Synopses & Reviews
From his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text. Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum
and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.
No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra, and scalars. Covers areas of parallelograms, triple products, moments, angular velocity, areas and vectorial addition, and more. Concludes with discussion of tensors. Includes 386 exercises.
No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra, and scalars. Includes 386 exercises.
Emphasizes unresolved issue of defining a vector. A provocative supplement (and corrective) to textbooks on vectors. 386 exercises.
About the Author
Banesh Hoffmann (1906-86) received his PhD from Princeton University. At Princeton's Institute for Advanced Study, he collaborated with Albert Einstein and Leopold Infeld on the classic paper "Gravitational Equations and the Problem of Motion." Hoffmann taught at Queens College for more than 40 years.
Table of Contents
1. Defining a vector
2. The parallelogram law
3. Journeys are not vectors
4. Displacements are vectors
5. Why vectors are important
6. The curious incident of the vectorial tribe
7. Some awkward questions
ALGEBRAIC NOTATION AND BASIC IDEAS
1. Equality and addition
2. Multiplication by numbers
4. Speed and velocity
6. Elementary statics in two dimensions
8. The problem of location. Vector fields
2. Unit orthogonal triads
3. Position vectors
5. Direction cosines
6. Orthogonal projections
7. Projections of areas
SCALARS. SCALAR PRODUCTS
1. Units and scalars
2. Scalar products
3. Scalar products and unit orthogonal triads
VECTOR PRODUCTS. QUOTIENTS OF VECTORS
1. Areas of parallelograms
2. "Cross products of i, j, and k"
3. "Components of cross products relative to i, j, and k"
4. Triple products
6. Angular displacements
7. Angular velocity
8. Momentum and angular momentum
9. Areas and vectorial addition
10. Vector products in right- and left-handed reference frames
11. Location and cross products
12. Double cross
13. Division of vectors
1. How components of vectors transform
2. The index notation
3. The new concept of a vector
5. Scalars. Contraction
6. Visualizing tensors
7. Symmetry and antisymmetry. Cross products
8. Magnitudes. The metrical tensor
9. Scalar products
10. What then is a vector?