The first thing I see in combination is as if I donated to us the college, a foreign version. It feels not too suitable for domestic books. Or read the classic "specific mathematics" of Graham and Knuth, etc., Xi'an University of Electronic Science and Technology Press has a translated version.
"Combined Mathematics", "Space Analysis Geometry" also has the "Topology". It is extremely cost-effective when it looks at these three books. The reason is a few, the first is that these three books have no exception, all use traditional Writing, the second is that the book is really too dirty. I look at the library's seat. The students are far away from me. I am very unnatural, I don't want to affect my classmates, but the school will not let the school borrow this book (huh, it is very interesting, others don't look at this book, only I am watching, the teacher is specially paying attention to me. Later, I told him the value of these books. He actually regarded them as a treasure of the shock, but the teacher is not allowed to borrow, but then they look like I really like it, just borrow the book to me, of course It is the name of the curator to borrow.) But the harvest is very big, and then many things in the computer theory are often used. Of course, if you haven't seen these books absolutely understand that level. Take the Tuology, our school seems to be the United States to open this course, but the importance of this course is obvious. I didn't expect that there are some reading notes in many pages of the book, and that notes Authors and some attainments, some ideas can be used in modern network design.
Abstract algebra, domestic classic is Mr. Mo Zongjian's "Mathematics". This book is heard that the Textbook of Peking University School is deeply praised. However, for undergraduates, this book is too deep. You can learn some other textbooks first, and then look back to see "Mathematics". The international classics can be more, and there is a lot of pile in the GTM series. It is recommended to talk about classics, but the simplest, easier to learn: http://www.math.miami.edu/~ec/book/ This "Introduction to linear and Abstract Algebra" is very easy to understand And combine the abstract algebra and linear algebra, which is ideal for beginners, and our school has a collection of cows. In terms of the fact that there is a classic and difficult to say the frozen 摹 摹 摹 摹 邸? (Pan's brothers, Peking University). Take another point, there are more classics (can be world-class) and more difficult "number of bodies" (Mr. Hua Geng's masterpiece, scientific version, nine bookstore's reprinting, "Traditional seems may be difficult). Take a basic chapter to get a probably, enough for undergraduates. But this is just the primary aumentation. After graduating from undergraduate, you must learn a number of words, you must read English, such as Bach's "Introduction to Algorithmic Number The". The fundamental of computer science theory is the algorithm. Nowadays, there are many systems to open algorithms design and analysis, which is indeed very correct. Way to Western world, there is approximately no three-flow computer system does not use the algorithm as a compulsory. The algorithm textbook is currently recognized as the "Introduction To Algorithms" waiting in Corman. This is enough for entry, it is already enough to refer to other books. What is deep is TAOCP known as common sense. That is, "The Art of Computer Programming" 3 volumes can be seen in the world, and Gates once said. "If you can understand the things above, please send me your resume. A "My Chief Secretary, Nan Xiong, once again bought this book from the American Trustee, not to mention, it can be seen in our computer science and technology system. Let me talk about the form language and automaton. I have seen the textbook of Bei Post, it should be clear. There is a good book that is easy to understand, "Introduction to Theory of Computation" in MIT's SIPSER. However, there is a little to emphasize: the role of form language and automators is mainly used as a computational model, not to be compiled. In fact, the front end of compilation is already the field of death. No Open Problems, Dr. Ban Xiaojuan, Northern University, has also said that compiled technology is quite mature. If this is, we don't have to go to school in the form of language - what is used in Yacc. The North Post is still better in China, but in the depth, there is a big limit in conjunctive links, and modern sense is not enough. Therefore, it is recommended that you have interested classmates to read English books, but there seems to be in this regard. You can go to the interactive publishing online to see. After getting started, the model language defined in the form of the automaton is more interesting with the model defined by the recursive function in the automaton, and can be said to be very interesting. I only know now, what is "the beauty of the palace, the rich" rich "!
Computer science and mathematics have a bit strange. Two-30 years ago, computer science basically or a branch of mathematics. Now, computer science has a wide range of research and many researchers, in many ways to promote mathematical development, from a sense to say that children are growing higher than mothers. But no matter what, this child always flows through the blood of the mother. This blood is the Mathematical Underpinning of Computer Science (Mathematical Basis of Computer Science), which is the theoretical computer science. It turned out that in the Oriental University City Library, I have seen a translation in the 1970s (the book skin is gone, but I love to pay attention to this book), probably call "computer mathematics". If the book is placed at the time, it is a good book, but now it seems that the scope covered is wide, the depth is a lot, but the recommended a big student can take a look, at least make you The calculation mathematics entry, that is, at least you can use mathematics to use where computer science is used. What is the word most common and theoretical computer science? A: Discrete mathematics. The relationship between the two is so close, so that they become synonyms in many cases. (This is also reflected in the previous book) traditionally, mathematics is analyzed centered. The classmates of mathematics must learn the mathematical analysis of the three or four semesters, then the retrieval function, the real change function, the function, and so on. Realism and functional letters are considered to be a modern mathematics. In physics, chemistry, engineering applications, also analyzed.
