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There is a foundational crisis in financial theory and professional investment practice: There is little, if any, credible evidence that active investment strategies and traditional institutional quantitative technologies are able to provide superior risk-adjusted, cost-adjusted return over investment relevant horizons.Economic and financial theory has been in error for more than fifty years and is the fundamental cause of the persistent ineffectiveness of professional asset management. Contemporary sociological and economic theory, agent-based modeling, and an appreciation of the social context for preference theory provides a rational and intuitive framework for understanding financial markets and economic behavior. The author narrates his long-term experience in the use and limitations of traditional tools of quantitative asset management as an institutional asset manager in practice and as a quantitative analyst and strategist on Wall Street. Monte Carlo simulation methods, modern statistical tools, and U.S. patented innovations are introduced to redefine portfolio optimality and procedures for enhanced professional asset management. A new social context for expected utility theory leads to a novel understanding of modern equity markets as a financial intermediary for purchasing power constant time-shift investing uniquely appropriate for meeting investor long-term investment objectives. This book addresses the limitations and indicated resolutions for more useful financial theory and more reliable asset management technology. In the process, it traces the major historical developments of theory and institutional asset management practice and their limitations over the course of the 20th century to the present, including Markowitz and the birth of modern finance, CAPM theory and emergence of institutional quantitative asset management, CAPM and VM theory limitations and ineffective iconic tools and strategies, andinnovations in statistical methodologies and financial market theory.

This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by |x|p + |y|p = 1 where p ¿ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric curves, and differential equations. Projects and opportunities for research abound, as we explore how similar (or different) the trigonometric and squigonometric worlds might be.Comprised of many short chapters, the book begins with core definitions and techniques. Successive chapters cover inverse squigonometric functions, the many possible re-interpretations of ¿, two deeper dives into parameterizing the squigonometric functions, and integration. Applications include a celebration of Piet Hein¿s work in design. From here, more technical pathways offer further exploration. Topicsinclude infinite series; hyperbolic, exponential, and logarithmic functions; metrics and norms; and lemniscatic and elliptic functions. Illuminating illustrations accompany the text throughout, along with historical anecdotes, engaging exercises, and wry humor.Squigonometry: The Study of Imperfect Circles invites readers to extend familiar notions from trigonometry into a new setting. Ideal for an undergraduate reading course in mathematics or a senior capstone, this book offers scaffolding for active discovery. Knowledge of the trigonometric functions, single-variable calculus, and initial-value problems is assumed, while familiarity with multivariable calculus and linear algebra will allow additional insights into certain later material.