Author: Kenneth H. RosenPublisher: McGraw-Hill
ISBN: 9781259676512
Category : Computer science
Languages : en
Pages : 0
Book Description
A precise, relevant, comprehensive approach to mathematical concepts...
Discrete Mathematics and Its Applications
Author: Kenneth H. RosenPublisher:
ISBN: 9780071244749
Category : Computer science
Languages : en
Pages : 109
Book Description
The companion Web site -- To the student -- The foundations : logic, sets, and functions -- The fundamentals : algorithms, the integers, and matrices -- Mathematical reasoning -- Counting -- Advanced counting techniques -- Relations -- Graphs -- Trees -- Boolean algebra -- Modeling computation
Discrete Mathematics and Its Applications
Author: Kenneth H. RosenPublisher: McGraw-Hill Science, Engineering & Mathematics
ISBN: 9780072899054
Category : Computers
Languages : en
Pages : 678
Book Description
This text is designed for the sophomore/junior level introduction to discrete mathematics taken by students preparing for future coursework in areas such as math, computer science and engineering. Rosen has become a bestseller largely due to how effectively it addresses the main portion of the discrete market, which is typically characterized as the mid to upper level in rigor. The strength of Rosen's approach has been the effective balance of theory with relevant applications, as well as the overall comprehensive nature of the topic coverage.
Discrete Mathematics with Applications, Metric Edition
Author: Susanna EppPublisher:
ISBN: 9780357114087
Category :
Languages : en
Pages : 984
Book Description
DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology.
Author: Kenneth RosenMathematical Statistics with Applications in R
Author: Kandethody M. RamachandranPublisher: Elsevier
ISBN: 012417132X
Category : Mathematics
Languages : en
Pages : 825
Book Description
Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner.This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students.Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. - Step-by-step procedure to solve real problems, making the topic more accessible - Exercises blend theory and modern applications - Practical, real-world chapter projects - Provides an optional section in each chapter on using Minitab, SPSS and SAS commands - Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods
Mathematical Modeling in Economics, Ecology and the Environment
Author: N.V. HritonenkoPublisher: Springer Science & Business Media
ISBN: 1441997334
Category : Mathematics
Languages : en
Pages : 225
Book Description
The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ...
Understanding Markov Chains
Author: Nicolas PrivaultPublisher: Springer
ISBN: 9811306591
Category : Mathematics
Languages : en
Pages : 379
Book Description
This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
Topological Crystallography
Author: Toshikazu SunadaPublisher: Springer Science & Business Media
ISBN: 4431541772
Category : Mathematics
Languages : en
Pages : 236
Book Description
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
All of Statistics
Author: Larry WassermanPublisher: Springer Science & Business Media
ISBN: 0387217363
Category : Mathematics
Languages : en
Pages : 446
Book Description
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
