© 2009

Explorations in Monte Carlo Methods


Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages 1-11
  2. Ronald W. Shonkwiler, Franklin Mendivil
    Pages 1-49
  3. Ronald W. Shonkwiler, Franklin Mendivil
    Pages 51-100
  4. Ronald W. Shonkwiler, Franklin Mendivil
    Pages 101-138
  5. Ronald W. Shonkwiler, Franklin Mendivil
    Pages 139-163
  6. Ronald W. Shonkwiler, Franklin Mendivil
    Pages 165-212
  7. Back Matter
    Pages 1-27

About this book


Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems.

Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material.

This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics. The problem-oriented approach makes it ideal for an applied course in basic probability and for a more specialized course in Monte Carlo methods. Topics include probability distributions, counting combinatorial objects, simulated annealing, genetic algorithms, option pricing, gamblers ruin, statistical mechanics, sampling, and random number generation.


Markov chain Markov chain Monte Carlo Matlab Monte Carlo Monte Carlo method Probability distribution algorithims algorithms genetic algorithms optimization probability random number generator random walk simulation stochastic processes

Authors and affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Dept. MathematicsAcadia UniversityWolfvilleCanada

About the authors

Ronald Shonkwiler is also publishing Mathematical Biology: An Introduction with Maple and Matlab, that will will be available in 2008. He is professor emeritus at Georgia Institute of Technology School of Mathematics. He received his PhD in 1970. His areas of expertise include: stochastic processes, optimization, computer simulation, Monte Carlo numerical methods, mathematical biology, and reproducing Kernel Hilbert spaces.

Franklin Mendevil is a professor at Acadia University in Nova Scotia. He received his PhD in 1996 at Georgia Institute of Technology. He has co-authored numerous papers and publications, several of which were with Dr. Shonkwiler.

Bibliographic information


From the reviews:

"Explorations in Monte Carlo Methods by Ronald Shonkwiler and Franklin Mendivil is an undergraduate text that is both practical and accessible. … Explorations would make a good text book and would also be suitable for independent study. … It gives numerous applications of Monte Carlo methods including applications in electrical engineering, finance, optimization, and statistical mechanics. Each chapter has numerous exercises and the book concludes with an appendix listing several ideas for student projects applying Monte Carlo methods." (John D. Cook, The Mathematical Association of America, October, 2009)

“This undergraduate text explores the world of Monte Carlo methods under two premises: it shall be algorithmically oriented, and the students shall have fun with the subject. … At the end of each chapter there are … references, and more importantly, a large number of problems … . The problems are clearly pointed out, and hence it is really fun to follow the text. There are not many undergraduate texts on Monte Carlo methods; this is one to recommend for use in a classroom.”­­­ (Peter Mathé, Mathematical Reviews, Issue 2010 i)

“This clearly presented, easy-to-understand book offers beginners a hands-on approach to Monte Carlo methods (MCM). These extensively used methods offer valuable computational tools together with very useful, efficient, and practical algorithms for resolving difficult, complex problems confronting researchers/investigators in numerous disciplines. Shonkwiler (emer., Georgia Institute of Technology) and Mendivil (Acadia Univ., Canada) present the material in five chapters, each ending with a carefully selected list of problems. … Summing Up: Highly recommended. Academic libraries serving upper-division undergraduates; professionals/practitioners.” (D. V. Chopra, Choice, Vol. 47 (7), March, 2010)