翻译一半累了…………我也是学习计算机的 以前学习离散现在都给忘

翻译一半累了…………我也是学习计算机的 以前学习离散现在都给忘 翻译一半累了…………..我也是学习计算机的 以前学习离散现在都给忘记了 先翻译这些吧 翻译不好 第一次.~~~~~ Computer Science 47//电脑科学 APPENDIX 2: Some Quotes from Curriculum 2001 目录2:课程2001的引述 This material is being added as this report goes to press in October, 2002. It was not available at the time of the Bowdoin meeting. 在Bowdoin会议上时, The full ACM, IEEE-CS report is available at: www.computer.org/education/cc2001/final/index.htm 所有的acm,ieee-cs的报告可以在www.computer.org/education/cc2001/final/index.htm 网站上看到. From Section 7.4 Integrating discrete mathematics into the introductory curriculum. 从第7.4整合离散数学的介绍性课程. As we discuss in , the CC2001 Task Force believes it is important for computer science students to study discrete mathematics early in their academic program, preferably in the first year. There are at least two workable strategies for accomplishing this goal: 在我们的讨论后, CC2001 Task Force认为就算机科学的学生在做他们的学术之前最好先学习离散数学,最好是在第一年里就学.并为了实现他的学术计划应该至少有2个可行的战略. From Appendix A: The CS body of knowledge. DS. Discrete Structures (43 core hours) 附录A:数学的一些知识。 DS. 分离结构(43个核心学时) DS1. Functions, relations and sets (6) 第一章.函数,逻辑,集合 DS2. Basic Logic (10) 第,章.基本逻辑 DS3. Proof Techniques (12) 第,章.证明 DS4. Basics of Counting (5) 第,章.基本运算 DS5. Graphs and trees (4) 第,章.图和数 DS6. Discrete Probability (6) 第,章.离散的可能性. From Appendix B: CS Course Descriptions 目录,:数学课程描述 CS115. Discrete Structures for Computer Science 关于电脑科学的离散数序 Offers an intensive introduction to discrete mathematics as it is used in computer science. 用于电脑科学技术的离散数学提供来了很详细的介绍 Topics include functions, relations, sets, propositional and predicate logic, simple circuit logic, proof techniques, elementary combinatorics, and discrete probability. 主要内容包括函数,逻辑集合,命题和谓词逻辑,简单的回路逻辑,证明的技术和基本的基本 的组合数学, 分离可能性 Prerequisites: Mathematical preparation sufficient to take calculus at the college level. 前提:在大学里要学习微积分做为数学准备. Syllabus: 教学大纲 • Fundamental structures: Functions (surjections, injections, inverses, composition); relations (reflexivity, symmetry, transitivity, equivalence relations); sets (Venn diagrams, complements, Cartesian products, power sets); pigeonhole principle; cardinality and countability 基本结构:函数(surjections、?、相反性，构成); 联系(自反性， 对称性，及物性，等价关系); 集合(Venn图，补全，笛卡儿积，幂集); 分类原理; 基数和可 数性 • Basic logic: Propositional logic; logical connectives; truth tables; normal forms (conjunctive and disjunctive); validity; predicate logic; limitations of predicate logic; universal and existential quantification; modus ponens and modus tollens 基本逻辑:命题逻辑;逻辑连词;真相;正常形式(合取和析取)有效性;谓词逻; 限制谓词逻辑;普遍和存在的量化,取式和作案推理 • Digital logic: Logic gates, flip-flops, counters; circuit minimization •数字逻辑:逻辑门，触发器，计数器;最小环路 • Proof techniques: Notions of implication, converse, inverse, contrapositive, negation, and contradiction; the structure of formal proofs; direct proofs; proof by counterexample; proof by contraposition; proof by contradiction; mathematical induction; strong induction; recursive mathematical definitions; well orderings 证 • Basics of counting: Counting arguments; pigeonhole principle; permutations and combinations; recurrence relations • Discrete probability: Finite probability spaces; conditional probability, independence, Bayes’ rule; random events; random integer variables; mathematical expectation. 48 The Curriculum Foundations Project Notes: This implementation of the Discrete Structures area (DS) compresses the core material into a single course. Although such a strategy is workable, many institutions will prefer to use two courses to cover this material in greater depth. For an implementation that uses the two-course model, see the descriptions of CS105 and CS106. CS105. Discrete Structures I Introduces the foundations of discrete mathematics as they apply to computer science, focusing on providing a solid theoretical foundation for further work. Topics include functions, relations, sets, simple proof techniques, Boolean algebra, propositional logic, digital logic, elementary number theory, and the fundamentals of counting. Prerequisites: Mathematical preparation sufficient to take calculus at the college level. Syllabus: • Introduction to logic and proofs: Direct proofs; proof by contradiction; mathematical induction • Fundamental structures: Functions (surjections, injections, inverses, composition); relations (reflexivity, symmetry, transitivity, equivalence relations); sets (Venn diagrams, complements, Cartesian products, power sets); pigeonhole principle; cardinality and countability • Boolean algebra: Boolean values; standard operations on Boolean values; de Morgan’s laws • Propositional logic: Logical connectives; truth tables; normal forms (conjunctive and disjunctive); validity • Digital logic: Logic gates, flip-flops, counters; circuit minimization • Elementary number theory: Factorability; properties of primes; greatest common divisors and least common multiples; Euclid’s algorithm; modular arithmetic; the Chinese Remainder Theorem • Basics of counting: Counting arguments; pigeonhole principle; permutations and combinations; binomial coefficients CS106. Discrete Structures II Continues the discussion of discrete mathematics introduced in CS105. Topics in the second course include predicate logic, recurrence relations, graphs, trees, matrices, computational complexity, elementary computability, and discrete probability. Prerequisites: CS105 Syllabus: • Review of previous course • Predicate logic: Universal and existential quantification; modus ponens and modus tollens; limitations of predicate logic • Recurrence relations: Basic formulae; elementary solution techniques • Graphs and trees: Fundamental definitions; simple algorithms ; traversal strategies; proof techniques; spanning trees; applications • Matrices: Basic properties; applications • Computational complexity: Order analysis; standard complexity classes • Elementary computability: Countability and uncountability; diagonalization proof to show uncountability of the reals; definition of the P and NP classes; simple demonstration of the halting problem • Discrete probability: Finite probability spaces; conditional probability, independence, Bayes’ rule; random events; random integer variables; mathematical expectation Computer Science 49 Notes: This implementation of the Discrete Structures area (DS) divides the material into two courses: CS105 and CS106. For programs that wish to accelerate the presentation of this material, there is also CS115, which covers the core topics in a single course. The two-course sequence, however, covers some additional material that is not in the compressed version, primarily in the Algorithms and Complexity area (AL). As a result, the introductory course in algorithmic analysis (CS210) can devote more time to advanced topics if an institution adopts the two-course implementation. Like CS105, this course introduces mathematical topics in the context of applications that require those concepts as tools. For this course, likely applications include transportation network problems (such as the traveling salesperson problem) and resource allocation.