Tsing Hua University Press has translated the book "Elements of Computation Theory". I trust everything has gone well in the translation.
It contains an extra page which was not in the original English version. The extra page has been translated by Xian Hu of University of Arkansas from Chinese to English. It is as follows:
Words from the Translators
Due to the constant change in information technology, importing outstanding foreign achievements such as textbooks meet the needs of China’s corresponding discipline’s development. After reading this book, we really appreciate the author’s wisdom and rigorous approach. Meanwhile, the way the author describes and illustrates things are rare in Chinese authors today. It starts with intuitive approaches and speculations which bring up the students’ enthusiasm for learning. After that, the book uses rigorous mathematical language and reasoning to prove or disprove the previous speculations. This method can not only stimulate students’ enthusiasm, initiative and creativity, but also help them build a rigorous, strict and serious attitude. This serious and lively style is not only beneficial for improving the Chinese teaching methods, but also provides a good example to build our teaching model. This serious and lively spirit is not only good for academics, but also motivates a nation to move forward.
The imported textbook should be authoritative, systematic, advanced and popular. Meanwhile, it should be beneficial for improving the levels of our academics, teaching, and way of thinking. This book is outstanding in all of the above areas. In addition, this book is also easy to understand. It explains profound theories in simple language with rigorous reasoning. It covers a large range of material with many inspiring exercises which are worth revisiting.
Indepth study of this book can reinforce the mathematical foundations of computer science, but more importantly, it benefits you with good methods, skills and tricks. This book combines good theory with excellent exercises, which will improve the readers’ problem solving ability. Overall, this is an excellent textbook, the kinds of which are not easy to find.
This book was mainly translated by Aiwen Cao, Peng Ye and Shaoshuai Li. The following people also participated in the work: Kun Cao, Zhiyun Li, Xiaochun Li, Anhua Chen, Jiayi Hou, Wei Xu, Wenya Dai, Fanpeng Yu, Peng Liu, Jiajia Wang, Wei Deng, Fanping Deng, Bo Li, Yunjian Cheng, Xiaozhe Xu, Ke Zhu, Xiao Wei, Hong Sun, Teng Li, Lei Chen, Yu Wei, Jingping Zhou, Dong Xun, Zhe Feng, Fei Li, Qiang Li, Donghui Zhao, Gang Zhou, Yuehua Zhang, Yan Sun, Qiang Gao, Xin Liu, Hongliang Wang, Feng Zhou, Hui Xie, Lin Li, Xiangyang Sun, Yuanyuan Li, Zhipeng Zhao, Jia Feng, CaiE Lin, Lei Sun, Baitao Zhang, Nan Zhao and Henan Chen.
During the translation, we tried our best to analyze the information in each word and sentence, not to guess. We respect the style and way of thinking of the original book and try to keep it. Due to the limitation of the translators’ knowledge and skill, it is inevitable to have errors and imperfections in the translation. We will highly appreciate the readers’ forgiveness and generous correction.
There ends the translator’s notes.
Introduction to Matrix Theory
The publisher of the book is Ane Books:
Ane Books Pvt. Ltd.
4821, Parwana Bhawan, 24, Ansari Road,
Daryaganj, New Delhi  110 002, India
Phones: 91112327 686344
Fax: 91112327 6863
EMail: kapoor@anebooks.com
Book’s ISBN : 9789386761217


Perhaps the best description about the book is the following extract from its preface.
Practising scientists and engineers feel that calculus and matrix theory form
the minimum mathematical requirement for their future work. Though it is
recommended to spread matrix theory or linear algebra over two semesters in
an early stage, the typical engineering curriculum allocates only one semester
for it. In addition, I found that science and engineering students are at a loss
in appreciating the abstract methods of linear algebra in the first year of their
undergraduate programme. This resulted in a curriculum that includes a thorough study of system of linear equations via Gaussian and/or GaussJordan
elimination comprising roughly one month in the first or second semester. It
needs a followup of one semester work in matrix theory ending in canonical
forms, factorizations of matrices, and matrix norms.
Initially, we followed the books such by Leon, Lewis, and Strang as possible texts, referring occasionally to papers and other books. None of these could be used as a text book on its own for our purpose. The requirement was a single text containing development of notions, one leading to the next, and without any distraction towards applications. It resulted in
creation of our own material. The students wished to see the material in a
book form so that they might keep it on their lap instead of reading it off the
laptop screens. Of course, I had to put some extra effort in bringing it to this
form; the effort is not much compared to the enjoyment in learning.
