Chengjiang Long 龙成江[CV]

Ph.D., Research Scientist
Meta Reality Labs (formerly Facebook Reality Labs)
322 Airport Blvd
Burlingame, CA 94010

Email: cjfykx AT


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ICEN/ICSI-210: Discrete Structures

Term: 2018 Fall 
Dr. Chengjiang Long
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 (
Student Assistant
: Jonathan P Mulhern( and Prachi D Vachhani(
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 (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. 


  • 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:

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 2 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
2210/22/2018Mathematical Induction Ch 5.1-5.2Homework 3 AssignedLecture_20
2310/24/2018Strong Induction and Well-OrderingCh 5.2Lecture_21
2410/26/2018Structural Recursion and InductionCh 5.3Lecture_22
2510/29/2018Recursive AlgorithmsCh 5.4Lecture_23
2610/31/2018Recursive Algorithms and Basic Counting RulesCh 5.4 and Ch 6.1Lecture_24
2711/2/2018Pigeonhole Principle, Permutations and CombinationCh 6.2-6.3Homework 3 DueLecture_25
2811/5/2018Binomial Coefficients and IdentitiesCh 6.4Homework 4 AssignedLecture_26
2911/7/2018Inclusion-exclusion PrincipleCh 6.4Lecture_27
3011/9/2018Discrete ProbabilityCh 7.1-7.2Lecture_28
3111/12/2018Conditional ProbabilityCh 7.2-7.3Lecture_29
3211/14/2018Midterm Exam 2Ch 3.1 - Ch 6.4Homework 4 Due and Midterm Exam 2
3311/16/2018No class
3411/19/2018Bayes Rules, Expected Value, Variance and Binorminal DistributionCh 7.3-7.4Lecture_30
11/21/2018Class Suspended -- Thanksgiving Break
11/23/2018Class Suspended -- Thanksgiving Break
3511/26/2018Relations (1)Ch 9.1-9.3Lecture_31
3611/28/2018Relations (2)Ch 9.4-9.5Homework 5 AssignedLecture_32
3711/30/2018Graph Theory (1)Ch 10.1-10.5Lecture_33
3812/3/2018Graph Theory (2)Ch 10.1-10.5Lecture_34
3912/5/2018TreesCh 11.1-11.5Lecture_35
4012/7/2018Recap and Review (1)Homework 5 Due
4112/10/2018Recap and Review (2)
4212/17/2018Final ExamCh 1-Ch 11 Final Exam

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