Chengjiang Long 龙成江[CV]

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

Email: cjfykx AT


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ICEN/ICSI-210: Discrete Structures

Term: 2019 Spring 
Dr. Chengjiang Long
Office Hour
: Wed 12:45 PM – 3:45 PM at UAB 412E (by appointment).
Teaching Assistant
: Siqian Zhao ( and Ronke Osipitan (
Student Assistant
: Mehrdad Mirzaei ( and Shalin Alfred (
Lecture Time:
Monday, Wednesday and Friday, 11:30 AM – 12:25 PM
Lecture Building/Room: Lecture Center 25, University at Albany, SUNY. 
TA Office Hour
  • Siqian, Zhao, Thu 2:50 PM – 5:50 PM at UAB 434.
  • Ronk Osiptan, Tue 1:20 PM - 2:20 PM at UAB 412D.
  • Ronk Osiptan, Thu 1:30 PM - 3:30 PM at UAB 412D.


  • Monday 9:20 AM - 10:15 AM, BB B010, by Siqian Zhao.
  • Wednesday 10:25 AM - 11:20 AM, ED 125, by Siqian Zhao.
  • Friday, 10:25 AM - 11:20 AM, BB B012, by Ronke Osipitan.
  • Friday, 12:35 PM - 1:30 PM, BB B012, by Ronke Osipitan.

Course Website

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

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. 

The students will be graded based on course/discussion participation (5%), homework assignments (50%), two midterm exams (15%), one final exam (30%). 

Extra points: 20% for each homework. Note that this is optional, the purposes of this design is to encourage the self-motivated students to challenge themselves and give them more chances to get a higher score.  

Attendance bounus: I would like to give the bonus to reward those students whose attendance is less than 3. For those who never miss any class, I will give them 5 extra points on the final grade. For those who miss only 1 class, I will give them 2 extra points. And for those who miss 2 classes, I will give them 1 extra point on the final grade.  

Final grade: A(>=92), A-(>=90), B+(>=87), B(>=82), B-(>=80), C+(>=77), C(>=72), C-(>=70) and F (<70).  

Late submission policy:
Exponential penalty -- late for one day loses 25%, two days loses 50%, and so on and so forth. 


  • 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:

21/25/2019Propositional LogicCh 1.1-1.2Lecture_2
31/28/2019Predicate Calculus and QuantifiersCh 1.3-1.4Homework_1Lecture_3
41/30/2019Quantifiers and Rules of Inference Ch 1.4-1.5Lecture_4
52/1/2019ProofsCh 1.5-1.8Lecture_5
62/4/2019Introduction to SetsCh 2.1Homework_2Lecture_6
72/6/2019Set Operations and Introduction to FunctionsCh 2.2-2.3Lecture_7
82/8/2019FunctionsCh 2.3Lecture_8
92/11/2019Sequences and Summation (1)Ch 2.4Homework_3Lecture_9
102/13/2019Sequences and Summation (2)Ch 2.4Lecture_10
112/15/2019Cardinality of SetsCh 2.5Lecture_11
122/18/2019MatricesCh 2.6Homework_4Lecture_12
132/20/2019AlgorithmsCh 3.1Lecture_13
142/22/2019Growth of Functions and ComplexityCh 3.2-3.3Lecture_14
152/25/2019Review for Mideterm 1 Homework_5
162/27/2019Integers and DivisionCh 4.1Lecture_15
173/1/2019Modular Arithmetic Ch 4.1Lecture_16
183/4/2019Integer Representations Ch 4.2Homework_6Lecture_17
193/6/2019Primes and Greatest Common DivisorsCh 4.3Lecture_18
203/8/2019Midterm Exam 1Ch 1.1 - Ch 3.3Midterm Exam 1
213/11/2019CryptographCh 4.6Homework_7Lecture_19
223/13/2019Mathematical Induction Ch 5.1-5.2Lecture_20
233/15/2019Strong Induction and Well-OrderingCh 5.2Lecture_21
3/18/2019Class Suspended -- Spring Break
3/20/2019Class Suspended -- Spring Break
3/22/2019Class Suspended -- Spring Break
243/25/2019Structural Recursion and InductionCh 5.3Homework_8Lecture_22
253/27/2019Recursive AlgorithmsCh 5.4Lecture_23
263/29/2019Recursive Algorithms and Basic Counting RulesCh 5.4 and Ch 6.1Lecture_24
274/1/2019Pigeonhole Principle, Permutations and CombinationCh 6.2-6.3Homework_9Lecture_25
284/3/2019Binomial Coefficients and IdentitiesCh 6.4Lecture_26
294/5/2019Inclusion-exclusion PrincipleCh 6.4Lecture_27
304/8/2019Review for Midterm Exam 2Homework_10
314/10/2019Discrete ProbabilityCh 7.1-7.2Lecture_28
324/12/2019Conditional ProbabilityCh 7.2-7.3Lecture_29
324/15/2019Bayes Rules, Expected Value, Variance and Binorminal DistributionCh 7.3-7.4Homework_11Lecture_30
334/17/2019Midterm Exam 2Ch 4.1 - Ch 6.4Midterm Exam 2
354/19/2019Relations (1)Ch 9.1-9.3Lecture_31
4/22/2019Class Suspended -- Easter
364/24/2019Relations (2)Ch 9.4-9.5Lecture_32
374/26/2019Graph Theory (1)Ch 10.1-10.5Lecture_33
384/29/2019Graph Theory (2)Ch 10.1-10.5Homework_12Lecture_34
395/1/2019TreesCh 11.1-11.5Lecture_35
405/3/2019Recap and Review (1)
415/6/2019Recap and Review (2)
425/8/2019Recap and Review (3)
435/13/2019 (3:30pm – 5:30pm) Final ExamCh 1-Ch 11 Final Exam

Note: The above course schedule may be subject to change. Please do check the latest update.

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