From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017 ()

Preface
	A Portrait of the Man as a Mathematician
	Overview of this Proceedings
	Nonlinear Analysis and Optimization
	Experimental Mathematics
	Number Theory, Special Functions and Pi
	Mathematical Finance
	Mathematical Education and Public Communication
	Visualization
	In Summary
	References
Acknowledgements
Contents
Part I Applied Analysis, Optimisation,  and Convexity
Introduction
	References
Symmetry and the Monotonicity of Certain Riemann Sums
	1 Introduction
	2 Szilárd\'s Theorems
	3 Extensions of Szilárd\'s Theorems
		3.1 Symmetrisation
	4 Monotonicity and Symmetrization
	5 Analysis of the Function 11-bx+x2
	6 Concluding Remarks
	References
Risk and Utility in the Duality Framework of Convex Analysis
	1 Preferences Under Uncertainty
	2 How Should ``Risk\'\' Be Understood?
	3 How Should Utility Be Understood?
	4 Risk Versus Utility
	References
Characterizations of Robust and Stable Duality for Linearly Perturbed Uncertain Optimization Problems
	1 Introduction
	2 Special Cases and Applications
	3 Robust Conjugate Duality
		3.1 Basic Lemmas
		3.2 Robust Duality
	4 Strong Robust Duality
	5 Reverse Strong and Min-Max Robust Duality
	6 Stable Robust Duality
	7 Stable Strong Robust Duality
	8 Exact Subdifferential Formulas: Robust Basic Qualification Condition
	References
Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples
	1 Introduction
	2 Background and preliminaries
	3 Convergence of Projection Methods
	4 Implementations
	5 Discussion
		5.1 Further Investigation
		5.2 Conclusion
	References
Part II Education
Introduction
On the Educational Legacies of Jonathan M. Borwein
	1 Introduction
		1.1 Introducing the Voices
	2 Issues: Practitioner Voices
		2.1 Overview
		2.2 Diversity
		2.3 Fear
		2.4 Transformation
	3 Schisms: A Theoretician\'s Voice
		3.1 Schisms, Theory, and Critical Examples
		3.2 The Micro and Macro Level
		3.3 Theory and Interdisciplinarity
		3.4 Standard Paradigms and Patterns
	4 Jon\'s Coda
		4.1 Experimental Mathematics in Education: Beauty and Philosophy
		4.2 From Littlewood to Dawkins
	5 Conclusion
	References
How Mathematicians Learned to Stop Worrying and Love the Computer
	References
Crossing Boundaries: Fostering Collaboration Between Mathematics Educators and Mathematicians in Initial Teacher Education Programmes
	1 Introduction
	2 Project Context and Overview
	3 Theoretical Background
	4 Research Methods
	5 Towards Integrated Models of Teacher Education
		5.1 Co-developed and Co-taught Courses Integrating Content and Pedagogy
		5.2 Communities of Pre-service Mathematics Teachers
	6 Concluding Comments
	References
Mathematics Education in the Computational Age: Challenges and Opportunities
	References
Mathematics Education for Indigenous Students in Preparation for Engineering and Information Technologies
	1 Introduction
	2 Development of the Curriculum and Schedule  for the Mathematics Workshop
		2.1 Analysis of the Students\' Backgrounds
		2.2 Initial Consideration of Topics and Pedagogy,  in Light of Background
		2.3 Providing a Means of Feedback to Establish Workshop Topics, Levels and Teaching Modes
		2.4 Results and Consequences of the Additional Questionnaire
		2.5 Resources Committed to Developing and Teaching the Workshop
	3 Teaching, Learning and Evolving the Workshop
		3.1 Setting Expectations that Students will Have a Genuine Voice
		3.2 Responding to Students Immediately and Continuously
		3.3 How a Culture of Inquiry was Shared Between Streams
		3.4 Incorporating Cooperation and Collaboration  in the Cryptography Session
		3.5 Promoting Inquisitive, Critical Thinking with the Rubik\'s Cube
	4 Assessing the Mathematics Workshop
	5 Conclusions
	References
Origami as a Teaching Tool for Indigenous Mathematics Education
	1 Introduction
	2 Origami: Definition and History
	3 Origami Mathematics
	4 Origami in Education
	5 Narratives in Education: Theory and Evidence
	6 Linking Story to Country and Culture
	7 Story, Culture and Artistic Expressions
	8 Narrative in Origami
	9 Origami and Indigenous Art
	10 Summary
	References
Dynamic Visual Models: Ancient Ideas and New Technologies
	1 Introduction
	2 Mathematical Proof in the Calculus Classroom
	3 The Sum of the First n Consecutive Odd Positive Integers
	4 The Sum of the First n Consecutive Positive Integers
	5 The Sum of Squares
	6 The Sum of Cubes
	7 Conclusion
	References
A Random Walk Through Experimental Mathematics
	1 Introduction
		1.1 The Confluence of Opportunities
		1.2 The Western Active Learning Space
		1.3 Active Learning Techniques
		1.4 Active Learning in Mathematics
	2 Choices of Topics
		2.1 Continued Fractions and Rational Approximations of sqrt2
		2.2 Newton\'s Method, sqrt2, and Solving Nonlinear Equations
		2.3 Backward Error
		2.4 Modified Equations
		2.5 Chaos Game Representation of DNA Sequences
	3 Concluding Remarks
	References
Part III Financial Mathematics
Introduction
	References
A Holistic Approach to Empirical Analysis: The Insignificance of P, Hypothesis Testing and Statistical Significance*
	1 Introduction
	2 What is the Problem
	3 P and Statistical Hypothesis Testing in Context
	4 Robust Samples, Analytical Significance and Impactfulness
	5 The Role of Non-Statistical Theory and Statistical Analysis
	6 Statistical Analysis: The Implications of Going Beyond Statistical Significance
	7 The Persistence of Inappropriate Approaches to Statistical Analysis
	8 Conclusion
	References
Do Financial Gurus Produce Reliable Forecasts?
