1. Probabilistic Programming and Bayesian Methods for Hackers
by Cameron Davidson-Pilon - GitHub, Inc., 2013
This book is designed as an introduction to Bayesian inference from a computational understanding-first, and mathematics-second, point of view. The book assumes no prior knowledge of Bayesian inference nor probabilistic programming.
2. Mathematics in the Age of the Turing Machine
by Thomas Hales - arXiv, 2013
Computers have rapidly become so pervasive in mathematics that future generations may look back to this day as a golden dawn. The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
3. The Life of Pi: From Archimedes to Eniac and Beyond
by Jonathan M. Borwein - DocServer, 2010
The desire to understand Pi, the challenge, and originally the need, to calculate ever more accurate values of Pi, has challenged mathematicians for many many centuries, and Pi has provided compelling examples of computational mathematics.
4. Pictures of Julia and Mandelbrot Sets
- Wikibooks, 2010
The purpose of this book is to show how the computer can draw technically perfect pictures of Julia and Mandelbrot sets. All the necessary theory is explained and some words are said about how to put the things into a computer program.
5. Think Stats: Probability and Statistics for Programmers
by Allen B. Downey - Green Tea Press, 2011
Think Stats is an introduction to Probability and Statistics for Python programmers. This new book emphasizes simple techniques you can use to explore real data sets and answer interesting statistical questions. Basic skills in Python are assumed.
6. Isabelle/HOL: A Proof Assistant for Higher-Order Logic
by T. Nipkow, L.C. Paulson, M. Wenzel - Springer, 2010
This book is a self-contained introduction to interactive proof in higher-order logic, using the proof assistant Isabelle. It is a tutorial for potential users. The book has three parts: Elementary Techniques; Logic and Sets; Advanced Material.
7. Computer Algebra, Algorithms, Systems and Applications
by Richard Liska, at al. - Czech Technical University, 1996
From the table of contents: Introduction; Algorithms for algebraic computation; Integrated mathematical systems; Basic possibilities of integrated mathematical systems; Applications of computer algebra; Another sources of study.
8. Algorithms in Real Algebraic Geometry
by S. Basu, R. Pollack, M. Roy - Springer, 2009
The monograph gives a detailed exposition of the algorithmic real algebraic geometry. It is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.
9. Implementing Mathematics with The Nuprl Proof Development System
by R. L. Constable, at al. - Prentice Hall, 1986
The authors offer a tutorial on the new mathematical ideas which underlie their research. Many of the ideas in this book will be accessible to a well-trained undergraduate with a good background in mathematics and computer science.
10. Algorithmic Algebra
by Bhubaneswar Mishra - Courant Institute of Mathematical Sciences, 1993
The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra.
11. An Architecture for Combinator Graph Reduction
by Philip J. Koopman, Jr. - Academic Press, 1990
The results of cache-simulation experiments with an abstract machine for reducing combinator graphs are presented. The abstract machine, called TIGRE, exhibits reduction rates that compare favorably with previously reported techniques.
12. Strange Attractors: Creating Patterns in Chaos
by Julien C. Sprott - M & T Books, 2000
Chaos and fractals have revolutionized our view of the world. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns.
13. Art Gallery Theorems and Algorithms
by Joseph O'Rourke - Oxford University Press, 1987
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas.
14. Axiom: The Scientific Computation System
by Richard D. Jenks, Robert S. Sutor - axiom-developer.org, 2003
Axiom is a free general purpose computer algebra system. The book gives a technical introduction to AXIOM, interacts with the system's tutorial, accesses algorithms developed by the symbolic computation community, and presents advanced techniques.
15. The Golden E-Book of Graphs of Mathematical Functions
by E. Pérez, 2008
This ebook is a visual introduction to the field of transcomplex numbers and an implicit comparison with the real surfaces counterpart. The reader is assumed to be a little related with the topics of graphing plane curves and surfaces.
16. Mathematics for Computer Scientists
by Gareth J. Janacek, Mark L. Close - BookBoon, 2008
In this textbook you will find the basic mathematics needed by computer scientists. It should help you to understand the meaning of mathematical concepts. Subjects as elementary logic, factorization, plotting functions and matrices are explained.
17. Mathematical Illustrations: A Manual of Geometry and PostScript
by Bill Casselman - Cambridge University Press, 2005
The author gives an introduction to basic features of the PostScript language and shows how to use it for producing mathematical graphics. The book includes the discussion computer graphics and some comments on good style in mathematical illustration.
18. Mathematics for Algorithm and Systems Analysis
by Edward A. Bender, S. Gill Williamson - Dover Publications, 2005
This text assists undergraduates in mastering the mathematical language to address problems in the field's many applications. It consists of 4 units: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory.
19. Vector Math for 3D Computer Graphics
by Bradley Kjell - Central Connecticut State University, 2003
A text on vector and matrix algebra from the viewpoint of computer graphics. It covers most vector and matrix topics needed for college-level computer graphics text books. Useful to computer science students interested in game programming.
20. Algorithmic Mathematics
by Leonard Soicher, Franco Vivaldi, 2004
This text is a course in mathematical algorithms, intended for second year mathematics students. It introduces the algorithms for computing with integers, polynomials and vector spaces. The course requires no computing experience.
21. A Computational Introduction to Number Theory and Algebra
by Victor Shoup - Cambridge University Press, 2005
This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes. It is accessible to a broad audience. Prerequisites are a typical undergraduate course in calculus and some experience in doing proofs.
by Cameron Davidson-Pilon - GitHub, Inc., 2013
This book is designed as an introduction to Bayesian inference from a computational understanding-first, and mathematics-second, point of view. The book assumes no prior knowledge of Bayesian inference nor probabilistic programming.
