Term: 2019 Spring
Instructor: Dr. Chengjiang Long
Email: clong2@albany.edu
Office Hour: Wed 12:45 PM – 3:45 PM at UAB 412E (by appointment).
Teaching Assistant: Siqian Zhao (szhao2@albany.edu) and
Ronke Osipitan (iosipitan@albany.edu)
Student Assistant: Mehrdad Mirzaei (mmirzaei@albany.edu) and Shalin Alfred (salfred@albany.edu)
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.
Lab/Discussions:
 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:
www.chengjianglong.com/teaching_UAlbanyDS2.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”, 7th Edition, Mc Graw Hill, 2012.
Grading: 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 selfmotivated 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.
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:
Class  Date  Topic  Reading  Homework/Exam  Slides 
1  1/23/2019  Introduction    Lecture_1 
2  1/25/2019  Propositional Logic  Ch 1.11.2   Lecture_2 
3  1/28/2019  Predicate Calculus and Quantifiers  Ch 1.31.4  Homework_1  Lecture_3 
4  1/30/2019  Quantifiers and Rules of Inference  Ch 1.41.5   Lecture_4 
5  2/1/2019  Proofs  Ch 1.51.8   Lecture_5 
6  2/4/2019  Introduction to Sets  Ch 2.1  Homework_2  Lecture_6 
7  2/6/2019  Set Operations and Introduction to Functions  Ch 2.22.3   Lecture_7 
8  2/8/2019  Functions  Ch 2.3   Lecture_8 
9  2/11/2019  Sequences and Summation (1)  Ch 2.4  Homework_3  Lecture_9 
10  2/13/2019  Sequences and Summation (2)  Ch 2.4   Lecture_10 
11  2/15/2019  Cardinality of Sets  Ch 2.5   Lecture_11 
12  2/18/2019  Matrices  Ch 2.6  Homework_4  Lecture_12 
13  2/20/2019  Algorithms  Ch 3.1   Lecture_13 
14  2/22/2019  Growth of Functions and Complexity  Ch 3.23.3   Lecture_14 
15  2/25/2019  Review for Mideterm 1   Homework_5  
16  2/27/2019  Integers and Division  Ch 4.1   Lecture_15 
17  3/1/2019  Modular Arithmetic  Ch 4.1   Lecture_16 
18  3/4/2019  Integer Representations  Ch 4.2  Homework_6  Lecture_17 
19  3/6/2019  Primes and Greatest Common Divisors  Ch 4.3   Lecture_18 
20  3/8/2019  Midterm Exam 1  Ch 1.1  Ch 3.3  Midterm Exam 1  
21  3/11/2019  Cryptograph  Ch 4.6  Homework_7  Lecture_19 
22  3/13/2019  Mathematical Induction  Ch 5.15.2   Lecture_20 
23  3/15/2019  Strong Induction and WellOrdering  Ch 5.2   Lecture_21 
 3/18/2019  Class Suspended  Spring Break    
 3/20/2019  Class Suspended  Spring Break    
 3/22/2019  Class Suspended  Spring Break    
24  3/25/2019  Structural Recursion and Induction  Ch 5.3  Homework_8  Lecture_22 
25  3/27/2019  Recursive Algorithms  Ch 5.4   Lecture_23 
26  3/29/2019  Recursive Algorithms and Basic Counting Rules  Ch 5.4 and Ch 6.1   Lecture_24 
27  4/1/2019  Pigeonhole Principle, Permutations and Combination  Ch 6.26.3  Homework_9  Lecture_25 
28  4/3/2019  Binomial Coefficients and Identities  Ch 6.4   Lecture_26 
29  4/5/2019  Inclusionexclusion Principle  Ch 6.4   Lecture_27 
30  4/8/2019  Review for Midterm Exam 2   Homework_10  
31  4/10/2019  Discrete Probability  Ch 7.17.2   Lecture_28 
32  4/12/2019  Conditional Probability  Ch 7.27.3   Lecture_29 
32  4/15/2019  Bayes Rules, Expected Value, Variance and Binorminal Distribution  Ch 7.37.4  Homework_11  Lecture_30 
33  4/17/2019  Midterm Exam 2  Ch 4.1  Ch 6.4  Midterm Exam 2  
35  4/19/2019  Relations (1)  Ch 9.19.3   Lecture_31 
 4/22/2019  Class Suspended  Easter    
36  4/24/2019  Relations (2)  Ch 9.49.5   Lecture_32 
37  4/26/2019  Graph Theory (1)  Ch 10.110.5   Lecture_33 
38  4/29/2019  Graph Theory (2)  Ch 10.110.5  Homework_12  Lecture_34 
39  5/1/2019  Trees  Ch 11.111.5   Lecture_35 
40  5/3/2019  Recap and Review (1)    
41  5/6/2019  Recap and Review (2)    
42  5/8/2019  Recap and Review (3)    
43  5/13/2019 (3:30pm – 5:30pm)  Final Exam  Ch 1Ch 11  Final Exam  
Note: The above course schedule may be subject to change. Please do check the latest update.