	1 Introduction and Background
	2 Methodology
	3 Results
		3.1 Forecaster Accuracy
		3.2 Time Frame and Specificity Analysis
		3.3 Ranking the Forecasters
	4 Conclusion
	References
Entropy Maximization in Finance
	1 Introduction
	2 Preliminaries
		2.1 Entropy Optimization Problem
		2.2 A Portfolio Model
	3 Markowitz Portfolio Theory
	4 Capital Asset Pricing Model
	5 Fundamental Theorem of Asset Pricing
	6 Selecting a Pricing Martingale Measure by Entropy Maximization
	7 Super/Sub-hedging Bounds
	8 Conclusion
	References
Part IV Number Theory, Special Functions,  and Pi
Introduction
	References
Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials
	1 Introduction
	2 Substitutions and their Fourier Matrices
	3 Lyapunov Exponents
	4 Proof of the Main Result
	5 Examples: From Polynomials to Substitutions
	6 Extensions and Outlook
	References
The Borwein Brothers, Pi and the AGM
	1 Introduction
	2 Preliminaries: Means, Elliptic Integrals and Theta Functions
	3 Historical Remarks
	4 Some Superlinearly Convergent Algorithms for π
	5 Equivalence of Some Algorithms for π
	6 Some Fast (but Linear) Algorithms for π
	7 Fast Algorithms for the Elementary Functions
	References
The Road to Quantum Computational Supremacy
	1 Fairy Tales or More Cautionary Tales?
	2 Quantum Algorithmics
	3 What Is Quantum Computational Supremacy?
	4 Criteria for Quantum Computational Supremacy
	5 Is the Quest for Quantum Computational Supremacy Worthwhile?
	6 Google Quantum Computational Supremacy
	7 IBM Challenge
	8 Latest Developments
	9 Closing Remarks
	10 P.S. Quantum Desperation
	References
Nonlinear Identities for Bernoulli  and Euler Polynomials
	1 Introduction
	2 Some Auxiliary Results
	3 The Proof of Theorem 1
	4 Further Remarks
	References
Metrical Theory for Small Linear Forms and Applications to Interference Alignment
	1 Metric Diophantine Approximation
	2 Statements of Results
		2.1 Mixed Type Linear Forms
		2.2 Diophantine Approximation Over Complex Numbers
	3 Some Proofs
		3.1 Proof of Theorem3
		3.2 Proof of Theorem4
		3.3 Proof of Theorem5
		3.4 Proofs of Theorems6 and 7
	4 Applications to Interference Alignment
	References
Improved Bounds on Brun\'s Constant
	1 Introduction
	2 Preparatory Results
		2.1 Bounds on the Number of Divisors
		2.2 A Large Sieve Inequality
	3 Riesel and Vaughan\'s Bounds on π2(x)
	4 Calculations
		4.1 Computing B(4cdot1018): The Lower Bound in Theorem 1
		4.2 The Upper Bound in Theorem 1
		4.3 Potential Improvements
	References
Extending the PSLQ Algorithm  to Algebraic Integer Relations
	1 Introduction
		1.1 Algorithm Overview
		1.2 Algebraic Number Theory
	2 Extension to Algebraic Integers
		2.1 Reduction
		2.2 Algebraic PSLQ
	3 Experimental Results
		3.1 Methodology
		3.2 Real and Complex PSLQ
		3.3 Real Quadratic Extension Fields
		3.4 Complex Quadratic Extension Fields
	4 Further Work
	References
Short Walk Adventures
	1 Introduction
	2 Uniform Random Walks
	3 Zeta Mahler Measures
	4 Generic Two-Step Random Walks
	5 Linear Mahler Measures
	6 Modular Parametrisation of p3(x) and Related Formulae
	7 Modular Computation for W5\'(0) and W6\'(0)
	8 Mahler Measures Related to a Variation of Random Walk
	9 Conclusion
	References