With the emergence of computer science, some mathematics branches that have not been attached to the past are suddenly important. It is found that the mathematical objects of these branches have obvious differences from traditional analysis: the problem solution for analysis and research is continuous, and thus differentials, points become basic operations; and the objects of these branches are discrete, thus very few Have the opportunity to conduct such calculations. It is thus called these branches to "Discrete Mathematics". The name of "Discrete Mathematics" is getting loud and losing, and finally, the traditional mathematical branch of analysis-centric mathematics is relatively referred to as "continuous mathematics."
After decades of development, discrete mathematics is basically stabilized. It is generally believed that discrete mathematics contains the following disciplines: 1) Collection, Mathematical Logic and Yuan Math. This is the basis of the entire mathematics, and it is also the foundation of computer science. 2) Figure theory, algorithm chart; combined mathematics, combined algorithm. The core of computer science, especially theoretical computer science is algorithm, and a large number of algorithms are based on graphs and combinations. 3) Abstract algebra. The algebra is inexpensive, which is very important in mathematics. In computer science, people surprised that modern numbers have more applications. However, the theoretical computer science is just that the top of "discrete" hats is simple in mathematics? It has been finally a master that I finally told us that one year ago. D.E.knuth (he has more great, I don't want me to say anything) I opened a new course in Stanford. Concrete Mathematics. Concrete The word has two levels here: First: For Abstract. Knuth believes that the object of traditional mathematical research is too abstract, causing not enough attention to specific problems. He complained that the mathematics he needs in research often does not exist, so he can only create some mathematics. In order to directly facilitate application, he should advocate "specific" mathematics. Here I am doing a simple explanation. For example, in the collection, mathematician care is the most fundamental problem - the various properties of the axiom system. And some of the specific collection of nature, all common collections, relationships, and mapping are what mathematics feel that it is not important. However, in computer science, it is precisely these specific things. Knuth can first see this, it is worthy of the first person of the world. Second, Concrete is Continuous plus Discrete (discrete). Regardless of continuous mathematics or discrete mathematics, it is useful mathematics as long as it can be hung hooks with us. 2, theory and actual combination - The science and technology research of computer science and technology is mainly from the perspective of mathematics. From a computer perspective, theoretical computer science currently the main research field includes: calculated theory, algorithm design and complexity analysis, cryptography and information security, distributed calculation theory, parallel calculation theory, network theory, biological information calculation, Calculate geometry, program language theory, etc. These areas are crossing each other, and new topics are constantly being put forward, so it is difficult to figure out a clue. I want to engage in this work, I recommend watching a series of books of the Chinese Computer Society, at least the authority of my country. Let's give some examples. Due to the promotion of application requirements, cryptography is now a hot spot study. Cryptography is based on numerical (especially calculating numbers), algebra, information theory, probability theory, and random processes, sometimes also used in the chart and composition. Many people think that cryptography is encrypted and decrypt, and encryption is to disrupted the data with a function. Such an understanding is too light. Modern cryptography includes at least the following levels: first, cryptographic basis.
For example, is it really difficult to break down a large number? Can there be a general tool certificate agreement? Second, the basic topics of cryptography. For example, better one-way functions, signature protocols, etc. Third, high-level issues of cryptography. For example, the length, secret sharing of zero knowledge certificates. Fourth, new application of cryptography. For example, digital cash, traitor tracking, etc. There is a "application cryptography" worth recommending to see the episode of the annual meeting. It feels that this material is relatively practical and will increase soon. There are also many important theoretical issues in a distributed system. For example, synchronization between processes, mutex protocols. A classic result is: When the communication channel is unreliable, there is no determination algorithm to achieve the same process. Therefore, it is almost meaningful to improve TCP three handshakes. For example, timing problems. One of the common sequences is due to fruit, but because of the ordered result, there is a theoretical result .... For example, there is no practical approach to the deadlock to perfectly. For example, ... operating system research, you will go! If the computer only has theory, it is just a branch of mathematics, not a separate science. In fact, in addition to theory, computer science has a broader sky. I have been thinking that four years is not enough to learn the basic knowledge of the computer, because the face is too wide, if you are learning, I think at least 8 years of learning can make you have certain scientific literacy ... I think this Let me talk about the "computer foundation" that we are universal in all schools. The "Computer Basic Course" in colleges and universities is the requirements of various professional compulsory courses stipulated in my country's Higher Education Division. The main content is to enable students to initially master the history of computer development, learn to simply use operating systems, text processing, table handling functions, and initial network application functions. However, the goal of teaching this course in the Computer Science Department will never be consistent with this. In the computer system, the target should be: let the students understand the development of computer disciplines, clearly grasp the direction of computer discipline research, the frontier of the development of each course is in the entire discipline system. Take the learning purpose, learning content, and application fields of each subject. Make students have a whole understanding of the whole discipline in the early days of the discipline, in order to learn what to learn in the future, how to learn. The location of the computer basic application skills should be placed in the second or more, as this should have this exploration ability for students in this department. this point is very important. It is recommended to give a book: New perspective of computer science, "New perspective of computer science" It is computer science. Scientific Press, "Calculation Science Introduction" (Mr. Zhao Zhizhu) can be said to have a lot of attempts in college computer education reform, which is also a book in this area. An excellent student of a first-class computer system should not be just a programming master, but he must first be a programming master. When I go to college, the first professional class is a C language program design, and people who read a computer from a certain point of view, a considerable number of people are based on the writing program. In our Beijing Institute of Technology Experimental Academy, there has always been such a debate (there is also 9CBS today), which is the first program design language.
