This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a "traditional" curriculum and takes the "traditional" (rather than "dynamical systems") approach.
Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Note that some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries depending on the school, course, or instructor.
Undergraduate students studying mathematics, biology, chemistry, economics, environmental sciences, physics, computer science and engineering
Introduction to Differential Equations;First-Order Equations; Applications of First-Order Equations; Higher Order Equations; Applications of Higher Order Equations; Systems of Differential Equationsl; Applications of First-Order Systems; Laplace Transforms; Eigenvalue Problems and Fourier Series; Partial Differential Equations; Answers, Hints and Solutions to Selected Exercises
This new handbook contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications.
Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 29A deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 29B is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects.
Part 1. Sampling and Survey Design
Introduction to Part 1
Ch. 1. Introduction to Survey Sampling
Ch. 2. Sampling with Unequal Probabilities
Ch. 3. Two-Phase Sampling
Ch. 4. Multiple-Frame Surveys
Ch. 5. Designs for Surveys over Time
Ch. 6. Sampling of Rare Populations
Ch. 7. Design, Conduct, and Analysis of Random-Digit Dialing Surveys
Part 2. Survey Processing
Introduction to Part 2
Ch. 8. Nonresponse andWeighting
Ch. 9. Statistical Data Editing
Ch. 10. Imputation and Inference in the Presence of Missing Data
Ch. 11. Dealing with Outliers in Survey Data
Ch. 12. Measurement Errors in Sample Surveys
Ch. 13. Computer Software for Sample Surveys
Ch. 14. Record Linkage
Ch. 15. Statistical Disclosure Control for Survey Data
Part 3. Survey Applications
Introduction to Part 3
Ch. 16. Sampling and Estimation in Household Surveys
Ch. 17. Sampling and Estimation in Business Surveys
Ch. 18. Sampling, Data Collection, and Estimation in Agricultural Surveys
Ch. 19. Sampling and Inference in Environmental Surveys
Ch. 20. Survey Sampling Methods in Marketing Research: A Review of Telephone,
Mall Intercept, Panel, andWeb Surveys
Ch. 21. Sample Surveys and Censuses
Ch. 22. Opinion and Election Polls
Series: New Mathematical Library
Hardback (ISBN-13: 9780883856475)
Page extent: 220 pages
Size: 228 x 152 mm
Most people, acquainted with cryptology either through sensational cloak and dagger stories or through newspaper cryptograms, are not aware that many aspects of this art may be treated systematically, by means of some elementary mathematical concepts and methods. In this introduction, Professor Sinkov explains some of the fundamental techniques at the heart of cryptanalytic endeavor from which much more sophisticated techniques have evolved, especially since the advent of computers. The mathematical topics relevant in these discussions include modular arithmetic, a little number theory, some linear algebra of two dimensions with matrices, some combinatorics, and a little statistics. This second edition has been revised and updated by Todd Fiel, and now includes discussion of the RSA method.
Author has professional experience breaking Japanese codes in Second World
War Suitable for self-study or course accompaniment Contains exercises
and answers
Contents
Part I. Monoalphabetic Ciphers: 1. The Caesar cipher; 2. Modular arithmetic; 3. Additive alphabets; 4. Solution of additive alphabets; 5. Frequency considerations; 6. Multiplications; 7. Solution of multiplicative alphabets; 8. Affine ciphers; Part II. General Substitution: 9. Mixed alphabets; 10. Solution of mixed alphabet ciphers; 11. Solution of five-letter groupings; 12. Monoalphabets with symbols; Part III. Polyalphabetic Substitution: 13. Polyalphabetic ciphers; 14. Recognition of polyalphabetic ciphers; 15. Determination of number of alphabets; 16. Solutions of additive subalphabets; 17. Mixed plain sequences; 18. Matching alphabets; 19. Reduction to a monoalphabet; 20. Mixed cipher sequences; 21. General comments; Part IV. Polygraphic Systems: 22. Linear transformations; 23. Multiplication of matrices - inverses; 24. Involutory transformations; 25. Recognition of digraphic ciphers; 26. Solution of a linear transformation; 27. How to make the Hill system more secure; Part V. Transposition: 28. Columnar transposition; 29. Completely filled rectangles; 30. Incompletely filled rectangles; 31. Probable word method; 32. General case; 33. Identical length messages; Part VI. RSA Encryption: 34. Public-key encryption; 35. The RSA method; 36. Creating the RSA keys; 37. Why RSA works - Fermat's Little Theorem; 38. Computational considerations; 39. Maple and Mathematica for RSA; 40. Breaking RSA and signatures; Part VII. Perfect Security - One-Time Pads: 41. One-time pads; 42. Pseudo-random number generators; A. Tables; B. ASCII codes; C. Binary numbers; D. Solutions to exercises; Further readings; Index.
