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1

Nickerson, Raymond S. Mathematical reasoning: Patterns, problems, conjectures, and proofs. New York: Psychology Press, 2010.

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2

Nickerson, Raymond S. Mathematical reasoning: Patterns, problems, conjectures, and proofs. New York: Psychology Press, 2010.

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3

E, Ladas G., ed. Dynamics of second order rational difference equations: With open problems and conjectures. Boca Raton, FL: Chapman & Hall/CRC, 2002.

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4

Graczyk, Jacek. The real Fatou conjecture. Princeton, N.J: Princeton University Press, 1998.

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5

Schwartz, Diane Driscoll. Conjecture & proof: An introduction to mathematical thinking. Fort Worth: Saunders College Pub., 1997.

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6

Charles, Figuieres, ed. Theory of conjectural variations. River Edge, NJ: World Scientific, 2004.

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7

Salamon, Peter. Facts, conjectures, and improvements for simulated annealing. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2003.

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8

Gessen, Masha. Perfect Rigour: A Genius and the Mathematical Breakthrough of a Lifetime. New York: Icon Books, 2011.

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9

Ecalle, Jean. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Paris: Hermann, 1992.

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10

Gul, Faruk. Foundation of dynamic monopoly and the Coase conjecture. Stanford, Calif: Institute for Mathematical Studies in the Social Sciences, Stanford University, 1985.

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11

Doxiadēs, Apostolos K. Uncle Petros and Goldbach's conjecture. New York: Bloomsbury, 2000.

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12

Doxiadēs, Apostolos K. Uncle Petros and Goldbach's conjecture. London: Faber and Faber, 2000.

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13

Stiebitz, Michael. Graph edge coloring: Vizing's theorem and Goldberg's conjecture. Hoboken, NJ: Wiley, 2012.

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14

Pogorzelski, H. A. Transtheoretic foundations of mathematics (general summary of results). Orono, Me: Research Institute for Mathematics, 2004.

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15

Pogorzelski, H. A. Transtheoretic foundations of mathematics (general summary of results). Orono: Research Institute for Mathematics, 2004.

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16

France) Séminaire sur les pinceaux arithmétiques (1984 Paris. Séminaire sur les pinceaux arithmétiques: La conjecture de Mordell. Paris: Société mathématique de France, 1985.

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17

Nickerson, Raymond. Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs. Taylor & Francis Group, 2011.

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18

Nickerson, Raymond. Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs. Taylor & Francis Group, 2011.

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19

Nickerson, Raymond. Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs. Taylor & Francis Group, 2015.

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20

Nickerson, Raymond. Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs. Taylor & Francis Group, 2011.

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21

Nickerson, Raymond. Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs. Taylor & Francis Group, 2011.

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22

Nickerson, Raymond. Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs. Taylor & Francis Group, 2011.

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23

Scientific computation on mathematical problems and conjectures. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1990.

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24

Mathematical reasoning: Patterns, problems, conjectures, and proofs. New York: Psychology Press, 2010.

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25

Lacort, Mercedes Orús. Fermat Equation over several fields and other historical mathematical conjectures. Lulu.com, 2019.

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26

Varga, Richard S. Scientific Computations on Mathematical Problems and Conjectures (CBMS-NSF Regional Conference Series in Applied Mathematics). Society for Industrial Mathematics, 1987.

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27

Kenney, Margaret J., and Stanley J. Bezuszka. Number Treasury 3: Investigations, Facts, and Conjectures about More Than 100 Number Families. World Scientific Publishing Co Pte Ltd, 2015.

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28

(Editor), Steven C. Ferry, Andrew Ranicki (Editor), and Jonathan M. Rosenberg (Editor), eds. Novikov Conjectures, Index Theorems, and Rigidity: Oberwolfach 1993 (London Mathematical Society Lecture Note Series). Cambridge University Press, 1996.

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29

Ladas, G. E. Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Taylor & Francis Group, 2001.

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30

Ladas, G. E. Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Taylor & Francis Group, 2001.

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31

Ladas, G. E. Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Chapman & Hall/CRC, 2001.

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32

Salamon, Peter, Paolo Sibani, and Richard Frost. Facts, Conjectures, and Improvements for Simulated Annealing (SIAM Monographs on Mathematical Modeling and Computation) (Monographs on Mathematical Modeling and Computation). Society for Industrial and Applied Mathematic, 2002.

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33

D'Agostino, Susan. How to Free Your Inner Mathematician. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.001.0001.

