The author was born and raised in San Francisco, California. He completed his Bachelor of Science in Chemistry at Stanford University and his PhD in Chemistry at Washington University, St. Louis, under the guidance of Professor Tien-Sung Lin. The author pursued his postdoctoral studies with Professor Richard H. Clarke at Boston University.The author’s independent career began as a chemistry faculty member at West Virginia University in Morgantown, West Virginia. He moved to Loyola University Chicago four years later, where he enjoyed a thirty-four-year sojourn. He is now Professor Emeritus.The author during his time in Chicago wrote two books published by Taylor & Francis: Chemical Thermodynamics and Information Theory with Applications (2011) and Invitation to Protein Sequence Analysis Through Probability and Information (2019).The Thermodynamics of Mathematical Representation is the author’s third book. His hope is that this book will be useful in special topics, classes, and seminars for math/science students and for faculty looking for ideas to incorporate into introductory chemistry, physical chemistry, and calculus classes. The author would have taught the classes and seminars himself, but the pandemic, retirement age, the curse of Zoom©teaching, and the wonderful call to be closer to family in Central New York intervened.

• Preface Acknowledgements Author Biography List of Principal Abbreviations Glossary of Principal Terms Chapter One: Aspects of the Thermodynamics of Mathematical Representation Chapter Two: A Tour of Thermodynamic Systems and Operational Laws Chapter Three: A Tour of the Real Number System and Thermodynamic Intertwining Chapter Four: The Information Bridge Joining Thermodynamics and the Number Systems Chapter Five: Information, Integer Partitions, and Small-System Thermodynamics Chapter Six: Information, Prime Number Representations, and Thermodynamic Overlays Chapter Seven: Information, Limit Operations, and Thermodynamic Overlays Chapter Eight: Special Limit Operations and Maximum Entropy Principles Chapter Nine: Points, Paths, and Horizons Epilogue Appendix A: A Synopsis of Thermodynamic Laws Appendix B: Notes and References Appendix C: A Précis on Point Sets and Operations Appendix D: Answers to Selected Exercises Appendix E: Bibliography Index

The author was born and raised in San Francisco, California. He completed his Bachelor of Science in Chemistry at Stanford University and his PhD in Chemistry at Washington University, St. Louis, under the guidance of Professor Tien-Sung Lin. The author pursued his postdoctoral studies with Professor Richard H. Clarke at Boston University.The author’s independent career began as a chemistry faculty member at West Virginia University in Morgantown, West Virginia. He moved to Loyola University Chicago four years later, where he enjoyed a thirty-four-year sojourn. He is now Professor Emeritus.The author during his time in Chicago wrote two books published by Taylor & Francis: Chemical Thermodynamics and Information Theory with Applications (2011) and Invitation to Protein Sequence Analysis Through Probability and Information (2019).The Thermodynamics of Mathematical Representation is the author’s third book. His hope is that this book will be useful in special topics, classes, and seminars for math/science students and for faculty looking for ideas to incorporate into introductory chemistry, physical chemistry, and calculus classes. The author would have taught the classes and seminars himself, but the pandemic, retirement age, the curse of Zoom©teaching, and the wonderful call to be closer to family in Central New York intervened.

• Preface Acknowledgements Author Biography List of Principal Abbreviations Glossary of Principal Terms Chapter One: Aspects of the Thermodynamics of Mathematical Representation Chapter Two: A Tour of Thermodynamic Systems and Operational Laws Chapter Three: A Tour of the Real Number System and Thermodynamic Intertwining Chapter Four: The Information Bridge Joining Thermodynamics and the Number Systems Chapter Five: Information, Integer Partitions, and Small-System Thermodynamics Chapter Six: Information, Prime Number Representations, and Thermodynamic Overlays Chapter Seven: Information, Limit Operations, and Thermodynamic Overlays Chapter Eight: Special Limit Operations and Maximum Entropy Principles Chapter Nine: Points, Paths, and Horizons Epilogue Appendix A: A Synopsis of Thermodynamic Laws Appendix B: Notes and References Appendix C: A Précis on Point Sets and Operations Appendix D: Answers to Selected Exercises Appendix E: Bibliography Index

The author was born and raised in San Francisco, California. He completed his Bachelor of Science in Chemistry at Stanford University and his PhD in Chemistry at Washington University, St. Louis, under the guidance of Professor Tien-Sung Lin. The author pursued his postdoctoral studies with Professor Richard H. Clarke at Boston University.The author’s independent career began as a chemistry faculty member at West Virginia University in Morgantown, West Virginia. He moved to Loyola University Chicago four years later, where he enjoyed a thirty-four-year sojourn. He is now Professor Emeritus.The author during his time in Chicago wrote two books published by Taylor & Francis: Chemical Thermodynamics and Information Theory with Applications (2011) and Invitation to Protein Sequence Analysis Through Probability and Information (2019).The Thermodynamics of Mathematical Representation is the author’s third book. His hope is that this book will be useful in special topics, classes, and seminars for math/science students and for faculty looking for ideas to incorporate into introductory chemistry, physical chemistry, and calculus classes. The author would have taught the classes and seminars himself, but the pandemic, retirement age, the curse of Zoom©teaching, and the wonderful call to be closer to family in Central New York intervened.

• Preface Acknowledgements Author Biography List of Principal Abbreviations Glossary of Principal Terms Chapter One: Aspects of the Thermodynamics of Mathematical Representation Chapter Two: A Tour of Thermodynamic Systems and Operational Laws Chapter Three: A Tour of the Real Number System and Thermodynamic Intertwining Chapter Four: The Information Bridge Joining Thermodynamics and the Number Systems Chapter Five: Information, Integer Partitions, and Small-System Thermodynamics Chapter Six: Information, Prime Number Representations, and Thermodynamic Overlays Chapter Seven: Information, Limit Operations, and Thermodynamic Overlays Chapter Eight: Special Limit Operations and Maximum Entropy Principles Chapter Nine: Points, Paths, and Horizons Epilogue Appendix A: A Synopsis of Thermodynamic Laws Appendix B: Notes and References Appendix C: A Précis on Point Sets and Operations Appendix D: Answers to Selected Exercises Appendix E: Bibliography Index