Chengjiang Long 龙成江[CV]

Ph.D.
Computer Vision Researcher/Senior R&D Engineer at Kitware Inc.
Adjunct Professor at University at Albany, SUNY

Email: cjfykx AT gmail.com




 

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ICEN/ICSI-210: Discrete Structures

Term: 2018 Fall 
Instructor:
Dr. Chengjiang Long
Email:
clong2@albany.edu
Time:
Monday, Wednesday and Friday, 9:20am – 10:15am
Building/Room: Lecture Center 25, University at Albany, SUNY. 
Office Hour
: Friday 10:30 am - 12:00 pm at UAB 412 B (by appointment).
TA Office Hour
: Thursday 12:00-3:00 pm at UAB 412 E.
Teaching Assistant
: Sourav Dutta (sdutta2@albany.edu)
Student Assistant
: Jonathan P Mulhern(jmulhern@albany.edu) and Prachi D Vachhani(pvachhani@albany.edu)
Course Website
: www.chengjianglong.com/teaching_UAlbanyDS.html

Course Overview:
The course is to introduce students to the techniques that may be used and enhanced later in professions related to Computer Science. Computer Science specialists could choose a career of developer, analyst, manager, etc. It is important for all of them to understand or to create formal (most often mathematical) description of the problem to be solved. This course covers a wide range of different aspects of discrete mathematics that are applicable to solving programming problems: proofs by induction; mathematical reasoning, propositions, predicates and quantifiers; sets; relations, graphs, and trees; functions; counting, permutations and combinations.

Prerequisites:
Students should have a fundamental understanding of mathematical reasoning as well as be competent in solving applied algebra problems. The most important prerequisites are interest in the subject, willingness to dedicate necessary resources in terms of time and intellectual effort, and willingness to actively participate in the learning process. No programming skills are required to pass the course.  

Text Books:
Kenneth Rosen, “ Discrete Mathematics and Its Applications”, 7-th Edition, Mc Graw Hill, 2012. 

Grading:
The students will be graded based on course/discussion participation (10%), homework assignments (40%), two midterm exams (20%), one final exam (30%). 
Final grade: A(>=92), A-(>=90), B+(>=87), B(>=82), B-(>=80), C+(>=77), C(>=72), C-(>=70), D+(>=67), D(>=62), D-(>=60) and F (<60).  

Late submission policy:
Exponential penalty -- late for one day loses half, two day loses another half of the remaining, and so on and so forth. 

Topics:

  • Introduction to Discrete Structures.
  • Logic Inference, Predicates, Qualifiers.
  • Boolean Algebra, Logic Gates, Logic Minimization.
  • Sets, Functions, Sequences, Sums, Matrices, Matrix Algebra.
  • Algorithms, Searching, Sorting, Complexity of Algorithms.
  • Number Theory, Cryptography, Modular Arithmetic.
  • Induction and Recursion.
  • Counting.
  • Relations.
  • Graphs.
  • Trees.


Course schedule:

ClassDateTopicReadingHomeworkSlides
18/27/2018IntroductionLecture_1
28/29/2018Propositional LogicCh 1.1-1.2Lecture_2
38/31/2018Predicate Calculus and QuantifiersCh 1.3-1.4Lecture_3
9/3/2018Class Suspended -- Labor Day
49/5/2018Quantifiers and Rules of Reference Ch 1.4-1.5Lecture_4
59/7/2018ProofsCh 1.5-1.8Homework 1 Assigned.Lecture_5
9/10/2018Class Suspended -- Rosh Hashanah
69/12/2018Introduction to SetsCh 2.1Lecture_6
79/14/2018Set Operations and Introduction to FunctionsCh 2.2-2.3Lecture_7
89/17/2018FunctionsCh 2.3Homework 1 Due.Lecture_8
9/19/2018Class Suspended -- Yom Kippur
99/21/2019Sequences and Summation (1)Ch 2.4Lecture_9
109/24/2019Sequences and Summation (2)Ch 2.4Lecture_10
119/26/2018Cardinality of SetsCh 2.5Lecture_11
129/28/2018MatricesCh 2.6Homework 2 AssignedLecture_12
1310/1/2018AlgorithmsCh 3.1Lecture_13
1410/3/2018Growth of Functions and ComplexityCh 3.2-3.3Lecture_14
1510/5/2018Integers and DivisionCh 4.1Lecture_15
1610/8/2018Midterm Exam 1Ch 1.1-1.8, Ch 2.1-2.6Homework 1 Due and Midterm Exam 1
1710/10/2018Modular Arithmetic Ch 4.1Lecture_16
1810/12/2018Integer Representations Ch 4.2Lecture_17
1910/15/2018Primes and Greatest Common DivisorsCh 4.3Lecture_18
2010/17/2018CryptographCh 4.6Lecture_19
2110/19/2018Cover Midterm Exam 1 and Homework
2210/22/2018Proof by Mathematical Induction Ch 5.1-5.2
2310/24/2018Proof by Strong InductionCh 5.2
2410/26/2018Some Aspects of Proof by InductionsCh 5.2
2510/29/2018Recursive/Inductive DefinitionsCh 5.3
2610/31/2018Structural Recursion and InductionCh 5.3
2711/2/2018Recursive Algorithms and Algorithm CorrectnessCh 5.4
2811/5/2018CountingCh 6.1
2911/7/2018Pigeonhole PrincipleCh 6.2
3011/9/2018Permutations and CombinationCh 6.3
3111/12/2018Midterm Exam 2
3211/14/2018Number of Permutations and CombinationsCh 6.3
3311/16/2018Binomial Coefficients. Pascal’s TriangleCh 6.4
3411/19/2018Generalized Permutations and CombinationsCh 6.5
3511/21/2018RelationsCh 9.1-9.5
11/23/2018Class Suspended -- Thanksgiving Break
11/26/2018Class Suspended -- Thanksgiving Break
3611/28/2018RelationsCh 9.1-9.5
3711/30/2018GraphsCh 10.1-10.5
3812/3/2018GraphsCh 10.1-10.5
3912/5/2018TreesCh 11.1-11.5
4012/7/2018TreesCh 11.1-11.5
4112/10/2018Recap and Review
42TBAFinal Exam








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