The approach is straight forward. Starting from the simple but intricate
problems that a system of linear equations presents, it introduces matrices
and operations on them. The elementary row operations comprise the basic tools in working with most of the concepts. Though the vector space
terminology is not required to study matrices, an exposure to the notions is
certainly helpful for an engineer’s future research. Keeping this in view, the
vector space terminology are introduced in a restricted environment of subspaces of finite dimensional real or complex spaces. It is felt that this direct
approach will meet the needs of scientists and engineers. Also, it will form a
basis for abstract function spaces, which one may study or use later.
Starting from simple operations on matrices this elementary treatment of
matrix theory characterizes equivalence and similarity of matrices. The other
tool of GramSchmidt orthogonalization has been discussed leading to best
approximations and least squares solution of linear systems. On the go we
discuss matrix factorizations such as rank factorization, QRfactorization,
Schur triangularization, diagonalization, Jordan form, singular value decomposition and polar decomposition. It includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix.
Keeping the modest goal of an introductory text book on matrix theory, which
may be covered in a semester, these topics are dealt with in a lively manner.
Though the earlier drafts were intended for use by science and engineering
students, many mathematics students used those as supplementary text for
learning linear algebra. This book will certainly fulfil that need.
Each section of the book has exercises to reinforce the concepts; and problems have been added at the end of each chapter for the curious student. Most of these problems are theoretical in nature and they do not fit into the running text linearly. Exercises and problems form an integral part of the book. Working them out may require some help from the teacher. It is hoped that the teachers and the students of matrix theory will enjoy the text the same way I and my students did.
Most engineering colleges in India allocate only one semester for Linear
Algebra or Matrix Theory. In such a case, the first two chapters of the book
can be covered in a rapid pace with proper attention to elementary row operations. If time does not permit, the last chapter on matrix norms may be omitted, or covered in numerical analysis under the veil of iterative solutions of linear systems.
The contents are:
Chapter 1  Matrix Operations:
1.1 Examples of linear equations 1.2 Basic matrix operations 1.3 Transpose and adjoint 1.4 Elementary row operations 1.5 Row reduced echelon form 1.6 Determinant 1.7 Computing inverse of a matrix & nbsp 1.8 Problems for Chapter 1
Chapter 2  Systems of Linear Equations:
2.1 Linear independence 2.2 Determining linear independence 2.3 Rank of a matrix 2.4 Solvability of linear equations 2.5 GaussJordan elimination 2.6 Problems for Chapter 2
Chapter 3  Matrix as a Linear Map:
3.1 Subspace and span 3.2 Basis and dimension 3.3 Linear transformations 3.4 Coordinate vectors 3.5 Coordinate matrices 3.6 Change of basis matrix 3.7 Equivalence and similarity 3.8 Problems for Chapter 3
Chapter 4  Orthogonality:
4.1 Inner products 4.2 GramSchmidt orthogonalization 4.3 QRfactorization 4.4 Orthogonal projection 4.5 Best approximation and least squares solution 4.6 Problems for Chapter 4
Chapter 5  Eigenvalues and Eigenvectors:
5.1 Invariant line 5.2 The characteristic polynomial 5.3 The spectrum 5.4 Special types of matrices 5.5 Problems for Chapter 5
Chapter 6  Canonical Forms:
6.1 Schur triangularization 6.2 Annihilating polynomials 6.3 Diagonalizability 6.4 Jordan form 6.5 Singular value decomposition 6.6 Polar decomposition 6.7 Problems for Chapter 6
Chapter 7  Norms of Matrices:
7.1 Norms 7.2 Matrix norms 7.3 Contraction mapping 7.4 Iterative solution of linear systems 7.5 Condition number 7.6 Matrix exponential 7.7 Estimating eigenvalues 7.8 Problems for Chapter 7
Short Bibliography
Index
Errata:
P.43, Line 25: Theorem 3.12 to be replaced with Theorem 1.1
P.109, Last two lines: a to be replaced with c, and (a,0,0) to be replaced with (0,0,c).
Extracts from its preface reads as follows:
In this revised version, the circularity in presenting logic via formal semantics is brought to the fore in a very elementary manner. Instead of developing everything from semantics, we now use an axiomatic system to model reasoning. Other proof methods are introduced and worked out later as alternative models.
Elimination of the equality predicate via equality sentences is dealt with semantically even before the axiomatic system for first order logic is presented. The replacement laws and the quantifier laws are now explicitly discussed along with the necessary motivation of using them in constructing proofs in mathematics. Adequacy of the axiomatic system is now proved in detail. An elementary proof of adequacy of Analytic Tableaux is now included.
