Copyright Year 2023
ISBN 9781032365053
May 22, 2023 Forthcoming
276 Pages 108 B/W Illustrations
The Baseball Mysteries: Challenging Puzzles for Logical Detectives is a book of baseball puzzles, logical baseball puzzles. To jump in, all you need is logic and a casual fanfs knowledge of the game. The puzzles are solved by reasoning from the rules of the game and a few facts.
The logic in the puzzles is like legal reasoning. A solution must argue from evidence (the facts) and law (the rules). Unlike legal arguments, however, a solution must reach an unassailable conclusion.
There are many puzzle books. But therefs nothing remotely like this book. The puzzles here, while rigorously deductive, are firmly attached to actual events, to struggles that are reported in the papers every day.
The puzzles offer a unique and scintillating connection between abstract logic and gritty reality.
Actually, this book offers the reader an unlimited number of puzzles. Once youfve solved a few of the challenges here, every boxscore you see in the papers or online is a new puzzle! It can be anywhere from simple, to complex, to impossible.
For anyone who enjoys logical puzzles.
For anyone interested in legal reasoning.
For anyone who loves the game of baseball.
Jerry Butters has a BA in mathematics from Oberlin College, and an MS in mathematics and a PhD in economics from the University of Chicago. He taught mathematics for two years at Mindanao State University in the Philippines as a Peace Corps volunteer. He taught economics for five years at Princeton University. For most of his career, he worked on consumer protection cases and policy issues at the Federal Trade Commission. In his retirement, he has become a piano teacher and performer. He enjoys hobbies ranging from reading Chinese to practicing Taiji. This book is an outgrowth of another of his hobbies?his love of designing and solving puzzles of all sorts.
Jim Henle has a BA in mathematics from Dartmouth College and a PhD from M.I.T. He taught for two years at U. P. Baguio in the Philippines as a Peace Corps volunteer, two years at a middle school as alternative service, and 42 years at Smith College. His research is primarily in logic and set theory, with additional papers in geometry, graph theory, number theory, games, economics, and music. He edited columns for The Mathematical Intelligencer. He authored or co-authored five books. His most recent book, The Proof and the Pudding, compares mathematics and gastronomy. He has collaborated with Jerry on puzzle papers and chamber music concerts.
1. The Game Begins. 1.1. In Plain Sight. 1.2. Working Backwards. 1.3. A Walk-Off. 1.4. An Imperfect Game. 1.5. The Five-Run Inning. 1.6. Casey At the Bat. 2. Historical Mysteries. 2.1. Substitutions. 2.2. Crazy Things Happen. 2.3. The Game-Winning RBI. 2.4 Number 299. 2.5. Number 400. 2.6. Who Scored When. 2.7. Earning and Unearning. 3. Steady Games. 3.1. A Steady Game. 3.2. Another Steady Game. 3.3. A Steady Double. 3.4. Cicioneddos. 3.5. Maltagliatti. 3.6. Lucca. 4. Secrets of the Past. 4.1. Ancient Rivalry. 4.2. Double Switches. 4.3. Switch Central. 4.4. A World Series Game. 4.5. The Other Side of The World. 4.6. Learyfs Bad Day. 5. Puzzles as Art. 5.1. Never Out, Never In. 5.2. Double Plays. 5.3. Mistakes Were Made. 5.4. The Two Rods. 5.5. The Guy Who Did It All. 5.6. Scraps. 6. Baseball Archaelogy. 6.1. At the Dawn of Time. 6.2. Later that Day. 6.3. Ancient History. 6.4. Baseball at War. 6.5. Twins Fall Short in Slugfest. 6.6. In Scoring Position. 7. More Puzzling Art. 7.1. Just Totals. 7.2 Two Guys. 7.3. Smedley. 7.4. Everybody Scores a Run. 7.5. Castro Homers in the First. 7.6. Brown Homers in the First. 7.7. Leftovers. 8. Missing Information. 8.1. Four Players Missing. 8.2. Four Missing, Again. 8.3. Six Missing. 8.4. Five Missing. 8.5. Who Won? 8.6. Sad Story. 9. Little League Games. 9.1. Kidsf Stuff. 9.2. Kids will be Kids. 9.3. Macy at the Bat. 9.4. Itfs an ERG. 9.5. Zhang and Li. 9.6. Li and Zhang. 9.7. Extreme ERGs. 9.8. Advanced Ergonomics. 10. The Final Problem. 10.1. Childfs Play. 10.2. Pitching In. 10.3. Team Spirit. 10.4. Three Odd Men. 10.5. The Muskratsf Pitching. 10.6. The Hornetfs Batting. 10.7. The Muskratsf Batting. Hints. Solutions. Crazy Things that donft happen in this Book.