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How to Free Your Inner Mathematician: Notes on Mathematics and Life offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. With practical insight and years of award-winning mathematics teaching experience, DAgostino offers more than 300 hand-drawn sketches alongside accessible descriptions of fractals, symmetry, fuzzy logic, knot theory, Penrose patterns, infinity, the Twin Prime Conjecture, Arrows Impossibility Theorem, Fermats Last Theorem, and other intriguing mathematical topics. Readers are encouraged to embrace change, proceed at their own pace, mix up their routines, resist comparison, have faith, fail more often, look for beauty, exercise their imaginations, and define success for themselves. Mathematics students and enthusiasts will learn advice for fostering courage on their journey regardless of age or mathematical background. How to Free Your Inner Mathematician delivers not only engaging mathematical content but provides reassurance that mathematical success has more to do with curiosity and drive than innate aptitude.
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34

Sylla, Edith. Probability in 17th- and 18th-century Continental Europe from the Perspective of Jacob Bernoulli’s Art of Conjecturing. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.4.

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Edith Dudley Sylla, “Probability in Seventeenth and Eighteenth Century Continental Europe from the perspective of Jacob Bernoulli’s Art of Conjecturing.” Abstract Jacob Bernoulli’s book The Art of Conjecturing, published in Basel in 1713 based on a carefully written manuscript left incomplete at the time of Bernoulli’s death in 1705, may be considered the founding document of mathematical probability. It brought together the mathematics of games of chance found in Christiaan Huygens’ On Reckoning in Games of Chance with approaches to weighing the probable truth of conjectures in civil, moral, or economic matters. The four parts of Bernoulli’s book are described. Whereas a key concept for Huygens and Bernoulli was expectation, Abraham De Moivre defined probability in terms of relative frequency. The chapter closes with a brief discussion of De Moivre’s De mensura sortis and The Doctrine of Chances.
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35

Speicher, Roland. Random banded and sparse matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.23.

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This article discusses some mathematical results and conjectures about random band matrix ensembles (RBM) and sparse matrix ensembles. Spectral problems of RBM and sparse matrices can be expressed in terms of supersymmetric (SUSY) statistical mechanics that provides a dual representation for disordered quantum systems. This representation offers important insights into nonperturbative aspects of the spectrum and eigenfunctions of RBM. The article first presents the definition of RBM ensembles before considering the density of states, the behaviour of eigenvectors, and eigenvalue statistics for RBM and sparse random matrices. In particular, it highlights the relations with random Schrödinger (RS) and the role of the dimension of the lattice. It also describes the connection between RBM and statistical mechanics, the spectral theory of large random sparse matrices, conjectures and theorems about eigenvectors and local spacing statistics, and the RS operator on the Cayley tree or Bethe lattice.
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36

Kythe, Prem K. Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture. Taylor & Francis Group, 2016.

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37

Kythe, Prem K. Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture. Taylor & Francis Group, 2016.

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38

Complex analysis: Conformal inequalities and the Bieberbach conjecture. Boca Raton: Taylor & Francis, 2016.

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39

Wang, Genxi. Triple-Number and Mathematical Conjecture. American Academic Press, 2019.

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40

Smart Medicine and Mathematical Conjecture. American Academic Press, 2022.

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41

Kepler's Conjecture. New York: John Wiley & Sons, Ltd., 2003.

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42

SMART MEDICINE and MATHEMATICAL CONJECTURE (Second Edition). American Academic Press, 2023.

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43

Lacort, Mercedes Orús. Mathematical Induction Method in Goldbach's Strong Conjecture. Lulu Press, Inc., 2017.

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44

Querou, Nicolas. Theory of Conjectural Variations. World Scientific Publishing Co Pte Ltd, 2004.

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45

Catalan's conjecture. London: Springer, 2008.

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46

Scheepers, Marion, and Ondrej Zindulka. Centenary of the Borel Conjecture. American Mathematical Society, 2020.

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47

Schwartz, Diane Driscoll. Conjecture and Proofs: An Introduction to Mathematical Thinking. Brooks Cole, 1996.

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48

Schwartz. Conjecture and Proofs: An Introduction to Mathematical Thinking. Brooks Cole, 1996.

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49

The Kepler Conjecture (London Mathematical Society Lecture Note). Cambridge University Press, 2008.

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50

Szpiro, George G. La Conjecture de Poincaré. LATTES, 2007.

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