离散数学英文版

1、Discrete Structures,CSCI-235 Dr. Kaitian Cao,Introduce Myself,What is my name? Where am I from? What are my current research fields?,Prerequisite and Description,Prerequisite: MATH 170 Calculus I and CSCI 185 Programming II Description: An introduction to discrete structures with applications to com

2、puting problems. Topics include logic, sets, functions, relations, proof techniques and algorithmic analysis. Graph theory and trees may be studied as well,Learning Outcomes,An ability to apply algorithmic concepts and constructs in problem analysis and design(Specific about algorithmic concepts and

3、 constructs) An ability to apply concepts of discrete mathematics, probability, and statistics(General about discrete mathematics) A knowledge of mathematics as it applies to solving problems in computer science(More general about mathematics),Course Objectives,Relate practical examples to the appro

4、priate set, function, or relation model, and interpret the associated operations and terminology in context Apply proof techniques, including logic, to problems Differentiate between dependent and independent events Apply the binomial theorem to independent events and Bayes theorem to dependent even

5、ts, and solve problems such as Hashing Relate ideas of mathematical induction(归纳) to recursion and apply it to problems in computer science setting Apply the basic counting principles, permutations and combinations to problems in computer science setting Implementing algorithms in C or C+ programs,A

6、ttendance Policy,A student is expected to attend each class session on a regular and punctual basis Students will be allowed to be late OR absent during the semester no more than three (3) times. Students who exceed these limits may be withdrawn from the course, or given an F grade Absence from a sc

7、heduled test is generally disallowed. Approval from the Department or College is required under extreme circumstances,Academic Honesty,Cheating or copying on an examination or an assignment will result in an F grade on the exam or assignment If it occurs the second time, the grade for the whole cour

8、se will be an F If it occurs the third time, the case will be brought to the university and the ultimate punishment could be a dismissal from the universities Please refer to the Cheating Policy being enforced by both NYIT and NUPT on the website,Homework Assignments or Exercises,Late homework assig

9、nments will be reduced by 10% if they are submitted within one week of the due date. They will not be accepted after that Exercises are usually due in one week in class following the one in which it is assigned Exercises will be checked and credited (based on the number of questions you attempted to

10、 answer) but not graded. Solutions will be provided and discussed in detail in class Prepare two notebooks for the assignments,Reading and Reviewing,Read the section or chapter of the textbook “before” and after the lecture that covers it. It will help in learning the material, answering questions i

11、n the homework and the exams Read and review the presentation slides (课件). It is most helpful in understanding the course contents and the focuses of the course Slides can be obtained in class through USB drive,Exams and Grading Policy,There is a midterm exam in week 7 or 8 There is a non-comprehens

12、ive final exam (week 15) There is a small programming in Visual Basic project Grading Homework andattendance: 20% Midterm exams35% Final exam 35% Project 10% Exams are always open book!,Importance of Homework and Attendance,Homework and attending the classes help you learn the course material and im

13、prove your grades in the exams Your final grade is calculated based on the formula HW+Attn (20) + Midterm (35) + Final (35) + Project (10) Example: Assume midterm grade is 20 out of 35 and your final is 20 out of 35. If you did not do any homework and failed to attend the class for three (not four!)

14、 times, your homework and attendance grade is 0, your project grade is 8, then your final grade is 0+20+20+8= 48, which is a Fail (F). If you did all the homework and attended all the classes (easy!), your final grade is 20+20+20+8 = 68, which is a C Missing one or two homework assignments sometimes

15、 makes a big difference!,Incomplete Grade: I,A grade of incomplete, I, is used when a student has been unable to complete all assigned work for the course because of some unavoidable circumstance. The instructor must certify that the students work is at least a pass at this point and the student mus

16、t agree to complete the missing work without paying the fee again A grade of I will become an F in the following situation: I is given in the semester and not made up by the end of the next semester,How I Can Help You,If you have a question, you can ask me face-to-face during the class, after the cl

17、ass, or in my office during my office hour, or by appointment You are encouraged to communicate with me in email at for appointments or questions. You have my promise to reply in 24 hours during week days (Dont use my email for inquiry about your final exam results!),How I Can Help You,Class Meeting

18、 Times: Thursday 1:45 PM 4: 15 PM Office Hours : Thursday: 9:15 AM- 11:15 AM (And by appointment) Office Address: Room 208(1), Teaching Building 1,Recommendation Requirements,The average grade you took all my courses is at least B+ Deep impression with your study and behavior Perform well in class a

19、nd after class.,Textbook: Kenneth H. Rosen, Discrete Mathematics and Its Applications, Seventh Edition, McGraw-Hill, 2012,Topics in Elements of Discrete Structures,Proof Techniques - Chapter 1,Propositional logic and equivalences Predicates and quantifiers Universal and existential quantification(存在

20、量化) Rules of inference Direct proofs, proofs by counter example(反例), by contraposition(对换) and by contradiction(矛盾),Sets, Functions and Relations Chapter 2 and Chapter 9,Sets: Venn diagrams, complements, Cartesian(笛卡尔) products, power sets(幂集/次子集) and set operations Functions: one-to-one, onto(映射),

21、inverses, and composition(合成) Relations and their properties: reflexivity(反射性), symmetry, transitivity(传递性) and equivalence (等价性),Algorithms and Integers Chapter 3 and Chapter 4,Growth of functions Complexity of algorithms Integers and division Primes(素数) and the greatest common divisors Integers and algorithms,Induction and Recursion Chapter 5,Mathem