Hardcover ISBN: 978-1-4704-4382-5
Product Code: TEXT/61
AMS/MAA Textbooks, Volume: 61
2022; 687 pp
The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian.
The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
Undergraduate and graduate students and researchers interested in the history of mathematics.
May 1, 2023
Paperback ISBN: 9780443151750
Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law considers so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and the operators acting on them. The book discusses their construction, considers spectral-theoretic properties of these operators, illustrate how gfree-Hilbert-spaceh Operator Theory is different from the classical Operator Theory, and demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how ginsideh actions of operator algebra deform the free-probabilistic information?in particular, the Semicircular Law.
Not yet published - available from March 2023
FORMAT: HardbackISBN: 9781009242431
General relativity is a subject that most undergraduates in physics are particularly curious about, but it has a reputation for being very difficult. This book provides as gentle an introduction to general relativity as possible, leading you through the necessary mathematics in order to arrive at important results. Of course, you cannot avoid the mathematics of general relativity altogether, but, using this book, you can gain an appreciation of tensors and differential geometry at a pace you can keep up with. Early chapters build up to a complete derivation of Einstein's Equations, while the final chapters cover the key applications on black holes, cosmology and gravitational waves. It is designed as a coursebook with just enough material to cover in a one-semester undergraduate class, but it is also accessible to any numerate readers who wish to appreciate the power and beauty of Einstein's creation for themselves.
Preface
1. The principle of equivalence
2. Tensors
3. Matter in space-time
4. Geodesics
5. Einstein's equations
6. Schwarzschild's solution
7. Cosmology
8. Gravitational waves
9. A guide to further reading
References
Index.
Not yet published - available from May 2023
FORMAT: HardbackISBN: 9781108837101
Using a modern matrix-based approach, this rigorous second course in linear algebra helps upper-level undergraduates in mathematics, data science, and the physical sciences transition from basic theory to advanced topics and applications. Its clarity of exposition together with many illustrations, 900+ exercises, and 350 conceptual and numerical examples aid the student's understanding. Concise chapters promote a focused progression through essential ideas. Topics are derived and discussed in detail, including the singular value decomposition, Jordan canonical form, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Each chapter ends with a bullet list summarizing important concepts. New to this edition are chapters on matrix norms and positive matrices, many new sections on topics including interpolation and LU factorization, 300+ more problems, many new examples, and color-enhanced figures. Prerequisites include a first course in linear algebra and basic calculus sequence. Instructor's resources are available.
Emphasizes matrix factorizations such as unitary triangularization, QR factorizations, spectral theorem, and singular value decomposition
Covers all relevant linear algebra material that students need to move on to advanced work in data science, such as convex optimization
Supplies 900 end-of-chapter problems, 350 conceptual and numerical examples, and many color illustrations to aid student understanding of concepts and help develop communication skills
Contains clear exposition and concise chapters that promote focused progression through essential ideas
Contents
Preface
Notation
1. Vector Spaces
2. Bases and Similarity
3. Block Matrices
4. Rank, Triangular Factorizations, and Row Equivalence
5. Inner Products and Norms
6. Orthonormal Vectors
7. Unitary Matrices
8. Orthogonal Complements and Orthogonal Projections
9. Eigenvalues, Eigenvectors, and Geometric Multiplicity
10. The Characteristic Polynomial and Algebraic Multiplicity
11. Unitary Triangularization and Block Diagonalization
12. The Jordan Form: Existence and Uniqueness
13. The Jordan Form: Applications
14. Normal Matrices and the Spectral Theorem
15. Positive Semidefinite Matrices
16. The Singular Value and Polar Decompositions
17. Singular Values and the Spectral Norm
18. Interlacing and Inertia
19. Norms and Matrix Norms
20. Positive and Nonnegative Matrices
References
Index.
available from May 2023
FORMAT: Hardback
ISBN: 9781009310949
Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemeredi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turan problem, Szemeredi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.
Provides readers with a clear understanding of various topics and their connections through intuitive language and commentary, leading them on a gentle path to exciting topics at the forefront of research
Uses graph theoretic perspectives to provide insights into the central results of additive combinatorics, including the cornerstone theorems of Roth, Szemeredi, Freiman, and Green-Tao, as well as key topics such as the Turan problem, Szemeredi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, structure of set addition, and the sum-product problem
Highlights important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods
Aids the readers' understanding with ~140 figures and illustrations, many classroom-tested exercises, chapter summaries, and complementary freely available MIT OpenCourseWare lecture videos
Preface
Notation and Conventions
Appetizer: triangles and equations
1. Forbidding a subgraph
2. Graph regularity method
3. Pseudorandom graphs
4. Graph limits
5. Graph homomorphism inequalities
6. Forbidding 3-term arithmetic progressions
7. Structure of set addition
8. Sum-product problem
9. Progressions in sparse pseudorandom sets
References
Index.