hand, yet I am determined to carry out my researches on my own at any cost under any circumstances, how hard my condition may be. Therefore considering all the constraints to research capacity as a solo researcher without the necessary supports and working atmosphere of a well established academic entity, I am determined to reorient myself as a number theorist, in connection with cryptography and Internet security. With my superb math foundation and learning capacity, I can step in the number theory and other math and science areas fairly quickly.

I chose number theory as my future research area because first all my previous attempts in other branches of science were failed and no universities and organizations were willing to support my researches, and second, without good experimental facilities and a good team I am unable to continue most of my research projects. Number theory on other hand depends mainly on my personal talent and intelligence. On other hand, any serious researches on whatever topics you may choose involves lots of math, and sometimes math is a determining tools in researches of other sciences. But I don’t have so much time to cope with both of them. I came to number theory also as a result of my combat to Internet blockade. In 2009 I was determined to work on Internet security in order to ensure my free access to and my security of my identity while using the Internet with various encryption services. I was attracted by the cryptographic technologies, and later it was found the its mathematical foundation is modern algebra (DES) and number theory (RSA). So it was a natural conclusion that these sciences will become parts of my studies objects.

During the first years, I will be focusing on prime number testing and integer factorization. But in my later years my researches will also extend to other branches of number theory. And finally I wish to join the world mathematician communities again with my researches on number theory, particularly those related to cryptography.

I plan first to propose my own improvements to existing deterministic, unconditional and polynomial time prime number tests – particularly the AKS test and go a step further to figure out my own. My second phase of research will be to benchmark the probabilistic and the deterministic primality tests based on complexity considerations in order to find out the threshold between these two and to put forward criteria of the real world optimal algorithms for various applications. I hope these studies will contribute to the development of practical cryptographic systems used for Internet security over the next years.

Currently I am doing my researches on my own – that is, I do not work in any university or any math institute in China. I also pay all the expenses in doing the researches, therefore I have to earn money to support my researches. But it is very difficult, if not impossible, to achieve what I have in mind when I continue to do this way, because during the day I have to earn money and only in the evening can I find 1 or 2 hours for number theory, if I still have to study number theory alone.

Therefore I would hope that someone could provide me with some help. I would appreciate it very much if he or she would provide me with a place where I can quietly conduct my researches on number theory and other related topics. It would also greatly help me if he or she could provide me with the recent development of the AKS algorithm.

Mathematics  (2010 -2011) see "Math" section for current research and further information

I arrived at mathematics mainly because without a research position in an university or institution, I am unable to conduct my researches on physical sciences such as thermodynamics, solar physics, fluiddynamics. And also because math is the basic science without a solid foundation one has no chance to carry out real world researches in any other sciences. And I am so busy that I cannot afford to maintain competences both in math and phyusical sciences. There are possibly other reasons why I finally chose math as my research area, either as hobby or as my academic career. I have tried

• differential equations
• functional analysis, in particular computational functional analysis and
• numerical computation

but without any publications yet, and now I am working mainly on number theory related to cryptography. See my other pages of this site.