2. Mathematics in the Age of the Turing Machine
by Thomas Hales - arXiv, 2013
Computers have rapidly become so pervasive in mathematics that future generations may look back to this day as a golden dawn. The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
3. The Life of Pi: From Archimedes to Eniac and Beyond
by Jonathan M. Borwein - DocServer, 2010
The desire to understand Pi, the challenge, and originally the need, to calculate ever more accurate values of Pi, has challenged mathematicians for many many centuries, and Pi has provided compelling examples of computational mathematics.
4. Pictures of Julia and Mandelbrot Sets
- Wikibooks, 2010
The purpose of this book is to show how the computer can draw technically perfect pictures of Julia and Mandelbrot sets. All the necessary theory is explained and some words are said about how to put the things into a computer program.
5. Think Stats: Probability and Statistics for Programmers
by Allen B. Downey - Green Tea Press, 2011
Think Stats is an introduction to Probability and Statistics for Python programmers. This new book emphasizes simple techniques you can use to explore real data sets and answer interesting statistical questions. Basic skills in Python are assumed.
6. Isabelle/HOL: A Proof Assistant for Higher-Order Logic
by T. Nipkow, L.C. Paulson, M. Wenzel - Springer, 2010
This book is a self-contained introduction to interactive proof in higher-order logic, using the proof assistant Isabelle. It is a tutorial for potential users. The book has three parts: Elementary Techniques; Logic and Sets; Advanced Material.
7. Computer Algebra, Algorithms, Systems and Applications
by Richard Liska, at al. - Czech Technical University, 1996
From the table of contents: Introduction; Algorithms for algebraic computation; Integrated mathematical systems; Basic possibilities of integrated mathematical systems; Applications of computer algebra; Another sources of study.
8. Algorithms in Real Algebraic Geometry
by S. Basu, R. Pollack, M. Roy - Springer, 2009
The monograph gives a detailed exposition of the algorithmic real algebraic geometry. It is well written and will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.
9. Implementing Mathematics with The Nuprl Proof Development System
by R. L. Constable, at al. - Prentice Hall, 1986
The authors offer a tutorial on the new mathematical ideas which underlie their research. Many of the ideas in this book will be accessible to a well-trained undergraduate with a good background in mathematics and computer science.
10. Algorithmic Algebra
by Bhubaneswar Mishra - Courant Institute of Mathematical Sciences, 1993
The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra.
11. An Architecture for Combinator Graph Reduction
by Philip J. Koopman, Jr. - Academic Press, 1990
The results of cache-simulation experiments with an abstract machine for reducing combinator graphs are presented. The abstract machine, called TIGRE, exhibits reduction rates that compare favorably with previously reported techniques.
12. Strange Attractors: Creating Patterns in Chaos
by Julien C. Sprott - M & T Books, 2000
Chaos and fractals have revolutionized our view of the world. This book shows examples of the artistic beauty that can arise from very simple equations, and teaches the reader how to produce an endless variety of such patterns.
13. Art Gallery Theorems and Algorithms
by Joseph O'Rourke - Oxford University Press, 1987
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas.
14. Axiom: The Scientific Computation System
by Richard D. Jenks, Robert S. Sutor - axiom-developer.org, 2003
Axiom is a free general purpose computer algebra system. The book gives a technical introduction to AXIOM, interacts with the system's tutorial, accesses algorithms developed by the symbolic computation community, and presents advanced techniques.
15. The Golden E-Book of Graphs of Mathematical Functions
by E. Pérez, 2008
This ebook is a visual introduction to the field of transcomplex numbers and an implicit comparison with the real surfaces counterpart. The reader is assumed to be a little related with the topics of graphing plane curves and surfaces.
16. Mathematics for Computer Scientists
by Gareth J. Janacek, Mark L. Close - BookBoon, 2008
In this textbook you will find the basic mathematics needed by computer scientists. It should help you to understand the meaning of mathematical concepts. Subjects as elementary logic, factorization, plotting functions and matrices are explained.
17. Mathematical Illustrations: A Manual of Geometry and PostScript
by Bill Casselman - Cambridge University Press, 2005
The author gives an introduction to basic features of the PostScript language and shows how to use it for producing mathematical graphics. The book includes the discussion computer graphics and some comments on good style in mathematical illustration.
18. Mathematics for Algorithm and Systems Analysis
by Edward A. Bender, S. Gill Williamson - Dover Publications, 2005
This text assists undergraduates in mastering the mathematical language to address problems in the field's many applications. It consists of 4 units: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory.
19. Vector Math for 3D Computer Graphics
by Bradley Kjell - Central Connecticut State University, 2003
A text on vector and matrix algebra from the viewpoint of computer graphics. It covers most vector and matrix topics needed for college-level computer graphics text books. Useful to computer science students interested in game programming.
20. Algorithmic Mathematics
by Leonard Soicher, Franco Vivaldi, 2004
This text is a course in mathematical algorithms, intended for second year mathematics students. It introduces the algorithms for computing with integers, polynomials and vector spaces. The course requires no computing experience.
21. A Computational Introduction to Number Theory and Algebra
by Victor Shoup - Cambridge University Press, 2005
This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes. It is accessible to a broad audience. Prerequisites are a typical undergraduate course in calculus and some experience in doing proofs.
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