Special attention is paid to the foundational questions such as decidability, expressibility, and incompleteness. These important and difficult topics are dealt with briefly and in an elementary manner.
The material on Program Verification, Modal Logics, and Other Logics in Chapters 9, 11 and 12 have undergone minimal change. Attempt has been made to correct all typographical errors pointed out by the readers. However, rearrangement of the old material and the additional topics might have brought in new errors. Numerous relevant results, examples, exercises and problems have been added. The correspondence of topics to chapters and sections have changed considerably, compared to the fist edition. A glance through the contents page will give you a comprehensive idea.
Its contents page reads as follows:
Chapter 1  Propositional Logic
1.1 Introduction 1.2 Syntax of PL 1.3 Is It a Proposition? 1.4 Interpretations, 1.5 Models 1.6 Equivalences and Consequences 1.7 More About Consequence 1.8 Summary and Problems
Chapter 2  A Propositional Calculus
2.1 Axiomatic System PC 2.2 Five theorems about PC 2.3 Using the metatheorems 2.4 Adequacy of PC to PL 2.5 Compactness of PL 2.6 Replacement Laws 2.7 Quasiproofs in PL 2.8 Summary and Problems
Chapter 3  Normal Forms and Resolution
3.1 Truth Functions 3.2 CNF and DNF 3.3 Logic Gates 3.4 Satisfiability Problem 3.5 2SAT and HornSAT 3.6 Resolution in PL 3.7 Adequacy of resolution in PL 3.8 Resolution Strategies 3.9 Summary and Problems
Chapter 4  Other Proof Systems for PL
4.1 Calculation 4.2 Natural Deduction 4.3 Gentzen Sequent Calculus 4.4 Analytic Tableaux 4.5 Adequacy of PT to PL 4.6 Summary and Problems
Chapter 5  First Order Logic
5.1 Syntax of FL 5.2 Scope and Binding 5.3 Substitutions 5.4 Semantics of FL 5.5 Translating into FL 5.6 Satisfiability and Validity 5.7 Some Metatheorems 5.8 Equality Sentences 5.9 Summary and Problems
Chapter 6  A First Order Calculus
6.1 Axiomatic System FC 6.2 Six theorems about FC 6.3 Adequacy of FC to FL 6.4 Compactness of FL 6.5 Laws in FL 6.6 Quasiproofs in FL 6.7 Summary and Problems
Chapter 7  Clausal Forms and Resolution
7.1 Prenex form 7.2 Quantifierfree forms 7.3 Clauses 7.4 Unification of clauses 7.5 Extending resolution 7.6 Factors and Pramodulants 7.7 Resolution for FL 7.8 Horn clauses in FL 7.9 Summary and Problems
Chapter 8  Other Proof Systems for FL
8.1 Calculation 8.2 Natural Deduction 8.3 Gentzen sequent calculus 8.4 Analytic Tableaux 8.5 Adequacy of FT to FL 8.6 Summary and Problems
Chapter 9  Program Verification
9.1 Debugging a Program 9.2 Issue of Correctness 9.3 The Core Language CL 9.4 Partial Correctness 9.5 Axioms And Rules 9.6 Hoare Proof 9.7 Proof Summary 9.8 Total Correctness 9.9 A Predicate Transformer 9.10 Summary and Problems
Chapter 10  First Order Theories
10.1 Structures and Axioms 10.2 Set Theory 10.3 Arithmetic 10.4 Herbrand Interpretation 10.5 Herbrand Expansion 10.6 SkolemLowenheim Theorems 10.7 Decidability 10.8 Expressibility 10.9 Provability predicate 10.10 Summary and Problems
Chapter 11  Modal Logic K
11.1 Introduction 11.2 Syntax and Semantics of K 11.3 Validity and Consequence in K 11.4 Axiomatic System KC 11.5 Adequacy of KC to K 11.6 Natural Deduction in K 11.7 Analytic Tableau for K 11.8 Other Modal Logics 11.9 Various Modalities 11.10 Computation Tree Logic 11.11 Summary and Problems
Chapter 12  Some Other Logics
12.1 Introduction 12.2 Intuitionistic Logic 12.3 Lukasiewicz Logics 12.4 Probabilistic Logics 12.5 Possibilistic and Fuzzy Logic 12.5.1 Crisp sentences and precise information 12.5.2 Crisp sentences and imprecise information 12.5.3 Crisp sentences and fuzzy Information 12.5.4 Vague sentences and fuzzy information 12.6 Default Logic 12.7 Autoepistemic Logics 12.8 Summary
References
Index
I will be happy to receive suggestions from you for improving the books.

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