Series: Cambridge Tracts in Mathematics (No. 181)
Hardback (ISBN-13: 9780521194082)
Page extent: 195 pages
Size: 228 x 152 mm
Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This modern account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject.
Up-to-date monograph detailing research in the area over the last twenty
years For researchers and graduate students in mathematics Contains complete
proofs
Foreword; 1. Basic properties of totally positive matrices; 2. Criteria for total positivity and strict total positivity; 3. Variation diminishing; 4. Examples; 5. Eigenvalues and eigenvectors; 6. Factorizations of totally positive matrices; Afterword; References; Subject index; Author index.
Series: Spectrum
Hardback (ISBN-13: 9780521769884)
Paperback (ISBN-13: 9780521759946)
35 line figures 9 tones 1 table
Page extent: 248 pages
Size: 228 x 152 mm
Flatland, Edwin Abbott’s story of a two-dimensional universe, as told by one of its inhabitants who is introduced to the mysteries of three-dimensional space, has enjoyed an enduring popularity from the time of its publication in 1884. This fully annotated edition enables the modern-day reader to understand and appreciate the many ‘dimensions’ of this classic satire. Mathematical notes and illustrations enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry. Historical notes show connections to late-Victorian England and to classical Greece. Citations from Abbott’s other writings as well as the works of Plato and Aristotle serve to interpret the text. Commentary on language and literary style includes numerous definitions of obscure words. An appendix gives a comprehensive account of the life and work of Flatland‘s remarkable author.
Annotations include historical notes, citations from the author’s other
writings as well as the works of Plato and Aristotle, and commentary on
language and literary style Mathematical notes and illustrations enhance
the usefulness of Flatland as an elementary introduction to higher-dimensional
geometry An appendix gives a comprehensive biographical account of the
life and work of Edwin Abbott
Introduction William F. Lindgren and Thomas F. Banchoff; Part I. This World:
1. Of the nature of Flatland; 2. Of the climate and houses in Flatland;
3. Concerning the inhabitants of Flatland; 4. Concerning the women; 5.
Of our methods of recognizing one another; 6. Of recognition by sight;
7. Concerning irregular figures; 8. Of the ancient practice of painting;
9. Of the universal colour bill; 10. Of the suppression of the chromatic
sedition; 11. Concerning our priests; 12. Of the doctrine of our priests;
Part II. Other Worlds: 13. How I had a vision of Lineland; 14. How in my
vision I endeavoured to explain the nature of Flatland, but could not;
15. Concerning a stranger from Spaceland; 16. How the stranger vainly endeavoured
to reveal to me in words the mysteries of Spaceland; 17. How the sphere,
having in vain tried words, resorted to deeds; 18. How I came to Spaceland
and what I saw there; 19. How, though the sphere showed me other mysteries
of Spaceland, I still desired more; and what came of it; 20. How the sphere
encouraged me in a vision; 21. How I tried to teach the theory of three
dimensions to my grandson, and with what success; 22. How I then tried
to diffuse the theory of three dimensions by other means, and of the result;
Appendix A. Critical reaction to Flatland; Appendix B. Biography and chronology