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CS233601: Discrete Mathematics

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Title: CS233601: Discrete Mathematics


1
CS233601 Discrete Mathematics
  • Department of Computer Science
  • National Tsing Hua University

2
  • Instructor
  • SHIH YU CHANG (???), shihyuch_at_cs.nthu.edu.tw
  • Office Number R743, EECS Building
  • Time and Location
  • Wednesday 1010 1200, Friday 1110 1200
  • EECS 236
  • Office Hours
  • Friday 15001700
  • Textbook
  • "Elements of Discrete Mathematics" (McGraw-Hill),
    by Prof. C. L. Liu
  • Reference
  • "Discrete Mathematics and Its Applications"
    (McGraw-Hill), by Kenneth H. Rosen

3
  • Teaching Assistant (TA)
  • ???, ???731, g9562637_at_oz.nthu.edu.tw
  • TA Office Hours
  • Thur. 420 620 pm

4
What is Discrete Mathematics?
  • Discrete mathematics is the part of mathematics
    devoted to the study of discrete objects.
  • Here discrete means consisting of distinct or
    unconnected elements.
  • The kind of problems solved using discrete
    mathematics include
  • How many ways are there to choose a valid
    password on a computer system?

5
What is Discrete Mathematics? (Cont.)
  • What is the probability of winning a lottery?
  • Is there a link between two computers in a
    network?
  • What is the shortest path between two cities
    using a transportation system?
  • How can a list of integers be sorted so that the
    integers are in increasing order?
  • How many steps are required to do such a sorting?
  • How can it be proved that a sorting algorithm
    correctly sorts a list?

6
What is Discrete Mathematics? (Cont.)
  • How can a circuit that adds two integers be
    designed?
  • How many valid Internet addresses are there?
  • You will learn the discrete structures and
    techniques needed to solve such problems.
  • More generally, discrete mathematics is used
    whenever objects are counted, when relationships
    between finite (or countable) sets are studied,
    and when processes involving a finite number of
    steps are analyzed.

7
Why Study Discrete Mathematics?
  • Through this course you can develop your
    mathematical maturity, that is, your ability to
    understand and create mathematical arguments.
  • Discrete mathematics provides the mathematical
    foundations for many computer science courses,
    including data structures, algorithms, database
    theory, automata theory, formal languages,
    compiler theory, computer security, and operating
    systems.

8
Five Themes in Discrete Mathematics?
  • Mathematical Reasoning
  • Understanding mathematical reasoning in order to
    read, comprehend, and construct mathematical
    arguments
  • Mathematical logic, methods of proof,
    mathematical induction
  • Combinatorial Analysis
  • The ability to count or enumerate objects
  • The basic techniques of counting, permutations,
    combinations
  • Discrete Structures
  • The abstract mathematical structures used to
    represent discrete objects and relationships
    between these objects
  • Sets, permutations, relations, graphs, trees, and
    finite-state machines

9
Five Themes in Discrete Mathematics?
  • Algorithmic Thinking
  • The specification of an algorithm that solves
    certain classes of problems
  • The specification of the algorithm, the
    verification of the algorithm, the analysis of
    the space and time complexities of the algorithm
  • Applications and Modeling
  • Computer science, data networking, chemistry,
    business, etc.
  • Modeling with discrete mathematics is an
    extremely important problem-solving skill

10
Course Outline
  • Sets and Propositions
  • Computability and Formal Languages
  • Permutations, Combinations, and Discrete
    Probability
  • Relations and Functions
  • Graphs and Planar Graphs
  • Trees and Cut-Sets
  • Finite State Machines

11
Course Outline (Cont.)
  • Analysis of Algorithms
  • Discrete Numeric Functions and Generating
    Functions
  • Recurrence Relations and Recursive Algorithms
  • Groups and Rings
  • Boolean Algebras

12
Grading
  • Homework 0
  • ?????????
  • Quiz 20
  • ??????, ??????????, ????10??
  • Midterm I 25
  • Midterm II 25
  • Final 30
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